The local heating of a selected region in a double-well potential alters the relative stability of the two wells and gives rise to an enhancement of population transfer to the cold well. We show that this Landauer's blowtorch effect may be considered in the spirit of a thermodynamic cross process linearly connecting the flux of particles and the thermodynamic force associated with the temperature difference and consequently ensuring the existence of a reverse cross effect. This reverse effect is realized by directing the thermalized particles in a double-well potential by application of an external bias from one well to the other, which suffers cooling.

In the lattice version of the multicomponent Widom-Rowlinson (WR) model, each site can be either empty or singly occupied by one of $M$ different particles, all species having the same fugacity $z$. The only nonzero interaction potential is a nearest-neighbor hard-core exclusion between unlike particles. For $M<M_0$ with some minimum $M_0$ dependent on the lattice structure, as $z$ increases from 0 to $\infty$ there is a direct transition from the disordered (gas) phase to a demixed (liquid) phase with one majority component at $z>z_d\left(M\right)$. If $M\ge M_0$, there is an intermediate ordered “crystal phase” (composed of two nonequivalent even and odd sublattices) for $z$ lying between $z_c\left(M\right)$ and $z_d\left(M\right)$ which is driven by entropy. We generalize the multicomponent WR model by replacing the hard-core exclusion between unlike particles by more realistic large (but finite) repulsion. The model is solved exactly on the Bethe lattice with an arbitrary coordination number. The numerical calculations, based on the corner transfer matrix renormalization group, are performed for the two-dimensional square lattice. The results for $M=4$ indicate that the second-order phase transitions from the disordered gas to the demixed phase become of first order, for an arbitrarily large finite repulsion. The results for $M\ge M_0$ show that, as the repulsion weakens, the region of the crystal phase diminishes itself. For weak enough repulsions, the direct transition between the crystal and demixed phases changes into a separate pair of crystal-gas and gas-demixed transitions; this is an example of a disorder-disorder reentrant transition via an ordered crystal phase. If the repulsion between unlike species is too weak, the crystal phase disappears from the phase diagram. It is shown that the generalized WR model belongs to the Ising universality class.

Diffusion of colloidal particles in a complex environment such as polymer networks or biological cells is a topic of high complexity with significant biological and medical relevance. In such situations, the interaction between the surroundings and the particle motion has to be taken into account. We analyze a simplified diffusion model that includes some aspects of a complex environment in the framework of a nonlinear friction process: at low particle speeds, friction grows linearly with the particle velocity as for regular viscous friction; it grows more than linearly at higher particle speeds; finally, at a maximum of the possible particle speed, the friction diverges. In addition to bare diffusion, we study the influence of a constant drift force acting on the diffusing particle. While the corresponding stationary velocity distributions can be derived analytically, the displacement statistics generally must be determined numerically. However, as a benefit of our model, analytical progress can be made in one case of a special maximum particle speed. The effect of a drift force in this case is analytically determined by perturbation theory. It will be interesting in the future to compare our results to real experimental systems. One realization could be magnetic colloidal particles diffusing through a shear-thickening environment such as starch suspensions, possibly exposed to an external magnetic field gradient.

Liquids are condensed matter in which atoms are strongly correlated in position and momentum. The atomic pair density function (PDF) is used often in describing such correlation. However, elucidation of many properties requires higher degrees of correlation than the pair correlation. For instance, viscosity depends upon the stress correlations in space and time. In this paper, we examine the cross correlation between the stress correlation at the atomic level and the PDF for two-dimensional liquids. We introduce the concept of the stress-resolved pair distribution function (SRPDF) that uses the sign of atomic-level stress as a selection rule to include particles from density correlations. The connection between SRPDFs and stress correlation function is explained through an approximation in which the shear stress is replaced by a pseudospin. We further assess the possibility of interpreting the long-range stress correlation as a consequence of short-range Ising-like pseudospin interactions.

