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- 摘要
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- 实验方案
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Incompressible limit for compressible nematic liquid crystal flows in a bounded domain
摘要： In this paper, we consider the incompressible limit of strong solution for the compressible nematic liquid crystal flows in a 3D bounded domain (cid:2) ? R3 where the the velocity field satisfies the Dirichlet boundary condition. We establish the uniform estimates with respect to the Mach number for the strong solutions with large initial data in a short time interval. Consequently, we obtain the convergence of the compressible nematic liquid crystal system to the incompressible nematic liquid crystals system as the Mach number tends to zero.
关键词： Incompressible limit,Dirichlet boundary condition,compressible nematic liquid crystal equations
更新于2025-09-23 15:23:52
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Relay-Zone Technique for Numerical Boundary Treatments in Simulating Dark Solitons
摘要： To simulate dark solitons in the defocusing nonlinear Schr?dinger equation, we introduce a relay-zone technique, by alternately using a Robin boundary condition to treat the nonzero far field, and a derivative boundary condition to match the dark soliton. Numerical tests and comparisons demonstrate the effectiveness of the proposed boundary treatment. Stability and interaction of dark solitons are also studied.
关键词： Nonlinear Schr?dinger equation,Artificial boundary condition,Dark soliton
更新于2025-09-23 15:22:29
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Graphene on an optical waveguide: comparison of simulation approaches
摘要： Recently, unusual properties of novel two-dimensional materials like graphene have revolutionized many branches of science and technology. Adequate numerical simulations of photonic devices comprising graphene layers require new approaches or modified methods. In this paper we present comparison of results obtained with three representations of a graphene monolayer: (1) an infinitely thin sheet with a finite surface complex conductivity, (2) a thin layer of a finite thickness exhibiting uniaxially anisotropic complex permittivity, and (3) anisotropic permittivity perturbation in an infinitely small volume. Numerical solutions of rigorous dispersion equations were compared to each other and also with the results obtained with several commercial as well as proprietary software packets. Under proper conditions, all approaches provide comparable results.
关键词： Perturbation method,Volumetric method,Optical waveguides,Graphene,Boundary condition method,Numerical simulations
更新于2025-09-23 15:21:01
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[IEEE 2019 PhotonIcs & Electromagnetics Research Symposium - Spring (PIERS-Spring) - Rome, Italy (2019.6.17-2019.6.20)] 2019 PhotonIcs & Electromagnetics Research Symposium - Spring (PIERS-Spring) - Spectrally Tunable Germanium-on-silicon Photodetectors: Design and Simulations
摘要： To avoid straightforward volumetric discretization, a discontinuous Galerkin time-domain (DGTD) method integrated with the impedance boundary condition (IBC) is presented in this paper to analyze the scattering from objects with finite conductivity. Two situations are considered. 1) The skin depth is smaller than the thickness of the conductive volume. 2) The skin depth is larger than the thickness of a thin conductive sheet. For the first situation, a surface impedance boundary condition (SIBC) is employed, wherein the surface impedance usually exhibits a complex relation with the frequency. To incorporate the SIBC into DGTD, the surface impedance is first approximated by rational functions in the Laplace domain using the fast relaxation vector-fitting (FRVF) technique. Via inverse Laplace transform, the time-domain DGTD matrix equations can be obtained conveniently in integral form with respect to time t. For the second situation, a transmission IBC (TIBC) is used to include the transparent effects of the fields. In the TIBC, the tangential magnetic field jump is related with the tangential electric field via the surface conductivity. In this work, a specifically designed DGTD algorithm with TIBC is developed to model the graphene up to the terahertz (THz) band. In order to incorporate the TIBC into DGTD without involving the time-domain convolution, an auxiliary surface polarization current governed by a first-order differential equation is introduced over the graphene. For open-region scattering problems, the DGTD algorithm is further hybridized with the time-domain boundary integral (TDBI) method to rigorously truncate the computational domain. To demonstrate the accuracy and applicability of the proposed algorithm, several representative examples are provided.
关键词： finite integral technique (FIT),surface/transmission impedance boundary condition (SIBC/TIBC),vector-fitting,time-domain boundary integral (TDBI) algorithm,Auxiliary differential equation (ADE),graphene,discontinuous Galerkin time-domain (DGTD) method
更新于2025-09-23 15:19:57
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Uniqueness and Direct Imaging Method for Inverse Scattering by Locally Rough Surfaces with Phaseless Near-Field Data
摘要： This paper is concerned with inverse scattering of plane waves by a locally perturbed infinite plane (which is called a locally rough surface) with the modulus of the total-field data (also called the phaseless near-field data) at a fixed frequency in two dimensions. We consider the case where a Dirichlet boundary condition is imposed on the locally rough surface. This problem models inverse scattering of plane acoustic waves by a one-dimensional sound-soft, locally rough surface; it also models inverse scattering of plane electromagnetic waves by a locally perturbed, perfectly reflecting, infinite plane in the transverse electric polarization case. We prove that the locally rough surface is uniquely determined by the phaseless near-field data generated by a countably infinite number of plane waves and measured on an open domain above the locally rough surface. Further, a direct imaging method is proposed to reconstruct the locally rough surface from the phaseless near-field data generated by plane waves and measured on the upper part of the circle with a sufficiently large radius. Theoretical analysis of the imaging algorithm is derived by making use of properties of the scattering solution and results from the theory of oscillatory integrals (especially the method of stationary phase). Moreover, as a by-product of the theoretical analysis, a similar direct imaging method with full far-field data is also proposed to reconstruct the locally rough surface. Finally, numerical experiments are carried out to demonstrate that the imaging algorithms with phaseless near-field data and full far-field data are fast, accurate, and very robust with respect to noise in the data.
