A significant decrease in the diffusivity of phospholipid molecules at an aqueous-oil monolayer was observed experimentally when the bathing solutions had different viscosities ${\eta }_1\ne {\eta }_2$. Near the point of isoviscosity ${\eta }_1\approx {\eta }_2$, the diffusion constant at the monolayer can be drastically affected by a slight change in the viscosity mismatch. We interpreted this phenomenon by considering the effect of vertical fluctuations which affect the long-term dynamics of two-dimensional lateral diffusion at the monolayer.

We present a sufficient condition for the presence of spontaneous magnetization for the Ising model on a general graph, related to its long-range topology. Applying this condition we are able to prove the existence of a phase transition at temperature $T>0$ on a wide class of general networks. The possibility of further extensions of our results is discussed.

We investigate the stationary spectral density of fractional bistable Klein-Kramers systems. First, we deduce a dissipation-fluctuation relation between the stationary spectral density at thermal equilibrium and the linear response of the system to an applied perturbation. Second, we describe how to obtain the linear dynamic susceptibility from the method of moments, and thus we derive the fluctuating spectral density from the dissipation-fluctuation relation. Finally, we exhibit the structure of this fluctuating spectral distribution and explore the effect of the subdiffusion on it. Compared with the standard bistable Klein-Kramers systems, our observation on the spectral distribution in fractional systems reveals that the subdiffusion weakens the oscillatory components of the intrawell oscillation and the above-barrier motion. This phenomenon should reflect a fact that the particles tend to stand still in separate wells in subdiffusive processes.

Transport of Brownian particles in a two-dimensional asymmetric tube is investigated by applying a polarized field. From the Brownian dynamics simulations, we find that the longitudinal current can be enhanced remarkably by applying a weakly transversal drive. Multiple current reversals can be realized by altering the driving frequency of the polarized field. By coupling the longitudinal and transversal forces together, one can control the particle transport flexibly.

It is an ever-growing challenge to develop nanodevices for controlling energy transport. An open question is whether we can create and control heat current at strict zero thermal bias, and if yes, how to do it. In this paper, we demonstrate that a nonlinear asymmetric system, when pushed out of equilibrium, can produce heat current in the absence of a thermal bias. The emergence and control of heat current over a broad range of parameters are studied. Our results reveal the following three necessary conditions: nonequilibrium source, symmetry breaking, and nonlinearity. We also demonstrate that when heat baths are correlated, symmetry breaking is sufficient to generate heat current.

In this paper a renormalization group (RG) scheme for the $q$-state Manna model is proposed based on the stochastic characteristic and the similarity of topplings at different scales. A full enumeration of the RG evolution events inside a $2\times 2$ RG cell for $q=2$, 3, and 4 was carried out. A fixed point analysis shows that the resulting height probabilities are very close to the results obtained by the numerical simulations. The calculations of the toppling number exponent $\tau$ and the dynamical exponent $z$ are also provided. It was found that the RG values of $\tau$ and $z$ for $q=4$ are very close to the simulation values.

We study the flow of a typical thixotropic material subjected to very different deformation histories (squeeze, shear, and extrusion) with either local (proton NMR and magnetic resonance imaging) or macroscopic measurements after different times of rest. Specifically, we measure the velocity fields and the spin-spin NMR relaxation of the material after different flow histories. The relaxation data exhibits a long relaxing component revealing information about the reversible microstructural evolution of the sample during aging-rejuvenation cycles. We show that for each deformation process, the evolution of the viscosity during the solid-liquid transition is similar by a factor related to the initial state of the material. Moreover, results examining the impact of the rate at which the deformation is imposed suggest that the state of the material during this transition may be described by a single parameter reflecting the average size and deformation of the material’s flocs. These results also show that localization of flow occurs as a result of a progressive differential evolution of the material in different regions of the flow, and thus are determined by the boundary conditions of the flow.

Recent experiments have shown that the striking structure formation in dewetting films of evaporating colloidal nanoparticle suspensions occurs in an ultrathin “postcursor” layer that is left behind by a mesoscopic dewetting front. Various phase change and transport processes occur in the postcursor layer that may lead to nanoparticle deposits in the form of labyrinthine, network, or strongly branched “finger” structures. We develop a versatile dynamical density functional theory to model this system which captures all these structures and may be employed to investigate the influence of evaporation or condensation, nanoparticle transport, and solute transport in a differentiated way. We highlight, in particular, the influence of the subtle interplay of decomposition in the layer and contact line motion on the observed particle-induced transverse instability of the dewetting front.

