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An approximate solution is presented for simple harmonic motion in the presence of damping by a force which is a general power-law function of the velocity. The approximation is shown to be quite robust, allowing for a simple way to investigate amplitude decay in the presence of general types of weak, nonlinear damping., 6 pages, 3 figures

BACKGROUND –: Short-term exposure to air pollution, particularly from vehicular sources, increases the risk of acute clinical cardiovascular events. However, cardiotoxicity is not always clearly discernible under ambient conditions; therefore, more subtle measures of cardiac dysfunction are necessary to elucidate the latent effects of exposure. OBJECTIVE –: Determine the effect of whole diesel exhaust (DE) exposure on reserve of refractoriness (RoR), an intrinsic electrophysiological measure of the heart’s minimum level of refractoriness relative to development of electrical conduction instability, in rats undergoing exercise-like stress. METHODS –: Wistar-Kyoto (WKY) and spontaneously hypertensive (SH) rats implanted with radiotelemeters to continuously collect electrocardiogram (ECG) and heart rate (HR) were exposed to 150 μg/m(3) of DE and challenged with dobutamine twenty-four hours later to mimic exercise-induced increases of the heart rate. The Chernyak-Starobin-Cohen (CSC) model was then applied to the ECG-derived QT and RR intervals collected during progressive increases in heart rate to calculate RoR for each rat. RESULTS –: Filtered air (FA)-exposed WKY and SH rats did not have any decrease in RoR, which indicates increased risk of cardiac conduction instability; however, DE caused a significant decrease in both strains. Yet, the decrease in RoR in SH rats was eight times steeper when compared to WKY rats indicating greater cardiac conduction instability in the hypertensive strain. CONCLUSION –: These data indicate that after exposure to DE, risk of cardiac instability increases during increasing stress, particularly in the presence of underlying cardiovascular disease. Furthermore, the CSC model, which was previously shown to reveal cardiac risk in humans, can be applied to rodent toxicology studies.

We present results obtained from electrocardiogram (ECG) measurements performed on mice exposed to single-walled carbon nanotubes and ceria nanoparticles through instillation. From these non-invasive ECG measurements, QT and RR intervals were obtained at various times after exposure and used to compute a novel metric for evaluating cardiac signal propagation stability, the reserve of refractoriness (RoR). It is demonstrated that while the isolated QT and RR intervals are essentially uncorrelated with histological data from hematoxylin and eosin stains of control and exposed tissue samples, the RoR is sensitive to cardiovascular effects from the exposure to nanoparticles.

The Seebeck coefficient S is a temperature- and material-dependent property, which linearly and causally relates the temperature difference △T between the “hot” and “cold” junctions of a thermoelectric power generator (TEC-PG) to the voltage difference △V. This phenomenon is the Seebeck effect (SE), and can be used to convert waste heat into usable energy. This work investigates the trends of the effective voltage output △V(t) and effective Seebeck coefficient S'(t) versus several hours of activity of a solid state TEC-PG device. The effective Seebeck coefficient S'(t) here is related to a device, not just to a material’s performance. The observations are pursued in an insulated compartment in various geometrical and environmental configurations. The results indicate that the SE does not substantially depend on the geometrical and environmental configurations. However, the effective Seebeck coefficient S'(t) and the produced effective △V(t) are affected by the environmental configuration, once the temperature is fixed. Heat transfer calculations do not completely explain this finding. Alternative explanations are hypothesized.

Out-of-equilibrium behavior is explored in the one-dimensional anisotropic $XY$ model. Initially preparing the system in the isotropic $XX$ model with a linearly varying magnetic field to create a domain-wall magnetization profile, dynamics is generated by rapidly changing the exchange interaction anisotropy and external magnetic field. Relaxation to a nonequilibrium steady state is studied analytically at the critical transverse Ising point, where correlation functions may be computed in closed form. For arbitrary values of anisotropy and external field, an effective generalized Gibbs' ensemble is shown to accurately describe observables in the long-time limit. Additionally, we find spatial oscillations in the exponentially decaying, transverse spin-spin correlation functions with wavelength set by the magnetization jump across the initial domain wall. This wavelength depends only weakly on anisotropy and magnetic field in contrast to the current, which is highly dependent on these parameters., Comment: typos corrected, references added

