882 research outputs found
The resonance spectrum of the cusp map in the space of analytic functions
We prove that the Frobenius--Perron operator of the cusp map
, (which is an approximation of the
Poincar\'e section of the Lorenz attractor) has no analytic eigenfunctions
corresponding to eigenvalues different from 0 and 1. We also prove that for any
the spectrum of in the Hardy space in the disk
\{z\in\C:|z-q|<1+q\} is the union of the segment and some finite or
countably infinite set of isolated eigenvalues of finite multiplicity.Comment: Submitted to JMP; The description of the spectrum in some Hardy
spaces is adde
Oldest known pantherine skull and evolution of the tiger
The tiger is one of the most iconic extant animals, and its origin and evolution have been intensely debated. Fossils attributable to extant pantherine species-lineages are less than 2 MYA and the earliest tiger fossils are from the Calabrian, Lower Pleistocene. Molecular studies predict a much younger age for the divergence of modern tiger subspecies at <100 KYA, although their cranial morphology is readily distinguishable, indicating that early Pleistocene tigers would likely have differed markedly anatomically from extant tigers. Such inferences are hampered by the fact that well-known fossil tiger material is middle to late Pleistocene in age. Here we describe a new species of pantherine cat from Longdan, Gansu Province, China, Panthera zdanskyi sp. nov. With an estimated age of 2.55–2.16 MYA it represents the oldest complete skull of a pantherine cat hitherto found. Although smaller, it appears morphologically to be surprisingly similar to modern tigers considering its age. Morphological, morphometric, and cladistic analyses are congruent in confirming its very close affinity to the tiger, and it may be regarded as the most primitive species of the tiger lineage, demonstrating the first unequivocal presence of a modern pantherine species-lineage in the basal stage of the Pleistocene (Gelasian; traditionally considered to be Late Pliocene). This find supports a north-central Chinese origin of the tiger lineage, and demonstrates that various parts of the cranium, mandible, and dentition evolved at different rates. An increase in size and a reduction in the relative size of parts of the dentition appear to have been prominent features of tiger evolution, whereas the distinctive cranial morphology of modern tigers was established very early in their evolutionary history. The evolutionary trend of increasing size in the tiger lineage is likely coupled to the evolution of its primary prey species
Discrete Symmetry and Stability in Hamiltonian Dynamics
In this tutorial we address the existence and stability of periodic and
quasiperiodic orbits in N degree of freedom Hamiltonian systems and their
connection with discrete symmetries. Of primary importance in our study are the
nonlinear normal modes (NNMs), i.e periodic solutions which represent
continuations of the system's linear normal modes in the nonlinear regime. We
examine the existence of such solutions and discuss different methods for
constructing them and studying their stability under fixed and periodic
boundary conditions. In the periodic case, we employ group theoretical concepts
to identify a special type of NNMs called one-dimensional "bushes". We describe
how to use linear combinations such NNMs to construct s(>1)-dimensional bushes
of quasiperiodic orbits, for a wide variety of Hamiltonian systems and exploit
the symmetries of the linearized equations to simplify the study of their
destabilization. Applying this theory to the Fermi Pasta Ulam (FPU) chain, we
review a number of interesting results, which have appeared in the recent
literature. We then turn to an analytical and numerical construction of
quasiperiodic orbits, which does not depend on the symmetries or boundary
conditions. We demonstrate that the well-known "paradox" of FPU recurrences may
be explained in terms of the exponential localization of the energies Eq of
NNM's excited at the low part of the frequency spectrum, i.e. q=1,2,3,....
Thus, we show that the stability of these low-dimensional manifolds called
q-tori is related to the persistence or FPU recurrences at low energies.
Finally, we discuss a novel approach to the stability of orbits of conservative
systems, the GALIk, k=2,...,2N, by means of which one can determine accurately
and efficiently the destabilization of q-tori, leading to the breakdown of
recurrences and the equipartition of energy, at high values of the total energy
E.Comment: 50 pages, 13 figure
Hydrodynamic dispersion within porous biofilms
Many microorganisms live within surface-associated consortia, termed biofilms, that can form intricate porous structures interspersed with a network of fluid channels. In such systems, transport phenomena, including flow and advection, regulate various aspects of cell behavior by controlling nutrient supply, evacuation of waste products, and permeation of antimicrobial agents. This study presents multiscale analysis of solute transport in these porous biofilms. We start our analysis with a channel-scale description of mass transport and use the method of volume averaging to derive a set of homogenized equations at the biofilm-scale in the case where the width of the channels is significantly smaller than the thickness of the biofilm. We show that solute transport may be described via two coupled partial differential equations or telegrapher's equations for the averaged concentrations. These models are particularly relevant for chemicals, such as some antimicrobial agents, that penetrate cell clusters very slowly. In most cases, especially for nutrients, solute penetration is faster, and transport can be described via an advection-dispersion equation. In this simpler case, the effective diffusion is characterized by a second-order tensor whose components depend on (1) the topology of the channels' network; (2) the solute's diffusion coefficients in the fluid and the cell clusters; (3) hydrodynamic dispersion effects; and (4) an additional dispersion term intrinsic to the two-phase configuration. Although solute transport in biofilms is commonly thought to be diffusion dominated, this analysis shows that hydrodynamic dispersion effects may significantly contribute to transport
Liquid-liquid equilibrium for monodisperse spherical particles
A system of identical particles interacting through an isotropic potential
that allows for two preferred interparticle distances is numerically studied.
