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Across a large range of scales, accreting sources show remarkably similar patterns of variability, most notably the log-normality of the luminosity distribution and the linear root-mean square (rms)-flux relationship. These results are…
Magnetic materials host a wealth of nonlinear dynamics, textures, and topological defects. This is possible due to the competition between strong nonlinearity and dispersion that act at the atomic scale as well as long-range interactions.…
In this paper, we consider the direct and inverse problem for time-fractional diffusion in a domain with an impenetrable subregion. Here we assume that on the boundary of the subregion the solution satisfies a generalized impedance boundary…
The general theoretical description of spin self-diffusion under nonlinear gradient is proposed, which extends the effective phase diffusion method for linear gradient field. Based on the phase diffusion, the proposed method reveals the…
The study of polarized radiation transfer in the highly-magnetized surface locales of neutron stars is of great interest to the understanding of accreting X-ray pulsars, rotation-powered pulsars and magnetars. This paper explores scattering…
The absorption cross section of M\"{o}ssbauer radiation in magnetic liquids is calculated, taking into consideration both translational and rotational Brownian motion of magnetic nanoparticles. Stochastic reversals of their magnetization…
We review, systematize and discuss models of diffusion in neuronal tissue, by putting them into an overarching physical context of coarse-graining over an increasing diffusion length scale. From this perspective, we view research on…
Particle transport, acceleration and energisation are phenomena of major importance for both space and laboratory plasmas. Despite years of study, an accurate theoretical description of these effects is still lacking. Validating models with…
Nuclear Magnetic Resonance (NMR) spectroscopy leverages nuclear magnetization to probe molecules' chemical environment, structure, and dynamics, with applications spanning from pharmaceuticals to the petroleum industry. Despite its utility,…
We consider Bloch states of weak spacetime-periodic perturbations of homogeneous materials in one spatial dimension. The interplay of space- and time-periodicity leads to an infinitely degenerate dispersion relation in the free case. We…
Application of fractional calculus to the description of anomalous diffusion and relaxation processes in complex media provided one of the most impressive impulses to the development of statistical physics during the last decade. In…
The acceleration of energetic particle transport in high amplitude magnetosonic and Alfvenic turbulence is considered using the method of Monte Carlo particle simulations, involving integration of particle equations of motion. We derive the…
The diffusion equation is the primary tool to study the movement dynamics of a free Brownian particle, but when spatial heterogeneities in the form of permeable interfaces are present, no fundamental equation has been derived. Here we…
We study the spectral properties of a class of random matrices where the matrix elements depend exponentially on the distance between uniformly and randomly distributed points. This model arises naturally in various physical contexts, such…
The introduction of nonlinearity alters the dispersion of elastic waves in solid media. In this paper, we present an analytical formulation for the treatment of finite-strain Bloch waves in one-dimensional phononic crystals. Considering…
In this paper we study nonlinear Helmholtz equations with sign-changing diffusion coefficients on bounded domains. The existence of an orthonormal basis of eigenfunctions is established making use of weak T-coercivity theory. All…
A method is proposed for the analysis of the propagation of electromagnetic waves through a homogeneous slab of a medium with Drude-Lorentz dispersion behavior, and excited by a causal sinusoidal source. An expression of the time dependent…
A survey is given on asymptotic diffusion coefficients of particles in lattices with random transition rates. Exact and approximate results for single particles are reviewed. A recent exact expression in $d = 1$ which includes occupation…
In the present article the diffusion equation is used to model the spatio-temporal dynamics of a tumor, taking into account the heterogeneous of the medium. This approach makes it possible to take into account the complex geometric shape of…
Unraveling real eigenfrequencies in non-Hermitian $\mathcal{PT}$-symmetric Hamiltonians has opened new avenues in quantum physics, photonics, and most recently, phononics. However, the existing literature squarely focuses on exploiting such…