The number of configurations of a polymer is reduced in the presence of a barrier or an obstacle. The resulting loss of entropy adds a repulsive component to other forces generated by interaction potentials. When the obstructions are scale invariant shapes (such as cones, wedges, lines, or planes) the only relevant length scales are the polymer size $R_0$ and characteristic separations, severely constraining the functional form of entropic forces. Specifically, we consider a polymer (single strand or star) attached to the tip of a cone, at a separation $h$ from a surface (or another cone). At close proximity, such that $h\ll R_0$, separation is the only remaining relevant scale and the entropic force must take the form $F=\mathcal{A}{k}_{B}T/h$. The amplitude $\mathcal{A}$ is universal and can be related to exponents $\eta$ governing the anomalous scaling of polymer correlations in the presence of obstacles. We use analytical, numerical, and $\epsilon$-expansion techniques to compute the exponent $\eta$ for a polymer attached to the tip of the cone (with or without an additional plate or cone) for ideal and self-avoiding polymers. The entropic force is of the order of 0.1 pN at 0.1 $\mu$m for a single polymer and can be increased for a star polymer.

The fluxes in transport processes expressed as a time derivative of state variables is a crucial requirement in Onsager's proof of his reciprocal relations, which is a much debated question existing in nonequilibrium thermodynamics. Thermomass theory is used to show that the linear decay of the fluctuation is a balance between the inertial forces and resistant force. Therefore, products of the drift velocities and relaxation times, namely, the displacements from equilibrium, can be used as the state variables, whose time derivatives give the transport fluxes. The Onsager reciprocal relations can be macroscopically derived from the principle that every action has an equal and opposite reaction, applicable in steady nonequilibrium systems and nonlinear couplings.

Recent studies on epistatic networks of model organisms have unveiled a certain type of modular property called monochromaticity in which the networks are clustered into functional modules that interact with each other through the same type of epistasis. Here, we propose and study three epistatic network models that are inspired by the duplication-divergence mechanism to gain insight into the evolutionary basis of monochromaticity and to test if it can be explained as the outcome of a neutral evolutionary hypothesis. We show that the epistatic networks formed by these stochastic evolutionary models have monochromaticity conflict distributions that are centered close to zero and are statistically significantly different from their randomized counterparts. In particular, the last model we propose yields a strictly monochromatic solution. Our results agree with the monochromaticity findings in real organisms and point toward the possible role of a neutral mechanism in the evolution of this phenomenon.

The absorbing-state transition in the three-dimensional contact process with and without quenched randomness is investigated by means of Monte Carlo simulations. In the clean case, a reweighting technique is combined with a careful extrapolation of the data to infinite time to determine with high accuracy the critical behavior in the three-dimensional directed percolation universality class. In the presence of quenched spatial disorder, our data demonstrate that the absorbing-state transition is governed by an unconventional infinite-randomness critical point featuring activated dynamical scaling. The critical behavior of this transition does not depend on the disorder strength, i.e., it is universal. Close to the disordered critical point, the dynamics is characterized by the nonuniversal power laws typical of a Griffiths phase. We compare our findings to the results of other numerical methods, and we relate them to a general classification of phase transitions in disordered systems based on the rare region dimensionality.

We discuss the decoding performance of error-correcting codes based on a model in which quantum fluctuations are introduced by means of a transverse field. The essential issue in this paper is whether quantum fluctuations improve the decoding quality compared with the conventional estimation based on thermal fluctuations, which is called finite-temperature decoding. We found that an estimation incorporating quantum fluctuations approaches the optimal performance of finite-temperature decoding. The results are illustrated by numerically solving saddle-point equations and performing a Monte Carlo simulation. We also evaluated the upper bound of the overlap between the original sequence and the decoded sequence derived from the equations of state for the order parameters, which is a measure of the decoding performance.

