Related papers: Some properties of the one-dimensional L\'{e}vy cr…
We report Monte Carlo studies of a two-dimensional soft colloidal crystal confined in a strip geometry by parallel walls. The wall-particle interaction has corrugations along the length of the strip. Compressing the crystal by decreasing…
We derive the fractional version of one-phase one-dimensional Stefan model. We assume that the diffusive flux is given by the time-fractional Riemann-Liouville derivative, i.e. we impose the memory effect in the examined model.
In this paper, we establish the existence of transition density for geometric $\alpha$-stable processes by using the property of self-decomposability--a fundamental concept in the theory of L\'evy processes. In contrast to traditional and…
Traditionally, skyrmions are treated as continuum magnetic textures of classical spins with a well-defined topological skyrmion number. Owing to their topological protection, skyrmions have attracted great interest as building blocks in…
We introduce a modification in the relativistic hamiltonian in such a way that (1) the relativistic Schr\"odinger equations can always be based on an underlying L\'evy process, (2) several families of particles with different rest masses…
We study such important properties of $f$-divergence minimal martingale measure as Levy preservation property, scaling property, invariance in time property for exponential Levy models. We give some useful decomposition for $f$-divergence…
The density-matrix and Heisenberg formulations of quantum mechanics follow--for unitary evolution--directy from the Schr"odinger equation. Nevertheless, the symmetries of the corresponding evolution operator, the Liouvillian L=i[.,H], need…
Conductance fluctuations, localization and statistics of Lyapunov exponents are studied numerically in pure metallic wires with rough boundaries (quasi-ballistic wires). We find that the correlation energy of conductance fluctuations scales…
We implement the so-called Weyl-Heisenberg covariant integral quantization in the case of a classical system constrained by a bounded or semi-bounded geometry. The procedure, which is free of the ordering problem of operators, is…
We study a one-dimensional stochastic differential equation driven by a stable L\'evy process of order $\alpha$ with drift and diffusion coefficients $b,\sigma$. When $\alpha\in (1,2)$, we investigate pathwise uniqueness for this equation.…
In this article we study the fractal Navier-Stokes equations by using stochastic Lagrangian particle path approach in Constantin and Iyer \cite{Co-Iy}. More precisely, a stochastic representation for the fractal Navier-Stokes equations is…
L\'evy Flights are paradigmatic generalised random walk processes, in which the independent stationary increments---the "jump lengths"---are drawn from an $\alpha$-stable jump length distribution with long-tailed, power-law asymptote. As a…
We study sums of independent and identically distributed random velocities in special relativity. We show that the resulting one-dimensional velocity distributions are not only stable under relativistic velocity addition but define a…
In this article, we are interested in the strong well-posedness together with the numerical approximation of some one-dimensional stochastic differential equations with a non-linear drift, in the sense of McKean-Vlasov, driven by a…
The semi-classical Lifshitz-Kosevich (LK) description of quantum oscillations is extended to a multiband two-dimensional Fermi liquid with a constant number of electrons. The amplitudes of novel oscillations with combination frequencies,…
We consider a fractional generalization of two-dimensional (2D) quantum-mechanical Kepler problem corresponding to 2D hydrogen atom. Our main finding is that the solution for discreet spectrum exists only for $\mu>1$ (more specifically $1 <…
The aim of this work is to prove existence and uniqueness of $L^{2}-$solutions of stochastic fractional partial differential equations in one spatial dimension. We prove also the equivalence between several notions of $L^{2}-$solutions. The…
In this paper we show the existence and form uniqueness of a solution for multidimensional backward stochastic differential equations driven by a multidimensional L\'{e}vy process with moments of all orders. The results are important from a…
Rayleigh-L\'evy flights are simplified cosmological tools which capture certain essential statistical properties of the cosmic density field, including hierarchical structures in higher-order correlations, making them a valuable reference…
The transformation of the partial fractional derivatives under spatial rotation in $R^2$ are derived for the Riemann-Liouville and Caputo definitions. These transformation properties link the observation of physical quantities, expressed…