1,340 research outputs found
Essential spectra and exponential estimates of eigenfunctions of lattice operators of quantum mechanics
This paper is devoted to estimates of the exponential decay of eigenfunctions
of difference operators on the lattice Z^n which are discrete analogs of the
Schr\"{o}dinger, Dirac and square-root Klein-Gordon operators. Our
investigation of the essential spectra and the exponential decay of
eigenfunctions of the discrete spectra is based on the calculus of so-called
pseudodifference operators (i.e., pseudodifferential operators on the group
Z^n) with analytic symbols and on the limit operators method. We obtain a
description of the location of the essential spectra and estimates of the
eigenfunctions of the discrete spectra of the main lattice operators of quantum
mechanics, namely: matrix Schr\"{o}dinger operators on Z^n, Dirac operators on
Z^3, and square root Klein-Gordon operators on Z^n
Essential spectra of difference operators on \sZ^n-periodic graphs
Let (\cX, \rho) be a discrete metric space. We suppose that the group
\sZ^n acts freely on and that the number of orbits of with respect to
this action is finite. Then we call a \sZ^n-periodic discrete metric
space. We examine the Fredholm property and essential spectra of band-dominated
operators on where is a \sZ^n-periodic discrete metric space.
Our approach is based on the theory of band-dominated operators on \sZ^n and
their limit operators.
In case is the set of vertices of a combinatorial graph, the graph
structure defines a Schr\"{o}dinger operator on in a natural way. We
illustrate our approach by determining the essential spectra of Schr\"{o}dinger
operators with slowly oscillating potential both on zig-zag and on hexagonal
graphs, the latter being related to nano-structures
Pattern formation without heating in an evaporative convection experiment
We present an evaporation experiment in a single fluid layer. When latent
heat associated to the evaporation is large enough, the heat flow through the
free surface of the layer generates temperature gradients that can destabilize
the conductive motionless state giving rise to convective cellular structures
without any external heating. The sequence of convective patterns obtained here
without heating, is similar to that obtained in B\'enard-Marangoni convection.
This work present the sequence of spatial bifurcations as a function of the
layer depth. The transition between square to hexagonal pattern, known from
non-evaporative experiments, is obtained here with a similar change in
wavelength.Comment: Submitted to Europhysics Letter
Administration of a peptide inhibitor of alpha4-integrin inhibits the development of experimental autoimmune uveitis
Recruitment of lymphocytes into the retina and to the vitreous during the development of experimental autoimmune uveitis (EAU) is governed by factors such as the state of activation of inflammatory cells and the repertoire of adhesion molecules expressed by the local vascular endothelia. alpha4 Integrins and their receptors play an important role during homing of cells to the inflammatory site. In the present study, the effect of alpha4-integrin inhibitor on the development of EAU was investigated.Fil: Martín, Andrea P.. Universidade de Sao Paulo; BrasilFil: Vieira de Moraes, Luciana. Universidade de Sao Paulo; BrasilFil: Tadokoro, Carlos E.. Universidade de Sao Paulo; BrasilFil: Commodaro, Alessandra G.. Universidade de Sao Paulo; BrasilFil: Urrets Zavalia, Enrique. Universidad Catolica de Córdoba. Facultad de Medicina. Clinica Universitaria Reina Fabiola; ArgentinaFil: Rabinovich, Gabriel Adrián. Universidad de Buenos Aires. Facultad de Medicina. Hospital de Clínicas General San Martín; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas. Instituto de Biología y Medicina Experimental. Fundación de Instituto de Biología y Medicina Experimental. Instituto de Biología y Medicina Experimental; ArgentinaFil: Urrets Zavalía, Julio Alberto. Universidad Catolica de Córdoba. Facultad de Medicina. Clinica Universitaria Reina Fabiola; ArgentinaFil: Rizzo, Luiz V.. Universidade de Sao Paulo; Brasil. Fundação Zerbini; BrasilFil: Serra, Horacio Marcelo. Universidad Nacional de Córdoba. Facultad de Ciencias Químicas; Argentin
Possibility of measuring the thermal Casimir interaction between a plate and a cylinder attached to a micromachined oscillator
We investigate the possibility of measuring the thermal Casimir force and its
gradient in the configuration of a plate and a microfabricated cylinder
attached to a micromachined oscillator. The Lifshitz-type formulas in this
configuration are derived using the proximity force approximation. The accuracy
for the obtained expressions is determined from a comparison with exact results
available in ideal metal case. Computations of the thermal correction to both
the Casimir force and its gradient are performed in the framework of different
theoretical approaches proposed in the literature. The correction to the
Casimir force and its gradient due to lack of parallelism of the plate and
cylinder is determined using the nonmultiplicative approach. The error
introduced in the theory due to the finite length of the cylinder is estimated.
