202 research outputs found
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
Realizability of metamaterials with prescribed electric permittivity and magnetic permeability tensors
We show that any pair of real symmetric tensors \BGve and \BGm can be
realized as the effective electric permittivity and effective magnetic
permeability of a metamaterial at a given fixed frequency. The construction
starts with two extremely low loss metamaterials, with arbitrarily small
microstructure, whose existence is ensured by the work of Bouchitt{\'e} and
Bourel and Bouchitt\'e and Schweizer, one having at the given frequency a
permittivity tensor with exactly one negative eigenvalue, and a positive
permeability tensor, and the other having a positive permittivity tensor, and a
permeability tensor having exactly one negative eigenvalue. To achieve the
desired effective properties these materials are laminated together in a
hierarchical multiple rank laminate structure, with widely separated length
scales, and varying directions of lamination, but with the largest length scale
still much shorter than the wavelengths and attenuation lengths in the
macroscopic effective medium.Comment: 12 pages, no figure
About curvature, conformal metrics and warped products
We consider the curvature of a family of warped products of two
pseduo-Riemannian manifolds and furnished with metrics of
the form and, in particular, of the type , where are smooth
functions and is a real parameter. We obtain suitable expressions for the
Ricci tensor and scalar curvature of such products that allow us to establish
results about the existence of Einstein or constant scalar curvature structures
in these categories. If is Riemannian, the latter question involves
nonlinear elliptic partial differential equations with concave-convex
nonlinearities and singular partial differential equations of the
Lichnerowicz-York type among others.Comment: 32 pages, 3 figure
Towards a unified theory of Sobolev inequalities
We discuss our work on pointwise inequalities for the gradient which are
connected with the isoperimetric profile associated to a given geometry. We
show how they can be used to unify certain aspects of the theory of Sobolev
inequalities. In particular, we discuss our recent papers on fractional order
inequalities, Coulhon type inequalities, transference and dimensionless
inequalities and our forthcoming work on sharp higher order Sobolev
inequalities that can be obtained by iteration.Comment: 39 pages, made some changes to section 1
Multidimensional Conservation Laws: Overview, Problems, and Perspective
Some of recent important developments are overviewed, several longstanding
open problems are discussed, and a perspective is presented for the
mathematical theory of multidimensional conservation laws. Some basic features
and phenomena of multidimensional hyperbolic conservation laws are revealed,
and some samples of multidimensional systems/models and related important
problems are presented and analyzed with emphasis on the prototypes that have
been solved or may be expected to be solved rigorously at least for some cases.
In particular, multidimensional steady supersonic problems and transonic
problems, shock reflection-diffraction problems, and related effective
nonlinear approaches are analyzed. A theory of divergence-measure vector fields
and related analytical frameworks for the analysis of entropy solutions are
discussed.Comment: 43 pages, 3 figure
Analysis of Oscillations and Defect Measures for the Quasineutral Limit in Plasma Physics
We perform a rigorous analysis of the quasineutral limit for a hydrodynamical
model of a viscous plasma represented by the Navier Stokes Poisson system in
. We show that as the velocity field strongly
converges towards an incompressible velocity vector field and the density
fluctuation weakly converges to zero. In general the limit
velocity field cannot be expected to satisfy the incompressible Navier Stokes
equation, indeed the presence of high frequency oscillations strongly affects
the quadratic nonlinearities and we have to take care of self interacting wave
packets. We shall provide a detailed mathematical description of the
convergence process by using microlocal defect measures and by developing an
explicit correctors analysis. Moreover we will be able to identify an explicit
pseudo parabolic pde satisfied by the leading correctors terms. Our results
include all the previous results in literature, in particular we show that the
formal limit holds rigorously in the case of well prepared data.Comment: Submitted pape
Character of Christ: A Proposal for Excellence in Christian Character Education
Moral teaching programs, such as character education, have been implemented nationwide in order to curb the growing trend of violence, abuse, and moral relativism within schools, both public and private. These programs represent a variety of moral training philosophies, and current research is revealing some best practices within the field. However, these programs do little to address the needs of distinctively Christian educators who seek to train their students toward the character of Jesus Christ. The research in this study promotes the development of a curriculum to meet this need. The following research indicates that character education\u27s premise and many of its practices are worthy of consideration when developing a Christian character curriculum. However, the foundation of the character traits promoted by a Christian character curriculum must not be based on the consensus of a pluralistic society. The foundation must be established solely on the person of Christ. Best practices within the field of character education are emerging through current research. These practices and the theories behind them are also examined in light of the development of a Christian character curriculum. Recommendations and implications for a Christian character curriculum are made in both theory and practice
Supportive care in the acute phase of Stevens-Johnson syndrome and toxic epidermal necrolysis : an international, multidisciplinary Delphi-based consensus
Background Supportive care is the cornerstone of management of adult and paediatric Stevens-Johnson syndrome (SJS) and toxic epidermal necrolysis (TEN). However, consensus on the modalities of supportive care is lacking. Objectives Our aim in this international multicentric Delphi exercise was to establish a multidisciplinary expert consensus to standardize recommendations regarding supportive care in the acute phase of SJS/TEN. Methods Participants were sent a survey via the online tool SurveyMonkey, consisting of 103 statements organized into 11 topics: multidisciplinary team composition, suspect drug management, infection prevention, fluid resuscitation and prevention of hypothermia, nutritional support, pain and psychological distress management, management of acute respiratory failure, local skincare, ophthalmological management, management of other mucosa, and additional measures. Participants evaluated the level of appropriateness of each statement on a scale of 1 (extremely inappropriate) to 9 (extremely appropriate). The results were analysed according to the RAND/UCLA Appropriateness Method. Results Forty-five participants from 13 countries (on three continents) participated. After the first round, a consensus was obtained for 82.5% of the 103 initially proposed statements. After the second round, a final consensus was obtained for 102 statements. Conclusions We have reached an international Delphi-based consensus on best supportive care practice for SJS/TEN. Our expert consensus should help guide physicians in treating patients with SJS/TEN and thereby improve short-term prognosis and the risk of sequelae.Peer reviewe
Histoplasma capsulatum Encodes a Dipeptidyl Peptidase Active against the Mammalian Immunoregulatory Peptide, Substance P
The pathogenic fungus Histoplasma capsulatum secretes dipeptidyl peptidase (Dpp) IV enzyme activity and has two putative DPPIV homologs (HcDPPIVA and HcDPPIVB). We previously showed that HcDPPIVB is the gene responsible for the majority of secreted DppIV activity in H. capsulatum culture supernatant, while we could not detect any functional contribution from HcDPPIVA. In order to determine whether HcDPPIVA encodes a functional DppIV enzyme, we expressed HcDPPIVA in Pichia pastoris and purified the recombinant protein. The recombinant enzyme cleaved synthetic DppIV substrates and had similar biochemical properties to other described DppIV enzymes, with temperature and pH optima of 42°C and 8, respectively. Recombinant HcDppIVA cleaved the host immunoregulatory peptide substance P, indicating the enzyme has the potential to affect the immune response during infection. Expression of HcDPPIVA under heterologous regulatory sequences in H. capsulatum resulted in increased secreted DppIV activity, indicating that the encoded protein can be expressed and secreted by its native organism. However, HcDPPIVA was not required for virulence in a murine model of histoplasmosis. This work reports a fungal enzyme that can function to cleave the immunomodulatory host peptide substance P
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