Recent zbMATH articles in MSC 78https://zbmath.org/atom/cc/782021-11-25T18:46:10.358925ZWerkzeugSmall permanent charge effects on individual fluxes via Poisson-Nernst-Planck models with multiple cationshttps://zbmath.org/1472.340862021-11-25T18:46:10.358925Z"Bates, Peter W."https://zbmath.org/authors/?q=ai:bates.peter-w"Wen, Zhenshu"https://zbmath.org/authors/?q=ai:wen.zhenshu"Zhang, Mingji"https://zbmath.org/authors/?q=ai:zhang.mingjiSummary: A quasi-one-dimensional Poisson-Nernst-Planck system for ionic flow through a membrane channel is studied. Nonzero but small permanent charge, the major structural quantity of an ion channel, is included in the model. The system includes three ion species, two cations with the same valences and one anion, which provides more correlations/interactions between ions compared to the case included only two oppositely charged particles. The cross-section area of the channel is included in the system, which provides certain information of the geometry of the three-dimensional channel. This is crucial for our analysis. Under the framework of geometric singular perturbation theory, more importantly, the specific structure of the model, the existence and local uniqueness of solutions to the system for small permanent charges is established. Furthermore, treating the permanent charge as a small parameter, through regular perturbation analysis, we are able to derive approximations of the individual fluxes explicitly, and this allows us to examine the small permanent charge effects on ionic flows in detail. Of particular interest is the competition between two cations, which is related to the selectivity phenomena of ion channels. Critical potentials are identified and their roles in characterizing ionic flow properties are studied. Some critical potentials can be estimated experimentally, and this provides an efficient way to adjust/control boundary conditions (electric potential and concentrations) to observe distinct qualitative properties of ionic flows. Mathematical analysis further indicates that to optimize the effect of permanent charges, a short and narrow filter, within which the permanent charge is confined, is expected, which is consistent with the typical structure of an ion channel.Effects on \(I-V\) relations from small permanent charge and channel geometry via classical Poisson-Nernst-Planck equations with multiple cationshttps://zbmath.org/1472.340992021-11-25T18:46:10.358925Z"Wen, Zhenshu"https://zbmath.org/authors/?q=ai:wen.zhenshu"Bates, Peter W."https://zbmath.org/authors/?q=ai:bates.peter-w"Zhang, Mingji"https://zbmath.org/authors/?q=ai:zhang.mingjiThe geometric average of curl-free fields in periodic geometrieshttps://zbmath.org/1472.350302021-11-25T18:46:10.358925Z"Poelstra, Klaas Hendrik"https://zbmath.org/authors/?q=ai:poelstra.klaas-hendrik"Schweizer, Ben"https://zbmath.org/authors/?q=ai:schweizer.ben"Urban, Maik"https://zbmath.org/authors/?q=ai:urban.maikSummary: In periodic homogenization problems, one considers a sequence \((u^{\eta})_{\eta}\) of solutions to periodic problems and derives a homogenized equation for an effective quantity \(\hat{u} \). In many applications, \( \hat{u}\) is the weak limit of \((u^{\eta})_{\eta} \), but in some applications \(\hat{u}\) must be defined differently. In the homogenization of Maxwell's equations in periodic media, the effective magnetic field is given by the geometric average of the two-scale limit. The notion of a geometric average has been introduced in [\textit{G. Bouchitté} et al., C. R., Math., Acad. Sci. Paris 347, No. 9--10, 571--576 (2009; Zbl 1177.35028)]; it associates to a curl-free field \(Y\setminus\overline{\Sigma}\to\mathbb{R}^3\), where \(Y\) is the periodicity cell and \(\Sigma\) an inclusion, a vector in \(\mathbb{R}^3 \). In this article, we extend previous definitions to more general inclusions, in particular inclusions that are not compactly supported in the periodicity cell. The physical relevance of the geometric average is demonstrated by various results, e.g., a continuity property of limits of tangential traces.Analysis of two transmission eigenvalue problems with a coated boundary conditionhttps://zbmath.org/1472.352612021-11-25T18:46:10.358925Z"Harris, I."https://zbmath.org/authors/?q=ai:harris.ian-g|harris.isaac|harris.irina|harris.isadore|harris.ian-rThe author of this article considers two transmission problems arising in scattering theory for a media with a coated boundary. Specifically, the electromagnetic transmission eigenvalue problem and the acoustic zero-index transmission eigenvalue problem is investigated. Transmission problems are new eigenvalue problems and the corresponding eigenvalues can be determined from scattering data. Additionally, they contain information on material properties of the media which one wants to obtain for example in non-destructive testing. In this work, it is proven that infinitely many real eigenvalues exists and that they depend monotonically both on the refractive index and the boundary parameters. Further, it is shown that the classical eigenvalue problem arises when the boundary parameter tends to zero or to infinity. Numerical results are given in two dimensions and support the theoretical findings.The existence and uniqueness result for a relativistic nonlinear Schrödinger equationhttps://zbmath.org/1472.353492021-11-25T18:46:10.358925Z"Cheng, Yongkuan"https://zbmath.org/authors/?q=ai:cheng.yongkuan"Yang, Jun"https://zbmath.org/authors/?q=ai:yang.jun.1|yang.jun.3|yang.jun.2|yang.junSummary: We study the existence and uniqueness of positive solutions for a class of quasilinear elliptic equations. This model has been proposed in the self-channeling of a high-power ultrashort laser in matter.Non-convex \(\ell_p\) regularization for sparse reconstruction of electrical impedance tomographyhttps://zbmath.org/1472.353692021-11-25T18:46:10.358925Z"Wang, Jing"https://zbmath.org/authors/?q=ai:wang.jing|wang.jing.13|wang.jing.1|wang.jing.11|wang.jing.14|wang.jing.2|wang.jing.3|wang.jing.6|wang.jing.17|wang.jing.16|wang.jing.5|wang.jing.15Summary: This work is to investigate the image reconstruction of electrical impedance tomography from the electrical measurements made on an object's surface. An \(\ell_p\)-norm \((0<p<1)\) sparsity-promoting regularization is considered to deal with the fully non-linear electrical impedance tomography problem, and a novel type of smoothing gradient-type iteration scheme is introduced. To avoid the difficulty in calculating its gradient in the optimization process, a smoothing Huber potential function is utilized to approximate the \(\ell_p\)-norm penalty. We then propose the smoothing algorithm in the general frame and establish that any accumulation point of the generated iteration sequence is a first-order stationary point of the original problem. Furthermore, one iteration scheme based on the homotopy perturbation technology is derived to find the minimizers of the Huberized approximated objective function. Numerical experiments show that non-convex \(\ell_p\)-norm sparsity-promoting regularization improves the spatial resolution and is more robust with respect to noise, in comparison with \(\ell_p\)-norm regularization.Numerical scheme for electromagnetic scattering on perturbed periodic inhomogeneous media and reconstruction of the perturbationhttps://zbmath.org/1472.353712021-11-25T18:46:10.358925Z"Konschin, Alexander"https://zbmath.org/authors/?q=ai:konschin.alexanderWeak solutions of the relativistic Vlasov-Maxwell system with external currentshttps://zbmath.org/1472.353722021-11-25T18:46:10.358925Z"Weber, Jörg"https://zbmath.org/authors/?q=ai:weber.jorgThe paper studies the Vlasov-Maxwell system and their weak solutions when the plasma is contained in a bounded domain \(\Omega\) while the electromagnetic fields are induced by external currents outside the container. Here, the main contribution is that boundary conditions on \(E\) and \(H\) fields is not set to perfect electric conductor (PEC) at the boundaries of container. This is much more difficult problem but makes it possible for interaction of the fields inside container with currents in the control coils.
The author uses a method similar to [\textit{Y. Guo}, Commun. Math. Phys. 154, No. 2, 245--263 (1993; Zbl 0787.35072)] to identity the proper sets of test functions and function spaces for particle densities as well as \(E\) and \(H\) fields. The first of main results of the article is about the existence of the weak solutions for such a Vlasov-Maxwell system. The second major outcome is the examination of the divergence equations and demonstration of the redundancy of the \(E\) field based on the proposed weak formulation.