The equilibrium Nernst potential plays a critical role in neural cell dynamics. A common approximation used in studying electrical dynamics of excitable cells is that the ionic concentrations inside and outside the cell membranes act as charge reservoirs and remain effectively constant during excitation events. Research into brain electrical activity suggests that relaxing this assumption may provide a better understanding of normal and pathophysiological functioning of the brain. In this paper we explore time-dependent ionic concentrations by allowing the ion-specific Nernst potentials to vary with developing transmembrane potential. As a specific implementation, we incorporate the potential-dependent Nernst shift into a one-dimensional Morris-Lecar reaction-diffusion model. Our main findings result from a region in parameter space where self-sustaining oscillations occur without external forcing. Studying the system close to the bifurcation boundary, we explore the vulnerability of the system with respect to external stimulations which disrupt these oscillations and send the system to a stable equilibrium. We also present results for an extended, one-dimensional cable of excitable tissue tuned to this parameter regime and stimulated, giving rise to complex spatiotemporal pattern formation. Potential applications to the emergence of neuronal bursting in similar two-variable systems and to pathophysiological seizure-like activity are discussed.

Low Density Lipoproteins (LDL) undergo a reversible order-disorder thermal transition close to biological temperature due to cooperative melting of the cholesteryl esters (CE) in the core of the LDL particle. We have noticed that chain-chain interactions between CE molecules are responsible for the stability of the ordered smectic phase; thus, we formulated a simple "coarse-grained" two-state model to describe the melting process. In this model only nearest neighbor interactions are allowed. On the basis of these assumptions we performed Metropolis Monte Carlo (MC) simulation in order to obtain the heat capacity curve. The resulting profile reveals well-known features of the systems with a finite size.

In this article, we present a framework for investigating the order-disorder transition in lipid droplets using the standard Ising model. While a single lipid droplet is itself a complex system whose constituent cholesteryl esters each possesses many degrees of freedom, we present justification for using this effective approach to isolate the underlying physics. It is argued that the behavior of the esters confined within lipid droplets is significantly different from that of a bulk system of similar esters, which is adequately described by continuum mean-field theory in the thermodynamic limit. When the droplet's shell is modeled as an elastic membrane, a simple picture emerges for a transition between two ordered phases within the core which is tuned by the strength of interactions between the esters. Triglyceride concentration is proposed as a variable which strongly influences the strength of interactions between cholesteryl esters within droplets. The possible relevance of this mechanism to the well known atherogenic nature of small low-density lipoprotein particles is discussed in detail.

We investigate dynamics arising after an interaction quench in the quantum sine-Gordon model for a one-dimensional system initially prepared in a spatially inhomogeneous domain wall state. We study the time-evolution of the density, current and equal time correlation functions using the truncated Wigner approximation (TWA) to which quantum corrections are added in order to set the limits on its validity. For weak to moderate strengths of the back-scattering interaction, the domain wall spreads out ballistically with the system within the light cone reaching a nonequilibrium steady-state characterized by a net current flow. A steady state current exists for a quench at the exactly solvable Luther-Emery point. The magnitude of the current decreases with increasing strength of the back-scattering interaction. The two-point correlation function of the variable canonically conjugate to the density reaches a spatially oscillating steady state at a wavelength inversely related to the current., 9 pages, 14 figures

Results are presented for the nonequilibrium dynamics of a quantum $XXZ$-spin chain whose spins are initially arranged in a domain wall profile via the application of a magnetic field in the $z$-direction which is spatially varying along the chain. The system is driven out of equilibrium in two ways: a). by rapidly turning off the magnetic field, b). by rapidly quenching the interactions at the same time as the magnetic field is turned off. The time-evolution of the domain wall profile as well as various two-point spin correlation functions is studied by the exact solution of the fermionic problem for the $XX$ chain and via a bosonization approach and a mean-field approach for the $XXZ$ chain. At long times the magnetization is found to equilibrate (reach the ground state value), while the two-point correlation functions in general do not. In particular, for quenches within the gapless $XX$ phase, the transverse spin correlation functions acquire a spatially inhomogeneous structure at long times whose details depend on the initial domain wall profile. The spatial inhomogeneity is also recovered for the case of classical spins initially arranged in a domain wall profile and shows that the inhomogeneities arise due to the dephasing of transverse spin components as the domain wall broadens. A generalized Gibbs ensemble approach is found to be inadequate in capturing this spatially inhomogeneous state., Comment: 17 pages, 9 figures. References added. Final published version

Excitable membranes are an important type of nonlinear dynamical system and their study can be used to provide a connection between physical and biological circuits. We discuss two models of excitable membranes important in cardiac and neural tissues. One model is based on the Fitzhugh-Nagumo equations and the other is based on a three-transistor excitable circuit. We construct a circuit that simulates reentrant tachycardia and its treatment by surgical ablation. This project is appropriate for advanced undergraduates as a laboratory capstone project, or as a senior thesis or honors project, and can also be a collaborative project, with one student responsible for the computational predictions and another for the circuit construction and measurements., 9 pages, twocolumn, revised and published in American Journal of Physics