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

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

Analytic bond-order potentials beyond TersoffBrenner

The accuracy of the analytic bond-order potentials ͑BOP's͒ that were derived in the previous paper within the tight-binding ͑TB͒ formalism is studied for the case of diamond, graphite, and the hydrocarbon molecules. The simplified four-level variant, BOP4S, is found to reproduce the TB bond orders of the C-H and C-C bonds to better than 6% due partly to the inclusion of the shape parameter (b 2 /b 1 ) 2 . The two-level matrixderived expression BOP2M is shown to provide a good description of the saturated and conjugate bonds, thereby overcoming the deficiencies of the Tersoff potential that are associated with overbinding of radicals and poor treatment of conjugacy. The analytic BOP's reproduce the C-H and C-C bond energies to better than 0.9 eV per bond. The errors would be reduced if the analytic potentials were fitted to experiment rather than predicted directly from known TB parameters. ͓S0163-1829͑99͒02813-1

Generalized sub band analysis and signal synthesis

The present paper introduces the basics of building a theory forsubband analysis/signal synthesis for various classes, and using transformations based on any orthonormal basis with weight.This proposed approach is based on the concept of Euclidean signal norm square fraction in a given subband of the transformant definition domain. It is shown that the basis for mathematical apparatus of subband analysis is a new class of matrices, called subband ones. Some eigenvalue properties of these matrices are established, and the problem of optimal selection for additive signal components is formulated and solve

Tumor microenvironment: the formation of the immune profile

Tumor microenvironment (TME) is formed as a result of interaction and cross-linking between the tumor cell and different types of surrounding cells. Recent studies have shown that the tumor reprograms the microenvironment so that TME promotes the development of primary tumors, their metastasis and becomes an important regulator of oncogenesis. Under the influence of the tumor, the immune profile in the TME undergoes significant changes, “editing". An immunosuppressive network is formed, which suppresses the activity of the main effector of cellular immunity — T lymphocytes. T cells in TMA are in a state of anergy and exhaustion. T cells in TME are characterized by increased expression of inhibitory receptors, decreased secretion of cytokines and cytolytic activity. Blocking inhibitory receptors with specific antibodies can lead to the restoration of the functions of exausted T cells. Therefore, the restoration of the functional activity of T lymphocytes is one of the important strategies in cancer immunotherapy. The formation of the immune profile is influenced by genetic aberrations accumulating in the tumor. They play an important role in creating a specific, characteristic only for this tumor immune environment in the TME. Genetic changes in tumor cells lead to phenotypic and functional rearrangements of lymphocytes, which allows the tumor to escape the reaction of immune cells. Since many tumors occur after prolonged inflammation or exhibit characteristics of chronic inflammation as they progress, inflammation is considered an important factor in the formation of immune profile in TME. Immune infiltrates from different human tumors associated with inflammation may contain valuable prognostic and pathophysiological information. Macrophages in the TME now began to be regarded as descriptive marker and as a therapeutic target. One of the main mechanisms by which tumor cells reprogram surrounding cells is the release of exosomes — small vesicles that carry and deliver proteins and nucleic acids to other cells. When exosomal cargo is absorbed, molecular, transcriptional and translational changes occur in the recipient non-tumor cells in the TME. Therefore, tumor exosomes are an effective means by which the functions of immune cells in TME are purposefully changed. Thus, along with individual molecular and genomic testing of the tumor, attention should be paid to a deeper analysis of the immune profile of TME. It is a large resource of biomarkers and targets for immunotherapy

Hydrodynamic limit for a boundary driven stochastic lattice gas model with many conserved quantities

We prove the hydrodynamic limit for a particle system in which particles may have different velocities. We assume that we have two infinite reservoirs of particles at the boundary: this is the so-called boundary driven process. The dynamics we considered consists of a weakly asymmetric simple exclusion process with collision among particles having different velocities

Essential self-adjointness for combinatorial Schr\"odinger operators II- Metrically non complete graphs

We consider weighted graphs, we equip them with a metric structure given by a weighted distance, and we discuss essential self-adjointness for weighted graph Laplacians and Schr\"odinger operators in the metrically non complete case.Comment: Revisited version: Ognjen Milatovic wrote to us that he had discovered a gap in the proof of theorem 4.2 of our paper. As a consequence we propose to make an additional assumption (regularity property of the graph) to this theorem. A new subsection (4.1) is devoted to the study of this property and some details have been changed in the proof of theorem 4.

MUTUAL IMAGE TRANSFORMATION ALGORITHMS FOR VISUAL INFORMATION PROCESSING AND RETRIEVAL

Subject of Research. The paper deals with methods and algorithms for mutual transformation of related pairs of images in order to enhance the capabilities of cross-modal multimedia retrieval (CMMR) technologies. We have thoroughly studied the problem of mutual transformation of face images of various kinds (e.g. photos and drawn pictures). This problem is widely represented in practice. Research is this area is based on existing datasets. The algorithms we have proposed in this paper can be applied to arbitrary pairs of related images due to the unified mathematical specification. Method. We have presented three image transformation algorithms. The first one is based on principal component analysis and Karhunen-Loève transform (1DPCA/1DKLT). Unlike the existing solution, it does not use the training set during the transformation process. The second algorithm assumes generation of an image population. The third algorithm performs the transformation based on two-dimensional principal component analysis and Karhunen-Loève transform (2DPCA/2DKLT). Main Results. The experiments on image transformation and population generation have revealed the main features of each algorithm. The first algorithm allows construction of an accurate and stable model of transition between two given sets of images. The second algorithm can be used to add new images to existing bases and the third algorithm is capable of performing the transformation outside the training dataset. Practical Relevance. Taking into account the qualities of the proposed algorithms, we have provided recommendations concerning their application. Possible scenarios include construction of a transition model for related pairs of images, mutual transformation of the images inside and outside the dataset as well as population generation in order to increase representativeness of existing datasets. Thus, the proposed algorithms can be used to improve reliability of face recognition performed on images of various kinds. Moreover, these techniques can be applied to address a wide variety of other CMMR problems