Dynamics of molecular motors that move along linear lattices and interact with them via reversible destruction of specific lattice bonds is investigated theoretically by analyzing exactly solvable discrete-state “burnt-bridge” models. Molecular motors are viewed as diffusing particles that can asymmetrically break or rebuild periodically distributed weak links when passing over them. Our explicit calculations of dynamic properties show that coupling the transport of the unbiased molecular motor with the bridge-burning mechanism leads to a directed motion that lowers fluctuations and produces a dynamic transition in the limit of low concentration of weak links. Interaction between the backward biased molecular motor and the bridge-burning mechanism yields a complex dynamic behavior. For the reversible dissociation the backward motion of the molecular motor is slowed down. There is a change in the direction of the molecular motor’s motion for some range of parameters. The molecular motor also experiences nonmonotonic fluctuations due to the action of two opposing mechanisms: the reduced activity after the burned sites and locking of large fluctuations. Large spatial fluctuations are observed when two mechanisms are comparable. The properties of the molecular motor are different for the irreversible burning of bridges where the velocity and fluctuations are suppressed for some concentration range, and the dynamic transition is also observed. Dynamics of the system is discussed in terms of the effective driving forces and transitions between different diffusional regimes.

We study the spin-1/2 Ising model on a Bethe lattice in the mean-field limit, with the interaction constants following one of two deterministic aperiodic sequences, the Fibonacci or period-doubling one. New algorithms of sequence generation were implemented, which were fundamental in obtaining long sequences and, therefore, precise results. We calculate the exact critical temperature for both sequences, as well as the critical exponents $\beta$, $\gamma$, and $\delta$. For the Fibonacci sequence, the exponents are classical, while for the period-doubling one they depend on the ratio between the two exchange constants. The usual relations between critical exponents are satisfied, within error bars, for the period-doubling sequence. Therefore, we show that mean-field-like procedures may lead to nonclassical critical exponents.

Using a field-theoretical representation of the Tanaka-Edwards integral, we develop a method to systematically compute the number $N_s$ of one-spin stable states (local energy minima) of a glassy Ising system with nearest-neighbor interactions and random Gaussian couplings on an arbitrary graph. In particular, we use this method to determine $N_s$ for $K$-regular random graphs and $d$-dimensional regular lattices for $d=2,3$. The method works also for other graphs. Excellent accuracy of the results allows us to observe that the number of local energy minima depends mainly on local properties of the graph on which the spin glass is defined.

We study the dynamics of a radioactive species flowing through a porous material, within the continuous-time random-walk (CTRW) approach to the modeling of stochastic transport processes. Emphasis is given to the case where radioactive decay is coupled to anomalous diffusion in locally heterogeneous media, such as porous sediments or fractured rocks. In this framework, we derive the distribution of the number of jumps each particle can perform before a decay event. On the basis of the obtained results, we compute the moments of the cumulative particle distribution, which can be then used to quantify the overall displacement and spread of the contaminant species.

