Related papers: Dynamics of wave packets in the functional mechani…
We review some applications of fractional calculus developed by the author (partly in collaboration with others) to treat some basic problems in continuum and statistical mechanics. The problems in continuum mechanics concern mathematical…
A coupled Volterra system is proposed. The model can be considered as one of the integrable discrete form of the coupled integrable KdV system which is a significant physical model. Many types of cnoidal waves, positons, negatons (solitons)…
We present a geometrical way of understanding the dynamics of wavefunctions in a free space, using the phase-space formulation of quantum mechanics. By visualizing the Wigner function, the spreading, shearing, the so-called "negative…
The continuum equations of fluid mechanics are rederived with the intention of keeping certain mechanical and thermodynamic concepts separate. A new "mechanical" mass density is created to be used in computing inertial quantities, whereas…
In this paper, we deal with fluid motion in terms of quantum mechanics. Mechanism accounting for the appearance of quantum behavior is discussed.
Presented here is the mathematical model describing the phenomenon of shock waves. The underlying concept is based on the time-space model of wave propagation.
Fractional calculus, in allowing integrals and derivatives of any positive order (the term "fractional" kept only for historical reasons), can be considered a branch of mathematical physics which mainly deals with integro-differential…
The mechanics of the structured particles develops. The substantiation of applicability of such mechanics for the description of processes of evolution in open nonequilibrium systems is offered. The consequences following from the equations…
We investigate the operator monotonicity of functions which was considered by V.E. Szabo.
The goals of the present work are to: (i) investigate the dynamics of oceanic frontogenesis by taking advantage of the geometric mechanics underlying the class of Vertical Slice Models (VSMs) of ocean dynamics; and (ii) illustrate the…
We show mathematical structure of the function dynamics, i.e., the dynamics of interval maps $f_{n+1} = (1-\e)f_n + \e f_n\circ f_n$ and clarify the types of fixed points, the self-referential structure and the hierarchical structure.
In quantum mechanics, spatial wavefunctions describe distributions of a particle's position or momentum, but not of angular momentum $j$. In contrast, here we show that a spatial wavefunction, $j_m (\phi,\theta,\chi)=~e^{i m \phi} \delta…
In the present work we deal with the dynamics of wave packets in a two-dimensional crystal under the action of magnetic and electric fields. The magnetic field is perpendicular to the plane and the electric field is on the plane. In the…
The wark is a contribution to the functional calculus constructed by of the author and A. A. Atvinovskii of closed operators on Banach spaces. The calculus is based on Markov and related functions as symbols. Estimates of bounded…
Complete analysis of quantum wave functions of linear systems in an arbitrary number of dimensions is given. It is shown how one can construct a complete set of stationary quantum states of an arbitrary linear system from purely classical…
The kinematic wave theory, originally proposed by (Lighthill and Whitham, 1955b; Richards, 1956), has been a good candidate for studying vehicular traffic. In this dissertation, we study kinematic wave models of network traffic, which are…
In quantum mechanics, one can express the evolution operator and other quantities in terms of functional integrals. The main goal of this paper is to prove corresponding results in the geometric approach to quantum theory. We apply these…
We present a new molecular-dynamics algorithm for integrating the equations of motion for a system of particles interacting with mixed continuous/impulsive forces. This method, which we call Impulsive Verlet, is constructed using operator…
For the first time weak turbulent theory was demonstrated for the surface gravity waves. Direct numerical simulation of the dynamical equations shows Kolmogorov turbulent spectra as predicted by analytical analysis from kinetic equation.
We propose a method for arbitrary manipulations of a quantum wavepacket in an optical lattice by a suitable modulation of the lattice amplitude. A theoretical model allows to determine the modulation corresponding to a given wavepacket…