The transition between a regime in which thermodynamic relations apply only to ensembles of small systems coupled to a large environment and a regime in which they can be used to characterize individual macroscopic systems is analyzed in terms of the change in behavior of the Jarzynski estimator of equilibrium free energy differences from nonequilibrium work measurements. Given a fixed number of measurements, the Jarzynski estimator is unbiased for sufficiently small systems. In these systems the directionality of time is poorly defined and the configurations that dominate the empirical average, but which are in fact typical of the reverse process, are sufficiently well sampled. As the system size increases the arrow of time becomes better defined. The dominant atypical fluctuations become rare and eventually cannot be sampled with the limited resources that are available. Asymptotically, only typical work values are measured. The Jarzynski estimator becomes maximally biased and approaches the exponential of minus the average work, which is the result that is expected from standard macroscopic thermodynamics. In the proper scaling limit, this regime change has been recently described in terms of a phase transition in variants of the random energy model. In this paper this correspondence is further demonstrated in two examples of physical interest: the sudden compression of an ideal gas and adiabatic quasistatic volume changes in a dilute real gas.

The ability of cells to undergo reversible shape changes is often crucial to their survival. For red blood cells (RBCs), irreversible alteration of the cell shape and flexibility often causes anemia. Here we show theoretically that RBCs may react irreversibly to mechanical perturbations because of tensile stress in their cytoskeleton. The transient polymerization of protein fibers inside the cell seen in sickle cell anemia or a transient external force can trigger the formation of a cytoskeleton-free membrane protrusion of $\mu$m dimensions. The complex relaxation kinetics of the cell shape is shown to be responsible for selecting the final state once the perturbation is removed, thereby controlling the reversibility of the deformation. In some case, tubular protrusion are expected to relax via a peculiar “pearling instability.”

Although commonly used materials are composed of irregular microstructures, most existing numerical methods for fracture dynamics are developed via regular discretizations. In the present Rapid Communication we investigate the dynamic fracture numerically by irregular domain discretizations. To explore the relationship between microscopic crack branching and the macroscopic instability of fracture dynamics, we simulate detailed diagrams for the crack branching and also calculate the crack speeds by varying the parameters of crack-tip cohesion. In particular, an equation to describe the relation between the crack speed and the fracture energy is proposed based on the simulation results. The present results indicate that the irregularities of mesoscopic structure contribute to the intrinsic instabilities of dynamic fracture and eventually to the crack speed. And the single-crack continuum theory should be at least carefully modified to describe the dynamic fracture governed by the complex branching and fluctuations.

When an ensemble of self-propelled camphor boats move in a one-dimensional channel, they exhibit a variety of collective behaviors. Under certain conditions, the boats tend to cluster together and move in a relatively tight formation. This type of behavior, referred to as clustering or swarming here, is one of three types recently observed in experiment. Similar clustering behavior is also reproduced in simulations based on a simple theoretical model. Here we examine this model to determine the clustering mechanism and the conditions under which clustering occurs. We also propose a method of quantifying the behavior that may be used in future experimental work.

Weight distribution greatly impacts the epidemic spreading taking place on top of networks. This paper presents a study of a susceptible-infected-susceptible model on regular random networks with different kinds of weight distributions. Simulation results show that the more homogeneous weight distribution leads to higher epidemic prevalence, which, unfortunately, could not be captured by the traditional mean-field approximation. This paper gives an edge-based mean-field solution for general weight distribution, which can quantitatively reproduce the simulation results. This method could be applied to characterize the nonequilibrium steady states of dynamical processes on weighted networks.

We experimentally investigate the ghost resonance phenomenon in the electronic circuit of Chua operating in the chaotic regime. The circuit can be stimulated to jump between two single-scroll attractors by an external periodic signal with an amplitude above an intrinsic threshold. For subthreshold signals, jumps between the chaotic attractors can be promoted by a superposed white noise. We show that the circuit output can exhibit a well-defined ghost resonance signature, i.e., a resonance on a frequency that is absent in a multicomponent input signal, when the amplitudes of the input components are properly related. Further, we show that ghost resonance can be induced by the Chua's circuit's own chaotic dynamics when it is driven by a suprathreshold multicomponent signal without the need of an external noise source.

