Related papers: Hashimoto transform for stochastic Landau-Lifshitz…
We present a general algorithm for constructing the holographic dictionary for Lifshitz and hyperscaling violating Lifshitz backgrounds for any value of the dynamical exponent $z$ and any value of the hyperscaling violation parameter…
We study the relativistic heat equation in one space dimension. We prove a local regularity result when the initial datum is locally Lipschitz in its support. We propose a numerical scheme that captures the known features of the solutions…
We study the two-dimensional stochastic nonlinear heat equation (SNLH) and stochastic damped nonlinear wave equation (SdNLW) with an exponential nonlinearity $\lambda\beta e^{\beta u }$, forced by an additive space-time white noise. We…
We construct finite time blow-up solutions to the Landau-Lifshitz-Gilbert equation (LLG) from ${\mathbb R}^2$ into $S^2$ \begin{equation*} \begin{cases} u_t= a(\Delta u+|\nabla u|^2u) -b u\wedge \Delta u &\ \mbox{ in }\ {\mathbb…
The equivalence between the Laplace transform [Landau L., J. Phys. USSR, 10 (1946), 25] and Hermite transform [Zocco and Schekochihin, Phys. Plasmas, 18, 102309 (2011)] solutions of the linear collisionless Landau damping problem is proven.
In this paper, we extend the results of [1] by proving exponential asymptotic $H^1$-convergence of solutions to a one-dimensional singular heat equation with $L^2$-source term that describe evolution of viscous thin liquid sheets while…
The Landau-Lifshitz-Gilbert (LLG) equation is widely used to describe magnetization dynamics. We develop a unified framework of the microscopic LLG equation based on the nonequilibrium Green's function formalism. We present a unified…
Admissible point transformations between Burgers equations with linear damping and time-dependent coefficients are described and used in order to exhaustively classify Lie symmetries of these equations. Optimal systems of one- and…
We present stochastic homogenization results for viscous Hamilton-Jacobi equations using a new argument which is based only on the subadditive structure of maximal subsolutions (solutions of the "metric problem"). This permits us to give…
The Landau-Lifshitz-Gilbert (LLG) equation is a widely used model for fast magnetization dynamics in ferromagnetic materials. Recently, the inertial LLG equation, which contains an inertial term, has been proposed to capture the ultra-fast…
We derive an It\^o's-type formula for the one dimensional stochastic heat equation driven by a space-time white noise. The proof is based on elementary properties of the $\mathcal{S}$-transform and on the explicit representation of the…
This is a series of studies devoted to modeling and solving heat and mass transfer problems occurring in electric contacts where we employ and develop mathematical apparatus along with quantum algorithms for solving moving boundary value…
In this paper, we consider Klein-Gordon equations with cubic nonlinearity in three spatial dimensions, which are Hamiltonian perturbations of the linear one with potential. It is assumed that the corresponding Klein-Gordon operator $B =…
The holographic complexity of a 3+1-dimensional Lifshitz spacetime having a scaling symmetry is computed. The change in the holographic complexity between the excited state and the ground state is then obtained. This is then related to the…
We introduce GBDT version of Darboux transformation for symplectic and Hamiltonian systems as well as for Shin-Zettl systems and Sturm-Liouville equations. These are the first results on Darboux transformation for general-type Hamiltonian…
Thermalization (generalized thermalization) in nonintegrable (integrable) quantum systems requires two ingredients: equilibration and agreement with the predictions of the Gibbs (generalized Gibbs) ensemble. We prove that observables that…
A necessary and sufficient condition for a parameter transformation that leaves invariant the energy of a one dimensional autonomous system is obtained. Using a parameter transformation the Hamilton-Jacobi equation is solved by a…
The fundamental purpose of this paper is to propose a new Laplace-type integral transform (NL-TIT) for solving steady heat-transfer problems. The proposed integral transform is a generalization of the Sumudu, and the Laplace transforms and…
In the paper we obtain equations for large-scale fluctuations of the mean field (the field of magnetization and quadrupole moments) in a magnetic system realized by a square (cubic) lattice of atoms with spin s >= 1 at each site. We use the…
We consider the solution to a stochastic heat equation. This solution is a random function of time and space. For a fixed point in space, the resulting random function of time, $F(t)$, has a nontrivial quartic variation. This process,…