911 research outputs found
Linear superposition in nonlinear wave dynamics
We study nonlinear dispersive wave systems described by hyperbolic PDE's in
R^{d} and difference equations on the lattice Z^{d}. The systems involve two
small parameters: one is the ratio of the slow and the fast time scales, and
another one is the ratio of the small and the large space scales. We show that
a wide class of such systems, including nonlinear Schrodinger and Maxwell
equations, Fermi-Pasta-Ulam model and many other not completely integrable
systems, satisfy a superposition principle. The principle essentially states
that if a nonlinear evolution of a wave starts initially as a sum of generic
wavepackets (defined as almost monochromatic waves), then this wave with a high
accuracy remains a sum of separate wavepacket waves undergoing independent
nonlinear evolution. The time intervals for which the evolution is considered
are long enough to observe fully developed nonlinear phenomena for involved
wavepackets. In particular, our approach provides a simple justification for
numerically observed effect of almost non-interaction of solitons passing
through each other without any recourse to the complete integrability. Our
analysis does not rely on any ansatz or common asymptotic expansions with
respect to the two small parameters but it uses rather explicit and
constructive representation for solutions as functions of the initial data in
the form of functional analytic series.Comment: New introduction written, style changed, references added and typos
correcte
The decay of turbulence in rotating flows
We present a parametric space study of the decay of turbulence in rotating
flows combining direct numerical simulations, large eddy simulations, and
phenomenological theory. Several cases are considered: (1) the effect of
varying the characteristic scale of the initial conditions when compared with
the size of the box, to mimic "bounded" and "unbounded" flows; (2) the effect
of helicity (correlation between the velocity and vorticity); (3) the effect of
Rossby and Reynolds numbers; and (4) the effect of anisotropy in the initial
conditions. Initial conditions include the Taylor-Green vortex, the
Arn'old-Beltrami-Childress flow, and random flows with large-scale energy
spectrum proportional to . The decay laws obtained in the simulations for
the energy, helicity, and enstrophy in each case can be explained with
phenomenological arguments that separate the decay of two-dimensional from
three-dimensional modes, and that take into account the role of helicity and
rotation in slowing down the energy decay. The time evolution of the energy
spectrum and development of anisotropies in the simulations are also discussed.
Finally, the effect of rotation and helicity in the skewness and kurtosis of
the flow is considered.Comment: Sections reordered to address comments by referee
Far-off-resonant wave interaction in one-dimensional photonic crystals with quadratic nonlinearity
We extend a recently developed Hamiltonian formalism for nonlinear wave
interaction processes in spatially periodic dielectric structures to the
far-off-resonant regime, and investigate numerically the three-wave resonance
conditions in a one-dimensional optical medium with nonlinearity.
In particular, we demonstrate that the cascading of nonresonant wave
interaction processes generates an effective nonlinear response in
these systems. We obtain the corresponding coupling coefficients through
appropriate normal form transformations that formally lead to the Zakharov
equation for spatially periodic optical media.Comment: 14 pages, 4 figure
Global attractors for strongly damped wave equations with displacement dependent damping and nonlinear source term of critical exponent
In this paper the long time behaviour of the solutions of 3-D strongly damped
wave equation is studied. It is shown that the semigroup generated by this
equation possesses a global attractor in H_{0}^{1}(\Omega)\times L_{2}(\Omega)
and then it is proved that this global attractor is a bounded subset of
H^{2}(\Omega)\times H^{2}(\Omega) and also a global attractor in
H^{2}(\Omega)\cap H_{0}^{1}(\Omega)\times H_{0}^{1}(\Omega)
Multi-scale analysis of compressible viscous and rotating fluids
We study a singular limit for the compressible Navier-Stokes system when the
Mach and Rossby numbers are proportional to certain powers of a small parameter
\ep. If the Rossby number dominates the Mach number, the limit problem is
represented by the 2-D incompressible Navier-Stokes system describing the
horizontal motion of vertical averages of the velocity field. If they are of
the same order then the limit problem turns out to be a linear, 2-D equation
with a unique radially symmetric solution. The effect of the centrifugal force
is taken into account
INTELLECTUAL PROPERTY PROTECTION AND ITS PRACTICAL APPLICATION IN EARLY-STAGE RUSSIAN TECHNOLOGY STARTUPS
The subject of the research in this article is the issue of protecting the intellectual property of the creators of early-stage Russian technology startups. This problem is important because any omissions and mistakes in this area can be crucial for newly established businesses
Anomalous diffusion in polymers: long-time behaviour
We study the Dirichlet boundary value problem for viscoelastic diffusion in
polymers. We show that its weak solutions generate a dissipative semiflow. We
construct the minimal trajectory attractor and the global attractor for this
problem.Comment: 13 page
Hygienic assessment of surface water quality in the territory of the cities of Irbit and Rezh
This article examines both the data on the surface waters of the city of Rezh and the city of Irbit, as well as the consequences of the content of certain components in volumes exceeding the sanitary-hygienic standards.В данной статье рассмотрены как данные о поверхностных водах г.Реж и г.Ирбит, так и последствия содержания тех или иных компонентов в объёмах, превышающих санитарно-гигиенические нормативы
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