The proposed weak formulation is used in a separate article by the same author [SIAM J. Math. Anal. 52, No. 3, 2895--2929 (2020; Zbl 1448.35499)] to find optimal external currents that control the plasma particles.Homogenization and diffusion approximation of the Vlasov-Poisson-Fokker-Planck system: a relative entropy approachhttps://zbmath.org/1472.353852021-11-25T18:46:10.358925Z"Addala, Lanoir"https://zbmath.org/authors/?q=ai:addala.lanoir"El Ghani, Najoua"https://zbmath.org/authors/?q=ai:el-ghani.najoua"Tayeb, Mohamed Lazhar"https://zbmath.org/authors/?q=ai:tayeb.mohamed-lazharSummary: We are concerned with the analysis of the approximation by diffusion and homogenization of a Vlasov-Poisson-Fokker-Planck system. Here we generalize the convergence result of the second author and \textit{N. Masmoudi} [Commun. Math. Sci. 8, No. 2, 463--479 (2010; Zbl 1193.35228)] where the same problem is treated without the oscillating electrostatic potential and we extend the one dimensional result of the third author [Ann. Henri Poincaré 17, No. 9, 2529--2553 (2016; Zbl 1456.82798)] to the case of several space dimensions. An averaging lemma and two scale convergence techniques are used to prove rigorously the convergence of the scaled Vlasov-Poisson-Fokker-Planck system to a homogenized Drift-Diffusion-Poisson system.Modeling the voltage distribution in a non-locally but globally electroneutral confined electrolyte medium: applications for nanophysiologyhttps://zbmath.org/1472.354092021-11-25T18:46:10.358925Z"Tricot, A."https://zbmath.org/authors/?q=ai:tricot.a"Sokolov, I. M."https://zbmath.org/authors/?q=ai:sokolov.igor-mikhailovich"Holcman, D."https://zbmath.org/authors/?q=ai:holcman.davidSummary: The distribution of voltage in sub-micron cellular domains remains poorly understood. In neurons, the voltage results from the difference in ionic concentrations which are continuously maintained by pumps and exchangers. However, it not clear how electro-neutrality could be maintained by an excess of fast moving positive ions that should be counter balanced by slow diffusing negatively charged proteins. Using the theory of electro-diffusion, we study here the voltage distribution in a generic domain, which consists of two concentric disks (resp. ball) in two (resp. three) dimensions, where a negative charge is fixed in the inner domain. When global but not local electro-neutrality is maintained, we solve the Poisson-Nernst-Planck equation both analytically and numerically in dimension 1 (flat) and 2 (cylindrical) and found that the voltage changes considerably on a spatial scale which is much larger than the Debye screening length, which assumes electro-neutrality. The present result suggests that long-range voltage drop changes are expected in neuronal microcompartments, probably relevant to explain the activation of far away voltage-gated channels located on the surface membrane.Boundary determination of electromagnetic and Lamé parameters with corrupted datahttps://zbmath.org/1472.354492021-11-25T18:46:10.358925Z"Caro, Pedro"https://zbmath.org/authors/?q=ai:caro.pedro"Lai, Ru-Yu"https://zbmath.org/authors/?q=ai:lai.ru-yu"Lin, Yi-Hsuan"https://zbmath.org/authors/?q=ai:lin.yi-hsuan"Zhou, Ting"https://zbmath.org/authors/?q=ai:zhou.tingSummary: We study boundary determination for an inverse problem associated to the time-harmonic Maxwell equations and another associated to the isotropic elasticity system. We identify the electromagnetic parameters and the Lamé moduli for these two systems from the corresponding boundary measurements. In a first step we reconstruct Lipschitz magnetic permeability, electric permittivity and conductivity on the surface from the ideal boundary measurements. Then, we study inverse problems for Maxwell equations and the isotropic elasticity system assuming that the data contains measurement errors. For both systems, we provide explicit formulas to reconstruct the parameters on the boundary as well as its rate of convergence formula.On the identification of the nonlinearity parameter in the Westervelt equation from boundary measurementshttps://zbmath.org/1472.354532021-11-25T18:46:10.358925Z"Kaltenbacher, Barbara"https://zbmath.org/authors/?q=ai:kaltenbacher.barbara"Rundell, William"https://zbmath.org/authors/?q=ai:rundell.williamSummary: We consider an undetermined coefficient inverse problem for a nonlinear partial differential equation occurring in high intensity ultrasound propagation as used in acoustic tomography. In particular, we investigate the recovery of the nonlinearity coefficient commonly labeled as \(B/A\) in the literature which is part of a space dependent coefficient \(\kappa\) in the Westervelt equation governing nonlinear acoustics. Corresponding to the typical measurement setup, the overposed data consists of time trace measurements on some zero or one dimensional set \(\Sigma\) representing the receiving transducer array. After an analysis of the map from \(\kappa\) to the overposed data, we show injectivity of its linearisation and use this as motivation for several iterative schemes to recover \(\kappa\). Numerical simulations will also be shown to illustrate the efficiency of the methods.A linear sampling method for inverse acoustic scattering by a locally rough interfacehttps://zbmath.org/1472.354572021-11-25T18:46:10.358925Z"Li, Jianliang"https://zbmath.org/authors/?q=ai:li.jianliang"Yang, Jiaqing"https://zbmath.org/authors/?q=ai:yang.jiaqing"Zhang, Bo"https://zbmath.org/authors/?q=ai:zhang.boSummary: This paper is concerned with the inverse problem of time-harmonic acoustic scattering by an unbounded, locally rough interface which is assumed to be a local perturbation of a plane. The purpose of this paper is to recover the local perturbation of the interface from the near-field measurement given on a straight line segment with a finite distance above the interface and generated by point sources. Precisely, we propose a novel version of the linear sampling method to recover the location and shape of the local perturbation of the interface numerically. Our method is based on a modified near-field operator equation associated with a special rough surface, constructed by reformulating the forward scattering problem into an equivalent integral equation formulation in a bounded domain, leading to a fast imaging algorithm. Numerical experiments are presented to illustrate the effectiveness of the imaging method.Asymptotic analysis and topological derivative for 3D quasi-linear magnetostaticshttps://zbmath.org/1472.490612021-11-25T18:46:10.358925Z"Gangl, Peter"https://zbmath.org/authors/?q=ai:gangl.peter"Sturm, Kevin"https://zbmath.org/authors/?q=ai:sturm.kevinSummary: In this paper we study the asymptotic behaviour of the quasilinear curl-curl equation of 3D magnetostatics with respect to a singular perturbation of the differential operator and prove the existence of the topological derivative using a Lagrangian approach. We follow the strategy proposed in [\textit{P. Gangl} and \textit{K. Sturm}, ESAIM, Control Optim. Calc. Var. 26, Paper No. 106, 20 p. (2020; Zbl 1459.49027)] where a systematic and concise way for the derivation of topological derivatives for quasi-linear elliptic problems in \(H^1\) is introduced. In order to prove the asymptotics for the state equation we make use of an appropriate Helmholtz decomposition. The evaluation of the topological derivative at any spatial point requires the solution of a nonlinear transmission problem. We discuss an efficient way for the numerical evaluation of the topological derivative in the whole design domain using precomputation in an offline stage. This allows us to use the topological derivative for the design optimization of an electrical machine.Non-intrusive reduced-order modeling of parameterized electromagnetic scattering problems using cubic spline interpolationhttps://zbmath.org/1472.651222021-11-25T18:46:10.358925Z"Li, Kun"https://zbmath.org/authors/?q=ai:li.kun.5"Huang, Ting-Zhu"https://zbmath.org/authors/?q=ai:huang.ting-zhu"Li, Liang"https://zbmath.org/authors/?q=ai:li.liang"Lanteri, Stéphane"https://zbmath.org/authors/?q=ai:lanteri.stephaneSummary: This paper presents a non-intrusive model order reduction (MOR) for the solution of parameterized electromagnetic scattering problems, which needs to prepare a database offline of full-order solution samples (snapshots) at some different parameter locations. The snapshot vectors are produced by a high order discontinuous Galerkin time-domain (DGTD) solver formulated on an unstructured simplicial mesh. Because the second dimension of snapshots matrix is large, a two-step or nested proper orthogonal decomposition (POD) method is employed to extract time- and parameter-independent POD basis functions. By using the singular value decomposition (SVD) method, the principal components of the projection coefficient matrices (also referred to as the reduced coefficient matrices) of full-order solutions onto the RB subspace are extracted. A cubic spline interpolation-based (CSI) approach is proposed to approximate the dominating time- and parameter-modes of the reduced coefficient matrices without resorting to Galerkin projection. The generation of snapshot vectors, the construction of POD basis functions and the approximation of reduced coefficient matrices based on the CSI method are completed during the offline stage. The RB solutions for new time and parameter values can be rapidly recovered via outputs from the interpolation models in the online stage. In particular, the offline and online stages of the proposed RB method, termed as the POD-CSI method, are completely decoupled, which ensures the computational validity of the method. Moreover, a surrogate error model is constructed as an efficient error estimator for the POD-CSI method. Numerical experiments for the scattering of plane wave by a 2-D dielectric cylinder and a multi-layer heterogeneous medium nicely illustrate the performance of POD-CSI method.A new numerical approach for single rational soliton solution of Chen-Lee-Liu equation with Riesz fractional derivative in optical fibershttps://zbmath.org/1472.651302021-11-25T18:46:10.358925Z"Ray, Santanu Saha"https://zbmath.org/authors/?q=ai:saha-ray.santanuThe author proposes a time-splitting spectral approximation technique for the Chen-Lee-Liu (CLL) equation involving Riesz fractional derivative, which is the nonlinear Schrodinger equation with Riesz fractional derivative, based on the Strang splitting spectral method. The proposed numerical technique is shown to be efficient, unconditionally stable, and of second-order accuracy in time and of spectral accuracy in space. It conserves the total density in the discretized level. To examine the results, the author also gives a Crank-Nicolson weighted and shifted Grünwald difference (CN-WSGD) scheme for the Riesz fractional CLL equation. By the comparison of numerical results, the proposed time-splitting spectral method shows to be effective and simple for obtaining single soliton numerical solution of the Riesz fractional CLL equation.Superconvergence of the second order cubic edge elements with Maxwell's equationshttps://zbmath.org/1472.651492021-11-25T18:46:10.358925Z"Wu, Chao"https://zbmath.org/authors/?q=ai:wu.chao"Huang, Yunqing"https://zbmath.org/authors/?q=ai:huang.yunqing"Yuan, Jinyun"https://zbmath.org/authors/?q=ai:yuan.jinyunSummary: Superconvergence of the second order cubic edge elements approximation is investigated on uniform and nonuniform mesh. Superconvergence of one order higher is established at the second order Gauss points for both the finite element solution and the curl of this solution. Numerical examples are presented to support our theoretical analysis.Complete separability of the Hamilton-Jacobi equation for the charged particle orbits in a Liénard-Wiechert fieldhttps://zbmath.org/1472.700412021-11-25T18:46:10.358925Z"McLenaghan, Raymond G."https://zbmath.org/authors/?q=ai:mclenaghan.raymond-g"Rastelli, Giovanni"https://zbmath.org/authors/?q=ai:rastelli.giovanni"Valero, Carlos"https://zbmath.org/authors/?q=ai:valero.carlosSummary: We classify all orthogonal coordinate systems in \(\mathbb{M}^4\), allowing complete additively separated solutions of the Hamilton-Jacobi equation for a charged test particle in the Liénard-Wiechert field generated by any possible given motion of a point-charge \(Q\). We prove that only the Cavendish-Coulomb field, corresponding to the uniform motion of \(Q\), admits separation of variables, precisely in cylindrical spherical and cylindrical conical-spherical coordinates. We show also that for some fields, the test particle with motion constrained into certain planes admits complete orthogonal separation, and we determine the separable coordinates.
{\copyright 2020 American Institute of Physics}Lie symmetry and conservation laws for magneto-static magnetic shape memory alloys systemhttps://zbmath.org/1472.740372021-11-25T18:46:10.358925Z"Haldar, Krishnendu"https://zbmath.org/authors/?q=ai:haldar.krishnendu"Lagoudas, Dimitris C."https://zbmath.org/authors/?q=ai:lagoudas.dimitris-cSummary: Magnetic shape memory alloys (MSMAs) have drawn significant research attention as potential high actuation energy multi-functional materials. Such a dissipative material system can be considered as a solid continuum interacting with a magnetic field. A continuum-based phenomenological model provides a magneto-mechanical system of equations that simulates and predicts primary MSMA behaviours. In this work, we investigate the local symmetries of the MSMA system equations through the Lie group analysis. Symmetry breaking due to stable-unstable transition is analysed. The conservation laws are derived, and their physical meaning is scrutinized.Coupled electrochemical-mechanical modeling with strain gradient plasticity for lithium-ion battery electrodeshttps://zbmath.org/1472.740542021-11-25T18:46:10.358925Z"Wang, Yan"https://zbmath.org/authors/?q=ai:wang.yan.4|wang.yan.5|wang.yan.2|wang.yan.1|wang.yan|wang.yan.6|wang.yan.3"Wu, Hui"https://zbmath.org/authors/?q=ai:wu.hui"Sun, Lizhong"https://zbmath.org/authors/?q=ai:sun.lizhong"Jiang, Wenjuan"https://zbmath.org/authors/?q=ai:jiang.wenjuan"Lu, Chunsheng"https://zbmath.org/authors/?q=ai:lu.chunsheng"Ma, Zengsheng"https://zbmath.org/authors/?q=ai:ma.zengshengSummary: We first present a model coupling the electrochemical reaction with strain gradient plasticity for a spherical electrode, which aims to analyze the evolutions and distributions of electrochemical-reaction dislocations and diffusion-induced stress during lithiation process. Several critical features viewed by \textit{in-situ} TEM are incorporated into this model, such as the two-phase boundary and high-density dislocations at the reaction front. It is shown that the microstructure evolution can impact the mechanical properties and electrochemical performances of electrode materials. The results obtained by a finite difference method indicate that, as lithiation proceeds, the circumferential stress on the surface of the lithiated shell changes from compression to tensile stress, which may cause fracture of the active materials. Especially, the electrochemical-reaction dislocation zone results in fairly large stresses at the front of the interface. Furthermore, the lithiation reaction displays a strong size effect, and the movement rate of reaction front reduces as the size of the particles decreases. This work provides a framework for large-capacity, multi-scale research on high-capacity lithium-ion battery electrodes.Review of rational electrodynamics: deformation and force models for polarizable and magnetizable matterhttps://zbmath.org/1472.740682021-11-25T18:46:10.358925Z"Rickert, Wilhelm"https://zbmath.org/authors/?q=ai:rickert.wilhelm"Müller, Wolfgang H."https://zbmath.org/authors/?q=ai:muller.wolfgang-hSummary: In this paper a rational derivation of Maxwell's equations is presented in a purely spatial description. On a macroscopic scale this can be done by means of localization of global balance laws. The mathematical tools for the localization in a spatial description are presented. Subsequently the balance laws of electric charge and magnetic flux are discussed and localized in order to obtain Maxwell's equations. Furthermore, short historical remarks on the origin of the governing laws in mechanics are presented. In order to illustrate the coupling of electrodynamics in matter to mechanics, two exemplary problems are analyzed. The procedure and the arising difficulties are discussed.
