515 research outputs found
Interior error estimate for periodic homogenization
In a previous article about the homogenization of the classical problem of
diff usion in a bounded domain with su ciently smooth boundary we proved that
the error is of order . Now, for an open set with su ciently
smooth boundary and homogeneous Dirichlet or Neuman limits conditions
we show that in any open set strongly included in the error is of order
. If the open set is of polygonal (n=2) or
polyhedral (n=3) boundary we also give the global and interrior error
estimates
Particle dynamics inside shocks in Hamilton-Jacobi equations
Characteristics of a Hamilton-Jacobi equation can be seen as action
minimizing trajectories of fluid particles. For nonsmooth "viscosity"
solutions, which give rise to discontinuous velocity fields, this description
is usually pursued only up to the moment when trajectories hit a shock and
cease to minimize the Lagrangian action. In this paper we show that for any
convex Hamiltonian there exists a uniquely defined canonical global nonsmooth
coalescing flow that extends particle trajectories and determines dynamics
inside the shocks. We also provide a variational description of the
corresponding effective velocity field inside shocks, and discuss relation to
the "dissipative anomaly" in the limit of vanishing viscosity.Comment: 15 pages, no figures; to appear in Philos. Trans. R. Soc. series
Homogenization of Maxwell's equations in periodic composites
We consider the problem of homogenizing the Maxwell equations for periodic
composites. The analysis is based on Bloch-Floquet theory. We calculate
explicitly the reflection coefficient for a half-space, and derive and
implement a computationally-efficient continued-fraction expansion for the
effective permittivity. Our results are illustrated by numerical computations
for the case of two-dimensional systems. The homogenization theory of this
paper is designed to predict various physically-measurable quantities rather
than to simply approximate certain coefficients in a PDE.Comment: Significantly expanded compared to v1. Accepted to Phys.Rev.E. Some
color figures in this preprint may be easier to read because here we utilize
solid color lines, which are indistinguishable in black-and-white printin
Turbulence for the generalised Burgers equation
In this survey, we review the results on turbulence for the generalised
Burgers equation on the circle: u_t+f'(u)u_x=\nu u_{xx}+\eta,\ x \in S^1=\R/\Z,
obtained by A.Biryuk and the author in \cite{Bir01,BorK,BorW,BorD}. Here, f is
smooth and strongly convex, whereas the constant 0<\nu << 1 corresponds to a
viscosity coefficient. We will consider both the case \eta=0 and the case when
\eta is a random force which is smooth in x and irregular (kick or white noise)
in t. In both cases, sharp bounds for Sobolev norms of u averaged in time and
in ensemble of the type C \nu^{-\delta}, \delta>=0, with the same value of
\delta for upper and lower bounds, are obtained. These results yield sharp
bounds for small-scale quantities characterising turbulence, confirming the
physical predictions \cite{BK07}.Comment: arXiv admin note: substantial text overlap with arXiv:1201.5567,
arXiv:1107.4866, arXiv:1208.524
Muon pair creation from positronium in a circularly polarized laser field
We study elementary particle reactions that result from the interaction of an
atomic system with a very intense laser wave of circular polarization. As a
specific example, we calculate the rate for the laser-driven reaction , where the electron and positron originate from a positronium
atom or, alternatively, from a nonrelativistic plasma. We distinguish
accordingly between the coherent and incoherent channels of the process. Apart
from numerical calculations, we derive by analytical means compact formulas for
the corresponding reaction rates. The rate for the coherent channel in a laser
field of circular polarization is shown to be damped because of the destructive
interference of the partial waves that constitute the positronium ground-state
wave packet. Conditions for the observation of the process via the dominant
incoherent channel in a circularly polarized field are pointed out
Somatoform disorders in the family doctor's practice.
Somatoform disorders – psychogenic diseases are characterized by pathological physical symptoms that resemble somatic illness. Thus, any organic manifestations, which can be attributed to known diseases are not detected, but there are non-specific functional impairments. Somatoform disorders include somatization disorder, undifferentiated somatoform disorder, hypochondriacal disorder, somatoform dysfunction of the autonomic nervous system and stable somatoform pain disorder. The first part of the article reviewes features of the clinical manifestations of somatization disorder and undifferentiated somatoform disorder. Role of non-benzodiazepine tranquilizers (ADAPTOL) and metabolic drugs (VASONAT) in the treatment of patients with somatoform disorders is discussed. In review article data of neurologists and cardiologists on the effectiveness of anxiolytic drug ADAPTOL and metabolic drug VASONAT in different clinical groups of patients (coronary artery disease, chronic ischemia of the brain), which can significantly improve quality of life, increase exercise tolerance, improve cognitive function and correct mental and emotional disorders are presented
X-ray generation during piezoelectric lighter operation in vacuum
The results of experimental studies on the generation of x-rays when operating a piezoelectric kitchen lighter in a vacuum are presented. For the first time, a new method for increasing the intensity of x-ray radiation in the piezoelectric effect in a high vacuum through the use of an additional electron emitter is proposed and demonstrated. The maximum energy of x-ray bremsstrahlung reaches 14 keV. This means that electrons are accelerated in vacuum in the field of a piezoelectric ceramic to energy of at least 14 ke
Strain Hardening of Polymer Glasses: Entanglements, Energetics, and Plasticity
Simulations are used to examine the microscopic origins of strain hardening
in polymer glasses. While stress-strain curves for a wide range of temperature
can be fit to the functional form predicted by entropic network models, many
other results are fundamentally inconsistent with the physical picture
underlying these models. Stresses are too large to be entropic and have the
wrong trend with temperature. The most dramatic hardening at large strains
reflects increases in energy as chains are pulled taut between entanglements
rather than a change in entropy. A weak entropic stress is only observed in
shape recovery of deformed samples when heated above the glass transition.
While short chains do not form an entangled network, they exhibit partial shape
recovery, orientation, and strain hardening. Stresses for all chain lengths
collapse when plotted against a microscopic measure of chain stretching rather
than the macroscopic stretch. The thermal contribution to the stress is
directly proportional to the rate of plasticity as measured by breaking and
reforming of interchain bonds. These observations suggest that the correct
microscopic theory of strain hardening should be based on glassy state physics
rather than rubber elasticity.Comment: 15 pages, 12 figures: significant revision
To the problems of modeling the brain ischemia in small animals
In the review article the problems of modeling cerebral ischemia in small mammals are consecrated. The advantages of experimental studies that are based on the similarity of the blood circulation of the brain in humans and animals are indicated. Classification of experimental models for the study of acute and chronic disorders of cerebral circulation, mechanisms of their development and preclinical approbation of new drugs is given. The authors indicate that all experimental models of brain ischemia can be divided into two groups: to study risk factors and pathophysiological studies of brain ischemia. And in the second case, the models of focal and global ischemia are described. In conclusion, the authors point out the difficulties and shortcomings of certain methods of ischemia reproduction, which await researchers to solve the above problems
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