Non-stationary heat conduction in one-dimensional chains with conserved momentum

The Letter addresses the relationship between hyperbolic equations of heat conduction and microscopic models of dielectrics. Effects of the non-stationary heat conduction are investigated in two one-dimensional models with conserved momentum: Fermi-Pasta-Ulam (FPU) chain and chain of rotators (CR). These models belong to different universality classes with respect to stationary heat conduction. Direct numeric simulations reveal in both models a crossover from oscillatory decay of short-wave perturbations of the temperature field to smooth diffusive decay of the long-wave perturbations. Such behavior is inconsistent with parabolic Fourier equation of the heat conduction. The crossover wavelength decreases with increase of average temperature in both models. For the FPU model the lowest order hyperbolic Cattaneo-Vernotte equation for the non-stationary heat conduction is not applicable, since no unique relaxation time can be determined.Comment: 4 pages, 5 figure

Energy exchange and localization in essentially nonlinear oscillatory systems: canonical formalism

Over recent years, a lot of progress has been achieved in understanding of the relationship between localization and transport of energy in essentially nonlinear oscillatory systems. In this paper we are going to demonstrate that the structure of the resonance manifold can be conveniently described in terms of canonical action-angle variables. Such formalism has important theoretical advantages: all resonance manifolds may be described at the same level of complexity, appearance of additional conservation laws on these manifolds is easily proven both in autonomous and non-autonomous settings. The harmonic balance - based complexification approach, used in many previous studies on the subject, is shown to be a particular case of the canonical formalism. Moreover, application of the canonic averaging allows treatment of much broader variety of dynamical models. As an example, energy exchanges in systems of coupled trigonometrical and vibro-impact oscillators are considered

A simple one-dimensional model of heat conduction which obeys Fourier's law

We present the computer simulation results of a chain of hard point particles with alternating masses interacting on its extremes with two thermal baths at different temperatures. We found that the system obeys Fourier's law at the thermodynamic limit. This result is against the actual belief that one dimensional systems with momentum conservative dynamics and nonzero pressure have infinite thermal conductivity. It seems that thermal resistivity occurs in our system due to a cooperative behavior in which light particles tend to absorb much more energy than the heavier ones.Comment: 5 pages, 4 figures, to be published in PR

Heat conduction in 1D lattices with on-site potential

The process of heat conduction in one-dimensional lattice with on-site potential is studied by means of numerical simulation. Using discrete Frenkel-Kontorova, $\phi$--4 and sinh-Gordon we demonstrate that contrary to previously expressed opinions the sole anharmonicity of the on-site potential is insufficient to ensure the normal heat conductivity in these systems. The character of the heat conduction is determined by the spectrum of nonlinear excitations peculiar for every given model and therefore depends on the concrete potential shape and temperature of the lattice. The reason is that the peculiarities of the nonlinear excitations and their interactions prescribe the energy scattering mechanism in each model. For models sin-Gordon and $\phi$--4 phonons are scattered at thermalized lattice of topological solitons; for sinh-Gordon and $\phi$--4 - models the phonons are scattered at localized high-frequency breathers (in the case of $\phi$--4 the scattering mechanism switches with the growth of the temperature).Comment: 26 pages, 18 figure

Nonstationary heat conduction in one-dimensional models with substrate potential

The paper investigates non-stationary heat conduction in one-dimensional models with substrate potential. In order to establish universal characteristic properties of the process, we explore three different models --- Frenkel-Kontorova (FK), phi4+ ($\phi^4$+) and phi4- ($\phi^4-$). Direct numeric simulations reveal in all these models a crossover from oscillatory decay of short-wave perturbations of the temperature field to smooth diffusive decay of the long-wave perturbations. Such behavior is inconsistent with parabolic Fourier equation of the heat conduction and clearly demonstrates the necessity of hyperbolic models. The crossover wavelength decreases with increase of average temperature. The decay patterns of the temperature field almost do not depend on the amplitude of the perturbations, so the use of linear evolution equations for temperature field is justified. In all model investigated, the relaxation of thermal perturbations is exponential -- contrary to linear chain, where it follows a power law. However, the most popular lowest-order hyperbolic generalization of the Fourier law, known as Cattaneo-Vernotte (CV) or telegraph equation (TE) is not valid for description of the observed behavior of the models with on-site potential. In part of the models a characteristic relaxation times exhibit peculiar scaling with respect to the temperature perturbation wavelength. Quite surprisingly, such behavior is similar to that of well-known model with divergent heat conduction (Fermi-Pasta-Ulam chain) and rather different from the model with normal heat conduction (chain of rotators). Thus, the data on the non-stationary heat conduction in the systems with on-site potential do not fit commonly accepted concept of universality classes for heat conduction in one-dimensional models.Comment: 9 pages, 7 figures, corrected versio

On the universality of anomalous one-dimensional heat conductivity

In one and two dimensions, transport coefficients may diverge in the thermodynamic limit due to long--time correlation of the corresponding currents. The effective asymptotic behaviour is addressed with reference to the problem of heat transport in 1d crystals, modeled by chains of classical nonlinear oscillators. Extensive accurate equilibrium and nonequilibrium numerical simulations confirm that the finite-size thermal conductivity diverges with the system size $L$ as $\kappa \propto L^\alpha$. However, the exponent $\alpha$ deviates systematically from the theoretical prediction $\alpha=1/3$ proposed in a recent paper [O. Narayan, S. Ramaswamy, Phys. Rev. Lett. {\bf 89}, 200601 (2002)].Comment: 4 pages, submitted to Phys.Rev.