For the entire collection see [Zbl 1468.74003].Plasmonic modes in cylindrical nanoparticles and dimershttps://zbmath.org/1472.741182021-11-25T18:46:10.358925Z"Downing, Charles A."https://zbmath.org/authors/?q=ai:downing.charles-a"Weick, Guillaume"https://zbmath.org/authors/?q=ai:weick.guillaumeSummary: We present analytical expressions for the resonance frequencies of the plasmonic modes hosted in a cylindrical nanoparticle within the quasi-static approximation. Our theoretical model gives us access to both the longitudinally and transversally polarized dipolar modes for a metallic cylinder with an arbitrary aspect ratio, which allows us to capture the physics of both plasmonic nanodisks and nanowires. We also calculate quantum mechanical corrections to these resonance frequencies due to the spill-out effect, which is of relevance for cylinders with nanometric dimensions. We go on to consider the coupling of localized surface plasmons in a dimer of cylindrical nanoparticles, which leads to collective plasmonic excitations. We extend our theoretical formalism to construct an analytical model of the dimer, describing the evolution with the inter-nanoparticle separation of the resultant bright and dark collective modes. We comment on the renormalization of the coupled mode frequencies due to the spill-out effect, and discuss some methods of experimental detection.Rayleigh-Bénard magnetoconvection with temperature modulationhttps://zbmath.org/1472.761262021-11-25T18:46:10.358925Z"Hazra, Suparna"https://zbmath.org/authors/?q=ai:hazra.suparna"Kumar, Krishna"https://zbmath.org/authors/?q=ai:kumar.krishna-b|kumar.krishna-dev"Mitra, Saheli"https://zbmath.org/authors/?q=ai:mitra.saheliSummary: Floquet analysis of modulated magnetoconvection in Rayleigh-Bénard geometry is performed. A sinusoidally varying temperature is imposed on the lower plate. As Rayleigh number Ra is increased above a critical value \(Ra_o\), the oscillatory magnetoconvection begins. The flow at the onset of magnetoconvection may oscillate either subhar- monically or harmonically with the external modulation. The critical Rayleigh number \(Ra_o\) varies non-monotonically with the modulation frequency \(\omega\) for appreciable value of the modulation amplitude \(a\). The temperature modulation may either postpone or prepone the appearance of magnetoconvection. The magnetoconvective flow always oscillates harmonically at larger values of \(\omega \). The threshold \(Ra_o\) and the corresponding wavenumber \(k_o\) approach to their values for the stationary magnetoconvection in the absence of modulation \((a = 0)\), as \(\omega \rightarrow \infty \). Two different zones of harmonic instability merge to form a single instability zone with two local minima for higher values of Chandrasekhar's number \(Q\), which is qualitatively new. We have also observed a new type of bicritical point, which involves two different sets of harmonic oscillations. The effects of variation of \(Q\) and Pr on the threshold \(Ra_o\) and critical wavenumber \(k_o\) are also investigated.Theoretical statistical opticshttps://zbmath.org/1472.780012021-11-25T18:46:10.358925Z"Korotkova, Olga"https://zbmath.org/authors/?q=ai:korotkova.olgaPublisher's description: This monograph overviews classic and recent developments in theoretical statistical optics in connection with stationary and non-stationary (pulsed) optical source characterization and modeling, discusses various phenomena occurring with random light propagating in free space, on its interaction with optical systems, extended media and particulate collections. The text includes scalar, beam-like and general electromagnetic treatment of light. A brief statistical description of four fundamental experiments relating to random light: spatial and temporal field interference, intensity interferometry and phase conjugation, is also included in order to relate the analytical descriptions with practical observations.
Rigorous mathematical methods for statistical manipulation of light sources useful for remote shaping of its various average properties, enhanced image resolution, optimized transmission in random media and for other applications are introduced. For illustration of efficient ways for manipulation of light polarization the generalized Stokes-Mueller calculus is applied for description of interaction of beam-like fields with classic and currently popular devices of polarization optics, including a spatial light modulator.
Random light plays a special role in the image formation process. Three imaging modalities including the classic intensity-based system with structured source correlations, the polarization-based imaging system and the ghost interference approach are discussed in detail.
Theoretical aspects of potential scattering of light from weakly scattering media are considered under a very broad range of assumptions: scalar/electromagnetic incident light, deterministic/random light/media, single/particulate media. Then, problems and methods in light characterization on interaction with extended, turbulent-like natural media, such as the Earth's atmosphere, oceans and soft bio-tissues that are currently widely used for communication, remote sensing and imaging purposes in these media, are provided.Analysis and implementation of isogeometric boundary elements for electromagnetismhttps://zbmath.org/1472.780022021-11-25T18:46:10.358925Z"Wolf, Felix"https://zbmath.org/authors/?q=ai:wolf.felixPublisher's description: This book presents a comprehensive mathematical and computational approach for solving electromagnetic problems of practical relevance, such as electromagnetic scattering and the cavity problems. After an in-depth introduction to the mathematical foundations of isogeometric analysis, which discusses how to conduct higher-order simulations efficiently and without the introduction of geometrical errors, the book proves quasi-optimal approximation properties for all trace spaces of the de Rham sequence, and demonstrates inf-sup stability of the isogeometric discretisation of the electric field integral equation (EFIE). Theoretical properties and algorithms are described in detail. The algorithmic approach is, in turn, validated through a series of numerical experiments aimed at solving a set of electromagnetic scattering problems. In the last part of the book, the boundary element method is combined with a novel eigenvalue solver, a so-called contour integral method. An algorithm is presented, together with a set of successful numerical experiments, showing that the eigenvalue solver benefits from the high orders of convergence offered by the boundary element approach. Last, the resulting software, called BEMBEL (Boundary Element Method Based Engineering Library), is reviewed: the user interface is presented, while the underlying design considerations are explained in detail. Given its scope, this book bridges an important gap between numerical analysis and engineering design of electromagnetic devices.Magnetic reconnection in partially ionized plasmashttps://zbmath.org/1472.780032021-11-25T18:46:10.358925Z"Ni, Lei"https://zbmath.org/authors/?q=ai:ni.lei"Ji, Hantao"https://zbmath.org/authors/?q=ai:ji.hantao"Murphy, Nicholas A."https://zbmath.org/authors/?q=ai:murphy.nicholas-a"Jara-Almonte, Jonathan"https://zbmath.org/authors/?q=ai:jara-almonte.jonathanSummary: Magnetic reconnection has been intensively studied in fully ionized plasmas. However, plasmas are often partially ionized in astrophysical environments. The interactions between the neutral particles and ionized plasmas might strongly affect the reconnection mechanisms. We review magnetic reconnection in partially ionized plasmas in different environments from theoretical, numerical, observational and experimental points of view. We focus on mechanisms which make magnetic reconnection fast enough to compare with observations, especially on the reconnection events in the low solar atmosphere. The heating mechanisms and the related observational evidence of the reconnection process in the partially ionized low solar atmosphere are also discussed. We describe magnetic reconnection in weakly ionized astrophysical environments, including the interstellar medium and protostellar discs. We present recent achievements about fast reconnection in laboratory experiments for partially ionized plasmas.Explicit Cartesian oval as a superconic surface for stigmatic imaging optical systems with real or virtual source or imagehttps://zbmath.org/1472.780042021-11-25T18:46:10.358925Z"Silva-Lora, Alberto"https://zbmath.org/authors/?q=ai:silva-lora.alberto"Torres, Rafael"https://zbmath.org/authors/?q=ai:torres.rafaelSummary: Cartesian ovals, also known as rigorously stigmatic surfaces, are the simplest optical systems capable of producing a perfect point image. Exist both implicit and explicit expressions to represent these surfaces, but they treat both refractive and reflective surfaces independently. Because of the complexity of explicit expressions, the ray-tracing techniques for these surfaces are implemented using third-party software. In this paper, we express Cartesian ovals as a degenerated superconic curve and get a new explicit formulation for Cartesian ovals capable of treating image formation using both object and image points, either real or virtual, and in this formulation can deal with both reflective and refractive rigorously stigmatic surfaces. Finally, using the resultant expressions and the vector Snell-Descartes Law, we propose a self-contained analytical ray-tracing technique for all these surfaces.The field of values of Jones matrices: classification and special caseshttps://zbmath.org/1472.780052021-11-25T18:46:10.358925Z"Gutiérrez-Vega, Julio C."https://zbmath.org/authors/?q=ai:gutierrez-vega.julio-cSummary: The concept of field of values (FoV), also known as the numerical range, is applied to the \(2 \times 2\) Jones matrices used in polarization optics. We discover the relevant interplay between the geometric properties of the FoV, the algebraic properties of the Jones matrices and the representation of polarization states on the Poincaré sphere. The properties of the FoV reveal hidden symmetries in the relationships between the eigenvectors and eigenvalues of the Jones matrices. We determine the main mathematical properties of the FoV, discuss the special cases that are relevant to polarization optics, and describe its application to calculate the Pancharatnam-Berry phase introduced by an optical system to the input state.Slender-body theory for plasmonic resonancehttps://zbmath.org/1472.780062021-11-25T18:46:10.358925Z"Ruiz, Matias"https://zbmath.org/authors/?q=ai:ruiz.matias"Schnitzer, Ory"https://zbmath.org/authors/?q=ai:schnitzer.orySummary: We develop a slender-body theory for plasmonic resonance of slender metallic nanoparticles, focusing on a general class of axisymmetric geometries with locally paraboloidal tips. We adopt a modal approach where one first solves the plasmonic eigenvalue problem, a geometric spectral problem which governs the surface-plasmon modes of the particle; then, the latter modes are used, in conjunction with spectral-decomposition, to analyse localized-surface-plasmon resonance in the quasi-static limit. We show that the permittivity eigenvalues of the axisymmetric modes are strongly singular in the slenderness parameter, implying widely tunable, high-quality-factor, resonances in the near-infrared regime. For that family of modes, we use matched asymptotics to derive an effective eigenvalue problem, a singular non-local Sturm-Liouville problem, where the lumped one-dimensional eigenfunctions represent axial voltage