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Inertial focusing in curved microfluidic ducts exploits the interaction of drag force from the Dean flow with the inertial lift force to separate particles or cells laterally across the cross-section width according to their size.…
Three numerical algorithms are proposed to solve the time-dependent elastodynamic equations in elastic solids. All algorithms are based on approximating the solution of the equations, which can be written as a matrix exponential. By…
The radial Schrodinger equation for a spherically symmetric potential can be regarded as a one dimensional classical harmonic oscillator with a time-dependent spring constant. For solving classical dynamics problems, symplectic integrators…
In this work, we derive particle schemes, based on micro-macro decomposition, for linear kinetic equations in the diffusion limit. Due to the particle approximation of the micro part, a splitting between the transport and the collision part…
In this methodology focused paper we scrutinize the application of the band-coherent Boltzmann equation approach to calculating the conductivity of chiral particles. As the ideal testing ground we use the two-band kinetic Hamiltonian with…
The Boltzmann collision operator for a dilute granular gas of inelastic rough hard spheres is much more intricate than its counterpart for inelastic smooth spheres. Now the one-body distribution function depends not only on the…
Quantum stochastic methods based on effective wave functions form a framework for investigating the generally non-Markovian dynamics of a quantum-mechanical system coupled to a bath. They promise to be computationally superior to the…
A cut of a graph can be represented in many different ways. Here we propose to represent a cut through a ``relation tree'', which is a spanning tree with signed edges. We show that this picture helps to classify the main greedy heuristics…
We use recent results regarding the geometry of the U(3) bosonic algebraic model to motivate a hybrid algebraic-Schr\"odinger approach to the 2D Franck-Condon problem analogous to 1D approaches. This approach allows one to analyze bent to…
We suggest a new derivation of a kinetic equation of Kolmogorov-Zakharov (KZ) type for the spectrum of the weakly nonlinear Schr\"odinger equation with stochastic forcing. The kynetic equation is obtained as a result of a double limiting…
We consider the problem of analyzing and designing gradient-based discrete-time optimization algorithms for a class of unconstrained optimization problems having strongly convex objective functions with Lipschitz continuous gradient. By…
We introduce a numerical method for solving Grad's moment equations or regularized moment equations for arbitrary order of moments. In our algorithm, we do not need explicitly the moment equations. As an instead, we directly start from the…
In this paper we have generalized the quantum mechanics on fractal time-space. The time is changing on Cantor-set like but space is considered as fractal curve like Von-Koch curve. The Feynman path method in quantum mechanics has been…
The wave kinetic equation has become an important tool in different fields of physics. In particular, for surface gravity waves, it is the backbone of wave forecasting models. Its derivation is based on the Hamiltonian dynamics of surface…
In the article, correct method for the kinetic Boltzmann equation asymptotic solution is formulated, the Hilbert method and the Enskog error are considered. The equations system of multi-component nonequilibrium gas-dynamics is derived,…
We introduce a new structure preserving, second order in time relaxation-type scheme for approximating solutions of the Schr\"odinger-Poisson system. More specifically, we use the Crank-Nicolson scheme as a time stepping mechanism, whilst…
Electric conductivity is sensitive to effective cross sections among the particles of the partonic medium. We investigate the electric conductivity of a hot plasma of quarks and gluons, solving the relativistic Boltzmann equation. In order…
Spectroscopic techniques are very essential tools in studying electronic structures, spectroscopic constants and energetic properties of diatomic molecules. These techniques are also required for parametrization of new method based on…
In this paper we deal with the extension of the Fast Kinetic Scheme (FKS) [J. Comput. Phys., Vol. 255, 2013, pp 680-698] originally constructed for solving the BGK equation, to the more challenging case of the Boltzmann equation. The scheme…
This article extends a recently introduced kinetic closure of turbulence by developing its theoretical framework, operational realizations, and validation. In contrast with filtered Navier--Stokes formulations, filtering the Boltzmann…