Wave Phenomena

Official Twitter account of the CRC1173 Wave Phenomena.

[Wave Phenomena @Wavephenomena]

We stand for respectful, democratic exchange and appreciative communication. We believe in facts and the values of science. Since the latest changes on X these values have come under severe pressure on this platform. Therefore, we say "bye bye, X".

[Wave Phenomena @Wavephenomena]

In https://t.co/lR0bUwBno8 we derive properties of the Calderon operator which is the analogue of the Dirichlet-to-Neumann operator for the scalar Helmholtz equation. We consider the cases where the boundary data decay or are quasi-periodic along the cylinder axis. #CRC1173

[Wave Phenomena @Wavephenomena]

In https://t.co/ubuNyPzIRR we study Maxwell’s equations with periodic coefficients (or local perturbations of periodic coefficients) in a closed waveguide. Particular emphasis is put on the radiation condition which follows from the limiting absorption principle. #CRC1173

[Wave Phenomena @Wavephenomena]

In the #CRC1173 preprint https://t.co/kl4ipMykdw we study Maxwell's equations for a Kerr-type optical material with instantaneous response that is of cylindrical or slab geometry. We show existence of breather solutions using variational methods.

[Wave Phenomena @Wavephenomena]

In https://t.co/nRq4M9qSB1 we derive radiation conditions for the Helmholtz equation in a closed wave-guide with periodic coefficients from the limiting absorption principle. We characterize the set of all bounded solutions of the homogeneous problem. #CRC1173

[Wave Phenomena @Wavephenomena]

In our #CRC1173 preprint https://t.co/0sHeEUlFUe we propose a multiscale approach for discrete minimizers of the Ginzburg-Landau energy. We choose different meshes and ansatz spaces for the order parameter and the vector potential and thus derive error bounds of optimal order.

[Wave Phenomena @Wavephenomena]

In https://t.co/jftk6KHR53 we study the magnetohydrodynamics equations in the non-resistive limit. We establish stability of small perturbations near an affine shear flow and a large constant magnetic field and show growth of the magnetic field. #CRC1173

[Wave Phenomena @Wavephenomena]

In our #CRC1173 preprint https://t.co/l6X3nlarvj we study the space and time discretization of Maxwell equations with an external surface current. This is the first step to simulate the interaction of Graphene with light pulses.

[Wave Phenomena @Wavephenomena]

In the #CRC1173 preprint https://t.co/uvAGngHYmi we present an IMEX scheme for semilinear wave equations. Our main results are error bounds of the full discretization combined with a general abstract space discretization.

[Wave Phenomena @Wavephenomena]

In https://t.co/wJGNvATnCK, we compare old and new Kirchhoff migration/inversion formulas for seismic tomography wrt their imaging properties. To this end, we analyze these formulas microlocally and illustrate the theoretical results with numerical examples. #CRC1173

[Wave Phenomena @Wavephenomena]

Delving into multi-scale effects of thermal radiative transfer equations and their computational challenges, a novel asymptotic-preserving & rank-adaptive dynamical low-rank scheme in https://t.co/cb40mCz0MY captures the correct limit with low memory requirements. #CRC1173

[Wave Phenomena @Wavephenomena]

Our new preprint https://t.co/qrK7lBqXMd on high-frequency wave propagation in nonlinear media is online. We prove new error bounds for the slowly varying envelope approximation and a related model. This is the result of years of work, and we are now very happy. #CRC1173

[Wave Phenomena @Wavephenomena]

In the #CRC1173 preprint https://t.co/fOaoYMD0J1 we obtain existence and decay of small solutions in the viscoelastic Klein-Gordon equation for large periods of time. This result extends previous work on the half Klein-Gordon equation.

[Wave Phenomena @Wavephenomena]

In our #CRC1173 preprint https://t.co/f7U243QvJW we study the space and time discretization of the Kuznetsov equation, a classical wave model of nonlinear acoustics. We show optimal order of convergence uniformly in the vanishing sound diffusivity parameter.

[Wave Phenomena @Wavephenomena]

Magnetic Schrödinger operators cannot have bound states in the continuum (BIC) under natural conditions solely on the magnetic field and potential and not on the vector potential. The Miller-Simon examples show that our condition in https://t.co/38uEbIBLkB is sharp. #CRC1173

[Wave Phenomena @Wavephenomena]

In https://t.co/HWhKFyyZWj we study the existence and dynamical stability of solitary waves in the Lugiato-Lefever equation. The solutions under consideration are highly nonlinear, localized waves and model Kerr frequency combs in nonlinear optics. #CRC1173

[Wave Phenomena @Wavephenomena]

In https://t.co/1MI0dbogBn we study time integration schemes for the 3D energy-(sub)critical semilinear wave equation. We use discrete-time Strichartz estimates to show first-order convergence for the Lie splitting and convergence order 3/2 for a corrected Lie splitting. #CRC1173

[Wave Phenomena @Wavephenomena]

In https://t.co/UFR0cS2mzW we study the magnetohydrodynamics equations with viscosity and horizontal resistivity. We establish stability of small perturbations near a combination of an affine shear flow and a large constant magnetic field. #CRC1173

[Wave Phenomena @Wavephenomena]

In https://t.co/qhhMOmKjO9 we give a proof of nonlinear Landau damping. Different time scales are shown to result in constrained plasma echo chains and different optimal regularity classes. #CRC1173

[Wave Phenomena @Wavephenomena]

In our recent preprint https://t.co/TnwWTROGhY, we consider Gaussian wave packets for the magnetic Schrödinger equation which reduce the computational effort dramatically. We prove convergence of the approximation and thereby generalize known results from the literature. #CRC1173