profiles (or charge line densities). We solve the effective eigenvalue problem in closed form for a prolate spheroid and numerically, by expanding the eigenfunctions in Legendre polynomials, for arbitrarily shaped particles. We apply the theory to plane-wave illumination in order to elucidate the excitation of multiple resonances in the case of non-spheroidal particles.Correction to: ``A doubly anharmonic oscillator in an induced electric dipole system''https://zbmath.org/1472.780072021-11-25T18:46:10.358925Z"Bakke, K."https://zbmath.org/authors/?q=ai:bakke.knut"Salvador, C."https://zbmath.org/authors/?q=ai:salvador.cCorrects several typos in [the authors, ibid. 474, No. 2217, Article ID 20170881, 7 p. (2018; Zbl 1407.78008)].Dynamics of a dipole in a stationary electromagnetic fieldhttps://zbmath.org/1472.780082021-11-25T18:46:10.358925Z"Maciejewski, Andrzej J."https://zbmath.org/authors/?q=ai:maciejewski.andrzej-j"Przybylska, Maria"https://zbmath.org/authors/?q=ai:przybylska.maria"Yaremko, Yurij"https://zbmath.org/authors/?q=ai:yaremko.yurijSummary: The non-relativistic dynamics of an electric dipole in a uniform and stationary electromagnetic field is considered. The equations of motion are derived \textit{ab initio}. It is shown that they are Hamiltonian with respect to a certain degenerated Poisson st+ructure. The system has a `hidden' symmetry which allows its dimension to be reduced. The reduced system is also Hamiltonian with respect to a degenerated Poisson structure. We show how to perform this reduction in the framework of the Lagrange formalism. Integrability of the reduced system is investigated. It was proved that the system is non-integrable except for two cases when, for specific values of parameters, the system admits an additional first integral.Homogenization of plasmonic crystals: seeking the epsilon-near-zero effecthttps://zbmath.org/1472.780092021-11-25T18:46:10.358925Z"Maier, M."https://zbmath.org/authors/?q=ai:maier.martin|maier.markus|maier.michael|maier.martina"Mattheakis, M."https://zbmath.org/authors/?q=ai:mattheakis.m"Kaxiras, E."https://zbmath.org/authors/?q=ai:kaxiras.efthimios"Luskin, M."https://zbmath.org/authors/?q=ai:luskin.mitchell"Margetis, D."https://zbmath.org/authors/?q=ai:margetis.dionisiosSummary: By using an asymptotic analysis and numerical simulations, we derive and investigate a system of homogenized Maxwell's equations for conducting material sheets that are periodically arranged and embedded in a heterogeneous and anisotropic dielectric host. This structure is motivated by the need to design plasmonic crystals that enable the propagation of electromagnetic waves with no phase delay (epsilon-near-zero effect). Our microscopic model incorporates the surface conductivity of the two-dimensional (2D) material of each sheet and a corresponding line charge density through a line conductivity along possible edges of the sheets. Our analysis generalizes averaging principles inherent in previous Bloch-wave approaches. We investigate physical implications of our findings. In particular, we emphasize the role of the vector-valued corrector field, which expresses microscopic modes of surface waves on the 2D material. We demonstrate how our homogenization procedure may set the foundation for computational investigations of: effective optical responses of reasonably general geometries, and complicated design problems in the plasmonics of 2D materials.Magnetic winding: what is it and what is it good for?https://zbmath.org/1472.780102021-11-25T18:46:10.358925Z"Prior, Christopher"https://zbmath.org/authors/?q=ai:prior.christopher-b"Mactaggart, David"https://zbmath.org/authors/?q=ai:mactaggart.davidSummary: Magnetic winding is a fundamental topological quantity that underpins magnetic helicity and measures the entanglement of magnetic field lines. Like magnetic helicity, magnetic winding is also an invariant of ideal magnetohydrodynamics. In this article, we give a detailed description of what magnetic winding describes, how to calculate it and how to interpret it in relation to helicity. We show how magnetic winding provides a clear topological description of magnetic fields (open or closed) and we give examples to show how magnetic winding and helicity can behave differently, thus revealing different and important information about the underlying magnetic field.Loss-less propagation, elastic and inelastic interaction of electromagnetic soliton in an anisotropic ferromagnetic nanowirehttps://zbmath.org/1472.780112021-11-25T18:46:10.358925Z"Senthil Kumar, V."https://zbmath.org/authors/?q=ai:kumar.v-senthil"Kavitha, L."https://zbmath.org/authors/?q=ai:kavitha.louis"Boopathy, C."https://zbmath.org/authors/?q=ai:boopathy.c"Gopi, D."https://zbmath.org/authors/?q=ai:gopi.dSummary: Nonlinear interaction of electromagnetic solitons leads to a plethora of interesting physical phenomena in the diverse area of science that include magneto-optics based data storage industry. We investigate the nonlinear magnetization dynamics of a one-dimensional anisotropic ferromagnetic nanowire. The famous Landau-Lifshitz-Gilbert equation (LLG) describes the magnetization dynamics of the ferromagnetic nanowire and the Maxwell's equations govern the propagation dynamics of electromagnetic wave passing through the axis of the nanowire. We perform a uniform expansion of magnetization and magnetic field along the direction of propagation of electromagnetic wave in the framework of reductive perturbation method. The excitation of magnetization of the nanowire is restricted to the normal plane at the lowest order of perturbation and goes out of plane for higher orders. The dynamics of the ferromagnetic nanowire is governed by the modified Korteweg-de Vries (mKdV) equation and the perturbed modified Korteweg-de Vries (pmKdV) equation for the lower and higher values of damping respectively. We invoke the Hirota bilinearization procedure to mKdV and pmKdV equation to construct the multi-soliton solutions, and explicitly analyze the nature of collision phenomena of the co-propagating EM solitons for the above mentioned lower and higher values of Gilbert-damping due to the precessional motion of the ferromagnetic spin. The EM solitons appearing in the higher damping regime exhibit elastic collision thus yielding the fascinating state restoration property, whereas those of lower damping regime exhibit inelastic collision yielding the solitons of suppressed intensity profiles. The propagation of EM soliton in the nanoscale magnetic wire has potential technological applications in optimizing the magnetic storage devices and magneto-electronics.Analytical model for electrohydrodynamic thrusthttps://zbmath.org/1472.780122021-11-25T18:46:10.358925Z"Vaddi, Ravi Sankar"https://zbmath.org/authors/?q=ai:vaddi.ravi-sankar"Guan, Yifei"https://zbmath.org/authors/?q=ai:guan.yifei"Mamishev, Alexander"https://zbmath.org/authors/?q=ai:mamishev.alexander-v"Novosselov, Igor"https://zbmath.org/authors/?q=ai:novosselov.igorSummary: Electrohydrodynamic (EHD) thrust is produced when ionized fluid is accelerated in an electric field due to the momentum transfer between the charged species and neutral molecules. We extend the previously reported analytical model that couples space charge, electric field and momentum transfer to derive thrust force in one-dimensional planar coordinates. The electric current density in the model can be expressed in the form of Mott-Gurney law. After the correction for the drag force, the EHD thrust model yields good agreement with the experimental data from several independent studies. The EHD thrust expression derived from the first principles can be used in the design of propulsion systems and can be readily implemented in the numerical simulations.Waves and vibrations in a finitely deformed electroelastic circular cylindrical tubehttps://zbmath.org/1472.780132021-11-25T18:46:10.358925Z"Dorfmann, Luis"https://zbmath.org/authors/?q=ai:dorfmann.luis"Ogden, Ray W."https://zbmath.org/authors/?q=ai:ogden.raymond-wSummary: In two recent papers, conditions for which axisymmetric incremental bifurcation could arise for a circular cylindrical tube subject to axial extension and radial inflation in the presence of an axial load, internal pressure and a radial electric field were examined, the latter being effected by a potential difference between compliant electrodes on the inner and outer radial surfaces of the tube. The present paper takes this work further by considering the incremental deformations to be time-dependent. In particular, both the axisymmetric vibration of a tube of finite length with appropriate end conditions and the propagation of axisymmetric waves in a tube are investigated. General equations and boundary conditions governing the axisymmetric incremental motions are obtained and then, for purposes of numerical evaluation, specialized for a Gent electroelastic model. The resulting system of equations is solved numerically and the results highlight the dependence of the frequency of vibration and wave speed on the tube geometry, applied deformation and electrostatic potential. In particular, the bifurcation results obtained previously are recovered as a special case when the frequency vanishes. Specification of an incremental potential difference in the present work ensures that there is no incremental electric field exterior to the tube. Results are also illustrated for a neo-Hookean electroelastic model and compared with those previously obtained for the case in which no incremental potential difference (or charge) is specified and an external field is required.Stability of a vacuum arc discharge on surfaces of hot-rolled steels and its frequency characteristicshttps://zbmath.org/1472.780142021-11-25T18:46:10.358925Z"Arustamov, V. N."https://zbmath.org/authors/?q=ai:arustamov.v-n"Ashurov, Kh. B."https://zbmath.org/authors/?q=ai:ashurov.kh-b"Mirkarimov, A. M."https://zbmath.org/authors/?q=ai:mirkarimov.a-m"Pozharov, S. L."https://zbmath.org/authors/?q=ai:pozharov.s-l"Kadirov, Kh. Kh."https://zbmath.org/authors/?q=ai:kadirov.kh-kh"Urisbekov, A. S."https://zbmath.org/authors/?q=ai:urisbekov.a-sSummary: The stability of a vacuum arc discharge (VAD) with allowance made for the parameters of an external circuit and a deduced equation of the heterogeneous kinetics of elementary cathode spots (ECSs) in the group cathode spot with one dimensional configuration is analyzed. It is theoretically and experimentally shown that a VAD with a rising voltage current characteristic (VCC) is stable independently of the parameters of the external circuit. Stability conditions for a VAD with falling VCC are found.A nonlinear moment model for radiative transfer equationhttps://zbmath.org/1472.780152021-11-25T18:46:10.358925Z"Li, Ruo"https://zbmath.org/authors/?q=ai:li.ruo"Song, Peng"https://zbmath.org/authors/?q=ai:song.peng"Zheng, Lingchao"https://zbmath.org/authors/?q=ai:zheng.lingchaoSmall deformation theory for two leaky dielectric drops in a uniform electric fieldhttps://zbmath.org/1472.780162021-11-25T18:46:10.358925Z"Zabarankin, Michael"https://zbmath.org/authors/?q=ai:zabarankin.michaelSummary: A small deformation theory for two non-identical spherical drops freely suspended in an ambient fluid and subjected to a uniform electric field is presented. The three phases are assumed to be leaky dielectric (slightly conducting) viscous incompressible fluids and the nonlinear effects of inertia and surface charge convection are neglected. The deformed shapes of the drops are linearized with respect to the electric capillary number that characterizes the balance between the electric stress and the surface tension. When the two