We measured shear thinning, a viscosity decrease ordinarily associated with complex liquids, near the critical point of xenon. The data span a wide range of reduced shear rate: ${10}^{-3}<\dot{\gamma }\tau <700$, where $\dot{\gamma }\tau$ is the shear rate scaled by the relaxation time $\tau$ of critical fluctuations. The measurements had a temperature resolution of 0.01 mK and were conducted in microgravity aboard the Space Shuttle Columbia to avoid the density stratification caused by Earth’s gravity. The viscometer measured the drag on a delicate nickel screen as it oscillated in the xenon at amplitudes $3\mu \text{m}<x_0<430\mu \text{m}$ and frequencies $1\text{Hz}<\omega /2\pi <5\text{Hz}$. To separate shear thinning from other nonlinearities, we computed the ratio of the viscous force on the screen at $\dot{\gamma }\tau$ to the force at $\dot{\gamma }\tau \approx 0$: $C_{\gamma }\equiv F\left(x_0,\omega \tau ,\dot{\gamma }\tau \right)/F\left(x_0,\omega \tau ,0\right)$. At low frequencies, ${\left(\omega \tau \right)}^2<\dot{\gamma }\tau$, $C_{\gamma }$ depends only on $\dot{\gamma }\tau$, as predicted by dynamic critical scaling. At high frequencies, ${\left(\omega \tau \right)}^2>\dot{\gamma }\tau$, $C_{\gamma }$ depends also on both $x_0$ and $\omega$. The data were compared with numerical calculations based on the Carreau-Yasuda relation for complex fluids: $\eta \left(\dot{\gamma }\right)/\eta \left(0\right)={\left[1+A_{\gamma }\left|\dot{\gamma }\tau \right|\right]}^{-x_{\eta }/\left(3+x_{\eta }\right)}$, where $x_{\eta }=0.069$ is the critical exponent for viscosity and mode-coupling theory predicts $A_{\gamma }=0.121$. For xenon we find $A_{\gamma }=0.137\pm 0.029$, in agreement with the mode coupling value. Remarkably, the xenon data close to the critical temperature $T_c$ were independent of the cooling rate (both above and below $T_c$) and these data were symmetric about $T_c$ to within a temperature scale factor. The scale factors for the magnitude of the oscillator’s response differed from those for the oscillator’s phase; this suggests that the surface tension of the two-phase domains affected the drag on the screen below $T_c$.

Employing simplified models in computer simulation is on the one hand often enforced by computer time limitations but on the other hand it offers insights into the molecular properties determining a given physical phenomenon. We employ this strategy to the determination of the phase behavior of quadrupolar fluids, where we study the influence of omitting angular degrees of freedom of molecules via an effective spherically symmetric potential obtained from a perturbative expansion. Comparing the liquid-vapor coexistence curve, vapor pressure at coexistence, interfacial tension between the coexisting phases, etc., as obtained from both the models with the full quadrupolar interactions and the (approximate) isotropic interactions, we find discrepancies in the critical region to be typically (such as in the case of carbon dioxide) of the order of 4%. However, when the Lennard-Jones parameters are rescaled such that critical temperatures and critical densities of both models coincide with the experimental results, almost perfect agreement between the above-mentioned properties of both models is obtained. This result justifies the use of isotropic quadrupolar potentials. We also present a detailed comparison of our simulations with a combined integral equation–density functional approach and show that the latter provides an accurate description except for the vicinity of the critical point.

A stochastic Lotka-Volterra model, a so-called pulse-type model, for the interaction between two species and their random natural environment is investigated. The effect of a random environment is modeled as random pulse trains in the birth rate of the prey and the death rate of the predator. The generalized cell mapping method is applied to calculate the probability distributions of the species populations at a state of statistical quasistationarity. The time evolution of the population densities is studied, and the probability of the near extinction time, from an initial state to a critical state, is obtained. The effects on the ecosystem behaviors of the prey self-competition term and of the pulse mean arrival rate are also discussed. Our results indicate that the proposed pulse-type model shows obviously distinguishable characteristics from a Gaussian-type model, and may confer a significant advantage for modeling the prey-predator system under discrete environmental fluctuations.

The signal transfer from nerve to muscle occurs by diffusion across the neuromuscular junction. The continuum level analysis of diffusion processes is based on the diffusion equation, which in one dimension is $\partial c∕\partial t=D({\partial }^{2}c∕\partial x^2)$, where $c$ is the molecular concentration and $D$ is the diffusivity. However, in confined systems such as the neuromuscular junction, the diffusion equation may not be valid, and even if valid the value of $D$ may be altered by the confinement. In this paper, Monte Carlo simulations are used to probe diffusion at the molecular level in a realistic model of a neuromuscular junction. The results show that diffusion is anomalous (i.e., not described by the diffusion equation) for time scales less than $\sim 0.01\mathrm{s}$, which is the time scale relevant for signaling processes in the synapse. At longer time scales, the diffusion is normal (i.e., described by the diffusion equation), but with a value of $D$ that is reduced by a factor of $\sim 5$ times compared to the value for diffusion in open space. As the width of the synaptic cleft decreases, these effects become even more pronounced. The physical basis of these results is described in terms of the structure of the neuromuscular junction.

