相关论文: A general numerical solution of dispersion relatio…
Starting from the Lorentzian inversion formula, we derive a dispersion relation which computes a four-point function in 1d CFTs as an integral over its double discontinuity. The crossing symmetric kernel of the integral is given explicitly…
We consider the numerical approximation of boundary conditions in radiative transfer problems by a perfectly matched layer approach. The main idea is to extend the computational domain by an absorbing layer and to use an appropriate…
Level-spacing distributions of the Gaussian Unitary Ensemble (GUE) of random matrix theory are expressed in terms of solutions of coupled differential equations. Series solutions up to order 50 in the level spacing are obtained, thus…
This paper presents a concurrent global-local numerical method for solving multiscale parabolic equations in divergence form. The proposed method employs hybrid coefficient to provide accurate macroscopic information while preserving…
The 2d one component gas of pointlike charges in a uniform neutralizing background interacting with a logarithmic potential is a common model for plasmas. In its classical equilibrium statistics at fixed temperature (canonical ensemble) it…
A hidden symmetry of the nonlinear wave equation is exploited to analyse the propagation of paraxial and uniform atom-laser beams in time-independent, quadratic and cylindrical potentials varying smoothly along the propagation axis. The…
We propose a numerical method for compensating dispersion effects in optical coherence tomography that does not require a priori knowledge of dispersive properties of the sample. The method is based on the generalized autoconvolution…
Fractional Gaussian noise models the time series with long-range dependence; when the Hurst index $H>1/2$, it has positive correlation reflecting a persistent autocorrelation structure. This paper studies the numerical method for solving…
The study gives a brief overview of existing modifications of the method of functional separation of variables for nonlinear PDEs. It proposes a more general approach to the construction of exact solutions to nonlinear equations of applied…
In this paper, the authors propose a numerical method to compute the solution of a nonlinear reaction-diffusion problem in the case of HS-regime. The initial condition is a nonnegative function with compact support. The problem is split in…
The interpolation of high-dimensional potential energy surfaces (PESs) is commonly done with physically-inspired deep-neural network models. In this work, we illustrate that Gaussian Processes (GPs) are also capable of interpolating…
The estimation of probability density functions (PDF) using approximate maps is a fundamental building block in computational probability. We consider forward problems in uncertainty quantification: the inputs or the parameters of a…
The model of laminated wave turbulence puts forth a novel computational problem - construction of fast algorithms for finding exact solutions of Diophantine equations in integers of order $10^{12}$ and more. The equations to be solved in…
We consider numerical methods for linear parabolic equations in one spatial dimension having piecewise constant diffusion coefficients defined by a one parameter family of interface conditions at the discontinuity. We construct immersed…
Boundary value problems in ODEs arise in modelling many physical situations from microscale to mega scale. Such two-point boundary value problems (BVPs) are complex and often possess no analytical closed form solutions. So, one has to rely…
Dispersion relations and amplitudes of collective pionic modes are derived in a pi + nucleon-hole + delta-hole model for use in transport descriptions by means of a local density approximation. It is discussed how pionic modes can be…
Many important applications are available for nonlinear reaction-diffusion equation especially in the area of biology and engineering. Therefore a mathematical model for Lie symmetry reduction of system of nonlinear reaction-diffusion…
Nonlinear optical responses are becoming increasingly relevant for characterizing the symmetries and quantum geometry of electronic phases in materials. Here, we develop an expanded diagrammatic scheme for calculating spatially dispersive…
Reaction-Diffusion systems arise in diverse areas of science and engineering. Due to the peculiar characteristics of such equations, analytic solutions are usually not available and numerical methods are the main tools for approximating the…
A detailed description and validation of a recently developed integration scheme is here reported for one- and two-dimensional reaction-diffusion models. As paradigmatic examples of this class of partial differential equations the complex…