8,650 research outputs found
Non polynomial conservation law densities generated by the symmetry operators in some hydrodynamical models
New extra series of conserved densities for the polytropic gas model and
nonlinear elasticity equation are obtained without any references to the
recursion operator or to the Lax operator formalism. Our method based on the
utilization of the symmetry operators and allows us to obtain the densities of
arbitrary homogenuity dimensions. The nonpolynomial densities with logarithmics
behaviour are presented as an example. The special attention is paid for the
singular case for which we found new non homogenious solutions
expressed in terms of the elementary functions.Comment: 11 pages, 1 figur
Space-Time Description of Scalar Particle Creation by a Homogeneous Isotropic Gravitational Field
We give the generalization of the method of the space-time description of
particle creation by a gravitational field for a scalar field with nonconformal
coupling to the curvature. The space-time correlation function is obtained for
a created pair of the quasi-particles, corresponding to a diagonal form of the
instantaneous Hamiltonian. The case of an adiabatic change of the metric of
homogeneous isotropic space is analyzed. We show that the created pairs of
quasi-particles in de Sitter space should be interpreted as pairs of virtual
particles.Comment: 7 pages, 3 figure
Waves in the Skyrme--Faddeev model and integrable reductions
In the present article we show that the Skyrme--Faddeev model possesses
nonlinear wave solutions, which can be expressed in terms of elliptic
functions. The Whitham averaging method has been exploited in order to describe
slow deformation of periodic wave states, leading to a quasi-linear system. The
reduction to general hydrodynamic systems have been considered and it is
compared with other integrable reductions of the system.Comment: 16 pages, 5 figure
Modeling of "groove" rolling defect on internal surface of pipes at lengthwise rolling
The research has been conducted in pipe forming at rolling off by lengthwise rolling mill with stub mandrel; the patterns of change in dimensionless parameters were determined, which characterize deformation in side angle depending on http://www.multitran.ru/c/m.exe?t=424995_2_1elongation ratio. The model of formation of lengthwise groove on internal surface of pipes has been proposed
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