A thorough analysis of the dynamics in a deterministic optical rocking ratchet [introduced in A. V. Arzola et al., Phys. Rev. Lett. 106, 168104 (2011)] and a comparison with experimental results are presented. The studied system consists of a microscopic particle interacting with a periodic and asymmetric light pattern, which is driven away from equilibrium by means of an unbiased time-periodic external force. It is shown that the asymmetry of the effective optical potential depends on the relative size of the particle with respect to the spatial period, and this is analyzed as an effective mechanism for particle fractionation. The necessary conditions to obtain current reversals in the deterministic regime are discussed in detail.

We have developed a technique for the simultaneous measurement of the surface tension and the viscosity of a liquid in a noncontact manner. In this method, a small linear deformation of the liquid surface is induced by a local dielectric force that is brought about by a knife-edge electrode. The surface tension and the viscosity are obtained from the shape of the induced meniscus and from the dynamic response of the surface, respectively. The surface tension obtained was examined in comparison with the values measured by the Wilhelmy plate method. We also measured time constants of the surface deformation for a variety of standard viscosity samples and obtained the relation between the time constant and the viscosity. The demonstrated advantage of the system is the ability to uniquely determine the surface tension and the viscosity.

In this work, the role of the hydrodynamic forces on a swimming microorganism near an air-liquid interface is studied. The lubrication theory is utilized to analyze hydrodynamic effects within the narrow gap between a flat interface and a small swimmer. By using an archetypal low-Reynolds-number swimming model called “squirmer,” we find that the magnitude of the vertical swimming velocity is on the order of $O\left(\epsilon \ln \epsilon \right)$, where $\epsilon$ is the ratio of the gap width to the swimmer's body size. The reduced swimming velocity near an interface can explain experimental observations of the aggregation of microorganisms near a liquid interface.

This article addresses the short-term decay of advecting-diffusing scalar fields in Stokes flows. The analysis is developed in two main subparts. In the first part, we present an analytic approach for a class of simple flow systems expressed mathematically by the one-dimensional advection-diffusion equation $w\left(y\right){\partial }_{\xi }\varphi =\varepsilon {\partial }_y^2\varphi +iV\left(y\right)\varphi -{\varepsilon }^{\prime }\varphi$, where $\xi$ is either time or axial coordinate and $iV\left(y\right)$ an imaginary potential. This class of systems encompasses both open- and closed-flow models and corresponds to the dynamics of a single Fourier mode in parallel flows. We derive an analytic expression for the short-time (short-length) decay of $\varphi$, and show that this decay is characterized by a universal behavior that depends solely on the singularity of the ratio of the transverse-to-axial velocity components $V_{\mathrm{eff}}\left(y\right)=V\left(y\right)/w\left(y\right)$, corresponding to the effective potential in the imaginary potential formulation. If $V_{\mathrm{eff}}\left(y\right)$ is smooth, then ${\left|\right|\varphi \left|\right|}_{L^2}\left(\xi \right)=\exp (-{\varepsilon }^{\prime }\xi -b{\xi }^3)$, where $b>0$ is a constant. Conversely, if the effective potential is singular, then ${\left|\right|\varphi \left|\right|}_{L^2}\left(\xi \right)=1-a{\xi }^{\nu }$ with $a>0$. The exponent $\nu$ attains the value $\frac{5}{3}$ at the very early stages of the process, while for intermediate stages its value is $\frac{3}{5}$. By summing over all of the Fourier modes, a stretched exponential decay is obtained in the presence of nonimpulsive initial conditions, while impulsive conditions give rise to an early-stage power-law behavior. In the second part, we consider generic, chaotic, and nonchaotic autonomous Stokes flows, providing a kinematic interpretation of the results found in the first part. The kinematic approach grounded on the warped-time transformation complements the analytical theory developed in the first part.

