Lattice Dynamics in the Half-Space, II. Energy Transport Equation

We consider the lattice dynamics in the half-space. The initial data are random according to a probability measure which enforces slow spatial variation on the linear scale $\varepsilon^{-1}$. We establish two time regimes. For times of order $\varepsilon^{-\gamma}$, $0<\gamma<1$, locally the measure converges to a Gaussian measure which is time stationary with a covariance inherited from the initial measure (non-Gaussian, in general). For times of order $\varepsilon^{-1}$, this covariance changes in time and is governed by a semiclassical transport equation.Comment: 35 page

Current reservoirs in the simple exclusion process

We consider the symmetric simple exclusion process in the interval $[-N,N]$ with additional birth and death processes respectively on $(N-K,N]$, $K>0$, and $[-N,-N+K)$. The exclusion is speeded up by a factor $N^2$, births and deaths by a factor $N$. Assuming propagation of chaos (a property proved in a companion paper "Truncated correlations in the stirring process with births and deaths") we prove convergence in the limit $N\to \infty$ to the linear heat equation with Dirichlet condition on the boundaries; the boundary conditions however are not known a priori, they are obtained by solving a non linear equation. The model simulates mass transport with current reservoirs at the boundaries and the Fourier law is proved to hold

Current large deviations in a driven dissipative model

We consider lattice gas diffusive dynamics with creation-annihilation in the bulk and maintained out of equilibrium by two reservoirs at the boundaries. This stochastic particle system can be viewed as a toy model for granular gases where the energy is injected at the boundary and dissipated in the bulk. The large deviation functional for the particle currents flowing through the system is computed and some physical consequences are discussed: the mechanism for local current fluctuations, dynamical phase transitions, the fluctuation-relation

Clinical, Biomechanical, and Physiological Translational Interpretations of Human Resting Myofascial Tone or Tension

Background: Myofascial tissues generate integrated webs and networks of passive and active tensional forces that provide stabilizing support and that control movement in the body. Passive [central nervous system (CNS)–independent] resting myofascial tension is present in the body and provides a low-level stabilizing component to help maintain balanced postures. This property was recently called “human resting myofascial tone” (HRMT). The HRMT model evolved from electromyography (EMG) research in the 1950s that showed lumbar muscles usually to be EMG-silent in relaxed gravity-neutral upright postures. Methods: Biomechanical, clinical, and physiological studies were reviewed to interpret the passive stiffness properties of HRMT that help to stabilize various relaxed functions such as quiet balanced standing. Biomechanical analyses and experimental studies of the lumbar multifidus were reviewed to interpret its passive stiffness properties. The lumbar multifidus was illustrated as the major core stabilizing muscle of the spine, serving an important passive biomechanical role in the body. Results: Research into muscle physiology suggests that passive resting tension (CNS-independent) is generated in sarcomeres by the molecular elasticity of low-level cycling cross-bridges between the actomyosin filaments. In turn, tension is complexly transmitted to intimately enveloping fascial matrix fibrils and other molecular elements in connective tissue, which, collectively, constitute the myofascial unit. Postural myofascial tonus varies with age and sex. Also, individuals in the population are proposed to vary in a polymorphism of postural HRMT. A few people are expected to have outlier degrees of innate postural hypotonicity or hypertonicity. Such biomechanical variations likely predispose to greater risk of related musculoskeletal disorders, a situation that deserves greater attention in clinical practice and research. Axial myofascial hypertonicity was hypothesized to predispose to ankylosing spondylitis. This often-progressive deforming condition of vertebrae and sacroiliac joints is characterized by stiffness features and particular localization of bony lesions at entheseal sites. Such unique features imply concentrations and transmissions of excessive force, leading to tissue micro-injury and maladaptive repair reactions. Conclusions: The HRMT model is now expanded and translated for clinical relevance to therapists. Its passive role in helping to maintain balanced postures is supported by biomechanical principles of myofascial elasticity, tension, stress, stiffness, and tensegrity. Further research is needed to determine the molecular basis of HRMT in sarcomeres, the transmission of tension by the enveloping fascial elements, and the means by which the myofascia helps to maintain efficient passive postural balance in the body. Significant deficiencies or excesses of postural HRMT may predispose to symptomatic or pathologic musculoskeletal disorders whose mechanisms are currently unexplained

Low temperature dynamics of kinks on Ising interfaces

The anisotropic motion of an interface driven by its intrinsic curvature or by an external field is investigated in the context of the kinetic Ising model in both two and three dimensions. We derive in two dimensions (2d) a continuum evolution equation for the density of kinks by a time-dependent and nonlocal mapping to the asymmetric exclusion process. Whereas kinks execute random walks biased by the external field and pile up vertically on the physical 2d lattice, then execute hard-core biased random walks on a transformed 1d lattice. Their density obeys a nonlinear diffusion equation which can be transformed into the standard expression for the interface velocity v = M[(gamma + gamma'')kappa + H]$, where M, gamma + gamma'', and kappa are the interface mobility, stiffness, and curvature, respectively. In 3d, we obtain the velocity of a curved interface near the orientation from an analysis of the self-similar evolution of 2d shrinking terraces. We show that this velocity is consistent with the one predicted from the 3d tensorial generalization of the law for anisotropic curvature-driven motion. In this generalization, both the interface stiffness tensor and the curvature tensor are singular at the orientation. However, their product, which determines the interface velocity, is smooth. In addition, we illustrate how this kink-based kinetic description provides a useful framework for studying more complex situations by modeling the effect of immobile dilute impurities.Comment: 11 pages, 10 figure

Phase Segregation Dynamics in Particle Systems with Long Range Interactions I: Macroscopic Limits

We present and discuss the derivation of a nonlinear non-local integro-differential equation for the macroscopic time evolution of the conserved order parameter of a binary alloy undergoing phase segregation. Our model is a d-dimensional lattice gas evolving via Kawasaki exchange dynamics, i.e. a (Poisson) nearest-neighbor exchange process, reversible with respect to the Gibbs measure for a Hamiltonian which includes both short range (local) and long range (nonlocal) interactions. A rigorous derivation is presented in the case in which there is no local interaction. In a subsequent paper (part II), we discuss the phase segregation phenomena in the model. In particular we argue that the phase boundary evolutions, arising as sharp interface limits of the family of equations derived in this paper, are the same as the ones obtained from the corresponding limits for the Cahn-Hilliard equation.Comment: amstex with macros (included in the file), tex twice, 20 page

WZ Sge-Type Star V592 Herculis

We observed the entire course of the 1998 outburst of V592 Her, which was originally reported as a nova in 1968. We have been able to construct a full light curve of the outburst, which is characterized by a rapid initial decline (0.98 mag/d), which smoothly developed into a plateau phase with a slower linear decline. We detected superhumps characteristic to SU UMa-type dwarf novae ~7 d after the optical maximum. The overall behavior of the light curve and the development of superhumps were characteristic to a WZ Sge-type dwarf nova. Combined with the past literature, we have been able to uniquely determine the superhump period to be 0.05648(2) d. From this period, together with a modern interpretation of the absolute magnitude of the outburst light curve, we conclude that the overall picture of V592 Her is not inconsistent with a lower main-sequence secondary star in contrast to a previous claim that V592 Her contains a brown dwarf.Comment: 10 pages, 7 figures, accepted for publication in Publ. Astron. Soc. Japa