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In this paper, we present the numerical solution of two-phase flow problems of engineering significance with a space-time finite element method that allows for local temporal refinement. Our basis is the method presented in [3], which…
We introduce an ansatz for force-free electrodynamics in Minkowski spacetime under which the nonlinear system reduces to a semilinear scalar wave equation depending on two spacetime variables. This reduction yields explicit time-dependent…
We investigate the representations of the solutions to Maxwell's equations based on the combination of hypercomplex function-theoretical methods with quantum mechanical methods. Our approach provides us with a characterization for the…
We construct new examples of embedded, complete minimal hypersurfaces in quaternionc hyperbolic space and also some minimal foliations. We introduce fans an construct analytic deformations of bisectors.
We consider the vacuum energy of the electromagnetic field in the background of spherically symmetric dielectrics, subject to a cut-off frequency in the dispersion relations. The effect of this frequency dependent boundary condition between…
Biomembranes and vesicles consisting of multiple phases can attain a multitude of shapes, undergoing complex shape transitions. We study a Cahn--Hilliard model on an evolving hypersurface coupled to Navier--Stokes equations on the surface…
The transient electroosmotic flow of Maxwell fluid in a rotating microchannel is investigated both analytically and numerically. We bring out the complex dynamics of the flow during the transience due to the combination of rotation and…
We construct space quasi-periodic standing wave solutions to the nonlinear Schr\"odinger equations on R^d for arbitrary d. This is a type of quasi-periodic nonlinear Bloch-Floquet waves.
We argue that the success of DFT can be understood in terms of a semiclassical expansion around a very specific limit. This limit was identified long ago by Lieb and Simon for the total electronic energy of a system. This is a universal…
This paper discusses the technical aspects - mathematical and numerical - associated with the numerical simulations of a mesoscopic system in the time domain (i.e. beyond the single frequency AC limit). After a short review of the state of…
The scalar wave equation in Kasner spacetime is solved, first for a particular choice of Kasner parameters, by relating the integrand in the wave packet to the Bessel functions. An alternative integral representation is also displayed,…
A novel description of kinetic theory dynamics is proposed in terms of resummed moments that embed information of both hydrodynamic and non-hydrodynamic modes. The resulting expansion can be used to extend hydrodynamics to higher orders in…
We study the propagation and scattering of electromagnetic waves by random arrays of dipolar cylinders in a uniform medium. A set of self-consistent equations, incorporating all orders of multiple scattering of the electromagnetic waves, is…
We discuss the irreversibility, nonlocality, and fluctuations, as well as the Lyapunov and hydrodynamic instabilities characterizing atomistic, smooth-particle, and finite-difference solutions of the two-dimensional Rayleigh-B\'enard…
The goal of this work is to study the existence of quasi-periodic solutions in time to nonlinear beam equations with a multiplicative potential. The nonlinearities are required to only finitely differentiable and the frequency is along a…
This dissertation describes the space of heteroclinic orbits for a class of semilinear parabolic equations, focusing primarily on the case where the nonlinearity is a second degree polynomial with variable coefficients. Along the way, a new…
We consider the description of a Fermi gas of free electrons given by the Boltzmann--Fermi--Dirac equation, and aim at providing a precise mathematical understanding of the Fermi ground state and its first-order approximation of excited…
We provide explicit commutative sequence space representations for classical function and distribution spaces on the real half-line. This is done by evaluating at the Fourier transforms of the elements of an orthonormal wavelet basis.
This work presents a comprehensive study of the microlocal energy decomposition and propagation of singularities for semiclassically adjusted dissipative pseudodifferential operators. The analysis focuses on the behavior of energy…
A novel semi-Lagrangian method is introduced to solve numerically the Euler equation for ideal incompressible flow in arbitrary space dimension. It exploits the time-analyticity of fluid particle trajectories and requires, in principle,…