Patterns and Stability of Coupled Multi-Stable Nonlinear Oscillators.

Nonlinear isolated and coupled oscillators are extensively studied as prototypical nonlinear dynamics models. Much attention has been devoted to oscillator synchronization or the lack thereof. Here, we study the synchronization and stability of coupled driven-damped Helmholtz-Duffing oscillators in bi-stability regimes. We find that despite the fact that the system parameters and the driving force are identical, the stability of the two states to spatially non-uniform perturbations is very different. Moreover, the final stable states, resulting from these spatial perturbations, are not solely dictated by the wavelength of the perturbing mode and take different spatial configurations in terms of the coupled oscillator phases.

Different time scales in dynamic systems with multiple outcomes.

Stochastic biochemical and transport processes have various final outcomes, and they can be viewed as dynamic systems with multiple exits. Many current theoretical studies, however, typically consider only a single time scale for each specific outcome, effectively corresponding to a single-exit process and assuming the independence of each exit process. However, the presence of other exits influences the statistical properties and dynamics measured at any specific exit. Here, we present theoretical arguments to explicitly show the existence of different time scales, such as mean exit times and inverse exit fluxes, for dynamic processes with multiple exits. This implies that the statistics of any specific exit dynamics cannot be considered without taking into account the presence of other exits. Several illustrative examples are described in detail using analytical calculations, mean-field estimates, and kinetic Monte Carlo computer simulations. The underlying microscopic mechanisms for the existence of different time scales are discussed. The results are relevant for understanding the mechanisms of various biological, chemical, and industrial processes, including transport through channels and pores.

The Red Kangaroo pericardium as a material source for the manufacture of percutaneous heart valves.

BACKGROUND: The kangaroo pericardium might be considered to be a good candidate material for use in the manufacture of the leaflets of percutaneous heart valves based upon the unique lifestyle. The diet consists of herbs, forbs and strubs. The kangaroo pericardium holds an undulated structure of collagen. MATERIAL AND METHOD: A Red Kangaroo was obtained after a traffic fatality and the pericardium was dissected. Four compasses were cut from four different sites: auricular (AUR), atrial (ATR), sternoperitoneal (SPL) and phrenopericardial (PPL). They were investigated by means of scanning electron microscopy, light microscopy and transmission electron microscopy. RESULTS: All the samples showed dense and wavy collagen bundles without vascularisation from both the epicardium and the parietal pericardium. The AUR and the ATR were 150±25µm thick whereas the SPL and the PPL were thinner at 120±20µm. The surface of the epicardium was smooth and glistening. The filaments of collagen were well individualized without any aggregation, but the banding was poorly defined and somewhat blurry. CONCLUSION: This detailed morphological analysis of the kangaroo pericardium illustrated a surface resistant to thrombosis and physical characteristics resistant to fatigue. The morphological characteristics of the kangaroo pericardium indicate that it represents an outstanding alternative to the current sources e.g., bovine and porcine. However, procurement of tissues from the wild raises supply and sanitary issues. Health concerns based upon sanitary uncertainty and reliability of supply of wild animals remain real problems.

Crowding effects in non-equilibrium transport through nano-channels.

Transport through nano-channels plays an important role in many biological processes and industrial applications. Gaining insights into the functioning of biological transport processes and the design of man-made nano-devices requires an understanding of the basic physics of such transport. A simple exclusion process has proven to be very useful in explaining the properties of several artificial and biological nano-channels. It is particularly useful for modeling the influence of inter-particle interactions on transport characteristics. In this paper, we explore several models of the exclusion process using a mean field approach and computer simulations. We examine the effects of crowding inside the channel and in its immediate vicinity on the mean flux and the transport times of single molecules. Finally, we discuss the robustness of the theory's predictions with respect to the crucial characteristics of the hindered diffusion in nano-channels that need to be included in the model.

Effects of jamming on nonequilibrium transport times in nanochannels.

Many biological channels perform highly selective transport without direct input of metabolic energy and without transitions from a "closed" to an "open" state during transport. Mechanisms of selectivity of such channels serve as an inspiration for creation of artificial nanomolecular sorting devices and biosensors. To elucidate the transport mechanisms, it is important to understand the transport on the single molecule level in the experimentally relevant regime when multiple particles are crowded in the channel. In this Letter we analyze the effects of interparticle crowding on the nonequilibrium transport times through a finite-length channel by means of analytical theory and computer simulations.

Random walk to a nonergodic equilibrium concept.

Random walk models, such as the trap model, continuous time random walks, and comb models, exhibit weak ergodicity breaking, when the average waiting time is infinite. The open question is, what statistical mechanical theory replaces the canonical Boltzmann-Gibbs theory for such systems? In this paper a nonergodic equilibrium concept is investigated, for a continuous time random walk model in a potential field. In particular we show that in the nonergodic phase the distribution of the occupation time of the particle in a finite region of space approaches U- or W-shaped distributions related to the arcsine law. We show that when conditions of detailed balance are applied, these distributions depend on the partition function of the problem, thus establishing a relation between the nonergodic dynamics and canonical statistical mechanics. In the ergodic phase the distribution function of the occupation times approaches a delta function centered on the value predicted based on standard Boltzmann-Gibbs statistics. The relation of our work to single-molecule experiments is briefly discussed.