We use numerical simulations to compute the equation of state of a suspension of spherical self-propelled nanoparticles in two and three dimensions. We study in detail the effect of excluded volume interactions and confinement as a function of the system's temperature, concentration, and strength of the propulsion. We find a striking nonmonotonic dependence of the pressure on the temperature and provide simple scaling arguments to predict and explain the occurrence of such anomalous behavior. We explicitly show how our results have important implications for the effective forces on passive components suspended in a bath of active particles.

Molecular dynamics simulations were carried out on a series of Lennard-Jones binary mixtures of rigid, asymmetric, dumbbell-shaped molecules. Below an onset temperature, the rotational and translational dynamics split into the slow structural α relaxation and a higher-frequency Johari-Goldstein β relaxation. Both processes are dynamically heterogeneous, having broad distributions of relaxation times. However, only the α relaxation shows strong dynamic correlations; correlations at the β time scale are weak, in particular for molecules having shorter bonds. Despite the close connection between the two processes, we find no correlation between the α and β relaxation times of individual molecules; that is, a molecule exhibiting slow β motion does not necessarily undergo slow α dynamics and likewise for fast molecules. However, the single-molecule α relaxation times do correlate with both the α and β relaxation strengths.

Polymer ejection from a capsid through a nanoscale pore is an important biological process with relevance to modern biotechnology. Here, we study generic capsid ejection using Langevin dynamics. We show that even when the ejection takes place within the drift-dominated region there is a very high probability for the ejection process not to be completed. Introducing a small aligning force at the pore entrance enhances ejection dramatically. Such a pore asymmetry is a candidate for a mechanism by which viral ejection is completed. By detailed high-resolution simulations we show that such capsid ejection is an out-of-equilibrium process that shares many common features with the much studied driven polymer translocation through a pore in a wall or a membrane. We find that the ejection times scale with polymer length, $\tau \sim N^{\alpha }$. We show that for the pore without the asymmetry the previous predictions corroborated by Monte Carlo simulations do not hold. For the pore with the asymmetry the scaling exponent varies with the initial monomer density (monomers per capsid volume) $\rho$ inside the capsid. For very low densities $\rho \le 0.002$ the polymer is only weakly confined by the capsid, and we measure $\alpha =1.33$, which is close to $\alpha =1.4$ obtained for polymer translocation. At intermediate densities the scaling exponents $\alpha =1.25$ and $1.21$ for $\rho =0.01$ and $0.02$, respectively. These scalings are in accord with a crude derivation for the lower limit $\alpha =1.2$. For the asymmetrical pore precise scaling breaks down, when the density exceeds the value for complete confinement by the capsid, $\rho ⪆0.25$. The high-resolution data show that the capsid ejection for both pores, analogously to polymer translocation, can be characterized as a multiplicative stochastic process that is dominated by small-scale transitions.

We study the effects of polymers in two-dimensional turbulent thermal convection using a shell model. In the absence of polymers, the inverse energy cascade in two dimensions leads to the observed Bolgiano-Obukhov scaling. When polymers are added, energy is extracted from the flow by the polymers, and as a result, the thermal balance between buoyancy and inertia in Bolgiano-Obukhov scaling is destroyed around the scales at which polymers interact strongly with the flow. This results in an increase in the Bolgiano scale and leads to a change in the scaling behavior of the velocity and temperature fluctuations for scales below the modified Bolgiano scale. We make theoretical estimates of the dependence of the mean rate of energy extracted by the polymers and the mean energy dissipation rate on the polymer relaxation time. Our theoretical analysis further leads to the prediction that the heat transport is not altered much by the polymers in two dimensions. We show that our theoretical estimates and prediction are in good agreement with the numerical results.

We study the influence of disjoining pressure for moving long bubbles inside cylindrical capillaries. Towards that end, consistent thin-film equations, for the annular region separating the bubble from the channel surface, are presented with specific emphasis on three different attributes: (a) the van der Waals interaction, formalized by the classical Lifshitz form of disjoining pressure; (b) the nonuniformity in film thickness, accommodated by the necessary corrections in the disjoining pressure; and (c) the electrostatic component of disjoining pressure, reminiscent of the electrostatic interactions in the presence of surface charges. The present thin-film analysis appositely uncovers the existence and the breakdown of the two-thirds power law for minimum film thickness behavior. This is attributed to the alteration in the characteristic length scales governing the underlying physics, as quantitatively established by our consistent scaling analysis. In the breakdown regimes, the characteristic length scales are found to be composed of the suitable combinations of the capillary number and the physics driven intrinsic length scales. The characteristics of the breakdown regime reported by us appear to match excellently with reported experimental data in the low capillary number regime. Towards unveiling the possible implications of slope and curvature dependence of disjoining pressure, our analysis reveals that the consequent correction term endorses an order two-thirds power of the capillary number contribution without alerting the governing length scales. The subsequent asymptotic analysis reveals that this correction may be neglected to the leading order approximation. Finally, we consider the electrostatic component of the disjoining pressure which may be realized in the presence of surface charges. Our analysis reveals that the significance of the electrostatic interaction is realized over a very small capillary number regime, leading towards the departure from the two-thirds power law type behavior. Reasonably good agreement is obtained with reported experimental data over this regime.

