pde2path is a free and easy to use Matlab continuation/bifurcation package for elliptic systems of PDEs with arbitrary many components,on general two dimensional domains,and with rather general boundary conditions.The...pde2path is a free and easy to use Matlab continuation/bifurcation package for elliptic systems of PDEs with arbitrary many components,on general two dimensional domains,and with rather general boundary conditions.The package is based on the FEM of the Matlab pdetoolbox,and is explained by a number of examples,including Bratu’s problem,the Schnakenberg model,Rayleigh-Bénard convection,and von Karman plate equations.These serve as templates to study new problems,for which the user has to provide,via Matlab function files,a description of the geometry,the boundary conditions,the coefficients of the PDE,and a rough initial guess of a solution.The basic algorithm is a one parameter arclength-continuation with optional bifurcation detection and branch-switching.Stability calculations,error control and mesh-handling,and some elementary timeintegration for the associated parabolic problem are also supported.The continuation,branch-switching,plotting etc are performed via Matlab command-line function calls guided by the AUTO style.The software can be downloaded from www.staff.uni-oldenburg.de/hannes.ue ker/pde2path,where also an online documentation of the software is provided such that in this paper we focus more on the mathematics and the example systems.展开更多
We develop a numerical method for approximating the surface modes of sphere-like nanoparticles in the quasi-static limit,based on an expansion of(the angular part of)the potentials into spherical harmonics.Comparisons...We develop a numerical method for approximating the surface modes of sphere-like nanoparticles in the quasi-static limit,based on an expansion of(the angular part of)the potentials into spherical harmonics.Comparisons of the results obtained in this manner with exact solutions and with a perturbation ansatz prove that the scheme is accurate if the shape deviations from a sphere are not too large.The method allows fast calculations for large numbers of particles,and thus to obtain statistics for nanoparticles with random shape fluctuations.As an application we present some statistics for the distribution of resonances,polariziabilities,and dipole axes for particles with random perturbations.展开更多
文摘pde2path is a free and easy to use Matlab continuation/bifurcation package for elliptic systems of PDEs with arbitrary many components,on general two dimensional domains,and with rather general boundary conditions.The package is based on the FEM of the Matlab pdetoolbox,and is explained by a number of examples,including Bratu’s problem,the Schnakenberg model,Rayleigh-Bénard convection,and von Karman plate equations.These serve as templates to study new problems,for which the user has to provide,via Matlab function files,a description of the geometry,the boundary conditions,the coefficients of the PDE,and a rough initial guess of a solution.The basic algorithm is a one parameter arclength-continuation with optional bifurcation detection and branch-switching.Stability calculations,error control and mesh-handling,and some elementary timeintegration for the associated parabolic problem are also supported.The continuation,branch-switching,plotting etc are performed via Matlab command-line function calls guided by the AUTO style.The software can be downloaded from www.staff.uni-oldenburg.de/hannes.ue ker/pde2path,where also an online documentation of the software is provided such that in this paper we focus more on the mathematics and the example systems.
基金supported in part by the DFG through Grant No.KI 438/8-1.
文摘We develop a numerical method for approximating the surface modes of sphere-like nanoparticles in the quasi-static limit,based on an expansion of(the angular part of)the potentials into spherical harmonics.Comparisons of the results obtained in this manner with exact solutions and with a perturbation ansatz prove that the scheme is accurate if the shape deviations from a sphere are not too large.The method allows fast calculations for large numbers of particles,and thus to obtain statistics for nanoparticles with random shape fluctuations.As an application we present some statistics for the distribution of resonances,polariziabilities,and dipole axes for particles with random perturbations.