We perform molecular dynamics simulations to demonstrate that when a nanodroplet is confined inside a carbon nanotube (CNT), unidirectional motion can be created by a nonzero surface energy gradient. It is found that the water nanodroplet moves along the direction of increasing surface energy. The transportation efficiency of the water nanodroplet is found to be dependent on the surface energy gradient; environmental temperature; and the flexibility, diameter, and defectiveness of the CNT. It is shown that higher surface energy gradient, the smaller diameter of the CNT, and fewer defects promote higher transportation efficiency. However, when the temperature is too high or too low, the water transport across the CNT is impeded. Except for the initial stage at the relatively low environmental temperature, higher flexibility of the CNT wall reduces the transportation efficiency. It is also found that the hydrogen bonds of water molecules play a role in the dynamic acceleration process with a wavelike feature. The present work provides insight for the development of CNT devices for applications such as drug delivery, nanopumps, chemical process control, and molecular medicine.

We investigate a dynamical interplay between interfacial electrokinetics and a combined dissipative and elastic behavior of flow through narrow confinements, in analogy with spatiotemporal hydrodynamics of porous media. In particular, we investigate the effects of streaming potential on the pertinent dynamic responses, by choosing a Maxwell fluid model for representing the consequent electro-hydrodynamic characteristics. We transform the pertinent governing equation to the frequency domain, so that a dynamic generalization of Darcy's law in the presence of streaming potential effects can be effectively realized. We show that the frequencies corresponding to local maxima in the dynamic permeability also correspond to local maxima in the induced streaming potential. We also bring out the effects of Stern layer conductivity on the dynamic permeability. Our analytical estimates do reveal that serious overestimations in the commonly portrayed notion of massive amplifications of dynamic permeability at resonating frequencies may be possible, if interactions between spontaneous electrochemical interfacial phenomena and pulsating pressure-gradient-driven viscoelastic transport are trivially ignored.

We continue our study of the statistical properties of particles in equilibrium obeying Smoluchowski dynamics. We show that the system is governed by a kinetic equation of the memory function form and that the memory function is given by one of the self-energies available via perturbation theory as introduced in previous work. We determine the memory function explicitly to second order in an expansion in a pseudopotential. The method we use allows for a straightforward computation of corrections via a formal expansion and we therefore view it as an improvement over the conventional mode-coupling theory (MCT) formalism where it is not clear how to make systematic corrections. In addition, the formalism we have introduced is flexible enough to allow for a wide array of different approximation schemes, including density expansions. The convergence criteria for our formal series are not worked out here, but the second-order equation that we derive is promising in the sense that it leads to analytic and numerical results consistent with expectations from computer simulations of the hard-sphere system in addition to replicating the desired features from conventional MCT (e.g., a two-step decay). These particular solutions will be discussed in forthcoming work.

The present paper investigates large sets of ceramic fibre failure strengths (500 to 1000 data) produced using tensile tests on tows that contained either 500 or 1000 filaments. The probability density function was determined through acoustic emission monitoring which allowed detection and counting of filament fractures. The statistical distribution of filament strengths was described using the normal distribution. The Weibull equation was then fitted to this normal distribution for estimation of statistical parameters. A perfect agreement between both distributions was obtained, and a quite negligible scatter in statistical parameters was observed, as opposed to the wide variability that is reported in the literature. Thus it was concluded that flaw strengths are distributed normally and that the statistical parameters that were derived are the true ones. In a second step, the conventional method of estimation of Weibull parameters was applied to these sets of data and, then, to subsets selected randomly. The influence of other factors involved in the conventional method of determination of statistical parameters is discussed. It is demonstrated that selection of specimens, sample size, and method of construction of so-called Weibull plots are responsible for statistical parameters variability.

