Resetting and annihilation of reentrant activity in a model of a one-dimensional loop of ventricular tissue

Resetting and annihilation of reentrant activity by a single stimulus pulse (S1) or a pair (S1-S2) of coupled pulses are studied in a model of one-dimensional loop of cardiac tissue using a Beeler-Reuter-type ionic model. Different modes of reentry termination are described. The classical mode of termination by unidirectional block, in which a stimulus produces only a retrograde front that collides with the activation front of the reentry, can be obtained for both S1 and S1-S2 applied over a small vulnerable window. We demonstrate that another scenario of termination-that we term collision block-can also be induced by the S1-S2 protocol. This scenario is obtained over a much wider range of S1-S2 coupling intervals than the one leading to a unidirectional block. In the collision block, S1 produces a retrograde front, colliding with the activation front of the pre-existing reentry, and an antegrade front propagating in the same direction as the initial reentry. Then, S2 also produces an antegrade and a retrograde front. However, the propagation of these fronts in the spatial profile of repolarization left by S1 leads to a termination of the reentrant activity. More complex behaviors also occur in which the antegrade fronts produced by S1 and S2 both persist for several turns, displaying a growing alternation in action potential duration ("alternans amplification") that may lead to the termination of the reentrant activity. The hypothesis that both collision block and alternans amplification depend on the interaction between the action potential duration restitution curve and the recovery curve of conduction velocity is supported by the fact that the dynamical behaviors were reproduced using an integro-delay equation based on these two properties. We thus describe two new mechanisms (collision block and alternans amplification) whereby electrical stimulation can terminate reentrant activity. (c) 2002 American Institute of Physics.     

Reentry wave formation in excitable media with stochastically generated inhomogeneities

Clinical research shows that the frequency of arrhythmia events depends on the number and area of the border zones of infarct scars. We investigate the possibility that arrhythmia is initiated by reentry waves generated by the inhomogeneity of conduction velocity at the border zone. The interaction of a plane wave with a spatially extended inhomogeneity is simulated in the FitzHugh- Nagumo model. The inhomogeneity is introduced into the model by modifying the spatial dependence of the diffusion coefficient in a stochastic manner. This results in a rich variety of spatial distributions of conductivity. A plane wave propagating through such a system may break up on the regions with low conductivity and produce numerous spiral waves. The frequency of reentry wave formation is studied as a function of the parameters of the inhomogeneity generation algorithm. Three main scenarios of reentry wave formation were found: unidirectional block, main wave-wavelet collision, and wave break up during collision, on a region in which a conduction velocity gradient occurs. These scenarios are likely candidates for the mechanisms of arrhythmia initiation in a damaged tissue, e.g., the border zone of an infarct scar.     

Dynamical heat channels

We consider heat conduction in a 1D dynamical channel. The channel consists of an ensemble of noninteracting particles, which move between two heat baths according to some dynamical process. We show that the essential thermodynamic properties of the heat channel can be obtained from the diffusion properties of the underlying particles. Emphasis is put on the conduction under anomalous diffusion conditions.     

Dynamical modelling of superstatistical complex systems

We show how to construct the optimum superstatistical dynamical model for a given experimentally measured time series. For this purpose we generalise the superstatistics concept and study a Langevin equation with a memory kernel whose parameters fluctuate on a large time scale. We show how to construct a synthetic dynamical model with the same invariant density and correlation function as the experimental data. As a main example we apply our method to velocity time series measured in high-Reynolds-number turbulent Taylor-Couette flow, but the method can be applied to many other complex systems in a similar way.     

Development of grain avalanches

We present a new theoretical approach aimed to describe the dynamical properties of avalanches. Starting from simple microscopic considerations, we propose an analytical derivation accounting for the avalanche growth as a function of time. The solution resembles very closely recent experimental observations. We show in particular that the two observed regimes of growth proceed from a singularity in the rear front velocity as a function of the slope.     

On the velocity distributions of granular gases

We present a new approach to determine velocity distributions in granular gases to improve the Sonine polynomial expansion of the velocity distribution function, at higher inelasticities, for the homogeneous cooling regime of inelastic hard spheres. The perturbative consistency is recovered using a new set of dynamical variables based on the characteristic function and we illustrate our approach by computing the first four Sonine coefficients for moderate and high inelasticities. The analytical coefficients are compared with molecular dynamics simulations results and with a previous approach by Huthmann et al.     

Dynamical Casimir–Polder atom-surface interaction

We have calculated dynamical Casimir–Polder force between a moving ground state atom and a flat polarizable surface. The velocity of an atom can be close to the velocity of light. The material properties are taken into account using a single oscillator model of the atomic dynamic polarizability and the Drude dielectric function of a metal substrate. The limit cases of nonrelativistic velocities and an ideal metal substrate are also considered. We have found specific dependence of the calculated forces on the velocity (energy), distance and material properties.     