For a gas confined between surfaces held at different temperatures the velocity distribution shows a significant deviation from the Maxwell distribution when the mean free path of the molecules is comparable to or larger than the channel dimensions. If one of the surfaces is suitably structured, this nonequilibrium distribution can be exploited for momentum transfer in a tangential direction between the two surfaces. This opens up the possibility to extract work from the system which operates as a heat engine. Since both surfaces are held at constant temperatures, the mode of momentum transfer is different from the thermal creep flow that has gained more attention so far. This situation is studied in the limit of free-molecular flow for the case that an unstructured surface is allowed to move tangentially with respect to a structured surface. Parameter studies are conducted, and configurations with maximum thermodynamic efficiency are identified. Overall, it is shown that significant efficiencies can be obtained by tangential momentum transfer between structured surfaces.

The fascinating and anomalous behavior of a chain that instead of falling straight down under gravity, first rises and then falls, acquiring a steady shape in space that resembles a fountain's spray, has recently attracted both popular and academic interest. The paper presents a complete mathematical solution of this problem, whose distinctive feature is the introduction of a number of dissipative shocks that can be resolved exactly.

The complexity of the primary structure of human DNA is explored using methods from nonequilibrium statistical mechanics, dynamical systems theory, and information theory. A collection of statistical analyses is performed on the DNA data and the results are compared with sequences derived from different stochastic processes. The use of ${\chi }^2$ tests shows that DNA can not be described as a low order Markov chain of order up to $r=6$. Although detailed balance seems to hold at the level of a binary alphabet, it fails when all four base pairs are considered, suggesting spatial asymmetry and irreversibility. Furthermore, the block entropy does not increase linearly with the block size, reflecting the long-range nature of the correlations in the human genomic sequences. To probe locally the spatial structure of the chain, we study the exit distances from a specific symbol, the distribution of recurrence distances, and the Hurst exponent, all of which show power law tails and long-range characteristics. These results suggest that human DNA can be viewed as a nonequilibrium structure maintained in its state through interactions with a constantly changing environment. Based solely on the exit distance distribution accounting for the nonequilibrium statistics and using the Monte Carlo rejection sampling method, we construct a model DNA sequence. This method allows us to keep both long- and short-range statistical characteristics of the native DNA data. The model sequence presents the same characteristic exponents as the natural DNA but fails to capture spatial correlations and point-to-point details.

We consider a freely movable solid that separates a long tube into two regions, each of which is filled with a dilute gas. The gases in each region are initially prepared at the same pressure but different temperatures. Under the assumption that the pressure and temperatures of gas particles before colliding with the solid are kept constant over time, we show that temperature gaps appearing on the solid surface generate a force. We provide a quantitative estimation of the force, which turns out to be large enough to be observed by a macroscopic measurement.

The hydrodynamic Burnett equations and the associated transport coefficients are exactly evaluated for generalized inelastic Maxwell models. In those models, the one-particle distribution function obeys the inelastic Boltzmann equation, with a velocity-independent collision rate proportional to the $\gamma$ power of the temperature. The pressure tensor and the heat flux are obtained to second order in the spatial gradients of the hydrodynamic fields with explicit expressions for all the Burnett transport coefficients as functions of $\gamma$, the coefficient of normal restitution, and the dimensionality of the system. Some transport coefficients that are related in a simple way in the elastic limit become decoupled in the inelastic case. As a byproduct, existing results in the literature for three-dimensional elastic systems are recovered, and a generalization to any dimension of the system is given. The structure of the present results is used to estimate the Burnett coefficients for inelastic hard spheres.

We analyze the electrorheological effect in immiscible fluid mixtures with dielectric mismatch. By taking the electric field effect into account, which couples to the dynamics of domain morphology under flow, we propose a set of electrorheological constitutive equations valid under the condition where the relative magnitude of the flow field is stronger than that of the electric field. Through comparison with recent experiments, we point out a unique dynamical stress response inherent in situations where the cross-coupling between different fields is essential.

When a globule with a complete symmetry (such as simple spherical droplets and concentric double emulsions) is transiting in a constriction tube, there is only one pattern of the transition. However, for a multiple-emulsion globule with asymmetric internal structures, there are many possible patterns with different pressure drops Δ$p$ due to various initial orientations of the inner droplets. In this paper, a boundary integral method developed recently is employed to investigate numerically the possible oriented transition of a globule with two unequal inner droplets in an axisymmetric microfluidic constriction. The transition is driven by an axisymmetric Poiseuille flow with a fixed volume flow rate, and the rheological behaviors of the globule are observed carefully. When the big inner droplet is initially located in the front of the globule, the maximum pressure drop during the transition is always lower than that when it is initially placed in the rear. Thus, a tropism—whereby a globule more easily gets through the constriction when its bigger inner droplet locates in its front initially—might exist, in which the orientating stimulus is the required pressure drops. The physical explanation of this phenomenon has also been analyzed in this paper.