This paper considers the time evolution of disperse systems in which binary coagulation is so rapid that it leads to formation of gels during a finite but nonzero interval of time. Right before the transition point an algebraic particle mass spectrum forms whose behavior at small particle masses does not permit one to define the total particle mass concentration as ${\int }_0^{\infty }gc(g,t)dg$, because the integral diverges at low limit. This divergency prevents the formulation of an asymptotic self–similarity spectrum in its traditional form. This difficulty is avoided by introducing the second moment of the particle mass spectrum as a basic scale defining its behavior at the pregelation stage. The equations for the universality mass spectra are formulated. It is shown that these equations correctly reproduce the asymptotic form of the particle mass spectrum for the system with the product kernel. The postcritical behavior in this case is investigated. The time dependencies of the gel mass, the second moment, and particle number concentrations in the postcritical period are found.

We performed numerical simulations of the $q$-state Potts model to compute the reduced conductivity exponent $t/\nu$ for the critical Coniglio-Klein clusters in two dimensions, for values of $q$ in the range $[1,4]$. At criticality, at least for $q<4$, the conductivity scales as $C\left(L\right)\sim L^{-\frac{t}{\nu }}$, where $t$ and $\nu$ are, respectively, the conductivity and correlation length exponents. For $q=1$, 2, 3, and 4, we followed two independent procedures to estimate $t/\nu$. First, we computed directly the conductivity at criticality and obtained $t/\nu$ from the size dependence. Second, using the relation between conductivity and transport properties, we obtained $t/\nu$ from the diffusion of a random walk on the backbone of the cluster. From both methods, we estimated $t/\nu$ to be $0.986\pm 0.012$, $0.877\pm 0.014$, $0.785\pm 0.015$, and $0.658\pm 0.030$, for $q=1$, 2, 3, and 4, respectively. We also evaluated $t/\nu$ for noninteger values of $q$ and propose the conjecture $40gt/\nu =72+20g-3g^2$ for the dependence of the reduced conductivity exponent on $q$, in the range $0⩽q⩽4$, where $g$ is the Coulomb gas coupling.

We investigate a driven, one-dimensional system of colloidal particles in a periodically corrugated narrow channel subject to a time-delayed feedback control. Our goal is to identify conditions under which the control induces oscillatory, time-periodic states. The investigations are based on the Fokker-Planck equation involving the density distribution of the system. First, by using the numerical continuation technique, we determine the linear stability of a stationary density. Second, the nonlinear regimes are analyzed by studying numerically the temporal evolution of the first moment of the density distribution. In this way we construct a bifurcation diagram revealing the nature of the instability. Apart from the case of a system with periodic boundary conditions, we also consider a microchannel of finite length. Finally, we study the influence of (repulsive) particle interactions based on dynamical density functional theory.

Electrochemical deposition (ECD) in thin cells in a vertical position relative to gravity, subject to an external uniform magnetic field, yields a growth pattern formation with dense branched morphology with branches tilted in the direction of the magnetic force. We study the nature of the inclined growth through experiments and theory. Experiments in ECD, in the absence of magnetic forces, reveal that a branch grows by allowing fluid to penetrate its tip and to be ejected from the sides through a pair of symmetric vortices attached to the tip. The upper vortices zone defines an arch separating an inner zone ion depleted and an outer zone in a funnel-like form with a concentrated solution through which metal ions are carried into the tip. When a magnetic field is turned on, vortex symmetry is broken, one vortex becoming weaker than the other, inducing an inclination of the funnel. Consequently, particles entering the funnel give rise to branch growth tilted in the same direction. Theory predicts, in the absence of a magnetic force, funnel symmetry induced through symmetric vortices driven by electric and gravitational forces; when the magnetic force is on, it is composed with the pair of clockwise and counterclockwise vortices, reducing or amplifying one or the other. In turn, funnel tilting modifies particle trajectories, thus, growth orientation.