Competition between unlimited and limited energy growth in a two-dimensional time-dependent billiard

Some dynamical properties for a dissipative time-dependent Lorentz gas are studied. We assume that the size of the scatterers change periodically in time. We show that for some combination of the control parameters the particles come to a complete stop between the scatterers, but for some other cases, the average velocity grows unbounded. This is the first time that the unlimited energy growth is observed in a dissipative system. Finally, we study the behavior of the average velocity as a function of the number of collisions and we show that the system is scaling invariant with scaling exponents well defined.     

Quantum Dynamics of Periodic and Limit-Periodic Jacobi and Block Jacobi Matrices with Applications to Some Quantum Many Body Problems

We investigate quantum dynamics with the underlying Hamiltonian being a Jacobi or a block Jacobi matrix with the diagonal and the off-diagonal terms modulated by a periodic or a limit-periodic sequence. In particular, we investigate the transport exponents. In the periodic case we demonstrate ballistic transport, while in the limit-periodic case we discuss various phenomena, such as quasi-ballistic transport and weak dynamical localization. We also present applications to some quantum many body problems. In particular, we establish for the anisotropic XY chain on \({\mathbb{Z}}\) with periodic parameters an explicit strictly positive lower bound for the Lieb–Robinson velocity.     

Controlling the heat flow: now it is possible

We discuss the problem of heat conduction in 1D nonlinear chains in relation to the dynamical properties of the system. We provide convincing numerical evidence for the validity of Fourier law of heat conduction in linear mixing systems. Therefore, deterministic diffusion and normal heat transport which are usually associated with full hyperbolicity, actually take place in systems without exponential instability. We then show that, acting on the parameter which controls the strength of the on site potential inside a segment of the chain, we induce a transition from conducting to insulating behavior in the whole system. The control of heat conduction by nonlinearity opens the possibility to propose new devices such as a thermal rectifier.     

From compact point defects to extended structures in silicon

We show that in contrast to the 1d Frenkel-Kontorova (FK) chain known to obey the Fourier law of heat conduction and several 2d models which show logarithmic dependence of conductivity on system size, a scalar 2d FK lattice with commensurate structure exhibits anomalous heat conduction, whose thermal conductivity displays a power law behavior. The dependence of thermal gradient on bulk temperature and noise correlation is critically analyzed. A dynamical contribution to conductivity when the system attains a nonequilibrium steady state of thermal conduction has been identified.     

Nonlinear dynamics of the heartbeat: I. The AV junction: Passive conduit or active oscillator?

Under physiologic conditions, the AV junction is traditionally regarded as a passive conduit for the conduction of impulses from the atria to the ventricles. An alternative view, namely that subsidiary pacemakers play an active role in normal electrophysiologic dynamics during sinus rhythm, has been suggested based on nonlinear models of cardiac oscillators. A central problem has been the development of a simple but explicit mathematical model for coupled nonlinear oscillators relevant both to stable and perturbed cardiac dynamics. We use equations describing an analog electrical circuit with an external d.c. voltage source (V₀) and two nonlinear oscillators with intrinsic frequencies in the ratio of 3:2, comparable to the SA node and AV junction rates. The oscillators are coupled by means of a resistor. 1:1 (SA:AV) phase-locking of the oscillators occurs over a critical range of V₀. Externally driving the SA oscillator at increasing rates results in 3:2 AV Wenckebach periodicity and a 2:1 AV block. These findings appear with no assumptions about conduction time or refractoriness. This dynamical model is consistent with the new interpretation that normal sinus rhythm may represent 1:1 coupling of two or more active nonlinear oscillators and also accounts for the appearance of an AV block with critical changes in a single parameter such as the pacing rate.     

Calculation of spectra of solids: Conduction electron susceptibility of Gd,Tb and Dy

The Gilat-Raubenheimer method simplified to tetrahedron division is used to calculate the real and imaginary part of the dynamical response function for electrons. A frequency expansion for the real part is discussed. The Lindhard function is calculated as a test for numerical accuracy. The conduction electron susceptibility is calculated for Gd, Tb and Dy using the RAPW energy bands by Keeton and Louks.     

Experimental measurement of acoustic plasmons in polycrystalline palladium

An experimental study of collective oscillations in Pd covering the region of very low energy and momentum transfers is reported. Through Dynamic Electron Scattering spectroscopy, structure factor spectra were measured from 80?K to 298?K on a bulk polycrystalline Pd sample. Here we report the first experimental evidence of damped acoustic plasmons and their evolution to the single-particle excitation continuum. The acoustic plasmons follow a linear dispersion and are experimentally shown to be a separate and distinct resonance mode from acoustic surface plasmons. Calculations of the dielectric function employed a model that incorporates complete mixing of two conduction bands with contributions from both interband and intraband transitions. The model was used in computational studies that focused on specific experimental results to aid the characterization and understanding of the plasmon behavior. We found that the Pd acoustic plasmon energy matched the longitudinal phonon anomaly that has sparked numerous theoretical reports on the possible energetic coupling of these modes. Further experimental evidence of plasmon and phonon dynamical processes are found in the linewidth analysis of the data. The primary decay mechanism of the plasmons is interpreted to be strong phonon-assisted interband transitions. Further spectral features and the plasmon velocity are also reported.     

