Related papers: Field distributions and effective-medium approxima…
We build an effective medium theory for two-dimensional photonic crystals comprising a rectangular lattice of dielectric cylinders with the incident electric field polarized along the axis of the cylinders. In particular, we discuss the…
The filtering distribution captures the statistics of the state of a dynamical system from partial and noisy observations. Classical particle filters provably approximate this distribution in quite general settings; however they behave…
We investigate the existence of weak type solutions for a class of aggregation-diffusion PDEs with nonlinear mobility obtained as large particle limit of a suitable nonlocal version of the follow-the-leader scheme, which is interpreted as…
This paper presents an efficient Bayesian framework for solving nonlinear, high-dimensional model calibration problems. It is based on a Variational Bayesian formulation that aims at approximating the exact posterior by means of solving an…
Light in a dielectric medium moves slower than in vacuum. The corresponding electromagnetic field equations are then no longer invariant under ordinary Lorentz transformations, but only under such transformations corresponding to this…
Inspired by the problem of Planckian scattering we describe a classical effective field theory for weak ultra relativistic scattering in which field propagation is instantaneous and transverse and the particles' equations of motion localize…
A new method to find the propagation equation system governing the scattering of an electromagnetic wave by a nonlinear medium is proposed. The aim is to let the effects appear spontaneously, deleting as far as possible the phenomenological…
We propose a general algorithm for approximating nonstandard Bayesian posterior distributions. The algorithm minimizes the Kullback-Leibler divergence of an approximating distribution to the intractable posterior distribution. Our method…
A hydrodynamic-type, macroscopic theory was set up recently to simultaneously account for dissipation and dispersion of electromagnetic field, in nonstationary condensed systems of nonlinear constitutive relations~\cite{JL}. Since it was…
The universe is smooth on large scales but very inhomogeneous on small scales. Why is the spacetime on large scales modeled to a good approximation by the Friedmann equations? Are we sure that small-scale non-linearities do not induce a…
This paper investigates the problem of time-harmonic acoustic scattering in an inhomogeneous medium with a complex topological structure. Specifically, the medium is anisotropic and contains several disjoint sound-soft obstacles. This model…
A mathematical model for the discrete nonlinear fragmentation (collision-induced breakage) equation with diffusion is studied. The existence of global weak solutions is established in arbitrary spatial dimensions without assuming a strictly…
Non-Gaussian likelihoods are essential for modelling complex real-world observations but pose significant computational challenges in learning and inference. Even with Gaussian priors, non-Gaussian likelihoods often lead to analytically…
Theoretical approach is proposed to description of dielectric properties of matrix disperse systems which consists of dielectric matrix with embedded in metallic inclusions. On the basis of effective differential medium approximation the…
Propagation of the extremely short electromagnetic pulse in non-linear dielectric media without the slowly varying envelope approximation is discussed. The models under consideration take into account both resonant and not-resonant…
Effective-medium theories for electromagnetic constitutive parameters of particulate composite materials are theories of averages. Standard deviations are absent because of the lack of rigorous theories. But ensemble averages and standard…
An integral-differential equation is derived for the self-consistent (effective) field in the medium consisting of many small bodies randomly distributed in some region. Acoustic and electromagnetic fields are considered in such a medium.…
We derive exact nonlocal expressions for the effective dielectric constant tensor ${\boldsymbol \varepsilon}_e({\bf k}_I, \omega)$ of disordered two-phase composites and metamaterials from first principles. This formalism extends the…
Diffuse domain methods (DDMs) have gained significant attention for solving partial differential equations (PDEs) on complex geometries. These methods approximate the domain by replacing sharp boundaries with a diffuse layer of thickness…
We find an explicit form of weak solutions to a Riemann problem for a degenerate semilinear parabolic equation with piecewise constant diffusion coefficient. It is demonstrated that the phase transition lines (free boundaries) correspond to…