While biological studies suggest that motility of cells is involved in cell segregation, few computational models have investigated this mechanism. We apply a simple Schelling model, modified to reflect biological conditions, demonstrating how differences in cell motility arising exclusively from differences in the composition of the local environment can be sufficient to drive segregation. The work presented here demonstrates that the segregation behavior observed in the original Schelling model is robust to a relaxation of the requirement for global information and that the Schelling model may yield insight in the context of biological systems. In the model, the time course of cell segregation follows a power law in accord with experimental observations and previous work.

In spin systems, the decay of the Loschmidt echo in the time-reversal experiment (evolution–perturbation–time-reversed evolution) is linked to the generation of multiple-quantum (MQ) coherences. Unlimited growth of the MQ coherences leads to irreversibility of dynamics. In some cases, one can expect that the deviation of the Loschmidt echo and the second moment of the MQ intensities distribution are linear in time. The criteria of such behavior, called weak irreversibility, are formulated. The proposed approach can be extended beyond spin systems, in order to analyze some general aspects of reversibility of many-body quantum dynamics.

Information theoretic geometry near critical points in classical and quantum systems is well understood for exactly solvable systems. Here, we show that renormalization group flow equations can be used to construct the information metric and its associated quantities near criticality for both classical and quantum systems in a universal manner. We study this metric in various cases and establish its scaling properties in several generic examples. Scaling relations on the parameter manifold involving scalar quantities are studied, and scaling exponents are identified. The meaning of the scalar curvature and the invariant geodesic distance in information geometry is established and substantiated from a renormalization group perspective.

The electrophoretic mobility of molecules such as $\lambda$-DNA depends on the conformation of the molecule. It has been shown that electrohydrodynamic interactions between parts of the molecule lead to a mobility that depends on conformation and can explain some experimental observations. We have developed a new coarse-grained model that incorporates these changes of mobility into a bead-spring chain model. Brownian dynamics simulations have been performed using this model. The model reproduces the cross-stream migration that occurs in capillary electrophoresis when pressure-driven flow is applied parallel or antiparallel to the electric field. The model also reproduces the change of mobility when the molecule is stretched significantly in an extensional field. We find that the conformation-dependent mobility can lead to a new type of unraveling of the molecule in strong fields. This occurs when different parts of the molecule have different mobilities and the electric field is large.

Transport of fluids and particles at the microscale is an important theme in both fundamental and applied science. One of the most successful approaches is to use an electric field, which requires the system to carry or induce electric charges. We describe a versatile approach to generate electrokinetic flows by using a liquid crystal (LC) with surface-patterned molecular orientation as an electrolyte. The surface patterning is produced by photoalignment. In the presence of an electric field, the spatially varying orientation induces space charges that trigger flows of the LC. The active patterned LC electrolyte converts the electric energy into the LC flows and transport of embedded particles of any type (fluid, solid, gaseous) along a predesigned trajectory, posing no limitation on the electric nature (charge, polarizability) of these particles and interfaces. The patterned LC electrolyte exhibits a quadratic field dependence of the flow velocities; it induces persistent vortices of controllable rotation speed and direction that are quintessential for micro- and nanoscale mixing applications.

One-dimensional sliding along DNA as a means to accelerate protein target search is a well-known phenomenon occurring in various biological systems. Using a biomimetic approach, we have recently demonstrated the practical use of DNA-sliding peptides to speed up bimolecular reactions more than an order of magnitude by allowing the reactants to associate not only in the solution by three-dimensional (3D) diffusion, but also on DNA via one-dimensional (1D) diffusion [A. Turkin et al., Chem. Sci. (2015)]. Here we present a mean-field kinetic model of a bimolecular reaction in a solution with linear extended sinks (e.g., DNA) that can intermittently trap molecules present in a solution. The model consists of chemical rate equations for mean concentrations of reacting species. Our model demonstrates that addition of linear traps to the solution can significantly accelerate reactant association. We show that at optimum concentrations of linear traps the 1D reaction pathway dominates in the kinetics of the bimolecular reaction; i.e., these 1D traps function as an assembly line of the reaction product. Moreover, we show that the association reaction on linear sinks between trapped reactants exhibits a nonclassical third-order behavior. Predictions of the model agree well with our experimental observations. Our model provides a general description of bimolecular reactions that are controlled by a combined 3D+1D mechanism and can be used to quantitatively describe both naturally occurring as well as biomimetic biochemical systems that reduce the dimensionality of search.