We study the manner in which the effect of quasiperiodic modulation is transmitted in a coupled nonlinear dynamical system. A system of Rössler oscillators is considered, one of which is subject to driving, and the dynamics of other oscillators which are, in effect, indirectly forced is observed. Strange nonchaotic dynamics is known to arise only in quasiperiodically driven systems, and thus the transmitted effect is apparent when such motion is seen in subsystems that are not directly modulated. We also find instances of imperfect phase synchronization with forcing, where the system transits from one phase synchronized state to another, with arbitrary phase slips. The stability of phase synchrony for arbitrary initial conditions with identical forcing is observed as a general property of strange nonchaotic motion.

Adaptation to environmental change is a common property of biological systems. Cells initially respond to external changes in the environment, but after some time, they regain their original state. By considering an element consisting of two variables that show such adaptation dynamics, we studied a coupled dynamical system containing such elements to examine the diverse dynamics in the system and classified the behaviors on the basis of the network structure that determined the interaction among elements. For a system with two elements, two types of behaviors, perfect adaptation and simple oscillation, were observed. For a system with three elements, in addition to these two types of dynamics, rapid-burst-type oscillation and a slow cycle were discovered; depending on the initial conditions, these two types of dynamics coexisted. These behaviors are a result of the characteristic dynamics of each element, i.e., fast response and slow adaptation processes. The behaviors depend on the network structure (in specific, a combination of positive or negative feedback among elements). Cooperativity among elements due to a positive feedback loop leads to simple oscillation, whereas frustration involving alternating positive and negative interactions among elements leads to the coexistence of rapid bursting oscillation and a slow cycle. These behaviors are classified on the basis of the frustration indices defined by the network structure. The period of the slow cycle is much longer than the original adaptation time scale, while the burst-type oscillation is a continued response that does not involve any adaptation. We briefly discuss the universal applicability of our results to a network of a larger number of elements and their possible relevance to biological systems.

The experimental data presented in this paper address the energy loss determination for argon at 4 MeV/u projectile energy in laser-generated carbon plasma covering a huge parameter range in density and temperature. Furthermore, a consistent theoretical description of the projectile charge state evolution via a Monte Carlo code is combined with an improved version of the CasP code that allows us to calculate the contributions to the stopping power of bound and free electrons for each projectile charge state. This approach gets rid of any effective charge description of the stopping power. Comparison of experimental data and theoretical results allows us to judge the influence of different plasma parameters.

In this work, closure of the Boltzmann–Bhatnagar-Gross-Krook (Boltzmann-BGK) moment hierarchy is accomplished via projection of the distribution function $f$ onto a space ${\mathbb{H}}^N$ spanned by $N$-order Hermite polynomials. While successive order approximations retain an increasing number of leading-order moments of $f$, the presented procedure produces a hierarchy of (single) $N$-order partial-differential equations providing exact analytical description of the hydrodynamics rendered by ($N$-order) lattice Boltzmann-BGK (LBBGK) simulation. Numerical analysis is performed with LBBGK models and direct simulation Monte Carlo for the case of a sinusoidal shear wave (Kolmogorov flow) in a wide range of Weissenberg number $\text{Wi}=\tau \nu k^2$ (i.e., Knudsen number $\text{Kn}=\lambda k=\sqrt{\text{Wi}}$); $k$ is the wave number, $\tau$ is the relaxation time of the system, and $\lambda \simeq \tau c_s$ is the mean-free path, where $c_s$ is the speed of sound. The present results elucidate the applicability of LBBGK simulation under general nonequilibrium conditions.

The strong-friction regime at low temperatures is analyzed systematically starting from the formally exact path-integral expression for the reduced dynamics. This quantum Smoluchowski regime allows for a type of semiclassical treatment in the inverse friction strength so that higher-order quantum corrections to the original quantum Smoluchowski equation [J. Ankerhold, P. Pechukas, and H. Grabert, Phys. Rev. Lett. 87, 086802 (2001); J. Ankerhold and H. Grabert, Phys. Rev. Lett. 101, 119903 (2008)] can be derived. Drift and diffusion coefficients are determined by the equilibrium distribution in position and are directly related to the corresponding action of extremal paths and fluctuations around them. It is shown that the inclusion of higher-order corrections reproduces the quantum enhancement above crossover for the decay rate out of a metastable well exactly.

We calculate numerically the normal modes of vibrations in three-dimensional jammed packings of soft spheres as a function of the packing fraction and obtain the energy diffusivity, a spectral measure of transport that controls sound propagation and thermal conductivity. The crossover frequency between weak and strong phonon scattering is controlled by the coordination and shifts to zero as the system is decompressed toward the critical packing fraction at which rigidity is lost. We present a scaling analysis that relates the packing fraction dependence of the crossover frequency to the anomalous scaling of the shear modulus with compression. Below the crossover, the diffusivity displays a power-law divergence with inverse frequency consistent with Rayleigh law, which suggests that the vibrational modes are primarily transverse waves, weakly scattered by disorder. Above it, a large number of modes appear whose diffusivity plateaus at a nearly constant value before dropping to zero above the localization frequency. The thermal conductivity of a marginally jammed solid just above the rigidity threshold is calculated and related to the one measured experimentally at room temperature for most glasses.

