Related papers: On the one--dimensional spectral Heat content for …
The spectral density function describes the second-order properties of a stationary stochastic process on $\mathbb{R}^d$. This paper considers the nonparametric estimation of the spectral density of a continuous-time stochastic process…
Consider anomalous energy spread in solid phases, i.e., $MSD= \int (x -{< x >}_E)^2 \rho_E(x,t)dx \propto t^{\beta}$, as induced by a small initial excess energy perturbation distribution $\rho_{E}(x,t=0)$ away from equilibrium. The…
The heat theorem (i.e. the second law of thermodynamics or the existence of entropy) is a manifestation of a general property of hamiltonian mechanics and of the ergodic Hypothesis. In nonequilibrium thermodynamics of stationary states the…
Consider non-linear time-fractional stochastic heat type equations of the following type, $$\partial^\beta_tu_t(x)=-\nu(-\Delta)^{\alpha/2} u_t(x)+I^{1-\beta}_t[\lambda \sigma(u)\stackrel{\cdot}{F}(t,x)]$$ in $(d+1)$ dimensions, where…
In this article, we investigate the asymptotic behavior of the solution to a one-dimensional stochastic heat equation with random nonlinear term generated by a stationary, ergodic random field. We extend the well-known central limit theorem…
We study the one-dimensional diffusion process which takes place between two reflecting boundaries and which is acted upon by a time-dependent and spatially-constant force. The assumed force possesses both the harmonically oscillating and…
Let $d \geq 2$, $\alpha \in (0,2)$, and $X$ be the rectilinear $\alpha$-stable process on $\mathbb{R}^d$. We first present a geometric characterization of an open subset $D\subset \mathbb{R}^d$ so that the part process $X^D$ of $X$ in $D$…
We study properties of solutions of the initial value problem for the nonlinear and nonlocal equation u_t+(-\partial^2_x)^{\alpha/2} u+uu_x=0 with alpha in (0,1], supplemented with an initial datum approaching the constant states u+/u-…
In this paper we obtain the precise description of the asymptotic behavior of the solution $u$ of $$ \partial_t u+(-\Delta)^{\frac{\theta}{2}}u=0\quad\mbox{in}\quad{\bf R}^N\times(0,\infty), \qquad u(x,0)=\varphi(x)\quad\mbox{in}\quad{\bf…
We define the heat capacity for steady periodically driven systems and as an example we compute it for dissipative two-level systems where the energy gap is time-modulated. There, as a function of ambient temperature, the Schottky peak…
de Haas-van Alphen oscillation spectrum of two-dimensional systems is studied for general power law energy dispersion, yielding a Fermi surface area of the form $S(E)\propto E^\alpha$ for a given energy $E$. The case $\alpha=1$ stands for…
We use a relationship between response and correlation function in nonequilibrium systems to establish a connection between the heat production and the deviations from the equilibrium fluctuation-dissipation theorem. This scheme extends the…
In this article, the small ball probability is obtained for the collision local time of two independent symmetric $\alpha-$stable processes with parameters $\alpha_1,\alpha_2\in(0,2]$ satisfying $\max\{\alpha_1,\alpha_2\}>1$. The proof is…
In this paper we consider the distribution of the location of the path supremum in a fixed interval for self-similar processes with stationary increments. To this end, a point process is constructed and its relation to the distribution of…
The statistical properties of coherent radiation scattered from phase-ordering materials are studied in detail using large-scale computer simulations and analytic arguments. Specifically, we consider a two-dimensional model with a…
For a two-level quantum mechanical system, we derive microscopically the exact expression for the fluctuation of microscopic work in a multi-step non-equilibrium process, and we rigorously prove that in an isothermal process, the…
Thermal convection in an inclined layer between two parallel walls kept at different fixed temperatures is studied for fixed Prandtl number Pr=1.07. Depending on the angle of inclination and the imposed temperature difference, the flow…
For the fractional diffusion-wave equation with the Caputo-Dzhrbashyan fractional derivative of order $\alpha \in (1,2)$ with respect to the time variable, we prove an analog of the principle of limiting amplitude (well-known for the wave…
This paper analyzes heat equation with memory in the case of kernels that are linear combinations of Gamma distributions. In this case, it is possible to rewrite the non-local equation as a local system of partial differential equations of…
A semilinear reaction-diffusion two-point boundary value problem, whose second-order derivative is multiplied by a small positive parameter $\eps^2$, is considered. It can have multiple solutions. An asymptotic expansion is constructed for…