When the parameters of the interaction potential are adequately chosen, the
system exhibits coexistence between two different liquid phases (in addition to
the usual liquid-gas coexistence). It is shown that this coexistence can occur
at equilibrium, namely, in the region where the liquid is thermodynamically
stable.Comment: 6 pages, 8 figures. Published versio
Path Integrals and Their Application to Dissipative Quantum Systems
Introduction
Path Integrals
- Introduction
- Propagator
- Free Particle
- Path Integral Representation of Quantum Mechanics
- Particle on a Ring
- Particle in a Box
- Driven Harmonic Oscillator
- Semiclassical Approximation
- Imaginary Time Path Integral
Dissipative Systems
- Introduction
- Environment as Collection of Harmonic Oscillators
- Effective Action
Damped Harmonic Oscillator
- Partition Function
- Ground State Energy and Density of States
- Position Autocorrelation FunctionComment: 55 pages, 13 figures. To be published in "Coherent Evolution in Noisy
Environments", Lecture Notes in Physics
(http://link.springer.de/series/lnpp/) (Springer Verlag,
Berlin-Heidelberg-New York
Threshold and linewidth of a mirrorless parametric oscillator
We analyze the above-threshold behavior of a mirrorless parametric oscillator
based on resonantly enhanced four wave mixing in a coherently driven dense
atomic vapor. It is shown that, in the ideal limit, an arbitrary small flux of
pump photons is sufficient to reach the oscillator threshold. We demonstrate
that due to the large group-velocity delays associated with coherent media, an
extremely narrow oscillator linewidth is possible, making a narrow-band source
of non-classical radiation feasible.Comment: revised version to appear in Phys.Rev.Lett., contains discussion on
threshold conditions and operation on few-photon leve
MRI plaque imaging reveals high-risk carotid plaques especially in diabetic patients irrespective of the degree of stenosis
<p>Abstract</p> <p>Background</p> <p>Plaque imaging based on magnetic resonance imaging (MRI) represents a new modality for risk assessment in atherosclerosis. It allows classification of carotid plaques in high-risk and low-risk lesion types (I-VIII). Type 2 diabetes mellitus (DM 2) represents a known risk factor for atherosclerosis, but its specific influence on plaque vulnerability is not fully understood. This study investigates whether MRI-plaque imaging can reveal differences in carotid plaque features of diabetic patients compared to nondiabetics.</p> <p>Methods</p> <p>191 patients with moderate to high-grade carotid artery stenosis were enrolled after written informed consent was obtained. Each patient underwent MRI-plaque imaging using a 1.5-T scanner with phased-array carotid coils. The carotid plaques were classified as lesion types I-VIII according to the MRI-modified AHA criteria. For 36 patients histology data was available.</p> <p>Results</p> <p>Eleven patients were excluded because of insufficient MR-image quality. DM 2 was diagnosed in 51 patients (28.3%). Concordance between histology and MRI-classification was 91.7% (33/36) and showed a Cohen's kappa value of 0.81 with a 95% CI of 0.98-1.15. MRI-defined high-risk lesion types were overrepresented in diabetic patients (n = 29; 56.8%). Multiple logistic regression analysis revealed association between DM 2 and MRI-defined high-risk lesion types (OR 2.59; 95% CI [1.15-5.81]), independent of the degree of stenosis.</p> <p>Conclusion</p> <p>DM 2 seems to represent a predictor for the development of vulnerable carotid plaques irrespective of the degree of stenosis and other risk factors. MRI-plaque imaging represents a new tool for risk stratification of diabetic patients.</p> <p>See Commentary: <url>http://www.biomedcentral.com/1741-7015/8/78/abstract</url></p
A Simple Model of Liquid-liquid Phase Transitions
In recent years, a second fluid-fluid phase transition has been reported in
several materials at pressures far above the usual liquid-gas phase transition.
In this paper, we introduce a new model of this behavior based on the
Lennard-Jones interaction with a modification to mimic the different kinds of
short-range orientational order in complex materials. We have done Monte Carlo
studies of this model that clearly demonstrate the existence of a second
first-order fluid-fluid phase transition between high- and low-density liquid
phases
Water-like anomalies for core-softened models of fluids: One dimension
We use a one-dimensional (1d) core-softened potential to develop a physical
picture for some of the anomalies present in liquid water. The core-softened
potential mimics the effect of hydrogen bonding. The interest in the 1d system
stems from the facts that closed-form results are possible and that the
qualitative behavior in 1d is reproduced in the liquid phase for higher
dimensions. We discuss the relation between the shape of the potential and the
density anomaly, and we study the entropy anomaly resulting from the density
anomaly. We find that certain forms of the two-step square well potential lead
to the existence at T=0 of a low-density phase favored at low pressures and of
a high-density phase favored at high pressures, and to the appearance of a
point at a positive pressure, which is the analog of the T=0 ``critical
point'' in the Ising model. The existence of point leads to anomalous
behavior of the isothermal compressibility and the isobaric specific heat
.Comment: 22 pages, 7 figure
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