drops are sufficiently far apart, their deformed shapes are predicted by Taylor's small deformation theory---depending on Taylor's discriminating function, the drops may become prolate, oblate or remain spherical. When the two drops get closer to each other, in addition to becoming prolate/oblate, they start translating and developing an egg shape. (Since there is no net charge, the centre of mass of the two drops remains stationary.) The extent of each of these `modes' of deformation depends on the distance between the drops' centres and on drop-to-ambient fluid ratios of electric conductivities, dielectric constants and viscosities. The predictions of the small deformation theory for two drops perfectly agree with the existing results of two-drop dynamics simulation based on a boundary-integral equation approach. Moreover, while previous works observed only three types of behaviour for two identical drops---the drops may either become prolate or oblate and move towards each other or become prolate and move away from each other---the small deformation theory predicts that non-identical drops may, in fact, become oblate and move away from each other when the drop-to-ambient fluid conductivity ratios are reciprocal and the drop-to-ambient fluid viscosity ratios are sufficiently large. The presented theory also readily yields an analytical insight into the interplay among different modes of drop deformation and can be used to guide the selection of the phases' electromechanical properties for two-drop dynamics simulations.Boundary-layer effects on electromagnetic and acoustic extraordinary transmission through narrow slitshttps://zbmath.org/1472.780172021-11-25T18:46:10.358925Z"Brandão, Rodolfo"https://zbmath.org/authors/?q=ai:brandao.rodolfo"Holley, Jacob R."https://zbmath.org/authors/?q=ai:holley.jacob-r"Schnitzer, Ory"https://zbmath.org/authors/?q=ai:schnitzer.orySummary: We study the problem of resonant extraordinary transmission of electromagnetic and acoustic waves through subwavelength slits in an infinite plate, whose thickness is close to a half-multiple of the wavelength. We build on the matched-asymptotics analysis of
the second and third author [Wave Motion 91, Article ID 102381, 9 p. (2019; Zbl 07222225)],
who considered a single-slit system assuming an idealized formulation where dissipation is neglected and the electromagnetic and acoustic problems are analogous. We here extend that theory to include thin dissipative boundary layers associated with finite conductivity of the plate in the electromagnetic problem and viscous and thermal effects in the acoustic problem, considering both single-slit and slit-array configurations. By considering a distinguished boundary-layer scaling where dissipative and diffractive effects are comparable, we develop accurate analytical approximations that are generally valid near resonance; the electromagnetic-acoustic analogy is preserved up to a single parameter that is provided explicitly for both scenarios. The theory is shown to be in excellent agreement with GHz-microwave and kHz-acoustic experiments in the literature.Dispersive and effective properties of two-dimensional periodic mediahttps://zbmath.org/1472.780182021-11-25T18:46:10.358925Z"Godin, Yuri A."https://zbmath.org/authors/?q=ai:godin.yuri-a"Vainberg, Boris"https://zbmath.org/authors/?q=ai:vainberg.boris-rSummary: We consider transverse propagation of electromagnetic waves through a two-dimensional composite material containing a periodic rectangular array of circular cylinders. Propagation of waves is described by the Helmholtz equation with the continuity conditions for the tangential components of the electric and magnetic fields on the boundaries of the cylinders. We assume that the cell size is small compared with the wavelength, but large compared with the radius \(a\) of the inclusions. Explicit formulae are obtained for asymptotic expansion of the solution of the problem in terms of the dimensionless magnitude \(q\) of the wavevector and radius \(a\). This leads to explicit formulae for the effective dielectric tensor and the dispersion relation with the rigorously justified error of order \(O((q^2 + a^2)^{5/2})\).Dyakonov-Voigt surface waveshttps://zbmath.org/1472.780192021-11-25T18:46:10.358925Z"Mackay, Tom G."https://zbmath.org/authors/?q=ai:mackay.tom-g"Zhou, Chenzhang"https://zbmath.org/authors/?q=ai:zhou.chenzhang"Lakhtakia, Akhlesh"https://zbmath.org/authors/?q=ai:lakhtakia.akhleshSummary: Electromagnetic surface waves guided by the planar interface of an isotropic dielectric medium and a uniaxial dielectric medium, both non-dissipative, were considered, the optic axis of the uniaxial medium lying in the interface plane. Whereas this interface is known to support the propagation of Dyakonov surface waves when certain constraints are satisfied by the constitutive parameters of the two partnering mediums, we identified a different set of constraints that allow the propagation of surface waves of a new type. The fields of the new surface waves, named Dyakonov-Voigt (DV) surface waves, decay as the product of a linear and an exponential function of the distance from the interface in the anisotropic medium, whereas the fields of the Dyakonov surface waves decay only exponentially in the anisotropic medium. In contrast to Dyakonov surface waves, the wavenumber of a DV surface wave can be found analytically. Also, unlike Dyakonov surface waves, DV surface waves propagate only in one direction in each quadrant of the interface plane.The general coupled Hirota equations: modulational instability and higher-order vector rogue wave and multi-dark soliton structureshttps://zbmath.org/1472.780202021-11-25T18:46:10.358925Z"Zhang, Guoqiang"https://zbmath.org/authors/?q=ai:zhang.guoqiang"Yan, Zhenya"https://zbmath.org/authors/?q=ai:yan.zhenya"Wang, Li"https://zbmath.org/authors/?q=ai:wang.li.5|wang.li.6|wang.li|wang.li.3|wang.li.2|wang.li.1|wang.li.4Summary: The general coupled Hirota equations are investigated, which describe the wave propagations of two ultrashort optical fields in a fibre. Firstly, we study the modulational instability for the focusing, defocusing and mixed cases. Secondly, we present a unified formula of high-order rational rogue waves (RWs) for the focusing, defocusing and mixed cases, and find that the distribution patterns for novel vector rational RWs of focusing case are more abundant than ones in the scalar model. Thirdly, the \(N\) th-order vector semirational RWs can demonstrate the coexistence of \(N\) th-order vector rational RWs and \(N\) breathers. Fourthly, we derive the multi-dark-dark solitons for the defocsuing and mixed cases. Finally, we derive a formula for the coexistence of dark solitons and RWs. These results further enrich and deepen the understanding of localized wave excitations and applications in vector nonlinear wave systems.Convolution quadrature methods for time-domain scattering from unbounded penetrable interfaceshttps://zbmath.org/1472.780212021-11-25T18:46:10.358925Z"Labarca, Ignacio"https://zbmath.org/authors/?q=ai:labarca.ignacio"Faria, Luiz M."https://zbmath.org/authors/?q=ai:faria.luiz-m"Pérez-Arancibia, Carlos"https://zbmath.org/authors/?q=ai:perez-arancibia.carlosSummary: This paper presents a class of boundary integral equation methods for the numerical solution of acoustic and electromagnetic time-domain scattering problems in the presence of unbounded penetrable interfaces in two spatial dimensions. The proposed methodology relies on convolution quadrature (CQ) schemes and the recently introduced windowed Green function (WGF) method. As in standard time-domain scattering from bounded obstacles, a CQ method of the user's choice is used to transform the problem into a finite number of (complex) frequency-domain problems posed, in our case, on the domains containing unbounded penetrable interfaces. Each one of the frequency-domain transmission problems is then formulated as a second-kind integral equation that is effectively reduced to a bounded interface by means of the WGF method---which introduces errors that decrease super-algebraically fast as the window size increases. The resulting windowed integral equations can then be solved by means of any (accelerated or unaccelerated) off-the-shelf Nyström or boundary element Helmholtz integral equation solvers capable of handling complex wavenumbers with large imaginary part. A high-order Nyström method based on Alpert's quadrature rules is used here. A variety of CQ schemes and numerical examples, including wave propagation in open waveguides as well as scattering from multiple layered media, demonstrate the capabilities of the proposed approach.On possible applications of media described by fractional-order models in electromagnetic cloakinghttps://zbmath.org/1472.780222021-11-25T18:46:10.358925Z"Stefański, Tomasz P."https://zbmath.org/authors/?q=ai:stefanski.tomasz-pAuthor's abstract: The purpose of this paper is to open a scientific discussion on possible applications of media described by fractional-order (FO) models (FOMs) in electromagnetic cloaking. A 2-D cloak based on active sources and the surface equivalence theorem is simulated. It employs a medium described by FOM in communication with sources cancelling the scattered field. A perfect electromagnetic active cloak is thereby demonstrated with the use of a finite-difference time-domain method combined with a simulation algorithm of non-monochromatic wave propagation in the media described by FOM. The application of constitutive relations based on FOMs in Maxwell's equations provides solutions which correspond to the results reported for the time-fractional diffusion-wave equation, which is non-relativistic, like the classical diffusion equation. This property is employed in the presented cloaking scheme for communication with active current sources around the cloak, which cancel the scattered field of an object inside the cloak. Although in the real world perfect invisibility is impossible to obtain due to the constraint of light speed, it is possible to obtain a perfect cloak in theoretical considerations by using FO formulation of electro-magnetism. It is worth noticing that numerous literature sources experimentally confirm the existence of electromagnetic media described by FOMs; hence, the presented numerical results should hopefully stimulate further investigations related to applications of FOMs in electromagnetic cloaking.Dielectric-induced surface wave radiation losshttps://zbmath.org/1472.780232021-11-25T18:46:10.358925Z"Schaich, Tobias"https://zbmath.org/authors/?q=ai:schaich.tobias"Rawi, Anas Al"https://zbmath.org/authors/?q=ai:rawi.anas-al"Morsman, Trevor"https://zbmath.org/authors/?q=ai:morsman.trevor"Payne, Mike"https://zbmath.org/authors/?q=ai:payne.mike-cSummary: We investigate a model which shows how the introduction of a perturbing dielectric close to an electromagnetic surface wave leads to radiation away from the surface through the dielectric. This resembles a surface waveguide passing through a wall or being deployed underground. Our theory, which is based on the mode-matching technique, allows quantitative determination of losses from a bound surface wave mode up to the point of its complete extinction. For a surface wave supported by a coated, conducting sheet the attenuation due to the perturbing dielectric is calculated for a number of frequencies, permittivities of the perturbation and separations between the sheet and the perturbing dielectric. The accuracy of our results is verified by simulation of the system with a full-wave numerical solution. Finally, we report experimental data of perturbed surface