4,636 research outputs found
Exact Solutions of a (2+1)-Dimensional Nonlinear Klein-Gordon Equation
The purpose of this paper is to present a class of particular solutions of a
C(2,1) conformally invariant nonlinear Klein-Gordon equation by symmetry
reduction. Using the subgroups of similitude group reduced ordinary
differential equations of second order and their solutions by a singularity
analysis are classified. In particular, it has been shown that whenever they
have the Painlev\'e property, they can be transformed to standard forms by
Moebius transformations of dependent variable and arbitrary smooth
transformations of independent variable whose solutions, depending on the
values of parameters, are expressible in terms of either elementary functions
or Jacobi elliptic functions.Comment: 16 pages, no figures, revised versio
Transformations of Heun's equation and its integral relations
We find transformations of variables which preserve the form of the equation
for the kernels of integral relations among solutions of the Heun equation.
These transformations lead to new kernels for the Heun equation, given by
single hypergeometric functions (Lambe-Ward-type kernels) and by products of
two hypergeometric functions (Erd\'elyi-type). Such kernels, by a limiting
process, also afford new kernels for the confluent Heun equation.Comment: This version was published in J. Phys. A: Math. Theor. 44 (2011)
07520
The vulnerable microcirculation in the critically ill pediatric patient
In neonates, cardiovascular system development does not stop after the transition from intra-uterine to extra-uterine life and is not limited to the macrocirculation. The microcirculation (MC), which is essential for oxygen, nutrient, and drug delivery to tissues and cells, also develops. Developmental changes in the microcirculatory structure continue to occur during the initial weeks of life in healthy neonates. The physiologic hallmarks of neonates and developing children make them particularly vulnerable during critical illness; however, the cardiovascular monitoring possibilities are limited compared with critically ill adult patients. Therefore, the development of non-invasive methods for monitoring the MC is necessary in pediatric critical care for early identification of impending deterioration and to enable the initiation and titration of therapy to ensure cell survival. To date, the MC may be non-invasively monitored at the bedside using hand-held videomicroscopy, which provides useful information regarding the microcirculation. There is an increasing number of studies on the MC in neonates and pediatric patients; however, additional steps are necessary to transition MC monitoring from bench to bedside. The recently introduced concept of hemodynamic coherence describes the relationship between changes in the MC and macrocirculation. The loss of hemodynamic coherence may result in a depressed MC despite an improvement in the macrocirculation, which represents a condition associated with adverse outcomes. In the pediatric intensive care unit, the concept of hemodynamic coherence may function as a framework to develop microcirculatory measurements towards implementation in daily clinical practice
On the Causality and Stability of the Relativistic Diffusion Equation
This paper examines the mathematical properties of the relativistic diffusion
equation. The peculiar solution which Hiscock and Lindblom identified as an
instability is shown to emerge from an ill-posed initial value problem. These
do not meet the mathematical conditions required for realistic physical
problems and can not serve as an argument against the relativistic
hydrodynamics of Landau and Lifshitz.Comment: 6 page
Critical behavior in Angelesco ensembles
We consider Angelesco ensembles with respect to two modified Jacobi weights
on touching intervals [a,0] and [0,1], for a < 0. As a \to -1 the particles
around 0 experience a phase transition. This transition is studied in a double
scaling limit, where we let the number of particles of the ensemble tend to
infinity while the parameter a tends to -1 at a rate of order n^{-1/2}. The
correlation kernel converges, in this regime, to a new kind of universal
kernel, the Angelesco kernel K^{Ang}. The result follows from the Deift/Zhou
steepest descent analysis, applied to the Riemann-Hilbert problem for multiple
orthogonal polynomials.Comment: 32 pages, 9 figure
Occurrence of periodic Lam\'e functions at bifurcations in chaotic Hamiltonian systems
We investigate cascades of isochronous pitchfork bifurcations of
straight-line librating orbits in some two-dimensional Hamiltonian systems with
mixed phase space. We show that the new bifurcated orbits, which are
responsible for the onset of chaos, are given analytically by the periodic
solutions of the Lam\'e equation as classified in 1940 by Ince. In Hamiltonians
with C_ symmetry, they occur alternatingly as Lam\'e functions of period
