Related papers: Some remarks on Relativistic Diffusion and the Spe…
In nematic liquid crystals light is strongly scattered from director fluctuations. We are interested in the limit where the incoming light wave is scattered many times. Then, the light transport can be described by a diffusion equation for…
The determination of the density parameter $\Omega_0$ from the large-scale distribution of galaxies is one of the major goals of modern cosmology. However, if galaxies are biased tracers of the underlying mass distribution, linear…
A new (scalar) spectral decomposition is found for the Dirac system in two dimensions associated to the focusing Davey--Stewartson II (DSII) equation. Discrete spectrum in the spectral problem corresponds to eigenvalues embedded into a…
The radiative transfer equation (RTE) is a cornerstone for describing the propagation of electromagnetic radiation in a medium, with applications spanning atmospheric science, astrophysics, remote sensing, and biomedical optics. Despite its…
Thermal decay rate over an edge-shaped barrier at high dissipation is studied numerically through the computer modeling. Two sorts of the stochastic Langevin type equations are applied: (i) the Langevin equations for the coordinate and…
Conventional cosmic-ray propagation models usually assume an isotropic diffusion coefficient to account for the random deflection of cosmic rays by the turbulent interstellar magnetic field. Such a picture is very successful in explaining…
In this paper, we develop a novel high-dimensional time-varying coefficient estimation method, based on high-dimensional It\^o diffusion processes. To account for high-dimensional time-varying coefficients, we first estimate local (or…
A model-independent parameterization of the low-energy scattering amplitude that incorporates the left-hand cut from one-particle exchange, an extension of the conventional effective-range expansion (ERE), was recently proposed and…
We study a relativistic diffusion equation on the Riemannian phase space defined by Franchi and Le Jan. We discuss stochastic Ito (Langevin) differential equations (defining the diffusion) as a perturbation by noise of the geodesic…
The mass spectra of $D_s$ meson is obtained in the framework of relativistic independent quark model using Martin like potential for the quark confinement. The predicted excited states are in good agreement with the experimental results as…
High-resolution stellar spectra offer valuable insights into atmospheric parameters and chemical compositions. However, their inherent complexity and high-dimensionality present challenges in fully utilizing the information they contain. In…
We study the Seebeck effect in the three-dimensional Dirac electron system based on the linear response theory with Luttinger's gravitational potential. The Seebeck coefficient $S$ is defined by $S = L_{12} / L_{11} T$, where $T$ is the…
The diffraction spectrum of coherent waves scattered from fractal supports is calculated exactly. The fractals considered are of the class generated iteratively by successive dilations and translations, and include generalizations of the…
The spectral energy distribution (SED) of observed stars in wide-field images is crucial for chromatic point spread function (PSF) modelling methods, which use unresolved stars as integrated spectral samples of the PSF across the field of…
Properties of two equations describing the evolution of the probability density function (PDF) of the relative dispersion in turbulent flow are compared by investigating their solutions: the Richardson diffusion equation with the drift term…
Penetrative turbulent Rayleigh-B\'enard convection which depends on the density maximum of water near $4^\circ\rm{C}$ is studied using two-dimensional (2D) and three-dimensional (3D) direct numerical simulations (DNS). The working fluid is…
We present three-dimensional, self-consistent radiative transfer solutions with a new Monte Carlo radiative equilibrium code. The code, RADISHE ($\bf{RAD}$iative transfer $\bf{I}$n $\bf{S}$moothed particle $\bf{H}$ydrodynamics and…
The reaction-diffusion master equation (RDME) is commonly used to model processes where both the spatial and stochastic nature of chemical reactions need to be considered. We show that the RDME in many cases is inconsistent with a…
Although the existence of cosmic rays with energies extending well above $10^{19}$ eV has been confirmed, their origin remains one of the most important questions in astro-particle physics today. Several source models have been proposed for…
We establish a simple criterion for locating points where the transition density of a degenerate diffusion is strictly positive. Throughout, we assume that the diffusion satisfies a stochastic differential equation (SDE) on $\mathbf{R}^d$…