waves on a cable, which are in qualitative agreement with our model.Guided electromagnetic waves for periodic arrays of thin metallic wires near an interface between two dielectric mediahttps://zbmath.org/1472.780242021-11-25T18:46:10.358925Z"Zalipaev, V. V."https://zbmath.org/authors/?q=ai:zalipaev.v-v"Kosulnikov, S. Yu."https://zbmath.org/authors/?q=ai:kosulnikov.s-yuSummary: Guided localized electromagnetic waves propagating along one-dimensional (1D) arrays of thin metallic parallel wires, finite and infinite, are studied. The arrays are embedded into the upper dielectric half-space close to the interface separating it from the lower dielectric medium with different permittivity and the same permeability. Firstly, a dependence of resonance frequencies of excited wave modes for finite array with respect to the array height above the interface is studied. The array is excited by a normally incident plane wave. It is important that the order of the resonance modes changes if the distance between the array and the interface becomes small. An analysis, based on the Pocklington system of integral equations to evaluate resonance frequencies and compute the fields of excited modes above the array, was applied. This approach is based on the longwave approximation of thin wires. Secondly, the waves propagating along infinite 1D array of thin metallic wires that is close to the interface are studied. Dispersion curves are presented for the lowest case of half-wave resonance for different heights of the array over the interface. When the array approaches very close to the interface an anomalous dispersion is observed. The results of the numerical analysis were tested against computations obtained by means of other independent CST Studio Suite simulations.Terahertz range resonances of metasurface formed by double-layer grating of microsize graphene strips inside dielectric slabhttps://zbmath.org/1472.780252021-11-25T18:46:10.358925Z"Zinenko, Tatiana L."https://zbmath.org/authors/?q=ai:zinenko.tatiana-l"Matsushima, Akira"https://zbmath.org/authors/?q=ai:matsushima.akira"Nosich, Alexander I."https://zbmath.org/authors/?q=ai:nosich.alexander-iSummary: We analyse, using integral equations and a previously developed in-house numerical algorithm, the scattering and absorption of the \(H\)-polarized plane wave by a metasurface consisting of a double-layer grating of flat graphene strips placed into a lossless dielectric slab. The algorithm is meshless and its convergence is guaranteed mathematically. It is a version of the method of analytical preconditioning; namely, it uses the set of weighted Chebyshev polynomials as expansion functions in the discretization of a hypersingular electric field integral equation for the on-strip current. Then the computational error is controlled by the matrix size and can be reduced to machine precision. Using this advanced tool, we plot the frequency dependences, in a huge range from 1 GHz to 10 THz, of the transmittance, reflectance and absorbance of such a metasurface. This accurate analysis reveals resonances on several types of natural modes, best understood via visualization of in-resonance near-fields. In addition to plasmon-mode resonances, special attention is paid to the ultra-high-\(Q\) resonances on the lattice modes, which are absent on the free-standing graphene strip gratings.Modelling and testing of a wave energy converter based on dielectric elastomer generatorshttps://zbmath.org/1472.780262021-11-25T18:46:10.358925Z"Moretti, Giacomo"https://zbmath.org/authors/?q=ai:moretti.giacomo"Papini, Gastone Pietro Rosati"https://zbmath.org/authors/?q=ai:papini.gastone-pietro-rosati"Daniele, Luca"https://zbmath.org/authors/?q=ai:daniele.luca"Forehand, David"https://zbmath.org/authors/?q=ai:forehand.david-i-m"Ingram, David"https://zbmath.org/authors/?q=ai:ingram.david-m"Vertechy, Rocco"https://zbmath.org/authors/?q=ai:vertechy.rocco"Fontana, Marco"https://zbmath.org/authors/?q=ai:fontana.marcoSummary: This paper introduces the analysis and design of a wave energy converter (WEC) that is equipped with a novel kind of electrostatic power take-off system, known as dielectric elastomer generator (DEG). We propose a modelling approach which relies on the combination of nonlinear potential-flow hydrodynamics and electro-hyperelastic theory. Such a model makes it possible to predict the system response in operational conditions, and thus it is employed to design and evaluate a DEG-based WEC that features an effective dynamic response. The model is validated through the design and test of a small-scale prototype, whose dynamics is tuned with waves at tank-scale using a set of scaling rules for the DEG dimensions introduced here in order to comply with Froude similarity laws. Wave-tank tests are conducted in regular and irregular waves with a functional DEG system that is controlled using a realistic prediction-free strategy. Remarkable average performance in realistically scaled sea states has been recorded during experiments, with peaks of power output of up to 3.8 W, corresponding to hundreds of kilowatts at full-scale. The obtained results demonstrated the concrete possibility of designing DEG-based WEC devices that are conceived for large-scale electrical energy production.The effect of an exterior electric field on the instability of dielectric plateshttps://zbmath.org/1472.780272021-11-25T18:46:10.358925Z"Su, Yipin"https://zbmath.org/authors/?q=ai:su.yipin"Chen, Weiqiu"https://zbmath.org/authors/?q=ai:chen.weiqiu"Dorfmann, Luis"https://zbmath.org/authors/?q=ai:dorfmann.luis"Destrade, Michel"https://zbmath.org/authors/?q=ai:destrade.michelSummary: We investigate the theoretical nonlinear response, Hessian stability, and possible wrinkling behaviour of a voltage-activated dielectric plate immersed in a tank filled with silicone oil. Fixed rigid electrodes are placed on the top and bottom of the tank, and an electric field is generated by a potential difference between the electrodes. We solve the associated incremental boundary value problem of superimposed, inhomogeneous small-amplitude wrinkles, signalling the onset of instability. We decouple the resulting bifurcation equation into symmetric and antisymmetric modes. For a neo-Hookean dielectric plate, we show that a potential difference between the electrodes can induce a thinning of the plate and thus an increase of its planar area, similar to the scenarios encountered when there is no silicone oil. However, we also find that, depending on the material and geometric parameters, an increasing applied voltage can also lead to a \textit{thickening} of the plate, and thus a shrinking of its area. In that scenario, Hessian instability and wrinkling bifurcation may then occur spontaneously once some critical voltages are reached.Exact and linearized refractive index stress-dependence in anisotropic photoelastic crystalshttps://zbmath.org/1472.780282021-11-25T18:46:10.358925Z"Daví, Fabrizio"https://zbmath.org/authors/?q=ai:davi.fabrizioSummary: For the permittivity tensor of photoelastic anisotropic crystals, we obtain the exact nonlinear dependence on the Cauchy stress tensor. We obtain the same result for its square root, whose principal components, the crystal principal refractive index, are the starting point for any photoelastic analysis of transparent crystals. From these exact results we then obtain, in a totally general manner, the linearized expressions to within higher-order terms in the stress tensor for both the permittivity tensor and its square root. We finish by showing some relevant examples of both nonlinear and linearized relations for optically isotropic, uniaxial and biaxial crystals.Nonlinear self-dual network equations: modulation instability, interactions of higher-order discrete vector rational solitons and dynamical behaviourshttps://zbmath.org/1472.780292021-11-25T18:46:10.358925Z"Wen, Xiao-Yong"https://zbmath.org/authors/?q=ai:wen.xiaoyong"Yan, Zhenya"https://zbmath.org/authors/?q=ai:yan.zhenya"Zhang, Guoqiang"https://zbmath.org/authors/?q=ai:zhang.guoqiangSummary: The nonlinear self-dual network equations that describe the propagations of electrical signals in nonlinear LC self-dual circuits are explored. We firstly analyse the modulation instability of the constant amplitude waves. Secondly, a novel generalized perturbation \((M, N - M)\)-fold Darboux transform (DT) is proposed for the lattice system by means of the Taylor expansion and a parameter limit procedure. Thirdly, the obtained perturbation \((1, N - 1)\)-fold DT is used to find its new higher-order rational solitons (RSs) in terms of determinants. These higher-order RSs differ from those known results in terms of hyperbolic functions. The abundant wave structures of the first-, second-, third- and fourth-order RSs are exhibited in detail. Their dynamical behaviours and stabilities are numerically simulated. These results may be useful for understanding the wave propagations of electrical signals.Numerical simulation of formation and evolution of dissipative breathers of the classical Heisenberg antiferromagnet modelhttps://zbmath.org/1472.780302021-11-25T18:46:10.358925Z"Muminov, Kh. Kh."https://zbmath.org/authors/?q=ai:muminov.kh-kh"Muhamedova, Sh. F."https://zbmath.org/authors/?q=ai:muhamedova.sh-fSummary: In the present paper we conduct numerical simulation of the breather (soliton-like) solutions of classical Heisenberg antiferromagnetic acted upon by the variable external electromagnetic fields pumping and dissipation. The numerical recipe of simulation on the basic of stereographic projection is suggested avoiding singularities on the poles of the Bloch sphere. Parameters of regime of formation of dissipative breathers are determined.Quantum information measures of the Aharonov-Bohm ring in uniform magnetic fieldshttps://zbmath.org/1472.810232021-11-25T18:46:10.358925Z"Olendski, O."https://zbmath.org/authors/?q=ai:olendski.olegSummary: Shannon quantum information entropies \(S_{\rho, \gamma}\), Fisher informations \(I_{\rho, \gamma}\), Onicescu energies \(O_{\rho, \gamma}\) and complexities \(e^S O\) are calculated both in the position (subscript \(\rho\)) and momentum (\(\gamma\)) spaces for the azimuthally symmetric two-dimensional nanoring that is placed into the combination of the transverse uniform magnetic field \(\mathbf{B}\) and the Aharonov-Bohm (AB) flux \(\phi_{AB}\) and whose potential profile is modelled by the superposition of the quadratic and inverse quadratic dependencies on the radius \(r\). The increasing intensity \(B\) flattens momentum waveforms \(\Phi_{nm}(\mathbf{k})\) and in the limit of the infinitely large fields they turn to zero: \(\Phi_{n m}(\mathbf{k}) \to 0\) at \(B \to \infty \), what means that the position wave functions \(\Psi_{n m}(\mathbf{r})\), which are their Fourier counterparts, tend in this limit to the \(\delta\)-functions. Position (momentum) Shannon entropy depends on the field \(B\) as a negative (positive) logarithm of \(\omega_{eff} \equiv (\omega_0^2 + \omega_c^2 / 4)^{1/2}\), where \(\omega_0\) determines the quadratic steepness of the confining potential and \(\omega_c\) is a cyclotron frequency. This makes the sum \(S_{\rho_{nm}} + S_{\gamma_{nm}}\) a field-independent quantity that increases with the principal \(n\) and azimuthal \(m\) quantum numbers and does satisfy entropic uncertainty relation. Position Fisher information does not depend on \(m\), linearly increases with \(n\) and varies as \(\omega_{eff}\) whereas its \(n\) and \(m\) dependent Onicescu counterpart \(O_{\rho_{nm}}\) changes as \(\omega_{eff}^{-1}\). The products \(I_{\rho_{nm}} I_{\gamma_{nm}}\) and \(O_{\rho_{nm}} O_{\gamma_{nm}}\) are \(B\)-independent quantities. A dependence of the measures on the ring geometry is discussed. It is argued that a variation of the position Shannon entropy or Onicescu energy with the AB field uniquely determines an associated persistent current as a function of \(\phi_{AB}\) at \(B = 0\). An inverse statement is correct too.Measuring space deformation via graphene under constraintshttps://zbmath.org/1472.810762021-11-25T18:46:10.358925Z"Jellal, Ahmed"https://zbmath.org/authors/?q=ai:jellal.ahmedSummary: We describe the lattice deformation in graphene under strain effect by considering the spacial-momenta coordinates do not commute. This later can be realized by introducing the star product to end up with a generalized Heisenberg algebra. Within such framework, we build a new model describing Dirac fermions interacting with an external source that is noncommutative parameter \(\kappa\) dependent. The solutions of energy spectrum are showing Landau levels in similar way to the case of a real magnetic field applied to graphene. We show that some strain configurations can be used to explicitly evaluate \(\kappa\) and then offer a piste toward its measurement.Dirac particle with memory: proper time non-localityhttps://zbmath.org/1472.810872021-11-25T18:46:10.358925Z"Tarasov, Vasily E."https://zbmath.org/authors/?q=ai:tarasov.vasily-eSummary: A generalization of the standard model of Dirac particle in external electromagnetic field is proposed. In the generalization we take into account interactions of this particle with environment, which is described by the memory function. This function takes into account that the behavior of the particle at proper time can depend not only at the present time, but also on the history of changes on finite time interval. In this case the Dirac particle can be considered an open quantum system with non-Markovian dynamics. The violation of the semigroup property of dynamic maps is a characteristic property of dynamics with memory. We use the Fock-Schwinger proper time method and derivatives of non-integer orders with respect to proper time. The fractional differential equation, which describes the Dirac particle with memory, and the expression of its exact solution are suggested. The asymptotic behavior of the proposed solutions is described.An interacting conformal chiral 2-form electrodynamics in six dimensionshttps://zbmath.org/1472.811962021-11-25T18:46:10.358925Z"Townsend, Paul K."https://zbmath.org/authors/?q=ai:townsend.paul-kingsleySummary: The strong-field limit for the 2-form potential on an M5-brane yields a conformal chiral 2-form electrodynamics in six dimensions, with gauge-invariant self-interactions but no adjustable coupling constant; the stress tensor is that of a null fluid. Lorentz invariance can be made manifest via an interpretation as a tensionless `space-filling M5-brane', or as a truncation of the infrared dynamics of an M5-brane in \(AdS_7 \times S^4\).Pion magnetic polarisability using the background field methodhttps://zbmath.org/1472.813082021-11-25T18:46:10.358925Z"Bignell, Ryan"https://zbmath.org/authors/?q=ai:bignell.ryan"Kamleh, Waseem"https://zbmath.org/authors/?q=ai:kamleh.waseem"Leinweber, Derek"https://zbmath.org/authors/?q=ai:leinweber.derek-bSummary: The magnetic polarisability is a fundamental property of hadrons, which provides insight into their structure in the low-energy regime. The pion magnetic polarisability is calculated using lattice QCD in the presence of background magnetic fields. The results presented are facilitated by the introduction of a new magnetic-field dependent quark-propagator eigenmode projector and the use of the background-field corrected clover fermion action. The magnetic polarisabilities are calculated in a relativistic formalism, and the excellent signal-to-noise property of pion correlation functions facilitates precise values.Diffraction pattern degradation driven by intense ultrafast X-ray pulse for \(H_2^+\)https://zbmath.org/1472.813182021-11-25T18:46:10.358925Z"Borovykh, S. V."https://zbmath.org/authors/?q=ai:borovykh.s-v"Mityureva, A. A."https://zbmath.org/authors/?q=ai:mityureva.a-a"Smirnov, V. V."https://zbmath.org/authors/?q=ai:smirnov.valerii-valentinovich|smirnov.valeri-v|smirnov.vitalii-vSummary: The drastic evolution of molecular systems exposed to ultrashort intense X-ray pulse is a fundamental obstacle for single-particle imaging (SPI) by means of X-ray free electron lasers (XFEL). Here we tackle the simplest molecule \(H_2^+\) and its diffraction pattern degradations in the strong ultrashort X-ray beam. The semiclassical method of the problem solution and its advantages are described in detail. We apply the method to calculate the electron density autocorrelation functions (ACF) for a few internuclear distances and then discuss numeric simulation data.Finite temperature aspect ratio in ultra-cold Bose gas for large Nhttps://zbmath.org/1472.813292021-11-25T18:46:10.358925Z"Kouidri, S."https://zbmath.org/authors/?q=ai:kouidri.smaineSummary: We present a detailed study of the temperature dependence of the condensate fraction, collective excitation and aspect ratio profiles of a Bose-condensed gas in a harmonic trap for large numbers of condensate atoms up to 85000. These quantities are calculated self-consistently using the generalized Hartree-Fock-Bogoliubov (GHFB) equations. We determine the evolution of the aspect ratio at zero and finite temperature \textit{via} the condensed fraction. We compare our results with experimental data and we find a good agreement.Spin orbit coupled Bose Einstein condensate in a two dimensional bichromatic optical latticehttps://zbmath.org/1472.813302021-11-25T18:46:10.358925Z"Oztas, Z."https://zbmath.org/authors/?q=ai:oztas.zSummary: We numerically investigate the localization of Bose Einstein condensate (BEC) with spin orbit coupling in a two dimensional bichromatic optical lattice. We study localization in weakly interacting and non-interacting regimes. The existence of stationary localized states in the presence of spin-orbit and Rabi couplings has been confirmed. We find that spin orbit coupling favors localization, whereas Rabi coupling has a slight delocalization effect.Theoretical approach to quantum cascade micro-laser broadband multimode emission in strong magnetic fieldshttps://zbmath.org/1472.813362021-11-25T18:46:10.358925Z"Gajić, Aleksandra"https://zbmath.org/authors/?q=ai:gajic.aleksandra"Radovanović, Jelena"https://zbmath.org/authors/?q=ai:radovanovic.jelena"Vuković, Nikola"https://zbmath.org/authors/?q=ai:vukovic.nikola"Milanović, Vitomir"https://zbmath.org/authors/?q=ai:milanovic.vitomir"Boiko, Dmitri L."https://zbmath.org/authors/?q=ai:boiko.dmitri-lSummary: We have theoretically explored the influence of the magnetic field on supporting the multimode Risken-Nummendal-Graham-Haken (RNGH) self-pulsations seen in the optical spectrum as two broad modulations sidebands at the Rabi flopping frequency [\textit{D. Smirnov} et al., Phys. rev. B 66, No. 12, Article ID 121305(R), 4 p. (2002; \url{doi:10.1103/PhysRevB.66.121305}), Article ID 125317, 4 p. (2002; \url{doi:10.1103/PhysRevB.66.125317})]. On the example of microcavity quantum cascade lasers (\(\mu\)-QCLs), we demonstrate that Landau quantization in an external magnetic field slows down the effective decoherence and diffusion rates. The pump current required to reach the broadband multimode RNGH self-pulsations is lowered with the magnetic field strength, while the Rabi flopping frequency and the overall optical spectrum width remain practically unchanged. Our theoretical results indicate that an external magnetic field can be a valuable tool for achieving high-power broadband QCL self-pulsations in practice.Complexity of the Einstein-Born-Infeld-massive black holeshttps://zbmath.org/1472.830472021-11-25T18:46:10.358925Z"Bahrami-Asl, B."https://zbmath.org/authors/?q=ai:bahrami-asl.b"Hendi, S. H."https://zbmath.org/authors/?q=ai:hendi.seyed-hosseinSummary: Motivated by interesting correspondence between computational complexity in a CFT and the action evaluated on a WDW patch in the bulk, we study the complexity of the Einstein-massive black holes in the presence of BI nonlinear electrodynamics. The upper limit of Lloyd's bound according to the WDW patch is investigated and it is found that there are some physical intervals for massive parameters in which Lloyd's bound is held.Testing the complexity conjecture in regular black holes geometryhttps://zbmath.org/1472.830502021-11-25T18:46:10.358925Z"El Moumni, H."https://zbmath.org/authors/?q=ai:el-moumni.hasan"Masmar, K."https://zbmath.org/authors/?q=ai:masmar.karimaSummary: Motived by the new complexity conjecture [\textit{A. R. Brown} et al., ``Holographic complexity equals bulk action?'', Phys. Rev. Lett. 116, No. 19, Article ID 191301, 5 p. (2016; \url{doi:10.1103/PhysRevLett.116.191301})] suggesting that the fastest computer in nature are the black holes. We study the action growth rate for a variety of four-dimensional regular black holes such as Hayward, Bardeen and the new class proposed in [\textit{Z. Y. Fan} and \textit{X. Wang}, ``Construction of regular black holes in general relativity'', Phys. Rev. D (3) 94, No. 12, Article ID 124027, 9 p. (2016; \url{doi:10.1103/PhysRevD.94.124027})]. Generally, we show that action growth rates of the Wheeler-De Witt patch are finite for such black hole configurations at the late time approach and satisfy the Lloyd bound on the rate of quantum computation. Also, the case of three dimensions space is investigated. In each regular black hole configuration, we found that the form of the Lloyd bound formula remains unaltered but the energy is modified due to the effect of the nonlinear electrodynamics where some extra-therm have appeared in the total growth action.Nonlinearly charged dyonic black holeshttps://zbmath.org/1472.830582021-11-25T18:46:10.358925Z"Panahiyan, Shahram"https://zbmath.org/authors/?q=ai:panahiyan.shahramSummary: In this paper, we investigate the thermodynamics of dyonic black holes in the presence of Born-Infeld electromagnetic field. We show that electric-magnetic duality reported for dyonic solutions with Maxwell field is omitted in case of Born-Infeld generalization. We also confirm that generalization to nonlinear field provides the possibility of canceling the effects of cosmological constant. This is done for nonlinearity parameter with \(10^{-33}\) \(\text{eV}^2\) order of magnitude which is high nonlinearity regime. In addition, we show that for small electric/magnetic charge and high nonlinearity regime, black holes would develop critical behavior and several phases. In contrast, for highly charged case and Maxwell limits (small nonlinearity), black holes have one thermal stable phase. We also find that the pressure of the cold black holes is bounded by some constraints on its volume while hot black holes' pressure has physical behavior for any volume. In addition, we report on possibility of existences of triple point and reentrant of phase transition in thermodynamics of these black holes. Finally, we show that if electric and magnetic charges are identical, the behavior of our solutions would be Maxwell like (independent of nonlinear parameter and field). In other words, nonlinearity of electromagnetic field becomes evident only when these black holes are charged magnetically and electrically different.Extensive layer clouds in the global electric circuit: their effects on vertical charge distribution and storagehttps://zbmath.org/1472.860162021-11-25T18:46:10.358925Z"Harrison, R. Giles"https://zbmath.org/authors/?q=ai:harrison.r-giles"Nicoll, Keri