About one automodel soliton
About one automodel soliton
P.V. Elyutin
An automodel solution of the soliton type, which, in propagating, conserves its shape though changes its parameters, has been obtained for the Corteweg-de Fries equation with an additional term that takes into account the nonlinear dissipation.
Show AbstractGeneration of tsunami by oscillations of a sea floor section
Generation of tsunami by oscillations of a sea floor section
M.A. Nosov
The problem of generation of surface waves in a layer of homogeneous heavy liquid by steady-state harmonic oscillations of a sea floor section is treated on the basis of the linear potential theory.
Show AbstractThe quantum Hall effect and the general principles of quantum field theory
The quantum Hall effect and the general principles of quantum field theory
V.R. Khalilov
The quantum Hall effect (QHE) is considered from the standpoint of the general theorems of quantum field theory and is interpreted as a quantum macroscopic phenomenon due to a spontaneous break of symmetry of the corresponding quantum system. An effective field model of QHE is suggested and a relationship between this model and the two-dimensional Higgs abelian model is established. This made it possible to determine what seems to be the true vacuum state in the case of the fractional quantum Hall effect, which turned out to be a nondegenerate $|\theta \rangle$-vacuum state.
Show AbstractInvariant regularization of infrared divergences in the background field method for two-dimensional nonlinear theories
Invariant regularization of infrared divergences in the background field method for two-dimensional nonlinear theories
V.V. Belokurov, V.E. Tarasov
Various methods for separating the ultraviolet and infrared divergences in two-dimensional nonlinear sigma models are discussed. An infrared regularization is proposed that takes into account the ultraviolet renormalization effect in the preceding orders and makes it possible to obtain invariant ultraviolet counterterms by the background field method.
Show AbstractSpace-time topology as a consequence of the dynamics of closed boson strings. I. The zeroth and first approximations
Space-time topology as a consequence of the dynamics of closed boson strings. I. The zeroth and first approximations
N.F. Nelipa, M.Yu. Pekar
The possibility of constructing a theory in which the space-time topology is determined by the dynamics of closed boson strings is analyzed. The initial object in the theory is a topological space of the contours which determines the form of the string interaction vertex. A cohomological complex and a topologically invariant action are constructed on the space of contours. The equations of motion obtained by varying the action coincide with the condition of closure of differential cohomology forms. The analysis is carried out in the form of an expansion with respect to the string coupling constant. The zeroth- and firstorder approximations are considered. Restrictions imposed on the space-time topology by the string dynamics are found. In what follows, by the space-time is meant an intermediate finite-dimensional space obtained from the original infinite-dimensional space of the contours and containing singularities. To pass to a smooth physical space-time it is necessary to pass to the massless limit, which will be the subject of another paper.
Show AbstractFiniteness of the effective action in the Chern-Simons theory and the conformal invariance
Finiteness of the effective action in the Chern-Simons theory and the conformal invariance
A.N. Kapustin, P.I. Pronin
The effective action in the gauge theory for the (2+1)-dimensional space-time was considered and its dilatational invariance was proved. Based on the dilatational invariance, we demonstrated the finiteness of the effective action in all orders of perturbation theory.
Show AbstractOn the uniqueness of the solution to the inverse carbonitriding problem
On the uniqueness of the solution to the inverse carbonitriding problem
V.B. Glasko, I.E. Stepanova, S.A. Yurasov
The problem of uniqueness of the determination of diffusion coefficient from data on the concentration field is investigated for carbonitriding models. For a more general inverse problem the uniqueness is proved for the normal solution with respect to the polynomial coefficients of the parabolic system of equations.
Show AbstractThe problem of introducing graphical information into a computer
The problem of introducing graphical information into a computer
B.M. Ibrahim, A.B. Knurenko, S.L. Men'shenin, Yu.P. Pyt'ev
In this paper consideration is given to the application of the measurement reduction method to the problem of introducing graphical information into a computer with a digitizer. An algorithm is described, which takes into account the errors arising in the graph pickup and the position of the graph on the digitizer plotting board. The algorithm makes it possible to obtain the most precise values of the coordinates of the graph points. Estimates for the concomitant error are presented.
Show AbstractEnvelope solitons in nonlinear coupled waveguides
Envelope solitons in nonlinear coupled waveguides
A.P. Sukhorukov, D.V. Persheev
Self-similar soliton-like solutions to a system of two nonlinear Schr$\stackrel{..}{o}$dinger-type equations (NSE) for various sets of coefficients have been studied theoretically and numerically. In the case of equality of the corresponding coefficients in the two equations of the system, a family of solitons of a new class with complex amplitude modulation has been found. The existence and uniqueness theorem for the NSE system has been proved and the related finite-difference scheme investigated.
Show AbstractDetermination of QCD condensates from the sum rules based on analytical properties of the pion formfactor
Determination of QCD condensates from the sum rules based on analytical properties of the pion formfactor
D.V. Meshcheryakov
Based on the analytical properties of the pion formfactor and the sum rules of quantum chromodynamics (QCD), the values of the gluon and the four-quark condensates are determined. The nonperturbative structure of the pion form-factor leads to an increase in the condensate values as compared to the standard ones.
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