This work describes an investigation of the static (or quasistatic) nuclear magnetic resonance (NMR) response in a nematic liquid crystal confined between two planar conducting plates and subject to a magnetic field and an electric field produced by a difference of voltage applied on the plates. Deuterium NMR spectroscopy of 4-pentyl-d${}_2$-4${}^{\prime }$-cyanobiphenyl (5CB-d${}_2$) under these conditions has revealed a voltage dependent inhomogeneous director distribution for a particular narrow range of voltages and for a fixed magnetic field (that of the spectrometer). In the ideal setup the two plates are assumed to be rigorously parallel, so that a difference of voltage applied on the plates leads to a constant electric field normal to them. When the magnetic field is parallel to the plates (orthogonal geometry) there exists a threshold value of the electric field for which the effect of both fields exactly compensate; moreover, for stronger electric field the director aligns with the electric field while for weaker electric field the director aligns with the magnetic field. If there is a lack of parallelism between the two plates, the electric field becomes inhomogeneous so that it may be larger than the threshold value in some region of the sample and smaller in the remaining part of the sample. In that case the director will adopt essentially two orientations within the sample, namely, parallel or perpendicular to the magnetic field, and the position of the frontier between the two domains depends on the voltage. This feature is clearly shown by deuterium NMR spectra that exhibit a transfer of intensity between two quadrupolar doublets with increase in the applied voltage. The coexistence of two director populations occurs for a range of voltages that depends on the degree of nonparallelism; accordingly, an estimation of this range by NMR yields an experimental estimation of the lack of parallelism. A tiny tilt of the magnetic field (nonorthogonal geometry) entrains a notably different behavior since a single doublet with voltage dependent splitting is observed in this case. In a first stage (simple model) of this work, the main features observed for the orthogonal and nonorthogonal geometries are interpreted within the framework of Leslie-Ericksen theory by employing the concept of a single effective field replacing the two real fields. However, the spectra reveal an additional director distribution, especially for the orthogonal geometry, that cannot be interpreted by this simple approach. In a second stage (advanced model), these less clear features have been investigated by numerical simulations of a two-dimensional model which includes the effects of inversion walls and of the high relative dielectric anisotropy of 5CB.

Neural synchronization plays a critical role in information processing, storage, and transmission. Characterizing the pattern of synchronization is therefore of great interest. It has recently been suggested that the brain displays broadband criticality based on two measures of synchronization, phase-locking intervals and global lability of synchronization, showing power-law statistics at the critical threshold in a classical model of synchronization. In this paper, we provide evidence that, within the limits of the model selection approach used to ascertain the presence of power-law statistics, the pooling of pairwise phase-locking intervals from a noncritically interacting system can produce a distribution that is similarly assessed as being power law. In contrast, the global lability of synchronization measure is shown to better discriminate critical from noncritical interaction.

We study the effects of nonzero time delays in stochastic synchronization problems with linear couplings in complex networks. We consider two types of time delays: transmission delays between interacting nodes and local delays at each node (due to processing, cognitive, or execution delays). By investigating the underlying fluctuations for several delay schemes, we obtain the synchronizability threshold (phase boundary) and the scaling behavior of the width of the synchronization landscape, in some cases for arbitrary networks and in others for specific weighted networks. Numerical computations allow the behavior of these networks to be explored when direct analytical results are not available. We comment on the implications of these findings for simple locally or globally weighted network couplings and possible trade-offs present in such systems.

Segregation and mixing of granular mixtures during heap formation has important consequences in industry and agriculture. This research investigates three different final particle configurations of bidisperse granular mixtures—stratified, segregated and mixed—during filling of quasi-two-dimensional silos. We consider a large number and wide range of control parameters, including particle size ratio, flow rate, system size, and heap rise velocity. The boundary between stratified and unstratified states is primarily controlled by the two-dimensional flow rate, with the critical flow rate for the transition depending weakly on particle size ratio and flowing layer length. In contrast, the transition from segregated to mixed states is controlled by the rise velocity of the heap, a control parameter not previously considered. The critical rise velocity for the transition depends strongly on the particle size ratio.