Entropy and heat capacity are calculated in phase sequence of crystal, hexatic smectic-$B$, and smectic-$A$ liquid crystals through constant pressure and temperature molecular-dynamics simulations of parallel soft spherocylinders. The transition from crystal to hexatic smectic-$B$ phase is continuous while the transition to smectic-$A$ phase is first order. The dependence of the phase sequence against the molecular shape anisotropy is investigated and there exists a triple point at a rather small anisotropy. Hopping diffusion of molecules is observed in the hexatic smectic-$B$ phase.

By use of the Landau–de Gennes phenomenological theory, we study the texture of a nematic liquid crystal confined within a hybrid cell. Precisely, we consider cylindrically symmetric solutions containing topological defects dictated by appropriate boundary conditions. We focus our attention on cells whose dimensions are comparable with the biaxial correlation length ${\xi }_b$. For such severe confinements the order reconstruction (OR) configuration could be stable. Its structural details reflect the balance among boundary-enforced frustration, elastic penalties, and finite-size effects. In particular, we analyze the interplay between finite-size effects and topological defects. We show that defects are always pinned to the negatively (planar) uniaxial sheet of the OR structure. The presence of a ring defect can dramatically increase the critical threshold below which the OR structure is stable.

Bundles of filamentous polymers are primary structural components of a broad range of cytoskeletal structures, and their mechanical properties play key roles in cellular functions ranging from locomotion to mechanotransduction and fertilization. We give a detailed derivation of a wormlike bundle model as a generic description for the statics and dynamics of polymer bundles consisting of semiflexible polymers interconnected by crosslinking agents. The elastic degrees of freedom include bending as well as twist deformations of the filaments and shear deformation of the crosslinks. We show that a competition between the elastic properties of the filaments and those of the crosslinks leads to renormalized effective bend and twist rigidities that become mode-number dependent. The strength and character of this dependence is found to vary with bundle architecture, such as the arrangement of filaments in the cross section and pretwist. We discuss two paradigmatic cases of bundle architecture, a uniform arrangement of filaments as found in $F$-actin bundles and a shell-like architecture as characteristic for microtubules. Each architecture is found to have its own universal ratio of maximal to minimal bending rigidity, independent of the specific type of crosslink-induced filament coupling; our predictions are in reasonable agreement with available experimental data for microtubules. Moreover, we analyze the predictions of the wormlike bundle model for experimental observables such as the tangent-tangent correlation function and dynamic response and correlation functions. Finally, we analyze the effect of pretwist (helicity) on the mechanical properties of bundles. We predict that microtubules with different number of protofilaments should have distinct variations in their effective bending rigidity.

Appropriate regulation of gene expression is essential to ensure that protein synthesis occurs in a selective manner. The control of transcription is the most dominant type of regulation mediated by a complex of molecules such as transcription factors. In general, regulatory molecules are of two types: activator and repressor. Activators promote the initiation of transcription whereas repressors inhibit transcription. In many cases, they regulate the gene transcription on binding the promoter mutually exclusively and the observed gene expression response is either graded or binary. In experiments, the gene expression response is quantified by the amount of proteins produced on varying the concentration of an external inducer molecules in the cell. In this paper, we study a gene regulatory network where activators and repressors both bind the same promoter mutually exclusively. The network is modeled by assuming that the gene can be in three possible states: repressed, unregulated, and active. An exact analytical expression for the steady-state probability distribution of protein levels is then derived. The exact result helps to explain the experimental observations that in the presence of activator molecules the response is graded at all inducer levels, whereas in the presence of both activator and repressor molecules, the response is graded at low and high inducer levels and binary at an intermediate inducer level.

Prediction of the statistics of scattering in typical wave-chaotic systems requires combining system-specific information with universal aspects of chaotic scattering as described by random matrix theory. This Rapid Communication shows that the average impedance matrix, which characterizes such system-specific properties, can be semiclassically calculated in terms of ray trajectories between ports. Theoretical predictions are compared with experimental results for a microwave billiard, demonstrating that the theory successfully uncovered universal statistics of wave-chaotic scattering systems.

In this Rapid Communication we investigate spatially constrained networks that realize optimal synchronization properties. After arguing that spatial constraints can be imposed by limiting the amount of “wire” available to connect nodes distributed in space, we use numerical optimization methods to construct networks that realize different trade offs between optimal synchronization and spatial constraints. Over a large range of parameters such optimal networks are found to have a link length distribution characterized by power-law tails $P\left(l\right)\propto l^{-\alpha }$, with exponents $\alpha$ increasing as the networks become more constrained in space. It is also shown that the optimal networks, which constitute a particular type of small world network, are characterized by the presence of nodes of distinctly larger than average degree around which long-distance links are centered.