Related papers: Semi-classical trace formula, isochronous case. Ap…
We study a class of semi-implicit Taylor-type numerical methods that are easy to implement and designed to solve multidimensional stochastic differential equations driven by a general rough noise, e.g. a fractional Brownian motion. In the…
We derive a semiclassical trace formula for a symmetry reduced part of the spectrum in axially symmetric systems. The classical orbits that contribute are closed in (\rho,z,p_\rho,p_z) and have p_\phi = m\hbar where m is the azimuthal…
In the present paper, we build up trace formulas for both the linear Hamiltonian systems and Sturm-Liouville systems. The formula connects the monodromy matrix of a symmetric periodic orbit with the infinite sum of eigenvalues of the…
We chart a path toward solving for the nonlinear gravitational dynamics of cold dark matter by relying on a semiclassical description using the propagator. The evolution of the propagator is given by a Schr\"odinger equation, where the…
We introduce the concept of a "transitory" dynamical system---one whose time-dependence is confined to a compact interval---and show how to quantify transport between two-dimensional Lagrangian coherent structures for the Hamiltonian case.…
We formulate a Hamiltonian description of the orbital motion of a point particle in Kerr spacetime for generic (eccentric, inclined) orbits, which accounts for the effects of the conservative part of the gravitational self-force. This…
Coherent sets are time-dependent regions in the physical space of nonautonomous flows that exhibit little mixing with their neighborhoods, robustly under small random perturbations of the flow. They thus characterize the global long-term…
We have proposed new algorithms for the numerical integration of the equations of motion for classical spin systems. In close analogy to symplectic integrators for Hamiltonian equations of motion used in Molecular Dynamics these algorithms…
Let F be a number field and $\widetilde{\mathrm{Sp}}(2n)$ be the metaplectic covering of Weil of $\mathrm{Sp}(2n, \mathbb{A}_F)$. We stabilize the elliptic semi-simple terms of the genuine part of trace formula for…
We further develop a thermal LB model for multiphase flows. In the improved model, we propose to use the FFT scheme to calculate both the convection term and external force term. The usage of FFT scheme is detailed and analyzed. By using…
In this paper we proceed with investigation of connections between Fokker - Planck equation and continuum mechanics. We base upon expressions from our work [2], based upon the spectral decomposition of Fokker - Planck equation solution. In…
A systematic analysis of the discrete conservation properties of non-dissipative, central-difference approximations of the compressible Navier-Stokes equations is reported. A general triple splitting of the nonlinear convective terms is…
A physically transparent and mathematically simple semiclassical model is employed to examine dynamics in the central-spin problem. The results reproduce a number of previous findings obtained by various quantum approaches and, at the same…
In non-degenerate integrable Hamiltonian systems, invariant tori can be parameterized equivalently by action variables or by their fundamental frequencies. We introduce an invariant-flow formulation for extracting fundamental frequencies of…
In this work, we develop a new compatible finite element formulation of the thermal shallow water equations that conserves energy and mathematical entropies given by buoyancy-related quadratic tracer variances. Our approach relies on…
As fractional diffusion equations can describe the early breakthrough and the heavy-tail decay features observed in anomalous transport of contaminants in groundwater and porous soil, they have been commonly employed in the related…
In this work, we study and extend a class of semi-Lagrangian exponential methods, which combine exponential time integration techniques, suitable for integrating stiff linear terms, with a semi-Lagrangian treatment of nonlinear advection…
We consider Hamiltonian PDEs that can be split into a linear unbounded operator and a regular non linear part. We consider abstract splitting methods associated with this decomposition where no discretization in space is made. We prove a…
In this paper we compare a classical finite-difference and a high order finite- volume scheme for barotropic ocean flows. We compare the schemes with respect to their accuracy, stability, and study various outflow and inflow boundary…
In this paper, we describe Bohr-Sommerfeld rules for semi-classical completely integrable systems with 2 degrees of freedom with non degenerate singularities (Morse-Bott singularities) under the assumption that the energy level of the first…