Paulius Miškinis

Some properties of fractional burgers equation

Abstract The fractional generalization of a one‐dimensional Burgers equation with initial conditions ?(x, 0) = ?0(x); ?t(x,0) = ψ0 (x), where ? = ?(x,t) ∈ C2(O): ?t = ??/?t; aDx p is the Riemann‐Liouville fractional derivative of the order p; O = (x,t) : x ∈ E 1, t > 0; and the explicit form of a particular analytical solution are suggested. Existing of traveling wave solution and conservation laws are considered. The relation with Burgers equation of integer order and properties of fractional generalization of the Hopf‐Cole transformation are discussed.

A Generalization of the Hopf-Cole Transformation

A generalization of the Hopf-Cole transformation and its relation to the Burgers equation of integer order and the diffusion equation with quadratic nonlinearity are discussed. The explicit form of a particular analytical solution is presented. The existence of the travelling wave solution and the interaction of nonlocal perturbation are considered. The nonlocal generalizations of the one-dimensional diffusion equation with quadratic nonlinearity and of the Burgers equation are analyzed.

The Havriliak–Negami susceptibility as a nonlinear and nonlocal process

A theoretical substantiation of the Cole–Cole, Cole–Davidson and Havriliak–Negami types of susceptibilities is presented. These types of susceptibility are shown to be a manifestation of weak nonlocality and nonlinearity. The Debye susceptibility corresponds to linear and local relaxation, the Cole–Cole susceptibility being linear and nonlocal; the Cole–Davidson susceptibility is nonlinear and local and the Havriliak–Negami susceptibility corresponds to nonlinear and nonlocal relaxation.

Rigid surface bag model

Abstract The surface bag model of hadrons with the term of surface rigidity is analyzed. It is shown that center-of-mass corrections together with the rigid term can be the required mass formula correction with a good prediction for light hadrons in the surface bag model. The obtained theoretical results of masses, radii and magnetic momenta of light hadrons, as well as the masses of exotic resonances are in good agreement with experimental data and with the results calculated in other models.

An example of a two-stage chemical reaction whose kinetics may be found in an analytical form

In the present work, on an example of the chemical reaction of the disodium ethylene glycol salt and acetyl chloride, a mathematical model has been formulated and the corresponding analytical solutions of four nonlinear evolutionary equations have been found. The phase portrait of the model has been constructed, and the half-life periods of the reagents have been determined. It has been emphasized that, for the analytical solvability, of significance are a rather high symmetry and the dimensionless form of the corresponding evolutionary equations of the presented mathematical model.

Modelling linear reactions in inhomogeneous catalytic systems

The kinetics of linear chemical reactions in an inhomogeneous medium is modeled as an evolutionary system characterized by a fractional derivative. The corresponding mathematical model depending on one nonlocal parameter

Electric properties of Y-Ba-Cu-O micro-diodes based on asymmetrically narrowed mesas

0< \alpha <1

One–parametric semigroups of diffeomorphisms and one‐sided vector fields

is proposed. Reactions with one degree of freedom are analyzed. Solutions of the corresponding kinetic equations are shown to depend on the nonlocality parameter