We study the deformation of a cavity around a large projectile moving with subsonic velocity in the cloud of small dust particles. To solve this problem, we employ the Navier-Stokes equation for a compressible fluid with due regard for friction between dust particles and atoms of neutral gas. The solution shows that due to friction, the pressure of a dust cloud at the surface of a cavity around the projectile can become negative, which entails the emergence of a considerable asymmetry of the cavity, i.e., the cavity deformation. Corresponding threshold velocity is calculated, which is found to decrease with increasing cavity size. Measurement of such velocity makes it possible to estimate the static pressure inside the dust cloud.

We describe a series of experiments on dust particles’ flows in a positive column of a horizontal dc discharge operating in laboratory and microgravity conditions. The main observation is that the particle flow velocities in laboratory experiments are systematically higher than in microgravity experiments for otherwise identical discharge conditions. The paper provides an explanation for this interesting and unexpected observation. The explanation is based on a physical model, which properly takes into account main plasma-particle interaction mechanisms relevant to the described experimental study. A comparison of experimentally measured particle velocities and those calculated using the proposed model demonstrates reasonable agreement, both in laboratory and microgravity conditions, in the entire range of discharge parameters investigated.

We consider developed turbulence in the Gross-Pitaevsky model, where a condensate appears due to an inverse cascade. Despite being fully turbulent, the system demonstrates nondecaying periodic oscillations around a steady state, when turbulence and condensate periodically exchange a small fraction of waves. We show that these collective oscillations are not of a predator-prey type, as was suggested earlier; rather, they are due to phase coherence and anomalous correlations imposed by the condensate.

Large-scale, time-asymptotic dispersion properties of diffusing tracers dragged by a uniform drive through a two-dimensional periodic lattice of hard-wall symmetric potentials are investigated. Dispersion is quantified by a typically anisotropic effective diffusivity tensor $\mathbb{D}$, whose eigenvalues and eigenvectors depend on the dimensionless bare diffusivity $1/\mathrm{Pe}$ for each given lattice geometry. Attention is focused on critical lattice geometries yielding sustained macroscale dispersion ${\mathcal{D}}_{\perp }$ along the direction orthogonal to the uniform drive in the limit where $\mathrm{Pe}\to \infty$. A simple one-dimensional model is proposed, which predicts the anomalous scaling ${\mathcal{D}}_{\perp }\sim 1/[A_1+A_2\log \left(\mathrm{Pe}\right)]$.

The ion-ion coupling parameter $\Gamma$ is estimated for tungsten along the $\rho =40$ g/cm${}^3$  isochore corresponding to twice the normal density with temperatures ranging from 10 eV to 5 keV. Using a variety of approaches from a spherical Thomas-Fermi ion to a full three-dimensional orbital-free method, we show that along an isochore the effective ionic coupling parameter is almost constant over a wide range of temperatures (in our case $\Gamma \simeq 20$) due to the competition between rising temperatures and increased ionization. This $\Gamma$-plateau effect depends on the chosen density and is well delineated at normal density but almost disappears at five times the normal density. This effect could be used to obtain well-defined and predictable experimental conditions.

We study a nonconserved one-dimensional stochastic process which involves two species of particles $A$ and $B$. The particles diffuse asymmetrically and react in pairs as $A\varnothing \leftrightarrow AA\leftrightarrow BA\leftrightarrow A\varnothing$ and $B\varnothing \leftrightarrow BB\leftrightarrow AB\leftrightarrow B\varnothing$. We show that the stationary state of the model can be calculated exactly by using matrix product techniques. The model exhibits a phase transition at a particular point in the phase diagram which can be related to a condensation transition in a particular zero-range process. We determine the corresponding critical exponents and provide a heuristic explanation for the unusually strong corrections to scaling seen in the vicinity of the critical point.