Sufficiently fine granular systems appear to exhibit continuum properties, though the precise continuum limit obtained can be vastly different depending on the particular system. In the present paper the continuum limit of an unconfined, dense granular flow is investigated. To do this a two-dimensional dense cohesionless granular jet impinging upon a target is used as a test system. This is simulated via a time-step-driven hard-sphere method and apply a mean-field theoretical approach to connect the macroscopic flow with the microscopic material parameters of the grains. It is observed that the flow separates into a cone with an interior cone angle determined by the conservation of momentum and the dissipation of energy. From the cone angle a dimensionless quantity $A-B$ that characterizes the flow is extracted. This quantity is found to depend both on whether or not a dead zone, i.e., a stationary region near the target, is present and on the value of the coefficient of dynamic friction. A theory is presented for the scaling of $A-B$ with the coefficient of friction that suggests that dissipation is primarily a perturbative effect in this flow rather than the source of qualitatively different behavior.

Granular solid hydrodynamics (GSH) is a broad-ranged continual mechanical description of granular media capable of accounting for static stress distributions, yield phenomena, propagation and damping of elastic waves, the critical state, shear band, and fast dense flow. An important input of GSH is an expression for the elastic energy needed to deform the grains. The original expression, though useful and simple, has some drawbacks. Therefore a slightly more complicated expression is proposed here that eliminates three of them: (1) The maximal angle at which an inclined layer of grains remains stable is increased from ${26}^{\circ }$ to the more realistic value of ${30}^{\circ }$. (2) Depending on direction and polarization, transverse elastic waves are known to propagate at slightly different velocities. The old expression neglects these differences, the new one successfully reproduces them. (3) Most importantly, the old expression contains only the Drucker-Prager yield surface. The new one contains in addition those named after Coulomb, Lade-Duncan, and Matsuoka-Nakai—realizing each, and interpolating between them, by shifting a single scalar parameter.

Spatially extended, excitable systems with resting, activated, and refractory states, and emergent localized propagating patterns, are widespread in nature. Here a unique type of three-state excitable network model is shown to generate such dynamic patterns with rich collective dynamics. It is shown that symmetry breaking leads to the formation of dynamical patterns, leading to a change from local subdiffusive wandering to directed superdiffusive propagation. Furthermore, the model yields a rich repertoire of collision dynamics between localized propagating patterns and between propagating patterns and the refractory wakes of others. This work is particularly motivated by recent experimental studies of neural systems that exhibit localized propagating patterns, exemplifying a far wider class of excitable systems.

We explore nanoscale hydrodynamical effects on synthesis and self-assembly of cadmium sulfide nanotubes oriented along one direction. These nanotubes are synthesized by horizontal capillary flow of two different chemical reagents from opposite directions through nanochannels of porous anodic alumina which are used primarily as nanoreactors. We show that uneven flow of different chemical precursors is responsible for directionally asymmetric growth of these nanotubes. On the basis of structural observations using scanning electron microscopy, we argue that chemohydrodynamic convective interfacial instability of multicomponent liquid-liquid reactive interface is necessary for sustained nucleation of these CdS nanotubes at the edges of these porous nanochannels over several hours. However, our estimates clearly suggest that classical hydrodynamics cannot account for the occurrence of such instabilities at these small length scales. Therefore, we present a case which necessitates further investigation and understanding of chemohydrodynamic fluid flow through nanoconfined channels in order to explain the occurrence of such interfacial instabilities at nanometer length scales.

We present an algebraic approach for determining the attractors and their basins of random Boolean networks under an asynchronous stochastic update based on the recently developed matrix semitensor product theory, which allows for converting the logical dynamics of a Boolean network into a standard iterative dynamics. In this setting, all attractors and basins are specified by the network transition matrices. We then devise procedures that can find all attractors and their basins exactly. We also discuss the issue of overlapping basins in asynchronous random Boolean networks, and we propose methods to compute the weight of each attractor and the basin entropy of the systems.

