Related papers: Spectral method for efficient computation of time-…
A number of physical processes in laser-plasma interaction can be described with the two-fluid plasma model. We report on a solver for the three-dimensional two-fluid plasma model equations. This solver is particularly suited for simulating…
High dimensional random dynamical systems are ubiquitous, including -- but not limited to -- cyber-physical systems, daily return on different stocks of S&P 1500 and velocity profile of interacting particle systems around McKeanVlasov…
Spectral methods have emerged as a simple yet surprisingly effective approach for extracting information from massive, noisy and incomplete data. In a nutshell, spectral methods refer to a collection of algorithms built upon the eigenvalues…
Supervised topic models simultaneously model the latent topic structure of large collections of documents and a response variable associated with each document. Existing inference methods are based on variational approximation or Monte…
The last decade has witnessed a rapid advancement in laser technology, enabling the direct monitoring and control of electronic motion on its natural attosecond to sub-femtosecond timescales. Ultrafast processes are conventionally studied…
We present an ab-initio treatment of the steady-state of lasers with injected signals that describes a regime, valid for micro lasers, in which the locking transition is dominated by cross-saturation and spatial hole-burning. The theory…
We review the spectral analysis and the time-dependent approach of scattering theory for manifolds with asymptotically cylindrical ends. For the spectral analysis, higher order resolvent estimates are obtained via Mourre theory for both…
This work models the propagation of an optical pulse in a 4-level atomic system in the electromagnetic induced transparency regime. By demonstrating that linear and nonlinear optical properties can be externally controlled and tailored by a…
Classical spectral methods are subject to two fundamental limitations: they only can account for covariance-related serial dependencies, and they require second-order stationarity. Much attention has been devoted lately to quantile-based…
We present a time-splitting spectral scheme for the Maxwell-Dirac system and similar time-splitting methods for the corresponding asymptotic problems in the semi-classical and the non-relativistic regimes. The scheme for the Maxwell-Dirac…
Semi-implicit semi-Lagrangian (SISL) methods are commonly used for the shallow water equations (SWE) because they allow for larger time steps than those permitted by the Courant-Friedrichs-Lewy (CFL) stability condition in Eulerian schemes.…
By means of quantum stochastic calculus we construct a model for an atom with two degenerate levels and stimulated by a laser and we compute its fluorescence spectrum; let us stress that, once the model for the unitary atom-field dynamics…
Coupled wave equations are popular tool for investigating longitudinal dynamical effects in semiconductor lasers, for example, sensitivity to delayed optical feedback. We study a model that consists of a hyperbolic linear system of partial…
Spontaneous emission of the quantum system driven by a high intensity classical laser field is analyzed. The study is based on the accurate consideration of quantum system interaction with vacuum quantized field modes in the first order of…
A large body of work has accumulated over the years in the study of the optical properties of single and coupled microcavities for a variety of applications, ranging from filters to sensors and lasers. The focus has been mostly on the…
The paper offers a discrete thermodynamic model of lasers. Laser is an open system; its equilibrium is based on a balance of two thermodynamic forces, one related to the incoming pumping power and another to the emitted light. The basic…
The ultrafast dynamic evolution of an atomic system under medium-strength laser fields is studied by performing transient absorption measurement. An analytical model developed from perturbation theory with a modified transition dipole…
There are two usual computational methods for linear (waves and instabilities) problem: eigenvalue (dispersion relation) solver and initial value solver. In fact, we can introduce an idea of the combination of them, i.e., we keep time…
Spectral methods provide highly accurate numerical solutions for partial differential equations, exhibiting exponential convergence with the number of spectral nodes. Traditionally, in addressing time-dependent nonlinear problems, attention…
In many mechanical, electrical, and general physical systems evolving over time or space, spectral analysis methods as Fast Fourier Transform (FFT), Short Term Fourier Transform (STFT), Power Spectrum Density (PSD) plays a very important…