The distributions of work for strongly nonequilibrium processes are studied using a very general form of a large-deviation approach, which allows one to study distributions down to extremely small probabilities of almost arbitrary quantities of interest for equilibrium, nonequilibrium stationary, and even nonstationary processes. The method is applied to quickly vary the external field in a wide range $B=3\leftrightarrow 0$ for a critical ($T=2.269$) two-dimensional Ising system of size $L\times L=128\times 128$. To obtain free-energy differences from the work distributions, they must be studied in ranges where the probabilities are as small as ${10}^{-240}$, which is not possible using direct simulation approaches. By comparison with the exact free energies, which are available for this model for the zero-field case, one sees that the present approach allows one to obtain the free energy with a very high relative precision of ${10}^{-4}$. This works well also for a nonzero field, i.e., for a case where standard umbrella-sampling methods are not efficient to calculate free energies. Furthermore, for the present case it is verified that the resulting distributions of work for forward and backward processes fulfill Crooks theorem with high precision. Finally, the free energy for the Ising magnet as a function of the field strength is obtained.

The physical properties of membrane necks are relevant in vesiculation, a process that plays an essential role in cellular physiology. Because the neck's radius is, in general, finite, membrane scission and the consequent pinching off of the vesicle can only occur if it is narrowed to permit the necessary membrane topological reformation. Here we examine, in a simple single phase lipid vesicle, how external forces can promote neck constriction not only by direct compression at the neck but also, counterintuitively, by dilation at remote locations. These results provide a new perspective on the role played by actin polymerization in the process of endocytosis.

In this paper we characterize the mixing properties in the advection of passive tracers by exploiting the extreme value theory for dynamical systems. With respect to classical techniques directly related to the Poincaré recurrences analysis, our method provides reliable estimations of the characteristic mixing times and distinguishes between barriers and unstable fixed points. The method is based on a check of convergence for extreme value laws on finite datasets. We define the mixing times in terms of the shortest time intervals such that extremes converge to the asymptotic (known) parameters of the generalized extreme value distribution. Our technique is suitable for applications in the analysis of other systems where mixing time scales need to be determined and limited datasets are available.

We study full counting statistics for transferred heat and entropy production between multiterminal systems in absence of a finite junction. The systems are modeled as collections of coupled harmonic oscillators, which are kept at different equilibrium temperatures and are connected via arbitrary time-dependent couplings. Following consistent quantum framework and two-time measurement concept we obtain analytical expressions for the generalized cumulant generating function. We discuss transient and steady-state fluctuation theorems for the transferred quantities. We also address the effect of coupling strength on the exchange fluctuation theorem.

Induced bulk orientation of nematic liquid crystal in contact with micron-scale patterned surfaces is investigated using the Landau-de Gennes theory by means of three-dimensional simulations. The effect of the size and spacing of square cross-sectional well and post patterns is investigated and shown to influence the orientation of the liquid crystal bulk, far removed from the surface. Additionally, the effective anchoring strength of the induced alignment is estimated using a modified version of the torque balance method. Both azimuthal and zenithal multistability are shown to exist within unique ranges of feature sizes.

In the last few years there have been many efforts in econophysics studying how network theory can facilitate understanding of complex financial markets. These efforts consist mainly of the study of correlation-based hierarchical networks. This is somewhat surprising as the underlying assumptions of research looking at financial markets are that they are complex systems and thus behave in a nonlinear manner, which is confirmed by numerous studies, making the use of correlations which are inherently dealing with linear dependencies only baffling. In this paper we introduce a way to incorporate nonlinear dynamics and dependencies into hierarchical networks to study financial markets using mutual information and its dynamical extension: the mutual information rate. We show that this approach leads to different results than the correlation-based approach used in most studies, on the basis of 91 companies listed on the New York Stock Exchange 100 between 2003 and 2013, using minimal spanning trees and planar maximally filtered graphs.

By invoking the famous Fortuin, Kasteleyn, and Ginibre (FKG) inequality, we prove the conjecture that the correlation of infection at the same time between any pair of nodes in a network cannot be negative for (exact) Markovian susceptible-infected-susceptible (SIS) and susceptible-infected-removed (SIR) epidemics on networks. The truth of the conjecture establishes that the $N$-intertwined mean-field approximation (NIMFA) upper bounds the infection probability in any graph so that network design based on NIMFA always leads to safe protections against malware spread. However, when the infection or/and curing are not Poisson processes, the infection correlation between two nodes can be negative.