Related papers: Periodic homogenisation for two dimensional genera…
In a previous work (N. H. Tong, Phys. Rev. B 92, 165126 (2015)), an equation-of-motion based series expansion formalism was used to do the second-order strong-coupling expansion for the single-particle Green function of the Anderson…
We establish two-sided Gaussian bounds for the fundamental solution of second-order parabolic operators in non-divergence form under minimal regularity assumptions. Specifically, we show that the upper and lower bounds follow from the local…
We study the localization properties of a disordered tight-binding Hamiltonian on a generic bipartite lattice close to the band center. By means of a fermionic replica trick method, we derive the effective non-linear $\sigma$-model…
Self-consistent perturbation expansion up to the second order in the interaction strength is used to study a single-level quantum dot with local Coulomb repulsion attached asymmetrically to two generally different superconducting leads. At…
We consider the heat equation in a multidimensional domain with nonlocal hysteresis feedback control in a boundary condition. Thermostat is our prototype model. We construct all periodic solutions with exactly two switching on the period…
We demonstrate the effectiveness of a generalized renormalized perturbational approach to calculate the induced magnetization for the single impurity Anderson model with a strong on-site interaction, using flow equations for renormalized…
We perform an all-orders resummation of the QCD Adler D-function for the vector correlator, in which the portion of perturbative coefficients involving the leading power of b, the first beta-function coefficient, is resummed. To avoid a…
A new type of perturbation expansion in the mixing $V$ of localized orbitals with a conduction-electron band in the $U\to\infty$ Anderson model is presented. It is built on Feynman diagrams obeying standard rules. The local correlations of…
This paper aims at an accurate and efficient computation of effective quantities, e.g., the homogenized coefficients for approximating the solutions to partial differential equations with oscillatory coefficients. Typical multiscale methods…
We deal with the regularity problem for linear, second order parabolic equations and systems in divergence form with measurable data over non-smooth domains, related to variational problems arising in the modeling of composite materials and…
Anderson acceleration (AA) is a technique for accelerating the convergence of fixed-point iterations. In this paper, we apply AA to a sequence of functions and modify the norm in its internal optimization problem to the $\mathcal{H}^{-s}$…
The averaging problem in general relativity concerns the difficulty of defining meaningful averages of tensor quantities and we consider various aspects of the problem. We first address cosmological backreaction which arises because the…
We develop a Magnus formalism for periodically driven systems which provides an expansion both in the driving term and the inverse driving frequency, applicable to isolated and dissipative systems. We derive explicit formulas for a driving…
In this article, we address singularly perturbed two-parameter parabolic problem of the reaction-convection-diffusion type in two dimensions. These problems exhibit discontinuities in the source term and convection coefficient at particular…
In this article, we study a two-dimensional singularly perturbed parabolic equation of the convection-diffusion type, characterized by discontinuities in the source term and convection coefficient at a specific point in the domain. These…
We find the normal forms of hyperbolic logarithmic transseries with respect to parabolic logarithmic normalizing changes of variables. We provide a necessary and sufficient condition on such transseries for the normal form to be linear. The…
The paper deals with homogenization problem for a non-local linear operator with a kernel of convolution type in a medium with a periodic structure. We consider the natural diffusive scaling of this operator and study the limit behaviour of…
We investigate and derive second solutions to linear homogeneous second-order difference equations using a variety of methods, in each case going beyond the purely formal solution and giving explicit expressions for the second solution. We…
In order to have a better description of homogenization for parabolic partial differential equations with periodic coefficients, we define the notion of parametric two-scale convergence. A compactness theorem is proved to justify this…
This paper is concerned with the study of solutions to discrete parabolic equations in divergence form with random coefficients, and their convergence to solutions of a homogenized equation. It has previously been shown that if the random…