We perform large-scale event-driven molecular dynamics (MD) simulations for granular gases of particles interacting with the impact-velocity-dependent restitution coefficient $\varepsilon \left(v_{\mathrm{imp}}\right)$. We use $\varepsilon \left(v_{\mathrm{imp}}\right)$ as it follows from the simplest first-principles collision model of viscoelastic spheres. Both cases of force-free and uniformly heated gases are studied. We formulate a simplified model of an effective constant restitution coefficient ${\varepsilon }_{\mathrm{eff}}$, which depends on a current granular temperature, and we compute ${\varepsilon }_{\mathrm{eff}}$ using the kinetic theory. We develop a theory of the velocity distribution function for driven gases of viscoelastic particles and analyze the evolution of granular temperature and of the Sonine coefficients, which characterize the form of the velocity distribution function. We observe that for not large dissipation the simulation results are in an excellent agreement with the theory for both the homogeneous cooling state and uniformly heated gases. At the same time, a noticeable discrepancy between the theory and MD results for the Sonine coefficients is detected for large dissipation. We analyze the accuracy of the simplified model based on the effective restitution coefficient ${\varepsilon }_{\mathrm{eff}}$, and we conclude that this model can accurately describe granular temperature. It provides also an acceptable accuracy for the velocity distribution function for small dissipation, but it fails when dissipation is large.

Nucleation is an out-of-equilibrium process that can be strongly affected by the presence of external fields. In this paper, we report a simple extension of classical nucleation theory to systems submitted to an homogeneous shear flow. The theory involves accounting for the anisotropy of the critical nucleus formation and introduces a shear-rate-dependent effective temperature. This extended theory is used to analyze the results of extensive molecular dynamics simulations that explore a broad range of shear rates and undercoolings. At fixed temperature, a maximum in the nucleation rate is observed, when the relaxation time of the system is comparable to the inverse shear rate. In contrast to previous studies, our approach does not require a modification of the thermodynamic description, as the effect of shear is mainly embodied into a modification of the kinetic prefactor and of the temperature.

Magnetophoresis (the motion of magnetic particles driven by the nonuniform magnetic field), that for a long time has been used for extracting magnetically susceptible objects in diverse industries, now attracts interest to develop more sophisticated microfluidic and batch techniques for separation and manipulation of biological particles, and magnetically assisted absorption and catalysis in organic chemistry, biochemistry, and petrochemistry. A deficiency of magnetic separation science is the lack of simple analytical models imitating real processes of magnetic separation. We have studied the motion of superparamagnetic (generally, soft magnetic) particles in liquid in the three-dimensional field of the diametrically polarized permanent cylindrical magnet; this geometry is basically representative of the batch separation mode. In the limit of the infinite-length magnet, we found the particle magnetophoresis proceeds independently of the magnet polarization direction, following the simple analytical relation incorporating all the relevant physical and geometrical parameters of the particle-magnet system. In experiments with a finite-length magnet we have shown applicability of the developed theory as to analyze the performance of the real batch separation systems in the noncooperative mode, and finally, we have presented an example of such analysis for the case of immunomagnetic cell separation and developed a criterion of the model limitation imposed by the magnetic aggregation of particles.

We use colloidal-probe atomic force microscope (AFM) to study the rheological behavior of polymer solutions confined between two surfaces: the surface of a sphere and a flat surface on which the fluid is deposited. Measurements of the hydrodynamic force exerted on the sphere by the flowing liquid allowed retrieving the viscosity of the solution for different distances between the sphere and the flat surface. This method has been experimentally tested for Newtonian fluids for which the viscosity does not vary versus the gap dimensions. On the other hand, for non-Newtonian fluids, such as the large molecular weight polymer solutions used here, the measured viscosity depends on the gap height $D$ between the flat surface and the sphere. The decrease of the viscosity versus gap height is similar to previously observed variations in colloidal suspensions. Depletion of polymers in the gap region due to the high shear rates involved is a possible cause for such a variation.