Dynamical regimes in the dissipative particle dynamics model

We discuss theoretically the behavior of the velocity autocorrelation function in the dissipative particle dynamics (DPD) model. Two dynamical regimes are identified depending on the dimensionless model parameters. For low values of the dimensional friction, a mean field behavior is observed in which the kinetic theory for the DPD model provides good predictions. For high values of the friction, collective hydrodynamic effects are dominant. We have performed numerical simulations that validate the theory presented.     

Transport in polygonal billiards

We present in this work a numerical study of the dynamics of ensembles of point particles within a polygonal billiard chain. This billiard is a system with no exponential instability. Our numerical results suggest that some members of the family exhibit normal diffusive behavior while others present anomalous diffusion. Our conclusions are drawn from the numerical evaluation of the mean square displacement, the velocity autocorrelation function and its spectral analysis. Furthermore we analyze the properties of the incoherent scattering function. The super Burnett coefficient seems to be ill defined in all systems. The multifractal analysis of the spectrum of the velocity autocorrelation functions is also reported. Finally, we study the heat conduction in our polygonal chain.     

Remodelling of cellular excitation (reaction) and intercellular coupling (diffusion) by chronic atrial fibrillation represented by a reaction-diffusion system

Human atrial tissue is an excitable system, in which myocytes are excitable elements, and cell-to-cell electrotonic interactions are via diffusive interactions of cell membrane potentials. We developed a family of excitable system models for human atrium at cellular, tissue and anatomical levels for both normal and chronic atrial fibrillation (AF) conditions. The effects of AF-induced remodelling of cell membrane ionic channels (reaction kinetics) and intercellular gap junctional coupling (diffusion) on atrial excitability, conduction of excitation waves and dynamics of re-entrant excitation waves are quantified. Both ionic channel and gap junctional coupling remodelling have rate dependent effects on atrial propagation. Membrane channel conductance remodelling allows the propagation of activity at higher rates than those sustained in normal tissue or in tissue with gap junctional remodelling alone. Membrane channel conductance remodelling is essential for the propagation of activity at rates higher than 300/min as seen in AF. Spatially heterogeneous gap junction coupling remodelling increased the risk of conduction block, an essential factor for the genesis of re-entry. In 2D and 3D anatomical models, the dynamical behaviours of re-entrant excitation waves are also altered by membrane channel modelling. This study provides insights to understand the pro-arrhythmic effects of AF-induced reaction and diffusion remodelling in atrial tissue.     

Specific features of oxygen-ionic conduction in oxide nanoceramics

The effect of surface tension on the activation energy for oxygen-ionic conduction in nanoceramics is considered. The activation energy is calculated for oxygen ion diffusion through oxygen vacancies, which are treated as dilatation centers. The activation energy is shown to decrease as the nanoparticle size decreases. Based on the size distribution function of nanoparticles, the activation energy distribution function is calculated. Analytical expressions are obtained for the dependences of the ionic conduction on temperature and nanoparticle size. The increase of two to three orders of magnitude in the oxygen-ionic conduction observed earlier in the ZrO₂: 16% Y nanoceramics is adequately described by these expressions. The surface tension of nanoparticles is shown to cause a substantial increase in the oxygen-ionic conduction observed in nanoceramics; the main contribution to the conductivity is related to a region near the particle surface.     

Vesicle propulsion in haptotaxis: A local model

We study theoretically vesicle locomotion due to haptotaxis. Haptotaxis is referred to motion induced by an adhesion gradient on a substrate. The problem is solved within a local approximation where a Rayleigh-type dissipation is adopted. The dynamical model is akin to the Rousse model for polymers. An invariant formulation is used to solve a dynamical model which includes a kind of dissipation due to bond breaking/restoring with the substrate. For a stationary situation where the vesicle acquires a constant drift velocity, we formulate the propulsion problem in terms of a nonlinear eigenvalue (the a priori unknown drift velocity) one of Barenblat-Zeldovitch type. A counting argument shows that the velocity belongs to a discrete set. For a relatively tense vesicle, we provide an analytical expression for the drift velocity as a function of relevant parameters. We find good agreement with the full numerical solution. Despite the oversimplification of the model it allows the identification of a relevant quantity, namely the adhesion length, which turns out to be crucial also in the nonlocal model in the presence of hydrodynamics, a situation on which we have recently reported (I. Cantat and C. Misbah, Phys. Rev. Lett. 83, 235 (1999)) and which constitutes the subject of a forthcoming extensive study. Received 10 February 2000     

简谐速度噪声及其与势场之间的频率共振

为了描述复杂的噪声环境，考虑了一种具有频率结构的噪声——简谐速度噪声，包括它的产生、关联函数、功率谱以及作为热噪声时的频率特性所导致的一些行为.结果表明：在频谱空间中简谐速度噪声是一种带通噪声，存在一个峰值频率，且噪声带宽由参量Γ控制.当简谐势中的一个布朗粒子受热简谐速度噪声驱动时，粒子能量极大值出现在两种频率相等的情况下.这表明噪声和势场的频率之间存在动力学共振，决定着粒子能量的大小. 关键词： 简谐噪声 简谐速度噪声 功率谱 频率共振