Vesicles and many biological membranes are made of two monolayers of lipid molecules and form closed lipid bilayers. The dynamical behavior of vesicles is very complex and a variety of forms and shapes appear. Lipid bilayers can be considered as a surface fluid and hence the governing equations for the evolution include the surface (Navier-)Stokes equations, which in particular take the membrane viscosity into account. The evolution is driven by forces stemming from the curvature elasticity of the membrane. In addition, the surface fluid equations are coupled to bulk (Navier-)Stokes equations. We introduce a parametric finite-element method to solve this complex free boundary problem and present the first three-dimensional numerical computations based on the full (Navier-)Stokes system for several different scenarios. For example, the effects of the membrane viscosity, spontaneous curvature, and area difference elasticity (ADE) are studied. In particular, it turns out, that even in the case of no viscosity contrast between the bulk fluids, the tank treading to tumbling transition can be obtained by increasing the membrane viscosity. Besides the classical tank treading and tumbling motions, another mode (called the transition mode in this paper, but originally called the vacillating-breathing mode and subsequently also called trembling, transition, and swinging mode) separating these classical modes appears and is studied by us numerically. We also study how features of equilibrium shapes in the ADE and spontaneous curvature models, like budding behavior or starfish forms, behave in a shear flow.

We study the generalized synchronization and its stability using the master stability function (MSF) in a network of coupled nearly identical dynamical systems. We extend the MSF approach for the case of degenerate eigenvalues of the coupling matrix. Using the MSF we study the size instability in star and ring networks for coupled nearly identical dynamical systems. In the star network of coupled Rössler systems we show that the critical size beyond which synchronization is unstable can be increased by having a larger frequency for the central node of the star. For the ring network we show that the critical size is not significantly affected by parameter variations. The results are verified by explicit numerical calculations.

This work is dedicated to the energy decomposition analysis of a viscous free-surface flow. In the presence of a free surface, the viscous dissipation for a Newtonian liquid can be decomposed into two terms: an enstrophy component and a free-surface deformation component. The latter requires the evaluation of volume and surface integrals in the meshless framework. The analysis is based on the weakly compressible smoothed particle hydrodynamics formalism. The behavior of the energy terms is studied in standing wave problems by changing the viscosity and the wave amplitude. Finally, an analysis of a complex shallow water breaking wave case is provided. It is shown that in presence of intense breaking phenomena the two energy components are always comparable, whereas generally the free surface component is dominant on the viscous dissipation of gravity waves.

A small mismatch between natural frequencies of unidirectionally coupled chaotic oscillators can induce coherence resonance in the slave oscillator for a certain coupling strength. This surprising phenomenon resembles “stabilization of chaos by chaos,” i.e., the chaotic driving applied to the chaotic system makes its dynamics more regular when the natural frequency of the slave oscillator is a little different than the natural frequency of the master oscillator. The coherence is characterized with the dominant component in the power spectrum of the slave oscillator, normalized standard deviations of both the peak amplitude and the interpeak interval, and Lyapunov exponents. The enhanced coherence is associated with increasing negative both the third and the fourth Lyapunov exponents, while the first and second exponents are always positive and zero, respectively.

We report experimental studies on the Saturn ring defect associated with a spherical microparticle across the nematic $\left(N\right)$ to smectic-$A$ $\left(\mathrm{Sm}A\right)$ phase transition. We observe that the director distortion around the microparticle changes rapidly with temperature. The equilibrium interparticle separation and the angle between two quadrupolar particles in the $N$ phase are larger than those of the $\mathrm{Sm}A$ phase. They are almost independent of the temperature in both phases, except for a discontinuous jump at the transition. We assembled a few particles using a laser tweezer to form a two-dimensional colloidal crystal in the $N$ phase. The lattice structure of the crystal dissolves irreversibly across the $N-\mathrm{Sm}A$ phase transition. The results on the pretransitional behavior of the defect are supported by the Landau–de Gennes $Q$-tensor modeling.

