相关论文: The Simplest Exact Solutions in the LTB Model

We introduce a quasi-local integral functional and scalar quasi-local variables to examine a wide class of spherically symmetric inhomogeneous spacetimes that generalize the Lemaitre-Tolman-Bondi (LTB) dust solutions ("LTB" spacetimes). By…

Recently, the zero-pairing limit of Hartree-Fock-Bogoliubov (HFB) mean-field theory was studied in detail in arXiv:2006.02871. It was shown that such a limit is always well-defined for any particle number A, but the resulting many-body…

We show that the GBW saturation model provides an exact solution to the one dimensional linear transport equation. We also show that it is motivated by the BK equation considered in the saturated regime when the diffusion and the splitting…

Let $\{b_H(t),t\in\mathbb{R}\}$ be the fractional Brownian motion with parameter $0<H<1$. When $1/2<H$, we consider diffusion equations of the type \[X(t)=c+\int_0^t\sigma\bigl(X(u)\bigr)\mathrm {d}b_H(u)+\int _0^t\mu\bigl(X(u)\bigr)\mathrm…

The Homotopy Perturbation Method (HPM) is used to solve the Burgers-Huxley non-linear differential equations. Three case study problems of Burgers-Huxley are solved using the HPM and the exact solutions are obtained. The rapid convergence…

The Tomonaga-Luttinger model with impurity is studied by means of flow equations for Hamiltonians. The system is formulated within collective density fluctuations but no use of the bosonization formula is made. The truncation scheme…

In this article we consider a class of nonlinear integro-differential equations of the form $$\inf_{\tau \in\mathcal{T}} \bigg\{\int_{\mathbb{R}^d} (u(x+y)+u(x-y)-2u(x))\frac{k_{\tau}(x,y)}{|y|^{d+2s}} \,dy+ b_{\tau}(x) \cdot \nabla…

A system of two cubic reaction-diffusion equations for two independent gene frequencies arising in population dynamics is studied. Depending on values of coefficients, all possible Lie and $Q$-conditional (nonclassical) symmetries are…

The solution of complex many-body lattice models can often be found by defining an energy functional of the relevant density of the problem. For instance, in the case of the Hubbard model the spin-resolved site occupation is enough to…

A novel explicit method to model Lorentz linear dispersive media with finite difference method are presented. The method shows an explicit method without any modification to the Leap-Frogging scheme. The polarizations of the Lorentz media…

Accuracy of a relativistic weak-coupling expansion procedure for solving the Hamiltonian bound-state eigenvalue problem in theories with asymptotic freedom is measured using a well-known matrix model. The model is exactly soluble and simple…

We examine a large class of inhomogeneous spherically symmetric spacetimes that generalize the Lemaitre-Tolman-Bondi dust solutions to nonzero pressure ("LTB spacetimes"). Local covariant LTB objects can be expressed as perturbations of…

It can be difficult to assess the quality of a fitted model when facing unsupervised learning problems. Latent variable models, such as variation autoencoders and Gaussian mixture models, are often trained with likelihood-based approaches.…

In this paper we present a survey concerning unconstrained free boundary problems of type $$ \left\{ \begin{array}{ll} F_1(D^2u,\nabla u,u,x)=0 & \text{in }B_1 \cap \Omega ,\\ F_2 (D^2 u,\nabla u,u,x)=0 & \text{in }B_1\setminus\Omega ,\\ u…

We study a class of nonlinear diffusion equations whose model is the classical porous media equation on domains $\Omega\subseteq{\mathbb R}^N$, $N\ge3$, with homogeneous Neumann boundary conditions. Firstly we improve some known results in…

On a nonrelativistic contact four-fermion model we have shown that the simple Lambda-cut-off prescription together with definite fine-tuning of the Lambda dependency of "bare"quantities lead to self-adjoint semi-bounded Hamiltonian in one-,…

A numerical approach to solve the perturbed Lambert's problem is presented. The proposed technique uses the Theory of Functional Connections, which allows the derivation of a constrained functional that analytically satisfies the boundary…

Analytic expressions for distance-redshift relations which have been corrected for the effects of inhomogeneities in the Friedmann-Lema\^itre-Robertson-Walker (FLRW) mass density are given in terms of Heun functions and are used to…

We propose to calculate spectral functions of quantum impurity models using the Time Evolving Block Decimation (TEBD) for Matrix Product States. The resolution of the spectral function is improved by a so-called linear prediction approach.…

An explicit and complete set of constants of the motion are constructed algorithmically for Friedmann-Lema\^{i}tre-Robertson-Walker (FLRW) models consisting of an arbitrary number of non-interacting species. The inheritance of constants of…