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 $\epsilon^{1/2}$. Now, for an open set with su ciently smooth boundary $C^{1,1}$ and homogeneous Dirichlet or Neuman limits conditions we show that in any open set strongly included in the error is of order $\epsilon$. If the open set $\Omega\subset R^n$ is of polygonal (n=2) or polyhedral (n=3) boundary we also give the global and interrior error estimates

Strain Hardening in Polymer Glasses: Limitations of Network Models

Simulations are used to examine the microscopic origins of strain hardening in polymer glasses. While traditional entropic network models can be fit to the total stress, their underlying assumptions are inconsistent with simulation results. There is a substantial energetic contribution to the stress that rises rapidly as segments between entanglements are pulled taut. The thermal component of stress is less sensitive to entanglements, mostly irreversible, and directly related to the rate of local plastic arrangements. Entangled and unentangled chains show the same strain hardening when plotted against the microscopic chain orientation rather than the macroscopic strain.Comment: 4 pages, 3 figure

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

Проблема инерции и антигравитация

The main aim of the present paper is to prove the possibility of the phenomenon of antigravity: as is shown by the example of plane curvilinear motion, the material bodies moving by inertia can repel each other. According to the criterion of antigravity obtained, the necessary condition for antigravity is the motion of a body by inertia along such a curvilinear trajectory on which the energy of the body is transferred from the rotational degree of freedom to the translational one. A control parameter is introduced with the change of which the character of particles motion changes: when the control parameter passes through some critical value, the force of attraction between particles is replaced by the repulsive force. Thus, the possibility to control the character of interaction between the particles of a physical system by redistributing the energy of the system between its degrees of freedom is unclosed. It is shown that the extension of the Newtonian scheme of mechanics by taking into consideration a broad class of curvilinear motions by inertia demands the refinement of the standard notion of inertia of the material body. The concept of inertia property should reflect the presence of dialectically opposite components of motion, associated with conservation of two characteristics of body motion — momentum and kinetic energy representing, accordingly, the force and energy measures of motion, mutually supplementing each other. The inertia property of body is that any body opposes to changing both momentum and kinetic energy. The tendency of the body to the conservation of momentum leads to the uniform and rectilinear motion (i. e. to translational inertia), and the tendency to kinetic energy conservation — to the curvilinear (accelerated) motion by inertia. Both types of inertial motion have a general feature — they can continue unrestrictedly long. The material bodies, moving along a curvilinear trajectory by inertia, are shown to generate electromagnetic field in environment. This field can be considered as a special physical medium which is created by bodies when they curvilinearly move by inertia and is capable to exert back action upon bodies. The results of the investigation presented in this paper allow one to make a guess that electromagnetism, as well as gravitation, is not a special kind of interaction. Electromagnetism is the interaction of material particles with mass that are in such states of curvilinear motion by inertia in which energy is transferred from some degrees of freedom to others.Главный результат настоящей работы состоит в доказательстве возможности явления антигравитации: на примере плоского криволинейного движения по инерции показано, что материальные тела, обладающие массой, могут отталкиваться друг от друга. Установлен критерий антигравитации, согласно которому необходимым условием антигравитации является перемещение тела по инерции по такому криволинейному пути, на котором происходит перекачка энергии тела из вращательной степени свободы в поступательную. Введен управляющий параметр, с изменением величины которого изменяется характер движения тел: при переходе управляющего параметра через некоторое критическое значение сила притяжения между телами сменяется силой отталкивания. Открывается, таким образом, возможность управления характером взаимодействия между частицами физической системы путем перераспределения энергии системы между ее степенями свободы. Показано, что расширение ньютоновской схемы механики путем включения в рассмотрение обширного класса криволинейных движений по инерции требует уточнения общепринятых представлений о свойстве инерции материального тела. Понятие «свойство инерции» должно отражать наличие диалектически противоположных составляющих движения, связанных с сохранением двух характеристик движения тела — импульса и кинетической энергии, которые представляют собой, соответственно, силовую и энергетическую меры движения, взаимно дополняющие друг друга. Свойство инерции тела заключается в том, что всякое тело сопротивляется изменению как импульса, так и кинетической энергии. Стремление тела к сохранению импульса приводит к равномерному и прямолинейному движению (т. е. к поступательной инерции), а стремление к сохранению кинетической энергии — к криволинейному (ускоренному) движению по инерции. Оба типа движения по инерции характеризуются тем, что они могут продолжаться сколь угодно долго. Показано, что материальные частицы, движущиеся по криволинейному пути по инерции, генерируют электромагнитное поле в окружающем пространстве. Это поле можно рассматривать как особую физическую среду, которая порождается телами при их криволинейном движении по инерции и способна оказывать обратное воздействие на тела. Представленные в работе результаты исследования позволяют предположить, что электромагнетизм, как и гравитация, не является особым видом взаимодействия. Электромагнетизм — это взаимодействие материальных частиц, обладающих массой и находящихся в особых состояниях криволинейного движения по инерции, в которых происходит перекачка энергии из одних степеней свободы в другие

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

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 $e^+e^- \to \mu^+\mu^-$, where the electron and positron originate from a positronium atom or, alternatively, from a nonrelativistic $e^+e^-$ 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

NUMERICAL STUDY OF OIL SPILL IN THE PATOS LAGOON ESTUARY REGION

The consumption pattern of the world population is based on petroleum derivatives, which despite contributing to the improvement of the quality of life, has negative aspects, mainly in the environmental scope. The number of oil spills in water slide has increased significantly in recent years. Considering the complexity of the marine environment, the present work aims to apply a identification system of the dynamics and dispersion of oil, using the numerical modeling in the region of Franceses Bridge, near to Patos Lagoon-RS, Brazil. The study of hypothetical events of oil leakage in the region is of fundamental importance, since the Riograndense Petroleum Refinery is located inside of the Patos Lagoon estuary. A data structure of atmospheric and oceanic circulation was organized and inserted in the coupling between the hydrodynamic module Telemac-3D and the ECOS oil model, during the period between 2010 and 2013. The coupling of these models provided satisfactory results, requiring a level of computational effort favorable to obtaining of results capable of giving technical and scientific support to studies such as those of environmental impacts and contingency plans