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In this work, we use the finite differences in time domain (FDTD) numerical method to compute and assess the validity of Hopf solutions, or hopfions, for the electromagnetic field equations. In these solutions, field lines form closed loops characterized by different knot topologies which are preserved during their time evolution. Hopfions have been studied extensively in the past from an analytical perspective but never, to the best of our knowledge, from a numerical approach. The implementation and validation of this technique eases the study of more complex cases of this phenomena; e.g. how these fields could interact with materials (e.g. anisotropic or non-linear), their coupling with other physical systems (e.g. plasmas), and also opens the path on their artificial generation by different means (e.g. antenna arrays or lasers).
We pursue here the development of models for complex (viscoelastic) fluids in shallow free-surface gravity flows which was initiated by [Bouchut-Boyaval, M3AS (23) 2013] for 1D (translation invariant) cases. The models we propose are hyperbolic quasi
It has been shown in the authors companion paper that solutions of Maxwell-Klein-Gordon equations in $mathbb{R}^{3+1}$ possess some form of global strong decay properties with data bounded in some weighted energy space. In this paper, we prove pointw
A simple model of random Brownian walk of a spherical mesoscopic particle in viscous liquids is proposed. The model can be both solved analytically and simulated numerically. The analytic solution gives the known Eistein-Smoluchowski diffusion law $<
We present a computer simulation of entangled polymer solutions at equilibrium. The chains repel each other via a soft Gaussian potential, appropriate for semi-dilute solutions at the scale of a correlation blob. The key innovation to suppress chain
In this article we develop a numerical scheme to deal with interfaces between touching numerical grids when solving the second-order wave equation. We show that it is possible to implement an interface scheme of penalty type for the second-order wave