Related papers: Scalable numerical approach for the steady-state a…
In this paper, we present a novel stochastic and spatially lumped multi-mode model to describe the nonlinear dynamics of actively Q-switched lasers and random perturbations due to amplified spontaneous emission. This model will serve as a…
The present work focuses on the numerical approximation of the weak solutions of the shallow water model over a non-flat topography. In particular, we pay close attention to steady solutions with nonzero velocity. The goal of this work is…
A new approach for analytically solving quantum nonlinear Langevin equations is proposed and applied to calculations of spectra of superradiant lasers where collective effects play an important role. We calculate lasing spectra for…
We investigate lasing thresholds in a representative photonic molecule composed of two coupled active cylinders of slightly different radii. Specifically, we use the recently formulated steady-state ab initio laser theory (SALT) to assess…
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…
A phase-space formulation of non-stationary nonlinear dynamics including both Hamiltonian (e.g., quantum-cosmological) and dissipative (e.g., dissipative laser) systems reveals an unexpected affinity between seemly different branches of…
We consider a variational problem for three-dimensional (3D) classical lattice models. We construct the trial state as a two-dimensional product of local variational weights that contain auxiliary variables. We propose a stable numerical…
The following document presents a possible solution and a brief stability analysis for a nonlinear system, which is obtained by studying the possibility of building a hybrid solar receiver; It is necessary to mention that the solution of…
In this paper, we consider the iterative solution of linear algebraic equations under the condition that matrix-vector products with the coefficient matrix are computed only partially. At the same time, non-computed entries are set to…
A brief review of the SIESTA project is presented in the context of linear-scaling density-functional methods for electronic-structure calculations and molecular-dynamics simulations of systems with a large number of atoms. Applications of…
This work introduces a systematic method for identifying analytical and semi-analytical solutions of force-free magnetic fields with plane-parallel and axial symmetry. The method of separation of variables is used, allowing the…
Fully kinetic simulations of the Vlasov equation require a careful numerical treatment of phase space advections to ensure accuracy and stability in six dimensions. To test the accuracy of full Vlasov codes, we have developed a surprisingly…
A new algorithm is presented for computing a direct solution to a system of consistent linear equations. It produces a minimum norm particular solution, a generalized inverse (of type {124}), and a null space projection operator. In…
A new iterative technique is presented for solving of initial value problem for certain classes of multidimensional linear and nonlinear partial differential equations. Proposed iterative scheme does not require any discretization,…
We investigate modified steepest descent methods coupled with a loping Kaczmarz strategy for obtaining stable solutions of nonlinear systems of ill-posed operator equations. We show that the proposed method is a convergent regularization…
In this paper, we introduce an iterative numerical method to solve systems of nonlinear equations. The third-order convergence of this method is analyzed. Several examples are given to illustrate the efficiency of the proposed method.
We present a general variational approach to determine the steady state of open quantum lattice systems via a neural network approach. The steady-state density matrix of the lattice system is constructed via a purified neural network ansatz…
In this paper, we propose a horizontal type method of lines numerical scheme for the unsteady Euler-Bernoulli beam equation. The problem is initially reformulated as a first order system of initial value problems and a suitable one-step…
We develop a stable and efficient numerical scheme for modeling the optical field evolution in a nonlinear dispersive cavity with counter propagating waves and complex, semiconductor physics gain dynamics that are expensive to evaluate. Our…
Non-linear state estimation and some related topics, like parametric estimation, fault diagnosis, and perturbation attenuation, are tackled here via a new methodology in numerical differentiation. The corresponding basic system theoretic…