The course of a peritrichous bacterium, such as E. coli, crucially depends on the level of synchronization and self-organization of several rotating flagella. However, the rotation of each flagellum generates countermovements of the body which in turn affect the flagellar dynamics. Using a detailed numerical model of an E. coli, we demonstrate that flagellar entanglement, besides fluid flow relative to the moving body, dramatically changes the dynamics of flagella from that compared to anchored flagella. In particular, bundle formation occurs through a zipping motion in a remarkably rapid time, affected little by initial flagellar orientation. A simplified analytical model supports our observations. Finally, we illustrate how entanglement, hydrodynamic interactions, and body movement contribute to zipping and bundling.

An efficient searcher needs to balance properly the trade-off between the exploration of new spatial areas and the exploitation of nearby resources, an idea which is at the core of scale-free Lévy search strategies. Here we study multiscale random walks as an approximation to the scale-free case and derive the exact expressions for their mean-first-passage times in a one-dimensional finite domain. This allows us to provide a complete analytical description of the dynamics driving the situation in which both nearby and faraway targets are available to the searcher, so the exploration-exploitation trade-off does not have a trivial solution. For this situation, we prove that the combination of only two movement scales is able to outperform both ballistic and Lévy strategies. This two-scale strategy involves an optimal discrimination between the nearby and faraway targets which is only possible by adjusting the range of values of the two movement scales to the typical distances between encounters. So, this optimization necessarily requires some prior information (albeit crude) about target distances or distributions. Furthermore, we found that the incorporation of additional (three, four, …) movement scales and its adjustment to target distances does not improve further the search efficiency. This allows us to claim that optimal random search strategies arise through the informed combination of only two walk scales (related to the exploitative and the explorative scales, respectively), expanding on the well-known result that optimal strategies in strictly uninformed scenarios are achieved through Lévy paths (or, equivalently, through a hierarchical combination of multiple scales).

We use a popular fictional disease, zombies, in order to introduce techniques used in modern epidemiology modeling, and ideas and techniques used in the numerical study of critical phenomena. We consider variants of zombie models, from fully connected continuous time dynamics to a full scale exact stochastic dynamic simulation of a zombie outbreak on the continental United States. Along the way, we offer a closed form analytical expression for the fully connected differential equation, and demonstrate that the single person per site two dimensional square lattice version of zombies lies in the percolation universality class. We end with a quantitative study of the full scale US outbreak, including the average susceptibility of different geographical regions.

In statistical data assimilation one evaluates the conditional expected values, conditioned on measurements, of interesting quantities on the path of a model through observation and prediction windows. This often requires working with very high dimensional integrals in the discrete time descriptions of the observations and model dynamics, which become functional integrals in the continuous-time limit. Two familiar methods for performing these integrals include (1) Monte Carlo calculations and (2) variational approximations using the method of Laplace plus perturbative corrections to the dominant contributions. We attend here to aspects of the Laplace approximation and develop an annealing method for locating the variational path satisfying the Euler-Lagrange equations that comprises the major contribution to the integrals. This begins with the identification of the minimum action path starting with a situation where the model dynamics is totally unresolved in state space, and the consistent minimum of the variational problem is known. We then proceed to slowly increase the model resolution, seeking to remain in the basin of the minimum action path, until a path that gives the dominant contribution to the integral is identified. After a discussion of some general issues, we give examples of the assimilation process for some simple, instructive models from the geophysical literature. Then we explore a slightly richer model of the same type with two distinct time scales. This is followed by a model characterizing the biophysics of individual neurons.

This article examines the hydrodynamic stability of various homogeneous three-dimensional flow topologies. The influence of inertial and pressure effects on the stability of flows undergoing strain, rotation, convergence, divergence, and swirl are isolated. In marked contrast to two-dimensional topologies, for three-dimensional flows the inertial effects are always destabilizing, whereas pressure effects are always stabilizing. In streamline topologies with a negative velocity-gradient third invariant, inertial effects prevail leading to instability. Vortex-stretching is identified as the underlying instability mechanism. In flows with positive velocity-gradient third derivative, pressure overcomes inertial effects to stabilize the flow.