We demonstrate numerically bidirectional sorting of flocking particles interacting with an array of V-shaped asymmetric barriers. Each particle aligns with the average swimming direction of its neighbors according to the Vicsek model and experiences additional steric interactions as well as repulsion from the fixed barriers. We show that particles preferentially localize to one side of the barrier array over time and that the direction of this rectification can be reversed by adjusting the particle-particle exclusion radius or the noise term in the equations of motion. These results provide a conceptual basis for isolation and sorting of single-cell and multicellular organisms that move collectively according to flocking-type interaction rules.

We propose an opinion model based on agents located at the vertices of a regular lattice. Each agent has an independent opinion (among an arbitrary, but fixed, number of choices) and its own degree of conviction. The latter changes every time two agents which have different opinions interact with each other. The dynamics leads to size distributions of clusters (made up of agents which have the same opinion and are located at contiguous spatial positions) which follow a power law, as long as the range of the interaction between the agents is not too short; i.e., the system self-organizes into a critical state. Short range interactions lead to an exponential cutoff in the size distribution and to spatial correlations which cause agents which have the same opinion to be closely grouped. When the diversity of opinions is restricted to two, a nonconsensus dynamic is observed, with unequal population fractions, whereas consensus is reached if the agents are also allowed to interact with those located far from them. The individual agents' convictions, the preestablished interaction range, and the locality of the interaction between a pair of agents (their neighborhood has no effect on the interaction) are the main characteristics which distinguish our model from previous ones.

We study the anomalous diffusion of a particle in an external force field whose motion is governed by nonrenewal continuous time random walks with correlated waiting times. In this model the current waiting time $T_i$ is equal to the previous waiting time $T_{i-1}$ plus a small increment. Based on the associated coupled Langevin equations the force field is systematically introduced. We show that in a confining potential the relaxation dynamics follows power-law or stretched exponential pattern, depending on the model parameters. The process obeys a generalized Einstein-Stokes-Smoluchowski relation and observes the second Einstein relation. The stationary solution is of Boltzmann-Gibbs form. The case of an harmonic potential is discussed in some detail. We also show that the process exhibits aging and ergodicity breaking.

We have performed extensive molecular dynamics simulations to study noise-power spectra of density and potential energy fluctuations of a Lennard-Jones model of a fluid in the supercritical region. Emanating from the liquid-vapor critical point, there is a locus of isobaric specific heat maxima, called the Widom line, which is often regarded as an extension of the liquid-vapor coexistence line. Our simulation results show that the noise-power spectrum of the density fluctuations on the Widom line of the liquid-vapor transition exhibits three distinct $1/f^{\gamma }$ behaviors with exponents $\gamma =0$, 1.2, and 2, depending on the frequency $f$. We find that the intermediate frequency region with an exponent $\gamma \sim$ 1 appears as the temperature approaches the Widom temperature from above or below. On the other hand, we do not find three distinct regions of $1/f^{\gamma }$ in the power spectrum of the potential energy fluctuations on the Widom line. Furthermore, we find that the power spectra of both the density and potential energy fluctuations at low frequency have a maximum on the Widom line, suggesting that the noise power can provide an alternative signature of the Widom line.

We study the dynamics of a homogeneous granular gas heated by a stochastic thermostat, in the low density limit. It is found that, before reaching the stationary regime, the system quickly “forgets” the initial condition and then evolves through a universal state that does not only depend on the dimensionless velocity, but also on the instantaneous temperature, suitably renormalized by its steady state value. We find excellent agreement between the theoretical predictions at the Boltzmann equation level for the one-particle distribution function and the direct Monte Carlo simulations. We conclude that at variance with the homogeneous cooling phenomenology, the velocity statistics should not be envisioned as a single-parameter, but as a two-parameter scaling form, keeping track of the distance to stationarity.

We examine the statics and dynamics of particles with repulsive Yukawa interactions in the presence of a two-dimensional triangular substrate for fillings of up to 12 particles per potential minimum. We term the ordered states Yukawa cluster crystals and show that they are distinct from the colloidal molecular crystal states found at low fillings. As a function of substrate and interaction strength at fixed particle density we find a series of novel crystalline states that we characterize using the structure factor. For fillings greater than four, shell and ring structures form at each potential minimum and can exhibit sample-wide orientational order. A disordered state can appear between ordered states as the substrate strength varies. Under an external drive, the onsets of different orderings produce clear changes in the critical depinning force, including a peak effect phenomenon that has generally only previously been observed in systems with random substrates. We also find a rich variety of dynamic ordering transitions that can be observed via changes in the structure factor and features in the velocity-force curves. The dynamical states encompass a variety of moving structures including one-dimensional stripes, smectic ordering, polycrystalline states, triangular lattices, and symmetry locking states. Despite the complexity of the system, we identify several generic features of the dynamical phase transitions which we map out in a series of phase diagrams. Our results have implications for the structure and depinning of colloids on periodic substrates, vortices in superconductors and Bose-Einstein condensates, Wigner crystals, and dusty plasmas.

