1,048 research outputs found
The Dirac equation in an external electromagnetic field: symmetry algebra and exact integration
Integration of the Dirac equation with an external electromagnetic field is
explored in the framework of the method of separation of variables and of the
method of noncommutative integration. We have found a new type of solutions
that are not obtained by separation of variables for several external
electromagnetic fields. We have considered an example of crossed electric and
magnetic fields of a special type for which the Dirac equation admits a
nonlocal symmetry operato
The Trajectory-Coherent Approximation and the System of Moments for the Hartree-Type Equation
The general construction of quasi-classically concentrated solutions to the
Hartree-type equation, based on the complex WKB-Maslov method, is presented.
The formal solutions of the Cauchy problem for this equation, asymptotic in
small parameter \h (\h\to0), are constructed with a power accuracy of
O(\h^{N/2}), where N is any natural number. In constructing the
quasi-classically concentrated solutions, a set of Hamilton-Ehrenfest equations
(equations for middle or centered moments) is essentially used. The nonlinear
superposition principle has been formulated for the class of quasi-classically
concentrated solutions of the Hartree-type equations. The results obtained are
exemplified by the one-dimensional equation Hartree-type with a Gaussian
potential.Comments: 6 pages, 4 figures, LaTeX Report no: Subj-class:
Accelerator PhysicsComment: 36 pages, LaTeX-2
An application of the Maslov complex germ method to the 1D nonlocal Fisher-KPP equation
A semiclassical approximation approach based on the Maslov complex germ
method is considered in detail for the 1D nonlocal
Fisher-Kolmogorov-Petrovskii-Piskunov equation under the supposition of weak
diffusion. In terms of the semiclassical formalism developed, the original
nonlinear equation is reduced to an associated linear partial differential
equation and some algebraic equations for the coefficients of the linear
equation with a given accuracy of the asymptotic parameter. The solutions of
the nonlinear equation are constructed from the solutions of both the linear
equation and the algebraic equations. The solutions of the linear problem are
found with the use of symmetry operators. A countable family of the leading
terms of the semiclassical asymptotics is constructed in explicit form.
The semiclassical asymptotics are valid by construction in a finite time
interval. We construct asymptotics which are different from the semiclassical
ones and can describe evolution of the solutions of the
Fisher-Kolmogorov-Petrovskii-Piskunov equation at large times. In the example
considered, an initial unimodal distribution becomes multimodal, which can be
treated as an example of a space structure.Comment: 28 pages, version accepted for publication in Int. J. Geom. Methods
Mod. Phy
Star Formation History in the Galactic Thin Disk
The behavior of the relative magnesium abundances in the thin-disk stars
versus their orbital radii suggests that the star formation rate in the thin
disk decreases with increasing Galactocentric distance, and there was no star
formation for some time outside the solar circle while this process was
continuous within the solar circle. The decrease in the star formation rate
with increasing Galactocentric distance is responsible for the existence of a
negative radial metallicity gradient in the thin disk. At the same time the
relative magnesium abundance exhibits no radial gradient. It is in detail
considered the influence of selective effects on the form of both age -
metallicity and age - relative magnesium abundance diagrams. It is shown that
the first several billion years of the formation of the thin disk interstellar
medium in it was on the average sufficiently rich in heavy elements ( =
-0.22), badly mixed (\sigma_[Fe/H] = 0.21), and the average relative magnesium
abundance was comparatively high ( = 0.10). Approximately 5 billion
years ago average metallicity began to systematically increase, and its
dispersion and the average relative magnesium abundance - to decrease. These
properties may be explained by an increase in star formation rate with the
simultaneous intensification of the processes of mixing the interstellar medium
in the thin disk, provoke possible by interaction the Galaxy with the
completely massive by satellite galaxy
The Shapovalov determinant for the Poisson superalgebras
Among simple Z-graded Lie superalgebras of polynomial growth, there are
several which have no Cartan matrix but, nevertheless, have a quadratic even
Casimir element C_{2}: these are the Lie superalgebra k^L(1|6) of vector fields
on the (1|6)-dimensional supercircle preserving the contact form, and the
series: the finite dimensional Lie superalgebra sh(0|2k) of special Hamiltonian
fields in 2k odd indeterminates, and the Kac--Moody version of sh(0|2k). Using
C_{2} we compute N. Shapovalov determinant for k^L(1|6) and sh(0|2k), and for
the Poisson superalgebras po(0|2k) associated with sh(0|2k). A. Shapovalov
described irreducible finite dimensional representations of po(0|n) and
sh(0|n); we generalize his result for Verma modules: give criteria for
irreducibility of the Verma modules over po(0|2k) and sh(0|2k)
The problem of turnover of the psychoactive substance al-cohol: abuse, consequences, countermeasures
The authors made a review of statistical data on the turnover of the psychoactive substance alcohol within the Russian Federation, Ukraine, United States, Moldova, Hungary, Czech Republic, and England. The authors studied the facts of negative consequences caused by the abuse of the psychoactive substance alcohol and dy-namics of alcohol dependence to develop the measures of resistence to the spread of alcoholism among the population. It was revealed that the WHO records only the quantitative indicators of abuse of alcohol. However, it is necessary to consider the qualitative indicators as well (strong or light alcoholic beverages)yesΠΠ΅Π»Π³ΠΎΡΠΎΠ΄ΡΠΊΠΈΠΉ Π³ΠΎΡΡΠ½ΠΈΠ²Π΅ΡΡΠΈΡΠ΅
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