Although it is well known that solid particles adsorb at interfaces, no consensus has been reached on whether the adsorbed nanoparticles affect interfacial tension. In this work the Wilhelmy plate method is implemented in mesoscale dissipative particle dynamics simulations to study the influence of nanoparticles on the water-oil interfacial tension. The results are compared with predictions that neglect nanoparticle-nanoparticle interactions at the interface. We find that the two estimates can differ significantly. In the regime where nanoparticle-nanoparticle repulsion is large, the Wilhelmy plate method suggests interfacial tension reduction, which appears to be a strong function of nanoparticle surface coverage. Some experimental data from the literature, in apparent disagreement, are reinterpreted based on this insight.

Among systems that display generic scale invariance, those whose asymptotic properties are anisotropic in space (strong anisotropy, SA) have received relatively less attention, especially in the context of kinetic roughening for two-dimensional surfaces. This is in contrast with their experimental ubiquity, e.g., in the context of thin-film production by diverse techniques. Based on exact results for integrable (linear) cases, here we formulate a SA ansatz that, albeit equivalent to existing ones borrowed from equilibrium critical phenomena, is more naturally adapted to the type of observables that are measured in experiments on the dynamics of thin films, such as one- and two-dimensional height structure factors. We test our ansatz on a paradigmatic nonlinear stochastic equation displaying strong anisotropy like the Hwa-Kardar equation [Phys. Rev. Lett. 62, 1813 (1989)], which was initially proposed to describe the interface dynamics of running sand piles. A very important role to elucidate its SA properties is played by an accurate (Gaussian) approximation through a nonlocal linear equation that shares the same asymptotic properties.

Kinesin is a processive molecular motor which transports various cellular cargos by converting chemical energy into mechanical movements. Although the motion of a single molecule has been characterized in several studies, the dynamics of collective transport remains controversial. Since the chemical reactions fueling molecular motors are stochastic processes, the movements of coupled motors are not perfectly synchronized. The goal of this study is to develop metrics to analyze the level of synchronization of coupled (stochastic) motors. The correlation among movements of coupled motors, the slackness, the cooperativity, and the power loss of kinesins are explored using the developed metrics. These metrics can be extended to characterize collective work done by other molecular motors also.

The self-assembly of polyhedral shells, each constructed from 60 trapezoidal particles, is simulated using molecular dynamics. The spatial organization of the component particles in this shell is similar to the capsomer proteins forming the capsid of a $T=1$ virus. Growth occurs in the presence of an atomistic solvent and, under suitable conditions, achieves a high yield of complete shells. The simulations provide details of the structure and lifetime of the particle clusters that appear as intermediate states along the growth pathway, and the nature of the transitions between them. In certain respects the growth of size-60 shells from trapezoidal particles resembles the growth of icosahedral shells from triangular particles studied previously, with reversible bonding playing a major role in avoiding incorrect assembly, although the details differ due to particle shape and bond organization. The strong preference for maximal bonding exhibited by the triangular particle clusters is also apparent for trapezoidal particles, but this is now confined to early growth and is less pronounced as shells approach completion along a variety of pathways.

Inverse power law distributions are generally interpreted as a manifestation of complexity, and waiting time distributions with power index $\mu <2$ reflect the occurrence of ergodicity-breaking renewal events. In this paper we show how to combine these properties with the apparently foreign clocklike nature of biological processes. We use a two-dimensional regular network of leaky integrate-and-fire neurons, each of which is linked to its four nearest neighbors, to show that both complexity and periodicity are generated by locality breakdown: Links of increasing strength have the effect of turning local interactions into long-range interactions, thereby generating time complexity followed by time periodicity. Increasing the density of neuron firings reduces the influence of periodicity, thus creating a cooperation-induced renewal condition that is distinctly non-Poissonian.