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Interferometric measurements of high-harmonics induced by multiple laser fields in an emerging field of research that promises optimized yield of harmonics, and time and space-resolved nonlinear spectroscopy. Most of the measurements have…
The paper is concerned with a node-based, gradient-driven, continuous adjoint two-phase flow procedure to optimize the shapes of free-floating vessels and discusses three topics. First, we aim to convey that elements of a Cahn-Hilliard…
We study the equilibrium correlations of a Bose gas in an elongated three-dimensional harmonic trap using a grand-canonical classical-field method. We focus in particular on the progressive transformation of the gas from the normal phase,…
This work introduces a simple and efficient linesearch method for composite minimization that accelerates proximal-gradient iterations with fast Newton-type directions. Our algorithm is based on simple operations and only requires the…
We present an efficient and accurate algorithm for solving the Poisson equation in spherical polar coordinates with a logarithmic radial grid and open boundary conditions. The method employs a divide-and-conquer strategy, decomposing the…
We provide a constructive algorithm to find the best separable approximation to an arbitrary density matrix of a composite quantum system of finite dimensions. The method leads to a condition of separability and to a measure of…
A conducting two-dimensional periodic composite of two anisotropic phases with anisotropic, not necessarily symmetric, conductivity tensors is considered. By finding approximate representations for the relevant operators, an approximation…
The thermodynamics of phase transitions of binary solutions into spatially inhomogeneous one-dimensional states is studied theoretically with taking into account nonlinear effects. It is shown that below the spinodal decomposition…
We consider adaptive finite element methods for second-order elliptic PDEs, where the arising discrete systems are not solved exactly. For contractive iterative solvers, we formulate an adaptive algorithm which monitors and steers the…
In this paper, we present a parallel numerical algorithm for solving the phase field crystal equation. In the algorithm, a semi-implicit finite difference scheme is derived based on the discrete variational derivative method. Theoretical…
We consider a composite open quantum system consisting of a fast subsystem coupled to a slow one. Using the time-scale separation, we develop an adiabatic elimination technique to derive at any order the reduced model describing the slow…
The evaluation of phase stabilities of unstable elemental phases is a long-standing problem in the computational assessment of phase diagrams. Here we tackle this problem by explicitly calculating phase diagrams of intermetallic systems…
We present a complexity reduction algorithm for a family of parameter-dependent linear systems when the system parameters belong to a compact semi-algebraic set. This algorithm potentially describes the underlying dynamical system with…
It has been conjectured that the relative phase between strong and electromagnetic amplitudes is universally $-90^{\circ}$ in charmonium decays. $\psi^{\prime}$ decaying into pseudoscalar pair provides a possibility to test this conjecture.…
In this paper, for solving a class of linear parabolic equations in rectangular domains, we have proposed an efficient Parareal exponential integrator finite element method. The proposed method first uses the finite element approximation…
Computational exploration of the compositional spaces of materials can provide guidance for synthetic research and thus accelerate the discovery of novel materials. Most approaches employ high-throughput sampling and focus on reducing the…
Results on continuous dependence on parameters, as well as on regularization, of solutions to linear systems of parabolic partial differential equations of second order with delay are given. One of the main features is that the topology on…
Numerically solving parabolic equations with quasiperiodic coefficients is a significant challenge due to the potential formation of space-filling quasiperiodic structures that lack translational symmetry or decay. In this paper, we…
In this paper, three efficient ensemble algorithms are proposed for fast-solving the random fluid-fluid interaction model. Such a model can be simplified as coupling two heat equations with random diffusion coefficients and a friction…
In this work, an efficient approximation scheme has been proposed for getting accurate approximate solution of nonlinear partial differential equations with constant or variable coefficients satisfying initial conditions in a series of…