We propose that both static and dynamic experiments measuring the thermal
Casimir interaction between a cylinder and a plate using a micromachined
oscillator can shed additional light on the thermal Casimir force problem.
Specifically, it is shown that the static experiment is better adapted for the
measurement of thermal effects.Comment: 29 pages, 4 figures, 1 table; minor additions are made in accordance
to the version accepted for publication; to appear in Phys. Rev.
Student’s Learning Profile as a Tool of Personal Learning Logistics
Increase of complexity and uncertainty as well as demand for personalization (including in education) urges universities to pay attention to educational subjectivity and its development; to transfer towards individual / collective-individual educational navigation and flexible systems of educational programs management (including formation of temporary learning groups, supply of required educational resources in due time, protocols of appraisal and mutual offset of educational results), what determines the relevance of the research. Usage of logistic approach enables to distinguish the pedagogical and management objectives of educational activity organization as well as to facilitate personalization of education. The article considers an educational profile as an instrument of personal educational logistics in digital educational environment, presents the preliminary terms “digital track”, “portfolio”, “profile”. The authors also dwell on the requirements to educational profiles development and scenarios of handling them in digital educational environment taking into account domestic and global experience of educational profiles’ implementation
Critical dimensions for random walks on random-walk chains
The probability distribution of random walks on linear structures generated
by random walks in -dimensional space, , is analytically studied
for the case . It is shown to obey the scaling form
, where is
the density of the chain. Expanding in powers of , we find that
there exists an infinite hierarchy of critical dimensions, ,
each one characterized by a logarithmic correction in . Namely, for
, ; for ,
; for , ; for , ; for , , {\it etc.\/} In particular, for
, this implies that the temporal dependence of the probability density of
being close to the origin .Comment: LATeX, 10 pages, no figures submitted for publication in PR
Frozen spatial chaos induced by boundaries
We show that rather simple but non-trivial boundary conditions could induce
the appearance of spatial chaos (that is stationary, stable, but spatially
disordered configurations) in extended dynamical systems with very simple
dynamics. We exemplify the phenomenon with a nonlinear reaction-diffusion
equation in a two-dimensional undulated domain. Concepts from the theory of
dynamical systems, and a transverse-single-mode approximation are used to
describe the spatially chaotic structures.Comment: 9 pages, 6 figures, submitted for publication; for related work visit
http://www.imedea.uib.es/~victo
Two Scenarios of Breaking Chaotic Phase Synchronization
Two types of phase synchronization (accordingly, two scenarios of breaking
phase synchronization) between coupled stochastic oscillators are shown to
exist depending on the discrepancy between the control parameters of
interacting oscillators, as in the case of classical synchronization of
periodic oscillators. If interacting stochastic oscillators are weakly detuned,
the phase coherency of the attractors persists when phase synchronization
breaks. Conversely, if the control parameters differ considerably, the chaotic
attractor becomes phase-incoherent under the conditions of phase
synchronization break.Comment: 8 pages, 7 figure
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