393 research outputs found
Quasiparticles for the one-dimensional nonlocal Fisher-Kolmogorov-Petrovskii-Piskunov equation
We construct quasiparticles-like solutions to the one-dimensional
Fisher-Kolmogorov-Petrovskii-Piskunov (FKPP) with a nonlocal nonlinearity using
the method of semiclassically concentrated states in the weak diffusion
approximation. Such solutions are of use for predicting the dynamics of
population patterns. The interaction of quasiparticles stems from nonlocal
competitive losses in the FKPP model. We developed the formalism of our
approach relying on ideas of the Maslov method. The construction of the
asymptotic expansion of a solution to the original nonlinear evolution equation
is based on solutions to an auxiliary dynamical system of ODEs. The asymptotic
solutions for various specific cases corresponding to various spatial profiles
of the reproduction rate and nonlocal competitive losses are studied within the
framework of the approach proposed.Comment: 27 pages, 2 figure
Semiclassical approach to the nonlocal kinetic model of metal vapor active media
A semiclassical approach based on the WKB–Maslov method is developed for the kinetic ionization equation in dense plasma with approximations characteristic of metal vapor active media excited by a contracted discharge. We develop the technique for constructing the leading term of the semiclassical asymptotics of the Cauchy problem solution for the kinetic equation under the supposition of weak diffusion. In terms of the approach developed, the local cubic nonlinear term in the original kinetic equation is considered in a nonlocal form. This allows one to transform the nonlinear nonlocal kinetic equation to an associated linear partial differential equation with a given accuracy of the asymptotic parameter using the dynamical system of moments of the desired solution of the equation. The Cauchy problem solution for the nonlinear nonlocal kinetic equation can be obtained from the solution of the associated linear partial differential equation and some algebraic equations for the coefficients of the linear equation. Within the developed approach, the plasma relaxation in metal vapor active media is studied with asymptotic solutions expressed in terms of higher transcendental functions. The qualitative analysis of such the solutions is given
Semiclassical approach to the nonlocal nonlinear Schr\"{o}dinger equation with a non-Hermitian term
The nonlinear Sch\"{o}dinger equation (NLSE) with a non-Hermitian term is the
model for various phenomena in nonlinear open quantum systems. We deal with the
Cauchy problem for the nonlocal generalization of multidimensional NLSE with a
non-Hermitian term. Using the ideas of the Maslov method, we propose the method
of constructing asymptotic solutions to this equation within the framework of
semiclassically concentrated states. The semiclassical nonlinear evolution
operator and symmetry operators for the leading term of asymptotics are
derived. Our approach is based on the solutions of the auxiliary dynamical
system that effectively linearize the problem under certain algebraic
conditions. The formalism proposed is illustrated with the specific example of
the NLSE with a non-Hermitian term that is the model of an atom laser. The
analytical asymptotic solution to the Cauchy problem is obtained explicitly for
this example.Comment: 29 pages, 1 figur
Family of asymptotic solutions to the two-dimensional kinetic equation with a nonlocal cubic nonlinearity
We apply the original semiclassical approach to the kinetic ionization
equation with the nonlocal cubic nonlinearity in order to construct the family
of its asymptotic solutions. The approach proposed relies on an auxiliary
dynamical system of moments of the desired solution to the kinetic equation and
the associated linear partial differential equation. The family of asymptotic
solutions to the kinetic equation is constructed using the symmetry operators
acting on functions concentrated in a neighborhood of a point determined by the
dynamical system. Based on these solutions, we introduce the nonlinear
superposition principle for the nonlinear kinetic equation. Our formalism based
on the Maslov germ method is applied to the Cauchy problem for the specific
two-dimensional kinetic equation. The evolution of the ion distribution in the
kinetically enhanced metal vapor active medium is obtained as the nonlinear
superposition using the numerical-analytical calculations.Comment: 29 pages, 3 figures, 1 table, minor improvements, the article is
published in Symmetr
Individual personality traits as predictors of intra-organizational vertical career growth of employees
The paper is devoted to the research on the influence of individual personality traits on the success of intra-organizational vertical career growth of employees, the indicator of which is the promotion of employees in their position (status) in the organization, taking into account their speed of passing the career levels.
The article analyzes the types of career, criteria and factors of career growth, including personality characteristics in the context of their influence on career processes. The article presents the results of an empirical study of the managers of JSC Concern Energomera, Stavropol (Russia), which determined the relationship between the success rate of intra-organizational vertical career growth and individual personality characteristics, manifested in the level of mental tension (anxiety, suspicion, inclination to risk, spontaneity and emotional sensitivity) and expressiveness.
The authors did not find statistically significant contribution of regulatory properties and indicators of general mental abilities to distinguishing groups of employees with high and low indicators of vertical career growth.
The averaged personal profiles of employees with high and low indicators of vertical career growth are presented.peer-reviewe
Investigation of the electric field distribution in the human brain based on MRI and EEG data
This work is devoted to the development of the approach to restoration of the spatial-temporal distribution of electric field in the human brain. This field was estimated from the model derived from the Maxwell’s equations with boundary conditions corresponding to electric potentials at the EEG electrodes, which are located on the surface of the head according to the standard “10-20” scheme. The MRI data were used for calculation of the spatial distribution of the electrical conductivity of biotissues in the human brain. The study of the electric field distribution using our approach was carried out for the healthy child and the child with autism. The research was carried out using the equipment of the Tomsk Regional Common Use Center of Tomsk State University
Representations of the Generalized Lie Algebra sl(2)_q
We construct finite-dimensional irreducible representations of two quantum
algebras related to the generalized Lie algebra \ssll (2)_q introduced by
Lyubashenko and the second named author. We consider separately the cases of
generic and at roots of unity. Some of the representations have no
classical analog even for generic . Some of the representations have no
analog to the finite-dimensional representations of the quantised enveloping
algebra , while in those that do there are different matrix
elements.Comment: 14 pages, plain-TEX file using input files harvmac.tex, amssym.de
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