Avalanche frontiers in Abelian sandpile model (ASM) are random simple curves whose continuum limit is known to be a Schramm-Loewner evolution with diffusivity parameter $\kappa =2$. In this paper we consider the dissipative ASM and study the statistics of the avalanche and wave frontiers for various rates of dissipation. We examine the scaling behavior of a number of functions, such as the correlation length, the exponent of distribution function of loop lengths, and the gyration radius defined for waves and avalanches. We find that they do scale with the rate of dissipation. Two significant length scales are observed. For length scales much smaller than the correlation length, these curves show properties close to the critical curves, and the corresponding diffusivity parameter is nearly the same as the critical limit. We interpret this as the ultraviolet limit where $\kappa =2$ corresponding to $c=-2$. For length scales much larger than the correlation length, we find that the avalanche frontiers tend to self-avoiding walk, and the corresponding driving function is proportional to the Brownian motion with the diffusivity parameter $\kappa =8/3$ corresponding to a field theory with $c=0$. We interpret this to be the infrared limit of the theory or at least a crossover.

We investigate the mechanical responses of dense granular materials, using a direct shear box combined with simultaneous acoustic measurements. Measured shear wave speeds evidence the structural change of the material under shear, from the jammed state to the flowing state. There is a clear acoustic signature when the shear band is formed. Subjected to cyclic shear, both shear stress and wave speed show the strong hysteretic dependence on the shear strain, likely associated with the geometry change in the packing structure. Moreover, the correlation function of configuration-specific multiply scattered waves reveals an intermittent behavior before the failure of material.

Populations of competing biological species exhibit a fascinating interplay between the nonlinear dynamics of evolutionary selection forces and random fluctuations arising from the stochastic nature of the interactions. The processes leading to extinction of species, whose understanding is a key component in the study of evolution and biodiversity, are influenced by both of these factors. Here, we investigate a class of stochastic population dynamics models based on generalized Lotka-Volterra systems. In the case of neutral stability of the underlying deterministic model, the impact of intrinsic noise on the survival of species is dramatic: It destroys coexistence of interacting species on a time scale proportional to the population size. We introduce a new method based on stochastic averaging which allows one to understand this extinction process quantitatively by reduction to a lower-dimensional effective dynamics. This is performed analytically for two highly symmetrical models and can be generalized numerically to more complex situations. The extinction probability distributions and other quantities of interest we obtain show excellent agreement with simulations.

Liquid drops start spreading directly after coming into contact with a partially wetting substrate. Although this phenomenon involves a three-phase contact line, the spreading motion is very fast. We study the initial spreading dynamics of low-viscosity drops using two complementary methods: molecular dynamics simulations and high-speed imaging. We access previously unexplored length and time scales and provide a detailed picture on how the initial contact between the liquid drop and the solid is established. Both methods unambiguously point toward a spreading regime that is independent of wettability, with the contact radius growing as the square root of time.

We develop and investigate a particle-based model for ski slope traffic. Skiers are modeled as particles with a mass that are exposed to social and physical forces, which define the riding behavior of skiers during their descents on ski slopes. We also report position and speed data of 21 skiers recorded with GPS-equipped cell phones on two ski slopes. A comparison of these data with the trajectories resulting from computer simulations of our model shows a good correspondence. A study of the relationship among the density, speed, and flow of skiers reveals that congestion does not occur even with arrival rates of skiers exceeding the maximum ski lift capacity. In a sensitivity analysis, we identify the kinetic friction coefficient of skis on snow, the skier mass, the range of repelling social forces, and the arrival rate of skiers as the crucial parameters influencing the simulation results. Our model allows for the prediction of speed zones and skier densities on ski slopes, which is important in the prevention of skiing accidents.