相关论文: Efficient numerical integration of neutrino oscill…
A procedure to numerically integrate non-autonomous linear delay differential equations is presented. It is based on the use of an spectral discretization of the delayed part to transform the original problem into a matrix linear ordinary…
We derive an analytical description of neutrino oscillations in matter based on the Magnus exponential representation of the time evolution operator. Our approach is valid in a wide range of the neutrino energies and properly accounts for…
We present new formalism for description of the neutrino oscillations in matter with varying density. The formalism is based on the Magnus expansion and has a virtue that the unitarity of the S-matrix is maintained in each order of…
We present a methodology for numerically integrating ordinary differential equations containing rapidly oscillatory terms. This challenge is distinct from that for differential equations which have rapidly oscillatory solutions: here the…
Approximate resolution of linear systems of differential equations with varying coefficients is a recurrent problem shared by a number of scientific and engineering areas, ranging from Quantum Mechanics to Control Theory. When formulated in…
We propose a third-order numerical integrator based on the Neumann series and the Filon quadrature, designed mainly for highly oscillatory partial differential equations. The method can be applied to equations that exhibit small or moderate…
In the present paper we consider numerical methods to solve the discrete Schr\"odinger equation with a time dependent Hamiltonian (motivated by problems encountered in the study of spin systems). We will consider both short-range…
We consider the problem of numerically integrating functions with hyperplane discontinuities over the entire Euclidean space in many dimensions. We describe a simple process through which the Euclidean space is partitioned into simplices on…
We present numerical schemes for the strong solution of linear stochastic differential equations driven by an arbitrary number of Wiener processes. These schemes are based on the Neumann (stochastic Taylor) and Magnus expansions. Firstly,…
In the following, we discuss nonlinear simulations of nonlinear dynamical systems, which are applied in technical and biological models. We deal with different ideas to overcome the treatment of the nonlinearities and discuss a novel…
We explore higher-dimensional generalizations of the Runge-Kutta-Wentzel-Kramers-Brillouin method for integrating coupled systems of first-order ordinary differential equations with highly oscillatory solutions. Such methods could improve…
We summarize our recent paper on neutrino oscillation probabilities in matter, explaining the importance, relevance and need for simple, highly accurate approximations to the neutrino oscillation probabilities in matter. Simple expressions…
The computation of the Schr\"odinger equation featuring time-dependent potentials is of great importance in quantum control of atomic and molecular processes. These applications often involve highly oscillatory potentials and require…
We study the dynamical equations for two-family neutrino oscillations in a medium of continuously-varying density. We can find explicit solutions to these equations in terms of series of nested integrals. These solutions can serve as a…
Within a conventional Hamiltonian description, we find accurate closed-form expressions for the oscillation probabilities of three coupled neutrinos propagating in matter. Subtle cancelations that occur in coefficients of our formulation…
In this paper, we show how the It\^o-stochastic Magnus expansion can be used to efficiently solve stochastic partial differential equations (SPDE) with two space variables numerically. To this end, we will first discretize the SPDE in space…
We demonstrate a multipole expansion method to calculate collective neutrino oscillations in supernovae using the neutrino bulb model. We show that it is much more efficient to solve multi-angle neutrino oscillations in multipole basis than…
A variety of problems in device and materials design require the rapid forward modeling of Maxwell's equations in complex micro-structured materials. By combining high-order accurate integral equation methods with classical multiple…
Inverse scattering involving microwave and ultrasound waves require numerical solution of nonlinear optimization problem. To alleviate the computational burden of a full three-dimensional (3-D) inverse problem, it is a common practice to…
We consider the efficient numerical solution of the three-dimensional wave equation with Neumann boundary conditions via time-domain boundary integral equations. A space-time Galerkin method with $C^\infty$-smooth, compactly supported basis…