Binding free energy is the most important physical parameter that describes the binding affinity of a receptor-ligand complex. Conventionally, it was obtained based on the thermodynamic cycle or alchemical reaction. These strategies have been widely used, but they would be problematic if the receptors and/or ligands have large conformational changes during the binding processes. In this paper, we present a way to calculate the binding free energy: constrained dynamics along a fragmental and high-dimensional transition path. This method directly considers unbound states in the simulation. The application to the calmodulin loop-calcium complexes shows that it is practical and the calculated relative binding affinities are in good agreement with experimental results.

There is growing interest in multiplex networks where individual nodes take part in several layers of networks simultaneously. This is the case, for example, in social networks where each individual node has different kinds of social ties or transportation systems where each location is connected to another location by different types of transport. Many of these multiplexes are characterized by a significant overlap of the links in different layers. In this paper we introduce a statistical mechanics framework to describe multiplex ensembles. A multiplex is a system formed by $N$ nodes and $M$ layers of interactions where each node belongs to the $M$ layers at the same time. Each layer $\alpha$ is formed by a network $G^{\alpha }$. Here we introduce the concept of correlated multiplex ensembles in which the existence of a link in one layer is correlated with the existence of a link in another layer. This implies that a typical multiplex of the ensemble can have a significant overlap of the links in the different layers. Moreover, we characterize microcanonical and canonical multiplex ensembles satisfying respectively hard and soft constraints and we discuss how to construct multiplexes in these ensembles. Finally, we provide the expression for the entropy of these ensembles that can be useful to address different inference problems involving multiplexes.

Here we consider the topological properties of the integrated networks emerging from the activity-driven model [N. Perra et al., Sci. Rep. 2, 469 (2012)], a temporal network model recently proposed to explain the power-law degree distribution empirically observed in many real social networks. By means of a mapping to a hidden-variable network model, we provide analytical expressions for the main topological properties of the integrated network, depending on the integration time and the distribution of activity potential characterizing the model. The expressions obtained, exacts in some cases, the results of controlled asymptotic expansions in others, are confirmed by means of extensive numerical simulations. Our analytical approach, which highlights the differences of the model with respect to the empirical observations made in real social networks, can be easily extended to deal with improved, more realistic modifications of the activity-driven network paradigm.

We present a theoretical study of surface proton mobility at a minimally hydrated array of protogenic surface groups. At dense packing, the array assembles into a 2D bicomponent lattice that is formed by sulfonate anions, which are only allowed to fluctuate about fixed equilibrium positions, and mobile hydronium ions. Proton transport on the lattice proceeds by collective translocations of hydronium ions. This type of motion is described within the framework of soliton theory. Our main objective in this article is to establish the relation between microscopic surface structure and effective proton mobility. To this end, we present an approach to calculate microscopic interaction parameters that determine hydronium ion motion. The developed formalism enables us to theoretically derive an expression for soliton mobility at a given surface structure and compare it with experimentally measured mobilities.

The social force model of Helbing and Molnár is one of the best known approaches to simulate pedestrian motion, a collective phenomenon with nonlinear dynamics. It is based on the idea that the Newtonian laws of motion mostly carry over to pedestrian motion so that human trajectories can be computed by solving a set of ordinary differential equations for velocity and acceleration. The beauty and simplicity of this ansatz are strong reasons for its wide spread. However, the numerical implementation is not without pitfalls. Oscillations, collisions, and instabilities occur even for very small step sizes. Classic solution ideas from molecular dynamics do not apply to the problem because the system is not Hamiltonian despite its source of inspiration. Looking at the model through the eyes of a mathematician, however, we realize that the right hand side of the differential equation is nondifferentiable and even discontinuous at critical locations. This produces undesirable behavior in the exact solution and, at best, severe loss of accuracy in efficient numerical schemes even in short range simulations. We suggest a very simple mollified version of the social force model that conserves the desired dynamic properties of the original many-body system but elegantly and cost efficiently resolves several of the issues concerning stability and numerical resolution.