A Generalization of Weak Law of Large Numbers

Kolmogorov's weak law of large numbers for i.i.d. random variables is generalized to a larger class distributions and to a wide class of normalizing sequences. The result is extended to maximal sums of negatively associated identically distributed random variables.     

Synchronization in complex networks by time-varying couplings

Synchronization in networks of complex topologies using couplings of time-varying strength is numerically investigated. The time-dependencies of coupling strengths are coupled to the dynamics of the nodes in a way to enhance synchronization. By time-varying couplings, oscillators are found to take quite a short time to reach synchronization state when the couplings are relatively strong. Even when a nearly regular networks of large-size with few shortcuts is difficult to be synchronized by fixed couplings, the time-varying couplings can easily enhance the emergence of synchronization.     

Domain wall delocalization,dynamics and fluctuations in an exclusion process with two internal states

We investigate the delocalization transition appearing in an exclusion process with two internal states, respectively on two parallel lanes. At the transition, delocalized domain walls form in the density profiles of both internal states, in agreement with a mean-field approach. Remarkably, the topology of the system’s phase diagram allows for the delocalization of a (localized) domain wall when approaching the transition. We quantify the domain wall’s delocalization close to the transition by analytic results obtained within the framework of the domain wall picture. Power law dependences of the domain wall width on the distance to the delocalization transition as well as on the system size are uncovered, they agree with numerical results.     

Active Brownian motion models and applications to ratchets

We give an overview over recent studies on the model of Active Brownian Motion (ABM) coupled to reservoirs providing free energy which may be converted into kinetic energy of motion. First, we present an introduction to a general concept of active Brownian particles which are capable to take up energy from the source and transform part of it in order to perform various activities. In the second part of our presentation we consider applications of ABM to ratchet systems with different forms of differentiable potentials. Both analytical and numerical evaluations are discussed for three cases of sinusoidal, staircaselike and Mateos ratchet potentials, also with the additional loads modelled by tilted potential structure. In addition, stochastic character of the kinetics is investigated by considering perturbation by Gaussian white noise which is shown to be responsible for driving the directionality of the asymptotic flux in the ratchet. This stochastically driven directionality effect is visualized as a strong nonmonotonic dependence of the statistics of the right versus left trajectories of motion leading to a net current of particles. Possible applications of the ratchet systems to molecular motors are also briefly discussed.     

Accounting for the energies and entropies of kinesin’s catalytic cycle

When the processive motor protein kinesin walks along the biopolymer microtubule it can occasionally make a backward step. Recent single molecule experiments on moving kinesin have revealed that the forward-to-backward step ratio decreases exponentially with the load force. Carter and Cross (Nature 435, 308-312, 2005) found that this ratio tightly followed 802 × exp[−0.95F], where F is the load force in piconewtons. A straightforward analysis of a Brownian step leads to L/(2k _B T) as the factor in front of the load force, where L is the 8 nm stepsize, k _B is the Boltzmann constant, and T is the temperature. The factor L/(2k _B T) does indeed equal 0.95 pN⁻¹. The same analysis shows how the 802 prefactor derives from the power stroke energy G as exp[G/(2k _B T)]. There are indications that the power stroke derives from the entropically driven coiling of the 30 amino acid neck linker that connects the two kinesin heads. This idea is examined and consequences are deduced.     

Lattice Lotka-Volterra model with long range mixing

A spatio-temporal process in the Lattice Lotka Volterra (LLV) model, when realized on low dimensional support, is studied. It is shown that the introduction of a long-range mixing causes a drastic change in the system’s behavior, which transits from small random-like fluctuations to global oscillations when the mixing rate transcends above a critical point. The amplitude of the induced oscillations is well defined by the mixing rate and is insensitive to the initial conditions and the lattice size variations. The observed behavior essentially differs from that predicted by the Mean-Field model which is conservative. The oscillations are of limit-cycle type and appear as a stochastic analog of a Hopf bifurcation.     

Re-weighted random series path integral simulations of molecular clusters: Applications to lithium solvated by a mixed Stockmayer cluster

Nuclear quantum effects in finite temperature simulations of molecular clusters are determined by taking advantage of a recently developed method based on the Feynman Path Integral. The structural and thermodynamic properties, including the nuclear quantum effects are determined for three Stockmayer clusters. The ionic system contain a lithium ion solvated by six strong dipoles and 12 weaker ones. The presence of the ion in the mixed Stockmayer cluster drastically enhances the fluxional nature of the less polar components which occupy the second solvation layer, whereas the neutral counterpart has the effect of reducing it. The nuclear quantum effects are significant at room temperature and above for the solvated ionic system. These are attributable to two factors: (a) the lightness of the lithium ion and (b) the stiffness of the ion-dipole interactions. At 300 K, the difference between the fully converged quantum and the classical heat capacities is about 1.3 K_B for the ionic cluster. This difference is about 10 SDs obtained from 95% confidence estimates of the statistical fluctuations. Cubic convergence is confirmed for temperatures as low as 50 K by regression analysis. The nuclear quantum effects do not change the peak melting temperature of the cluster.     

Twice Scattered Particles in a Plane Are Uniformly Distributed

It was recently shown (Physica A 216:299–315, 1995) that in two dimensions the sum of three vectors each of whose lengths is exponentially distributed, whose direction is uniformly distributed and such that the sum of their lengths is l, is uniformly distributed on a disk of radius l. We state here this random walk result in terms of scattering of particles as follows: in two dimensions twice isotropically scattered particles by random (i.e., Poisson distributed) scatterers are uniformly distributed. We show that there is no other dimension d and no other number of scatterings s for which the corresponding result (i.e., uniform distribution on a d-dimensional sphere after s scatterings) holds.     

Microscopic Approach to Random Walks

In the present paper the microscopic approach to random walk models is introduced. For any particular model it provides a rigorous way to derive the transport equations for the macroscopic density of walking particles. Although it is not more complicated than the standard random walk framework it has virtually no limitations with respect to the initial distribution of particles. As a consequence, the transport equations derived with this method almost automatically give answers to such important problems as aging and two point probability distribution.     

Enhanced Synchronization of Intercellular Calcium Oscillations by Noise Contaminated Signals

We consider the dynamics of locally coupled calcium oscillation systems, each cell is subjected to extracellular contaminated signal, which contains common sub-threshold signal and independent Gaussian noise. It is found that intermediate noise can enhance synchronized oscillations of calcium ions, where the frequency of noise-induced oscillations is matched with the one of sub-threshold external signal. We show that synchronization is enhanced as a result of the entrainment of external signal. Furthermore, the effect of coupling strength is considered. We find above-mentioned phenomenon exists only when coupling strength is very small. Our findings may exhibit that noise can enhance the detection of feeble external signal through the mechanism of synchronization of intercellular calcium ions.