The critical behavior of self-assembled rigid rods on a square lattice was recently reinvestigated by Almarza et al. [Phys. Rev. E 82, 061117 (2010)]. Based on the Binder cumulants and the value of the critical exponent of the correlation length, the authors found that the isotropic-nematic phase transition occurring in the system is in the two-dimensional Ising universality class. This conclusion contrasts with that of a previous study [López et al., Phys. Rev. E 80, 040105(R) (2009)] which indicates that the transition at intermediate density belongs to the $q=1$ Potts universality class. Almarza et al. attributed the discrepancy to the use of the density as the control parameter by López et al. The present work shows that this suggestion is not sufficient, and that the discrepancy arises solely from the use of different statistical ensembles. Finally, the necessity of making corrections to the scaling functions in the canonical ensemble is discussed.

We comment on the nature of the ordering transition of a model of equilibrium polydisperse rigid rods on the square lattice, which is reported by López et al. to exhibit random percolation criticality in the canonical ensemble, in sharp contrast to (i) our results of Ising criticality for the same model in the grand canonical ensemble [Phys. Rev. E 82, 061117 (2010)] and (ii) the absence of exponent(s) renormalization for constrained systems with logarithmic specific-heat anomalies predicted on very general grounds by Fisher [Phys. Rev. 176, 257 (1968)].

We investigate the persistence probability of a Brownian particle in a harmonic potential, which decays to zero at long times, leading to an unbounded motion of the Brownian particle. We consider two functional forms for the decay of the confinement, an exponential decay and an algebraic decay. Analytical calculations and numerical simulations show that for the case of the exponential relaxation, the dynamics of Brownian particle at short and long times are independent of the parameters of the relaxation. On the contrary, for the algebraic decay of the confinement, the dynamics at long times is determined by the exponent of the decay. Finally, using the two-time correlation function for the position of the Brownian particle, we construct the persistence probability for the Brownian walker in such a scenario.

We explore, in the quantum regime, the stochastic dynamics of a time-periodic, rapidly oscillating potential (having a characteristic frequency of $\omega$) within the framework of a time-dependent system-reservoir Hamiltonian. We invoke the idea of a quantum gauge transformation in light of the standard Floquet theorem in an attempt to construct a Langevin equation (bearing a time-independent effective potential) by employing a systematic perturbative expansion in powers of ${\omega }^{-1}$ using the natural time-scale separation. The time-independent effective potential (corrected to ${\omega }^{-2}$ in leading order) that acts on the slow motion of the driven particle can be employed for trapping. We proceed further to evaluate the rate of escape of the driven particle from the metastable state in the high-temperature limit. We also envisage a resonance phenomena, a true hallmark of the system-reservoir quantization. This development would thus serve as a model template to investigate the trapping mechanism, as well as an appropriate analog to understand the dynamics of a fluctuation-induced escape process from the trap.

Using the time dependence of density fluctuations in a supercooled liquid obtained from the solutions of the equations of nonlinear fluctuating hydrodynamics (NFH), the evolution of the system in the free energy landscape is studied. A crossover from a continuous fluid type dynamics to that of hopping between different free energy minima is observed as the liquid is increasingly supercooled. We demonstrate that our results are also in agreement with equilibrium density functional analysis of the same system. The density field obtained in the numerical solution of the NFH equations are further analyzed to introduce complimentary density of voids in the supercooled liquid state and its static and dynamic correlations are computed. The nature of the relaxation of vacancy correlations are observed to be similar to that of the density fluctuations.

Various microorganisms use chemotaxis for signaling among individuals—a common strategy for communication that is responsible for the formation of microcolonies. We model the microorganisms as autochemotactic active random walkers and describe them by an appropriate Langevin dynamics. It consists of rotational diffusion of the walker's velocity direction and a deterministic torque that aligns the velocity direction along the gradient of a self-generated chemical field. To account for finite size, each microorganism is treated as a soft disk. Its velocity is modified when it overlaps with other walkers according to a linear force-velocity relation and a harmonic repulsion force. We analyze two-walker collisions by presenting typical trajectories and by determining a state diagram that distinguishes between free walker, metastable, and bounded cluster states. We mention an analogy to Kramer's escape problem. Finally, we investigate relevant properties of many-walker systems and describe characteristics of cluster formation in unbounded geometry and in confinement.

In the field of network dynamics it has been suggested that statistical information of motifs, small subnetworks, can help in understanding global activity of the entire network. We present a counterexample where the relation between the stable synchronized activity modes and network connectivity was studied using the Hodgkin-Huxley brain dynamics model. Simulations indicate that small motifs of three nodes exhibit different synchronization modes depending on their local parameters such as delays, synaptic strength, and external drives. Thus the activity of a complex network composed of interconnected motifs cannot be extracted from the activity mode of each individual motif and is governed by local parameters. Finally, we exemplify how local dynamics ultimately enriches the ability of a network to generate diverse modes with a given motif structure.