Identification of Differentially Expressed Proteins in Murine Embryonic and Postnatal Cortical Neural Progenitors

BACKGROUND: The central nervous system (CNS) develops from a heterogeneous pool of neural stem and progenitor cells (NSPC), the underlying differences among which are poorly understood. The study of NSPC would be greatly facilitated by the identification of additional proteins that mediate their function and that would distinguish amongst different progenitor populations. METHODOLOGY/PRINCIPAL FINDINGS: To identify membrane and membrane-associated proteins expressed by NSPC, we used a proteomics approach to profile NSPC cultured as neurospheres (NS) isolated from the murine cortex during a period of neurogenesis (embryonic day 11.5, E11.5), as compared to NSPC isolated at a peak of gliogenesis (postnatal day 1, P0) and to differentiated E11.5 NS. 54 proteins were identified with high expression in E11.5 NS, including the TrkC receptor, several heterotrimeric G proteins, and the Neogenin receptor. 24 proteins were identified with similar expression in E11.5 and P0 NS over differentiated E11.5 NS, and 13 proteins were identified with high expression specifically in P0 NS compared to E11.5 NS. To illustrate the potential relevance of these identified proteins to neural stem cell biology, the function of Neogenin was further studied. Using Fluorescence Activated Cell Sorting (FACS) analysis, expression of Neogenin was associated with a self-renewing population present in both E11.5 and adult subventricular zone (SVZ) NS but not in P0 NS. E11.5 NS expressed a putative Neogenin ligand, RGMa, and underwent apoptosis when exposed to a ligand-blocking antibody. CONCLUSIONS/SIGNIFICANCE: There are fundamental differences between the continuously self-renewing and more limited progenitors of the developing cortex. We identified a subset of differentially expressed proteins that serve not only as a set of functionally important proteins, but as a useful set of markers for the subsequent analysis of NSPC. Neogenin is associated with the continuously self-renewing and neurogenic cells present in E11.5 cortical and adult SVZ NS, and the Neogenin/RGMa receptor/ligand pair may regulate cell survival during development

Finite thermal conductivity in 1D models having zero Lyapunov exponents

Heat conduction in three types of 1D channels are studied. The channels consist of two parallel walls, right triangles as scattering obstacles, and noninteracting particles. The triangles are placed along the walls in three different ways: (a) periodic, (b) disordered in height, and (c) disordered in position. The Lyapunov exponents in all three models are zero because of the flatness of triangle sides. It is found numerically that the temperature gradient can be formed in all three channels, but the Fourier heat law is observed only in two disordered ones. The results show that there might be no direct connection between chaos (in the sense of positive Lyapunov exponent) and the normal thermal conduction.Comment: 4 PRL page

Regional Brain Stem Atrophy in Idiopathic Parkinson's Disease Detected by Anatomical MRI

Idiopathic Parkinson's disease (PD) is a neurodegenerative disorder characterized by the dysfunction of dopaminergic dependent cortico-basal ganglia loops and diagnosed on the basis of motor symptoms (tremors and/or rigidity and bradykinesia). Post-mortem studies tend to show that the destruction of dopaminergic neurons in the substantia nigra constitutes an intermediate step in a broader neurodegenerative process rather than a unique feature of Parkinson's disease, as a consistent pattern of progression would exist, originating from the medulla oblongata/pontine tegmentum. To date, neuroimaging techniques have been unable to characterize the pre-symptomatic stages of PD. However, if such a regular neurodegenerative pattern were to exist, consistent damages would be found in the brain stem, even at early stages of the disease. We recruited 23 PD patients at Hoenn and Yahr stages I to II of the disease and 18 healthy controls (HC) matched for age. T1-weighted anatomical scans were acquired (MPRAGE, 1 mm3 resolution) and analyzed using an optimized VBM protocol to detect white and grey matter volume reduction without spatial a priori. When the HC group was compared to the PD group, a single cluster exhibited statistical difference (p<0.05 corrected for false detection rate, 4287 mm3) in the brain stem, between the pons and the medulla oblongata. The present study provides in-vivo evidence that brain stem damage may be the first identifiable stage of PD neuropathology, and that the identification of this consistent damage along with other factors could help with earlier diagnosis in the future. This damage could also explain some non-motor symptoms in PD that often precede diagnosis, such as autonomic dysfunction and sleep disorders

To Reach the Light: The Monumental Byzantine Stairs of Caesarea, a Conservation and Restoration Project

Ancient Caesarea has founded in the years 25-10 BC and named after Emperor Augustus. Throughout history, from the early Roman until the Byzantine period, Caesarea was a major city and one of the largest and most important port cities in the Mediterranean. During the Byzantine period, the city encompassed an area three times larger than that delimited by the Herodian wall and became an important center of Christianity. The monumental stairs led to the Byzantine Octagonal Church built upon giant arch above the remains of the enormous Roman stairs of Augustus temple. Stairs led a large number of people from the vast harbor, to the Temple platform. The Byzantine arch located 17 meters from the ancient quay, is 8 meters width and 4-meter long, built with specific technology from local sandstone named Kurkar. The arch fall after the Byzantine period and the staircases severely damaged due to the long exposure of almost 1500 years and environmental conditions such as capillary rise, daily winds carrying sand, high temperature, moisture, salts, and deliberate destruction, for instance, stones robber and collapse parts from the wall. The characteristics of the Kurkar with sustained deterioration and this environmental condition have led to different conservation problems, at various levels of severity erosion, the disintegration in both bonding materials and stones. The conservation measures' purpose is to stop the ongoing weathering process and prevent a deterioration state of the staircases, to restore the arch and stabilize the structure of the stairs to carry 48 tons of the restore arch. The findings of the project show that a suitable solution to ensure effective and sustainable protection of complicated staircases structure from destruction and various weathering condition to carry new massive arch depends on understanding the ancient application of building technologies and techniques, the use of original bonding material, integrated monitoring, and ongoing maintenance