2K and 4K, respectively, where 4K is the period of the Jacobi elliptic function
appearing in the Lam\'e equation. We also show that the two pairs of orbits
created at period-doubling bifurcations of touch-and-go type are given by two
different linear combinations of algebraic Lam\'e functions with period 8K.Comment: LaTeX2e, 22 pages, 14 figures. Version 3: final form of paper,
accepted by J. Phys. A. Changes in Table 2; new reference [25]; name of
bifurcations "touch-and-go" replaced by "island-chain
Applications of Information Theory to Analysis of Neural Data
Information theory is a practical and theoretical framework developed for the
study of communication over noisy channels. Its probabilistic basis and
capacity to relate statistical structure to function make it ideally suited for
studying information flow in the nervous system. It has a number of useful
properties: it is a general measure sensitive to any relationship, not only
linear effects; it has meaningful units which in many cases allow direct
comparison between different experiments; and it can be used to study how much
information can be gained by observing neural responses in single trials,
rather than in averages over multiple trials. A variety of information
theoretic quantities are commonly used in neuroscience - (see entry
"Definitions of Information-Theoretic Quantities"). In this entry we review
some applications of information theory in neuroscience to study encoding of
information in both single neurons and neuronal populations.Comment: 8 pages, 2 figure
Black Hole Thermodynamics from Near-Horizon Conformal Quantum Mechanics
The thermodynamics of black holes is shown to be directly induced by their
near-horizon conformal invariance. This behavior is exhibited using a scalar
field as a probe of the black hole gravitational background, for a general
class of metrics in D spacetime dimensions (with ). The ensuing
analysis is based on conformal quantum mechanics, within a hierarchical
near-horizon expansion. In particular, the leading conformal behavior provides
the correct quantum statistical properties for the Bekenstein-Hawking entropy,
with the near-horizon physics governing the thermodynamic properties from the
outset. Most importantly: (i) this treatment reveals the emergence of
holographic properties; (ii) the conformal coupling parameter is shown to be
related to the Hawking temperature; and (iii) Schwarzschild-like coordinates,
despite their ``coordinate singularity,''can be used self-consistently to
describe the thermodynamics of black holes.Comment: 16 pages. Sections 2 and 3 and sections 4 and 5 of version 1 were
merged and reduced; a few typos were corrected. The original central results
and equations remain unchange
Quasi-doubly periodic solutions to a generalized Lame equation
We consider the algebraic form of a generalized Lame equation with five free
parameters. By introducing a generalization of Jacobi's elliptic functions we
transform this equation to a 1-dim time-independent Schroedinger equation with
(quasi-doubly) periodic potential. We show that only for a finite set of
integral values for the five parameters quasi-doubly periodic eigenfunctions
expressible in terms of generalized Jacobi functions exist. For this purpose we
also establish a relation to the generalized Ince equation.Comment: 15 pages,1 table, accepted for publication in Journal of Physics
Adiabatic-antiadiabatic crossover in a spin-Peierls chain
We consider an XXZ spin-1/2 chain coupled to optical phonons with non-zero
frequency . In the adiabatic limit (small ), the chain is
expected to spontaneously dimerize and open a spin gap, while the phonons
become static. In the antiadiabatic limit (large ), phonons are
expected to give rise to frustration, so that dimerization and formation of
spin-gap are obtained only when the spin-phonon interaction is large enough. We
study this crossover using bosonization technique. The effective action is
solved both by the Self Consistent Harmonic Approximation (SCHA)and by
Renormalization Group (RG) approach starting from a bosonized description. The
SCHA allows to analyze the lowfrequency regime and determine the coupling
constant associated with the spin-Peierls transition. However, it fails to
describe the SU(2) invariant limit. This limit is tackled by the RG. Three
regimes are found. For , where is the gap in
the static limit , the system is in the adiabatic regime, and
the gap remains of order . For , the system enters
the antiadiabatic regime, and the gap decreases rapidly as
increases. Finally, for , where is an
increasing function of the spin phonon coupling, the spin gap vanishes via a
Berezinskii-Kosterlitz-Thouless transition. Our results are discussed in
relation with numerical and experimental studies of spin-Peierls systems.Comment: Revtex, 21 pages, 5 EPS figures (v1); 23 pages, 6 EPS figures, more
detailed comparison with ED results, referenes added (v2
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