Neurons are subject to synaptic inputs from many other cells. These inputs consist of spikes changing the conductivity of the target cell, i.e., they enter the neural dynamics as multiplicative shot noise. Up to now, only for simplified models like current-based (additive-noise) point neurons or models with Gaussian white-noise input, exact solutions are available. We present a method to calculate the exact time-dependent moments for the voltage of a point neuron with conductance-based shot noise and a passive membrane. The exact solutions show features (for instance, maxima of the moments vs time) which are also confirmed by numerical simulations. The theoretical analysis of subthreshold membrane fluctuations may contribute to a better comprehension of neural noise in general. We also discuss how the analytical results may provide additional conditions for estimating parameters from experimental data.

The dynamical response of a population of interconnected objects, when exposed to external perturbations, is of great interest to physicists working on complex systems. Here we focus on human systems, by analyzing the dynamical response of the world’s financial community to various types of unexpected events—including the 9/11 terrorist attacks as they unfolded on a minute-by-minute basis. For the unfolding events of 9/11, our results show that there was a gradual collective understanding of what was happening, rather than an immediate realization. More generally, we find that for news items which are not simple economic statements—and hence whose implications for the market are not immediately obvious—there are periods of collective discovery during which opinions seem to vary in a remarkably synchronized way.

The load of a node in a network is the total traffic going through it when every node pair sustains a uniform bidirectional traffic between them on shortest paths. We express nodal load in terms of the more elementary notion of a node’s descents in breadth-first-search [(BFS) or shortest-path] trees and study both the descent and nodal-load distributions in the case of scale-free networks. Our treatment is both semianalytical (combining a generating-function formalism with simulation-derived BFS branching probabilities) and computational for the descent distribution; it is exclusively computational in the case of the load distribution. Our main result is that the load distribution, even though it can be disguised as a power law through subtle (but inappropriate) binning of the raw data, is in fact a succession of sharply delineated probability peaks, each of which can be clearly interpreted as a function of the underlying BFS descents. This find is in stark contrast with previously held belief, based on which a power law of exponent $-2.2$ was conjectured to be valid regardless of the exponent of the power-law distribution of node degrees.

Identifying strongly connected substructures in large networks provides insight into their coarse-grained organization. Several approaches based on the optimization of a quality function, e.g., the modularity, have been proposed. We present here a multistep extension of the greedy algorithm (MSG) that allows the merging of more than one pair of communities at each iteration step. The essential idea is to prevent the premature condensation into few large communities. Upon convergence of the MSG a simple refinement procedure called “vertex mover” (VM) is used for reassigning vertices to neighboring communities to improve the final modularity value. With an appropriate choice of the step width, the combined MSG-VM algorithm is able to find solutions of higher modularity than those reported previously. The multistep extension does not alter the scaling of computational cost of the greedy algorithm.

Two schemes are proposed to detect phase synchronization from chaotic data contaminated by noise. The first is a neighborhood-based method which links time delay embedding with instantaneous phase estimation. The second adopts the local projection method as a preprocessing filter to noisy data. Both schemes utilize the state recurrence, an important feature of chaotic data. The proposed schemes are applied to data measured from two typical chaotic systems, i.e., the coupled Rössler systems and the coupled Lorenz systems, respectively. The results show that phase synchronization, which may be buried by noise, is detected even when the noise level is high. Moreover, the overestimation of the degree of phase synchronization, which may be introduced by the Hilbert transform combined with a traditional linear bandpass filter, can be avoided when the data are contaminated by only measurement noise.

Signal transmission delays tend to destabilize dynamical networks leading to oscillation, but their dispersion contributes oppositely toward stabilization. We analyze an integrodifferential equation that describes the collective dynamics of a neural network with distributed signal delays. With the $\Gamma$ distributed delays less dispersed than exponential distribution, the system exhibits reentrant phenomena, in which the stability is once lost but then recovered as the mean delay is increased. With delays dispersed more highly than exponential, the system never destabilizes.