A."https://zbmath.org/authors/?q=ai:nicoll.keri-a"Mareev, Evgeny"https://zbmath.org/authors/?q=ai:mareev.evgeny"Slyunyaev, Nikolay"https://zbmath.org/authors/?q=ai:slyunyaev.nikolay-n"Rycroft, Michael J."https://zbmath.org/authors/?q=ai:rycroft.michael-jSummary: A fair-weather electric field has been observed near the Earth's surface for over two centuries. The field is sustained by charge generation in distant disturbed weather regions, through current flow in the global electric circuit. Conventionally, the fair-weather part of the global circuit has disregarded clouds, but extensive layer clouds, important to climate, are widespread globally. Such clouds are not electrically inert, becoming charged at their upper and lower horizontal boundaries from vertical current flow, in a new electrical regime---neither fair nor disturbed weather; hence it is described here as \textit{semi-fair weather}. Calculations and measurements show the upper cloud boundary charge is usually positive, the cloud interior positive and the lower cloud boundary negative, with the upper charge density larger, but of the same magnitude \(( \sim\) nC \(m^{-2} )\) as cloud base. Globally, the total positive charge stored by layer clouds is approximately \(10^{5 }\) C, which, combined with the positive charge in the atmospheric column above the cloud up to the ionosphere, balances the total negative surface charge of the fair-weather regions. Extensive layer clouds are, therefore, an intrinsic aspect of the global circuit, and the resulting natural charging of their cloud droplets is a fundamental atmospheric feature.A trio of simple optimized axisymmetric kinematic dynamos in a spherehttps://zbmath.org/1472.860172021-11-25T18:46:10.358925Z"Holdenried-Chernoff, D."https://zbmath.org/authors/?q=ai:holdenried-chernoff.d"Chen, L."https://zbmath.org/authors/?q=ai:chen.letian|chen.liuyi|chen.liang-ho|chen.liangguo|chen.li.1|chen.liangyan|chen.lidong|chen.lu|chen.lina|chen.liuxin|chen.lincong|chen.liangpeng|chen.liuhua|chen.lingli|chen.linsong|chen.lianhan|chen.lihuan|chen.liangyun|chen.lirong|chen.liqun|chen.laihuan|chen.liming.1|chen.lin.5|chen.longxiang|chen.lianghua|chen.lu.2|chen.lanxiang|chen.ling|chen.liqiang|chen.lizhong|chen.lujie|chen.lian|chen.lifeng.1|chen.lizhen|chen.linjue|chen.liangzhe|chen.lifan|chen.lang|chen.lin|chen.lichun|chen.liuhong|chen.luodan|chen.liqiong|chen.lu.3|chen.lonkey|chen.like|chen.leping|chen.lanlang|chen.li.7|chen.le.1|chen.lingyun|chen.liangzhi|chen.lianchang|chen.lienwen|chen.liyuan|chen.louisa|chen.lilin|chen.linghua|chen.lixing|chen.liujuan|chen.lijia|chen.lixiang|chen.lidi|chen.lusheng|chen.luo|chen.lujuan|chen.li.2|chen.liying|chen.liu-juan|chen.longjie|chen.lianlin|chen.liangsheng|chen.longfei|chen.lv|chen.lijuan|chen.licong|chen.liucai|chen.lingen|chen.lei|chen.liwen|chen.linhong|chen.leizhi|chen.lingxin|chen.lanjue|chen.liangjun|chen.lijiang|chen.lanqing|chen.lanxing|chen.lifen|chen.liqing|chen.luefeng|chen.libei|chen.lan|chen.lyping|chen.lianfu|chen.linxiao|chen.liuzhu|chen.liufeng|chen.lanping|chen.liqun.1|chen.linan|chen.linchong|chen.leisong|chen.luxi|chen.liwei|chen.leiwen|chen.liwei.1|chen.longxuan|chen.lanfeng|chen.lifei|chen.longqing|chen.libin|chen.liangliang|chen.lin.6|chen.longyong|chen.longzhu|chen.lingkun|chen.li.6|chen.linjie|chen.lixia|chen.longsheng|chen.lisha|chen.laming|chen.leilei|chen.lingshen|chen.lejun|chen.lingju|chen.linchun|chen.liu|chen.li.3|chen.lingji|chen.lihai|chen.lihong|chen.lejin|chen.libo|chen.lingjie|chen.linhui|chen.lipeng|chen.lingfa|chen.licheng|chen.lianzi|chen.lingjuan|chen.laijun|chen.linfeng|chen.liman|chen.liangyu|chen.likai|chen.linyu|chen.lin.3|chen.liangchen|chen.lizhou|chen.leitao|chen.lishing|chen.lianmeng|chen.liangming|chen.ligeng|chen.liebin|chen.lingyu|chen.liya|chen.linda|chen.lijing|chen.lianglu|chen.lifeng|chen.li.4|chen.luyuan|chen.liangfan|chen.laijiu|chen.lyu|chen.lou|chen.larry|chen.leon|chen.linlin|chen.lin.1|chen.lili|chen.lifang|chen.limin|chen.liangbo|chen.linhung|chen.luowu|chen.libing|chen.liang|chen.lansun|chen.longxi|chen.li.5|chen.lizhi|chen.lilian|chen.lixue|chen.linbin|chen.liangbiao|chen.lin.4|chen.linqiang|chen.lixin|chen.luoping|chen.lvzhou|chen.lingling|chen.liyan|chen.linna|chen.liju|chen.lu.1|chen.liguo|chen.liqian|chen.leiting|chen.liujun|chen.luyi|chen.lijian|chen.linshu|chen.lifu|chen.liangxiao|chen.ligang|chen.liuhao|chen.lianmu|chen.longwei|chen.leiming|chen.liuhe|chen.liquan|chen.luonan|chen.lianjun|chen.lihui|chen.liyong|chen.longgang|chen.liping|chen.liliang|chen.liangquan|chen.liangjie|chen.lanxin|chen.long|chen.lihua|chen.lisheng|chen.lie|chen.lingxia|chen.lungkee|chen.liangsen|chen.liansheng|chen.lunming|chen.liyu|chen.lijun|chen.lichao|chen.lin.2|chen.le-shan|chen.lingqiao|chen.lele|chen.linya|chen.lamei|chen.longkang|chen.lairong|chen.liuyuan|chen.liam|chen.liangxu|chen.lianna|chen.luyun|chen.luming|chen.liansong|chen.lanlan|chen.liyin|chen.lijie|chen.lingjun|chen.linbo|chen.liangzhou|chen.laiwen|chen.luping|chen.linfei|chen.lianrong|chen.liangqun|chen.lide|chen.lunting|chen.leichen|chen.le|chen.liangkang|chen.lixuan|chen.liting|chen.luting|chen.lu-san|chen.liheng|chen.liming|chen.lily"Jackson, A."https://zbmath.org/authors/?q=ai:jackson.a-mcn|jackson.a-p|jackson.adrian|jackson.alexander-h|jackson.aaron-s|jackson.aaron-l|jackson.andrew-d|jackson.alan|jackson.allyn|jackson.a-nSummary: Planetary magnetic fields are generated by the motion of conductive fluid in the planet's interior. Complex flows are not required for dynamo action; simple flows have been shown to act as efficient kinematic dynamos, whose physical characteristics are more straightforward to study. Recently,
the second author et al. [J. Fluid Mech. 839, 1--32 (2018; Zbl 1419.76704)]
found the optimal, unconstrained kinematic dynamo in a sphere, which, despite being of theoretical importance, is of limited practical use. We extend their work by restricting the optimization to three simple two-mode axisymmetric flows based on the kinematic dynamos of
\textit{M. L. Dudley} and \textit{R. W. James} [``Time-dependent kinematic dynamos with stationary flows'', Proc. R. Soc. Lond., A, Math. Phys. Eng. Sci. 425, No. 1869, 407--429 (1989; \url{doi:10.1098/rspa.1989.0112})].
Using a Lagrangian optimization, we find the smallest critical magnetic Reynolds number for each flow type, measured using an enstrophy-based norm. A Galerkin method is used, in which the spectral coefficients of the fluid flow and magnetic field are updated in order to maximize the final magnetic energy. We consider the \(t^0_1s^0_1\), \(t^0_1s^0_2\) and \(t^0_2s^0_2\) flows and find enstrophy-based critical magnetic Reynolds numbers of 107.7, 142.4 and 125.5 (13.7, 19.6 and 16.4, respectively, with the energy-based definition). These are up to four times smaller than the original flows. These simple and efficient flows may be used as benchmarks in future studies.Plesio-geostrophy for Earth's core: I. Basic equations, inertial modes and inductionhttps://zbmath.org/1472.860182021-11-25T18:46:10.358925Z"Jackson, Andrew"https://zbmath.org/authors/?q=ai:jackson.andrew-d"Maffei, Stefano"https://zbmath.org/authors/?q=ai:maffei.stefanoSummary: An approximation is developed that lends itself to accurate description of the physics of fluid motions and motional induction on short time scales (e.g. decades), appropriate for planetary cores and in the geophysically relevant limit of very rapid rotation. Adopting a representation of the flow to be columnar (horizontal motions are invariant along the rotation axis), our characterization of the equations leads to the approximation we call \textit{plesio-geostrophy}, which arises from dedicated forms of integration along the rotation axis of the equations of motion and of motional induction. Neglecting magnetic diffusion, our self-consistent equations collapse all three-dimensional quantities into two-dimensional scalars in an exact manner. For the isothermal magnetic case, a series of fifteen partial differential equations is developed that fully characterizes the evolution of the system. In the case of no forcing and absent viscous damping, we solve for the normal modes of the system, called inertial modes. A comparison with a subset of the known three-dimensional modes that are of the least complexity along the rotation axis shows that the approximation accurately captures the eigenfunctions and associated eigenfrequencies.Phase retrieval from Fourier measurements with maskshttps://zbmath.org/1472.940092021-11-25T18:46:10.358925Z"Li, Huiping"https://zbmath.org/authors/?q=ai:li.huiping"Li, Song"https://zbmath.org/authors/?q=ai:li.songSummary: This paper concerns the problem of phase retrieval from Fourier measurements with random masks. Here we focus on researching two kinds of random masks. Firstly, we utilize the Fourier measurements with real masks to estimate a general signal \(\mathfrak{x}_0\in \mathbb{R}^d\) in noiseless case when \(d\) is even. It is demonstrated that \(O(\log^2d)\) real random masks are able to ensure accurate recovery of \(\mathfrak{x}_0\). Then we find that such real masks are not adaptable to reconstruct complex signals of even dimension. Subsequently, we prove that \(O(\log^4d)\) complex masks are enough to stably estimate a general signal \(\mathfrak{x}_0\in \mathbb{C}^d\) under bounded noise interference, which extends \textit{E. J. Candès} et al.'s work [SIAM Rev. 57, No. 2, 225--251 (2015; Zbl 1344.49057)]. Meanwhile, we establish tighter error estimations for real signals of even dimensions or complex signals of odd dimensions by using \(O(\log^2d)\) real masks. Finally, we intend to tackle with the noisy phase problem about an \(s\)-sparse signal by a robust and efficient approach, namely, two-stage algorithm. Based on the stable guarantees for general signals, we show that the \(s\)-sparse signal \(\mathfrak{x}_0\) can be stably recovered from composite measurements under near-optimal sample complexity up to a \(\log\) factor, namely, \(O(s\log(\frac{ed}{s})\log^4(s\log(\frac{ed}{s})))\).The antenna spacetime system theory of wireless communicationshttps://zbmath.org/1472.940282021-11-25T18:46:10.358925Z"Mikki, Said"https://zbmath.org/authors/?q=ai:mikki.said-mSummary: A general deterministic spacetime system theory of antennas suitable for the analysis and design of wireless communication links is rigorously developed using the recently introduced antenna current Green's function formalism. We provide the first complete derivation of the antenna spatio-temporal response to a delta source using only electromagnetic Green's functions, effectively eliminating all field and current distributions in the final expressions. While the theory works well in both space and time, it puts into sharper focus how the spatio-temporal structure of electromagnetic processes imposes restrictions on the signal processing capabilities of antenna systems by constraining the allowable mathematical form of the effective impulse response of the global wireless communication link. It is shown that the antenna current Green's functions of both the receive and transmit terminals, plus the propagation environment Green's functions, are the only quantities needed to obtain the single input-single output link response function in closed form. One of the results deduced from the theory is that an exact impulse response cannot be ascribed to an arbitrary antenna in general, but may be approximated for many applications. The theory can be deployed for future antenna systems research to boost up spectral efficiency (without increasing physical bandwidth) by directly incorporating electromagnetic knowledge into the design of the communication system's signal processing functions.