关键词： Dirichlet boundary condition,phaseless near-field data,inverse scattering,full far-field data,locally rough surface
更新于2025-09-19 17:15:36
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[IEEE 2018 IEEE International Symposium on Antennas and Propagation & USNC/URSI National Radio Science Meeting - Boston, MA, USA (2018.7.8-2018.7.13)] 2018 IEEE International Symposium on Antennas and Propagation & USNC/URSI National Radio Science Meeting - Analysis of Waves Propagation on Magnetized Graphenes Using Surface Boundary Condition FDTD
摘要： In this paper, the finite-difference time-domain (FDTD) method is presented to study the magnetically biased graphene. With the introduction of the surface resistivity, the biased graphene can be taken as a two-dimensional anisotropic surface with zero thickness, which avoids the tiny spatial cell in FDTD simulation. Because of gyrotropy of the material, we calculate the average electric field over the sheet and reconstruct the electric fields after every time-marching step. The derived difference equations result in easy programming. Numerical results are presented to show the accuracy of our approach.
关键词： surface boundary condition,magnetized graphene,surface conductivity,Finite-difference time-domain
更新于2025-09-19 17:15:36
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[IEEE 2019 IEEE International Conference on Microwaves, Antennas, Communications and Electronic Systems (COMCAS) - Tel-Aviv, Israel (2019.11.4-2019.11.6)] 2019 IEEE International Conference on Microwaves, Antennas, Communications and Electronic Systems (COMCAS) - Terahertz Range Elementary Dipole Excitation of a Thin Dielectric Disk Sandwiched between Two Graphene Covers: Integral Equation Analysis
摘要： We study, using the integral equation technique, the scattering of the field radiated by an elementary dipole, by a thin dielectric disk sandwiched between two conformal graphene covers, on the top and bottom faces. To build a mathematical model of such scatterer, we use the generalized boundary condition in the form first obtained by Mitzner and Bleszynski et al. and generalized by Karlsson. This enables us to derive dual integral equations in the disk plane for the Hankel transforms of the tangential electric and magnetic field components, and cast it to a set of two coupled Fredholm second-kind integral equations. The latter equations are discretized and solved numerically with the guaranteed convergence. We compute and plot the power radiated by an elementary magnetic dipole placed above such a composite disk, in the THz range. This reveals that the studied scatterer is a complicated open resonator supporting the low-frequency plasmon modes and the high-frequency dielectric-disk modes.
关键词： generalized boundary condition,radiated power,thin disk,graphene,plasmon resonances
更新于2025-09-16 10:30:52
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Modal Expansion Analysis of T-Shaped Waveguide
摘要： The T-shaped waveguide (T-waveguide for short) is a new kind of wideband waveguide which is easier to fabricate than conventional wideband waveguides. This paper presents the modal expansion analysis of the T-waveguide. The T-waveguide is ?rst divided into four rectangular domains. The electromagnetic ?elds in each domain are expressed by suitable mode functions. The continuity of tangential electromagnetic ?elds along the interface of neighboring regions is enforced by the Galerkin’s matching process and a matrix equation is thus derived. The cutoff wavenumbers of the T-waveguide are then found from the matrix. The results are in good agreement with those obtained by CST Microwave Studio. The proposed method provides fast calculation of the T-waveguide cutoff wavenumber, which is of guiding signi?cance to the design of T-waveguide.
关键词： T-waveguide,boundary condition,modal expansion,cutoff wavenumber,Galerkin matching
更新于2025-09-11 14:15:04
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Experimental and Theoretical Research on Bending Behavior of Photovoltaic Panels with a Special Boundary Condition
摘要： Currently, the photovoltaic (PV) panels widely manufactured on market are composed of stiff front and back layers and the solar cells embedded in a soft polymeric interlayer. The wind and snow pressure are the usual loads to which working PV panels need to face, and it needs the panels keep undamaged under those pressure when they generate electricity. Therefore, an accurate and systematic research on bending behavior of PV panels is important and necessary. In this paper, classical lamination theory (CLT) considering soft interlayer is applied to build governing equations of the solar panel. A Rayleigh–Rita method is modified to solve the governing equations and calculate the static deformation of the PV panel. Different from many previous researches only analyzing simply supported boundary condition for four edges, a special boundary condition which consists of two opposite edges simply supported and the others two free is studied in this paper. A closed form solution is derived out and used to do the numerical calculation. The corresponding bending experiments of PV panels are completed. Comparing the numerical results with experiment results, the accuracy of the analytical solutions are verified.
关键词： bending behavior,classical lamination theory,bending experiment,photovoltaic panel,Rayleigh–Rita method,special boundary condition
更新于2025-09-11 14:15:04
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Simulation of Circular Cylindrical Metasurfaces using GSTC-MoM
摘要： Modeling of circular cylindrical metasurfaces using Method of Moments (MoM) based on Generalized Sheet Transition Conditions (GSTCs) is presented. GSTCs are used to link the integral equations for fields on the inner and outer contour of the circular cylindrical metasurface. The GSTC-MoM is validated by two examples: (1) anisotropic, gyrotropic metasurface capable of two field transformations, (2) non-gyrotropic metasurface capable of transforming field generated by an infinite electric line source at origin to field generated by a displaced electric line source. The formulations presented here can be used as a platform for deriving GSTC-MoM for 3D spherical and conformal metasurfaces.
关键词： GSTC,Integral Equation,Metasurface,MoM,Electromagnetic discontinuity,Boundary condition,Susceptibility,Bianisotropy,Cylindrical
更新于2025-09-10 09:29:36