We report experimental results on the maximum angle of stability, i.e., the so-called avalanche angle, of a granular medium subjected to an inner water flow controlled by a constant pressure drop. A unique avalanche threshold is derived by two alternative theoretical developments, namely a continuum and a discrete approach, and is successfully confronted to many measurements in a large experimental range. A qualitative analysis of the instability triggering reveals different dynamical behaviors depending on whether the water flow is downward or upward in the granular layer, namely stabilizing versus destabilizing regime. Contrary to the purely hydrostatic situation, the free surface following an avalanche departs from a linear shape because the dynamical pressure gradient is no longer constant in the medium. A simple model is proposed that can satisfactorily predict the postavalanche height profile as well as its subsequent evolution for higher inclinations.

Thermally induced particle flow in a charged colloidal suspension is studied in a fluid-mechanical approach. The force density acting on the charged boundary layer is derived in detail. From Stokes’ equation with no-slip boundary conditions at the particle surface, we obtain the particle drift velocity and the thermophoretic transport coefficients. The results are discussed in view of previous work and available experimental data.

When a system undergoes a first-order phase transition from a disordered to an ordered state, the local energy is first minimized. This local energy minimization often prevents a system from reaching the global energy minimum state and leads to trapping in an imperfectly ordered state with many defects. In soft matter, however, a system can further relax to the global energy minimum state via slow relaxation due to its softness and fluidity. We study this relaxation process, using a lyotropic lamellar phase in a wedge-shaped cell as a model system. A lyotropic smectic liquid crystal has a large repeat unit (here, an interlayer spacing $d$) up to $\sim 0.1\mu \text{m}$, and thus the motion of an individual edge dislocation in the lamellar phase can be directly observed with optical microscopy. Furthermore, a rather macroscopic spatial confinement (size $h$) can produce strong confinement effects, since $d/h$ can still be large due to the largeness of $d$. These properties allow us to study the detailed kinetics of the relaxation process. We follow the time evolution of an edge dislocation array over 100 h from its initial stage. We reveal that the pattern evolution of an edge-dislocation array is the relaxation process of excess dislocation lines that formed initially toward the equilibrium configuration, and it is characterized by the motion of “nodes” of the topologically connected edge-dislocation network. We clarify the elementary process of this relaxation from a local to the global energy minimum state.

During development, cells grow, differentiate, divide, and die according to their spatial positions, yet the positional information given to cells by morphogens (diffusive chemicals) includes considerable noises from various origins. In this paper, we examine a relationship between fluctuations in morphogen concentrations that the cells receive and the precision of positional specification by the morphogens in multidimensional space. As a method to quantify the precision, we introduce a measure of “ambiguity of positional information,” based on the information entropy. We discover that the location of morphogen sources crucially affects the ambiguity, and that the ambiguity becomes minimum when the angle made by gradient vectors of different morphogens cross at a right angle in a target region under a given organ geometry (orthogonality principle). We conjecture that morphogen sources in development might be placed at the nearly optimal position that minimizes the ambiguity of positional information. This is supported by experimental data on the configurations of two major sources of spatial patterning, the apical ectodermal ridge (AER) and the zone of polarizing activity (ZPA), in vertebrate limb development. Indeed, their predicted configuration agrees very well with the one observed in experiments. We believe that the placement of morphogen sources to minimize the ambiguity of positional information is a basic principle in development of multicellular organisms beyond this particular example.

The artificial microswimmer [R. Dreyfus et al., Nature (London) 437, 862 (2005)] whose mechanism of propulsion is the magnetically driven undulation of a flagellum-like tail composed of chemically linked paramagnetic beads can be used as a physical model with which to study low-Reynolds-number swimming. Understanding how such swimmers interact provides insight into the related problem of quantifying the hydrodynamic interactions between microorganisms. In this study, particle-based numerical simulations are conducted of two comoving artificial swimmers. The resulting swimming speeds are determined over a range of separations for swimmers driven by planar and rotational magnetic fields. The far-field hydrodynamic interactions are analyzed and found to decay as $h^{-2}$ where $h$ is the separation distance. Additionally, the role of the interswimmer magnetic forces is determined.

The onset of spatiotemporal chaos in a damped sine-Gordon system subjected to a plane wave field as well as its suppression by an additional small-amplitude plane wave field are proposed theoretically and confirmed numerically. The relevance of these findings in the context of nonlinear magnetization waves is discussed.