Remarks on NonHamiltonian Statistical Mechanics: Lyapunov Exponents and Phase-Space Dimensionality Loss

The dissipation associated with nonequilibrium flow processes is reflected by the formation of strange attractor distributions in phase space. The information dimension of these attractors is less than that of the equilibrium phase space, corresponding to the extreme rarity of nonequilibrium states. Here we take advantage of a simple model for heat conduction to demonstrate that the nonequilibrium dimensionality loss can definitely exceed the number of phase-space dimensions required to thermostat an otherwise Hamiltonian system.Comment: 5 pages, 2 figures, minor typos correcte

Device measures conductivity and velocity of ionized gas streams

Coaxial arrangement of primary coil and two sensing secondary coils contained inside slender quartz tube inserted into ionized stream permits simultaneous determination of conductivity and linear velocity. System results agree favorably with theory

Sds22 regulates aurora B activity and microtubule-kinetochore interactions at mitosis

Sds22 defines protein phosphatase 1 location and function at kinetochores and subsequent activity of aurora B in mitosis

Time-reversal focusing of an expanding soliton gas in disordered replicas

We investigate the properties of time reversibility of a soliton gas, originating from a dispersive regularization of a shock wave, as it propagates in a strongly disordered environment. An original approach combining information measures and spin glass theory shows that time reversal focusing occurs for different replicas of the disorder in forward and backward propagation, provided the disorder varies on a length scale much shorter than the width of the soliton constituents. The analysis is performed by starting from a new class of reflectionless potentials, which describe the most general form of an expanding soliton gas of the defocusing nonlinear Schroedinger equation.Comment: 7 Pages, 6 Figure

Lyapunov instability of fluids composed of rigid diatomic molecules

We study the Lyapunov instability of a two-dimensional fluid composed of rigid diatomic molecules, with two interaction sites each, and interacting with a WCA site-site potential. We compute full spectra of Lyapunov exponents for such a molecular system. These exponents characterize the rate at which neighboring trajectories diverge or converge exponentially in phase space. Quam. These exponents characterize the rate at which neighboring trajectories diverge or converge exponentially in phase space. Qualitative different degrees of freedom -- such as rotation and translation -- affect the Lyapunov spectrum differently. We study this phenomenon by systematically varying the molecular shape and the density. We define and evaluate ``rotation numbers'' measuring the time averaged modulus of the angular velocities for vectors connecting perturbed satellite trajectories with an unperturbed reference trajectory in phase space. For reasons of comparison, various time correlation functions for translation and rotation are computed. The relative dynamics of perturbed trajectories is also studied in certain subspaces of the phase space associated with center-of-mass and orientational molecular motion.Comment: RevTeX 14 pages, 7 PostScript figures. Accepted for publication in Phys. Rev.

Lyapunov spectra of billiards with cylindrical scatterers: comparison with many-particle systems

The dynamics of a system consisting of many spherical hard particles can be described as a single point particle moving in a high-dimensional space with fixed hypercylindrical scatterers with specific orientations and positions. In this paper, the similarities in the Lyapunov exponents are investigated between systems of many particles and high-dimensional billiards with cylindrical scatterers which have isotropically distributed orientations and homogeneously distributed positions. The dynamics of the isotropic billiard are calculated using a Monte-Carlo simulation, and a reorthogonalization process is used to find the Lyapunov exponents. The results are compared to numerical results for systems of many hard particles as well as the analytical results for the high-dimensional Lorentz gas. The smallest three-quarters of the positive exponents behave more like the exponents of hard-disk systems than the exponents of the Lorentz gas. This similarity shows that the hard-disk systems may be approximated by a spatially homogeneous and isotropic system of scatterers for a calculation of the smaller Lyapunov exponents, apart from the exponent associated with localization. The method of the partial stretching factor is used to calculate these exponents analytically, with results that compare well with simulation results of hard disks and hard spheres.Comment: Submitted to PR

Molecular genetics of congenital atrial septal defects

Congenital heart defects (CHD) are the most common developmental errors in humans, affecting 8 out of 1,000 newborns. Clinical diagnosis and treatment of CHD has dramatically improved in the last decades. Hence, the majority of CHD patients are now reaching reproductive age. While the risk of familial recurrence has been evaluated in various population studies, little is known about the genetic pathogenesis of CHD. In recent years significant progress has been made in uncovering genetic processes during cardiac development. Data from human genetic studies in CHD patients indicate that the genetic aetiology was presumably underestimated in the past. Inherited mutations in genes encoding cardiac transcription factors and sarcomeric proteins were found as an underlying cause for familial recurrence of non-syndromic CHD in humans, in particular cardiac septal defects. Notably, the cardiac phenotypes most frequently seen in mutation carriers are ostium secundum atrial septal defects (ASDII). This review outlines experimental approaches employed for the detection of CHD-related genes in humans and summarizes recent findings in molecular genetics of congenital cardiac septal defects with an emphasis on ASDII

Time-reversed symmetry and covariant Lyapunov vectors for simple particle models in and out of thermal equilibrium

Recently, a new algorithm for the computation of covariant Lyapunov vectors and of corresponding local Lyapunov exponents has become available. Here we study the properties of these still unfamiliar quantities for a number of simple models, including an harmonic oscillator coupled to a thermal gradient with a two-stage thermostat, which leaves the system ergodic and fully time reversible. We explicitly demonstrate how time-reversal invariance affects the perturbation vectors in tangent space and the associated local Lyapunov exponents. We also find that the local covariant exponents vary discontinuously along directions transverse to the phase flow.Comment: 13 pages, 11 figures submitted to Physical Review E, 201