Related papers: A fast Fourier spectral method for wave kinetic eq…
Wavelet basis functions are a natural tool for analyzing turbulent flows containing localized coherent structures of different spatial scales. Here, wavelets are used to study the onset and subsequent transition to fully developed…
In the study of subsurface seismic imaging, solving the acoustic wave equation is a pivotal component in existing models. The advancement of deep learning enables solving partial differential equations, including wave equations, by applying…
This paper presents a novel methodology for the direct numerical modeling and simulation of turbulent flows. The kinetic model equation is firstly extended to turbulent flow with the account of coupled evolution of kinetic, thermal, and…
A single-wavenumber representation of nonlinear energy spectrum, i.e., stretching energy spectrum is found in elastic-wave turbulence governed by the F\"oppl-von K\'arm\'an (FvK) equation. The representation enables energy decomposition…
Fourier transform-based methods enable accurate, dispersion-free simulations of time-domain scattering problems by evaluating solutions to the Helmholtz equation at a discrete set of frequencies sufficient to approximate the inverse Fourier…
A high-frequency recovered fully discrete low-regularity integrator is constructed to approximate rough and possibly discontinuous solutions of the semilinear wave equation. The proposed method, with high-frequency recovery techniques, can…
The internal-wave (IW) continuum of a regional ocean model is studied in terms of the vertical spectral kinetic-energy (KE) fluxes and transfers at high vertical wavenumbers. Previous work has shown that this model permits a partial…
In this paper we present a parallelization strategy on distributed memory systems for the Fast Kinetic Scheme --- a semi-Lagrangian scheme developed in [J. Comput. Phys., Vol. 255, 2013, pp 680-698] for solving kinetic equations. The…
Synthetic turbulence models are a useful tool that provide realistic representations of turbulence, necessary to test theoretical results, to serve as background fields in some numerical simulations, and to test analysis tools. Models of 1D…
Difference Kinetic Equations are derived quantum mechanically in a plane wavelets representation with account of two-particle correlations. It is shown that the set of plane wavelet orthonormal functions is complete. The set of ket vectors…
The linear stability analysis of the Boltzmann kinetic equation has recently garnered research interest due to its potential applications in space exploration, where rarefaction effects can render the Navier Stokes equations invalid. Since…
This paper presents a new numerical model based on the highly nonlinear potential flow theory for simulating the propagation of water waves in variable depth. A new set of equations for estimating the surface vertical velocity is derived…
We present a new method for the generation of atmospheric turbulence phase screens based on the frequency shift property of the Fourier transform. This method produces low spatial frequency distortions without additional computation time…
Oscillatory rarefied gas flows are frequently encountered in MEMS, and their efficient numerical simulation remains a major challenge due to the time dependent nature of the problem and the high dimensionality of the Boltzmann kinetic…
The known nonlinear kinetic equations (in particular, the wave kinetic equation and the quantum Nordheim -- Uehling -- Uhlenbeck equations) are considered as a natural generalization of the classical spatially homogeneous Boltzmann…
We present a spectral Petrov-Galerkin method for the Boltzmann collision operator. We expand the density distribution $f$ to high order orthogonal polynomials multiplied by a Maxwellian. By that choice, we can approximate on the whole…
To avoid instabilities in the continuum semi-classical limit of loop quantum cosmology models, refinement of the underlying lattice is necessary. The lattice refinement leads to new dynamical difference equations which, in general, do not…
The development of accurate and fast numerical schemes for the five fold Boltzmann collision integral represents a challenging problem in scientific computing. For a particular class of interactions, including the so-called hard spheres…
We re-use some original ideas of de~Broglie, Schr\"odiger, Dirac and Feynman to revise the ensemble interpretation of wave function in quantum mechanics. To this end we introduce coherence (auto-concordance) of ensembles of quantum…
Maxwell equations describe the propagation of electromagnetic waves and are therefore fundamental to understanding many problems encountered in the study of antennas and electromagnetics. The aim of this paper is to propose and analyse an…