All possible symmetry-determined nonlinear normal modes (also called simple periodic orbits, one-mode solutions, etc.) in both hard and soft Fermi-Pasta-Ulam $\beta$ chains are discussed. A general method for studying their stability in the thermodynamic limit as well as its application for each of the above nonlinear normal modes are presented.

In this article we replace the semiheuristic derivation of the Rosenfeld functional of hard convex particles with the systematic calculation of Mayer clusters. It is shown that each cluster integral further decomposes into diagrams of intersection patterns that we classify by their loop number. This extends the virial expansion of the free energy by an expansion in the loop order, with the Rosenfeld functional as its leading contribution. Rosenfeld's weight functions then follow from the derivation of the intersection probability by generalizing the equation of Blaschke, Santalo, and Chern. It is found that the 0-loop order can be derived exactly and reproduces the Rosenfeld functional. We further discuss the influence of particle dimensions, topologies, and geometries on the mathematical structure of the calculation.

The dynamics of an induced lamellar microemulsion adjacent to a planar hydrophilic surface (45 ns) were found to be three times faster compared to the bicontinuous bulk structure (133 ns). For these investigations the grazing incidence technique for neutron spin echo spectroscopy has been developed to resolve the depth dependent near surface dynamics. The observation is rationalized in terms of membrane hydrodynamics, where the flow fields reflected by the surface lead to a crossover from classical to confined fluctuations, and faster dynamics on large length scales (also known as “lubrication”) are predicted.

Optical stretchers can be used to quantify elastic and homeostatic properties of cells. Because they can apply forces to cells without requiring direct contact, they may noninvasively measure mechanical properties related to cell and membrane health. Present-day optical stretchers are, however, limited to measurements on individual stationary cells, limiting throughput. To overcome this limitation and allow study of variations in cell populations, we recently developed and tested a microfluidic chamber that measures optical stretching parameters for erythrocytes under dynamic flowing conditions. The method uses a single linear diode laser bar and permitted measurements at low flow rates and higher throughput. Here, we numerically investigate the feasibility of further increasing the measurement rates of the optical stretcher in parameter domains where hydrodynamic and optical forces are of comparable magnitude. To do this we couple a recently implemented dynamic optical ray-tracing technique with a fluid-structure interaction solver to simulate the deformation of osmotically swollen erythrocytes in fluid flow of variable rate. Our results demonstrate that a detectable steady-state stretch is induced at nominal optical powers and flow rates. In addition, we find that flow rates can be increased significantly with no major effect on net cell stretch showing the feasibility of application of this technique at greatly increased throughputs.

We describe a method for the analysis of the distribution of displacements, i.e., the propagators, of single-particle tracking measurements for the case of obstructed subdiffusion in two-dimensional membranes. The propagator for the percolation cluster is compared with a two-component mobility model against Monte Carlo simulations. To account for diffusion in the presence of obstacle concentrations below the percolation threshold, a propagator that includes the transient motion in finite percolation clusters and hopping between obstacle-induced compartments is derived. Finally, these models are shown to be effective in the analysis of Kv2.1 channel diffusive measurements in the membrane of living mammalian cells.

We generalize the standard Hopfield model to the case when a weight is assigned to each input pattern. The weight can be interpreted as the frequency of the pattern occurrence at the input of the network. In the framework of the statistical physics approach we obtain the saddle-point equation allowing us to examine the memory of the network. In the case of unequal weights our model does not lead to the catastrophic destruction of the memory due to its overfilling (that is typical for the standard Hopfield model). The real memory consists only of the patterns with weights exceeding a critical value that is determined by the weights distribution. We obtain the algorithm allowing us to find this critical value for an arbitrary distribution of the weights, and analyze in detail some particular weights distributions. It is shown that the memory decreases as compared to the case of the standard Hopfield model. However, in our model the network can learn online without the catastrophic destruction of the memory.

By introducing a small backward dedifferentiation probability of postmitotic cells to progenitor cells in a recently proposed skin cell proliferation model, the homeostasis of the system can be disrupted resulting in uncontrolled growth. It is found that when the dedifferentiation probability exceeds a small critical value, the stable fixed point of the system vanishes leading to unlimited cell growth resembling scenarios in carcinogenesis. Explicit expression for the critical dedifferentiation probability and phase diagram are calculated analytically and the associated nonlinear dynamics is analyzed. In the presence of stochastic fluctuations, our model predicts that the escape rate from homeostatic growth to uncontrolled growth is greatly enhanced by a small but finite dedifferentiation probability. These results are verified by numerical solutions of the dynamical system and chemical Langevin equations.