Inspiral of binary black holes occurs over a time-scale of many orbits,far longer than the dynamical time-scale of the individual black holes.Explicit evolutions of a binary system therefore require excessively many t...Inspiral of binary black holes occurs over a time-scale of many orbits,far longer than the dynamical time-scale of the individual black holes.Explicit evolutions of a binary system therefore require excessively many time-steps to capture interesting dynamics.We present a strategy to overcome the Courant-Friedrichs-Lewy condition in such evolutions,one relying on modern implicit-explicit ODE solvers and multidomain spectral methods for elliptic equations.Our analysis considers the model problem of a forced scalar field propagating on a generic curved background.Nevertheless,we encounter and address a number of issues pertinent to the binary black hole problem in full general relativity.Specializing to the Schwarzschild geometry in KerrSchild coordinates,we document the results of several numerical experiments testing our strategy.展开更多
We explore the use of PDE constrained nonlinear optimization techniques to optimize and design electromagnetic crystals which exhibit frozen mode behavior.This is characterized by Van Hove singularities in the dispers...We explore the use of PDE constrained nonlinear optimization techniques to optimize and design electromagnetic crystals which exhibit frozen mode behavior.This is characterized by Van Hove singularities in the dispersion relation,e.g.,stationary reflection points and degenerate band edge points.Hence,the optimization process modifies the dispersion relation by adjusting the geometries and material parameters.The resulting algorithm is found to be capable of recovering all known crystal configurations as well as many new configurations,some of which display dramatically improved properties over previously used configuration.We investigate both gyrotropic photonic crystals and degenerate band edge crystals as well as the more complex case of the oblique incidence.In this latter case,we extend the investigation to the three-dimensional case to identify the first three-dimensional crystal exhibiting frozen mode behavior.展开更多
We investigate the behavior and sensitivity of the frozen mode phenomenon in finite structures with anisotropic materials,including both magnetic materials and non-normal incidence.The studies are done by using a high...We investigate the behavior and sensitivity of the frozen mode phenomenon in finite structures with anisotropic materials,including both magnetic materials and non-normal incidence.The studies are done by using a high-order accurate discontinuous Galerkin method for solving Maxwells equations in the time domain.We confirm the existence of the phenomenon also in the time-domain and study carefully the impact of the finite crystal on the frozen mode.This sets the stage for a thorough study of the robustness of the frozen mode phenomenon,resulting in guidelines for which design parameters are most sensitive and acceptable tolerances.展开更多
文摘Inspiral of binary black holes occurs over a time-scale of many orbits,far longer than the dynamical time-scale of the individual black holes.Explicit evolutions of a binary system therefore require excessively many time-steps to capture interesting dynamics.We present a strategy to overcome the Courant-Friedrichs-Lewy condition in such evolutions,one relying on modern implicit-explicit ODE solvers and multidomain spectral methods for elliptic equations.Our analysis considers the model problem of a forced scalar field propagating on a generic curved background.Nevertheless,we encounter and address a number of issues pertinent to the binary black hole problem in full general relativity.Specializing to the Schwarzschild geometry in KerrSchild coordinates,we document the results of several numerical experiments testing our strategy.
基金the U.S.Air Force Office of Scientific Research under the grant FA9550-04-1-0359.
文摘We explore the use of PDE constrained nonlinear optimization techniques to optimize and design electromagnetic crystals which exhibit frozen mode behavior.This is characterized by Van Hove singularities in the dispersion relation,e.g.,stationary reflection points and degenerate band edge points.Hence,the optimization process modifies the dispersion relation by adjusting the geometries and material parameters.The resulting algorithm is found to be capable of recovering all known crystal configurations as well as many new configurations,some of which display dramatically improved properties over previously used configuration.We investigate both gyrotropic photonic crystals and degenerate band edge crystals as well as the more complex case of the oblique incidence.In this latter case,we extend the investigation to the three-dimensional case to identify the first three-dimensional crystal exhibiting frozen mode behavior.
基金supported by the U.S.Air Force Office of Scientific Research under the grant FA9550-04-1-0359.
文摘We investigate the behavior and sensitivity of the frozen mode phenomenon in finite structures with anisotropic materials,including both magnetic materials and non-normal incidence.The studies are done by using a high-order accurate discontinuous Galerkin method for solving Maxwells equations in the time domain.We confirm the existence of the phenomenon also in the time-domain and study carefully the impact of the finite crystal on the frozen mode.This sets the stage for a thorough study of the robustness of the frozen mode phenomenon,resulting in guidelines for which design parameters are most sensitive and acceptable tolerances.
