Several single-molecule studies aim to reliably extract parameters characterizing molecular confinement or transient kinetic trapping from experimental observations. Pioneering works from single-particle tracking (SPT) in membrane diffusion studies [Kusumi et al., Biophys. J. 65, 2021 (1993)] appealed to mean square displacement (MSD) tools for extracting diffusivity and other parameters quantifying the degree of confinement. More recently, the practical utility of systematically treating multiple noise sources (including noise induced by random photon counts) through likelihood techniques has been more broadly realized in the SPT community. However, bias induced by finite-time-series sample sizes (unavoidable in practice) has not received great attention. Mitigating parameter bias induced by finite sampling is important to any scientific endeavor aiming for high accuracy, but correcting for bias is also often an important step in the construction of optimal parameter estimates. In this article, it is demonstrated how a popular model of confinement can be corrected for finite-sample bias in situations where the underlying data exhibit Brownian diffusion and observations are measured with non-negligible experimental noise (e.g., noise induced by finite photon counts). The work of Tang and Chen [J. Econometrics 149, 65 (2009)] is extended to correct for bias in the estimated “corral radius” (a parameter commonly used to quantify confinement in SPT studies) in the presence of measurement noise. It is shown that the approach presented is capable of reliably extracting the corral radius using only hundreds of discretely sampled observations in situations where other methods (including MSD and Bayesian techniques) would encounter serious difficulties. The ability to accurately statistically characterize transient confinement suggests additional techniques for quantifying confined and/or hop diffusion in complex environments.

We study ensembles of globally coupled, nonidentical phase oscillators subject to correlated noise, and we identify several important factors that cause noise and coupling to synchronize or desynchronize a system. By introducing noise in various ways, we find an estimate for the onset of synchrony of a system in terms of the coupling strength, noise strength, and width of the frequency distribution of its natural oscillations. We also demonstrate that noise alone can be sufficient to synchronize nonidentical oscillators. However, this synchrony depends on the first Fourier mode of a phase-sensitivity function, through which we introduce common noise into the system. We show that higher Fourier modes can cause desynchronization due to clustering effects, and that this can reinforce clustering caused by different forms of coupling. Finally, we discuss the effects of noise on an ensemble in which antiferromagnetic coupling causes oscillators to form two clusters in the absence of noise.

Time scales of turbulent strain activity, denoted as the strain persistence times of first and second order, are obtained from time-dependent expectation values and correlation functions of Lagrangian rate-of-strain eigenvalues taken in particularly defined statistical ensembles. Taking into account direct numerical simulation data, our approach relies on heuristic closure hypotheses which allow us to establish a connection between the statistics of vorticity and strain. It turns out that softly divergent prefactors correct the usual “$1/s$” strain time-scale estimate of standard turbulence phenomenology, in a way which is consistent with the phenomenon of vorticity intermittency.

We show that memristive networks, namely networks of resistors with memory, can efficiently solve shortest-path optimization problems. Indeed, the presence of memory (time nonlocality) promotes self organization of the network into the shortest possible path(s). We introduce a network entropy function to characterize the self-organized evolution, show the solution of the shortest-path problem and demonstrate the healing property of the solution path. Finally, we provide an algorithm to solve the traveling salesman problem. Similar considerations apply to networks of memcapacitors and meminductors, and networks with memory in various dimensions.

Anomalous diffusion with a sublinear growth of the particles' mean-square displacement (subdiffusion) has been observed frequently in crowded fluids, e.g., in the cytoplasm of living cells or in artificial solutions. Based on a recently reported set of single-particle tracking data, it is shown here that trajectories of nanoparticles immersed in artificial crowded fluids display all signatures of anticorrelated fractional Brownian motion. Moreover, the trajectories' power spectrum follows a scaling that reports on the fluid's viscoelasticity. Macromolecular crowding therefore renders fluids viscoelastic which in turn leads to subdiffusion of immersed tracer particles with all the characteristics of fractional Brownian motion.

This paper explores how pairs of spherical particles with homeotropic (normal) surface anchoring cluster when immersed in nematic liquid crystal. By means of the Landau-de Gennes continuum theory we calculate how the equilibrium separation of a particle pair depends on the anchoring energy at the particle surface and the elastic anisotropy of the liquid crystal. We find that, for modest to strong anchoring strengths, the particle separation depends linearly on the elastic anisotropy and the inverse of the anchoring strength. Thus, the anchoring strength can be estimated by measuring the particle-pair separation.

The fluctuation pressure of a lipid-bilayer membrane is important for the stability of lamellar phases and the adhesion of membranes to surfaces. In contrast to many theoretical studies, which predict a decrease of the pressure with the cubed inverse distance between the membranes, Freund suggested very recently a linear inverse distance dependence [Proc. Natl. Acad. Sci. USA 110, 2047 (2013)]. We address this discrepancy by performing Monte Carlo simulations for a membrane model discretized on a square lattice and employ the wall theorem to evaluate the pressure for a single membrane between parallel walls. For distances that are small compared with the lattice constant, the pressure indeed depends on the inverse distance as predicted by Freund. For intermediate distances, the pressure depends on the cubed inverse distance as predicted by Helfrich [Z. Naturforsch. A 33, 305 (1978)]. Here, the crossover length between the two regimes is a molecular length scale. Finally, for distances large compared with the mean squared fluctuations of the membrane, the entire membrane acts as a soft particle and the pressure on the walls again depends linearly on the inverse distance.

Destabilization of soft interfaces into thin cylindrical filaments under external stresses is ubiquitous and is generally the first step toward breakup. We show that such filaments, called tethers, emerge from a vesicle subjected to gravity. Contrary to the pendant drop experiment, we demonstrate that the bending rigidity, a specific membrane property of vesicles, ensures the tethers reach a stationary state. Moreover, unlike point-like force experiments, we show that the family of shapes is continuous.

Channel transport of different species of particles is viewed usually only in terms of competition and selectivity. In this paper we show that transport of one species may be promoted by the presence of another and that both may even mutually cooperate. We investigate a discretized Markovian model of nanochannel transport via in-channel sites, allowing for the simultaneous transport of several different species of particles; interaction between transported particles is included via the condition of single occupancy on a channel site. By numerically solving the model exactly, particularly an analysis of situations of crowding in the channel is possible and we observe three situations: mutual cooperation, promotion of one species at the cost of the other, and mutual competition. The physical situation has a strong nonequilibrium character as Onsager's relations on coupled flows do not hold.

We investigate the localization of stiff directed lines with bending energy by a short-range random potential. We apply perturbative arguments, Flory scaling arguments, a variational replica calculation, and functional renormalization to show that a stiff directed line in $1+d$ dimensions undergoes a localization transition with increasing disorder for $d>2/3$. We demonstrate that this transition is accessible by numerical transfer matrix calculations in 1+1 dimensions and analyze the properties of the disorder-dominated phase in detail. On the basis of the two-replica problem, we propose a relation between the localization of stiff directed lines in $1+d$ dimensions and of directed lines under tension in $1+3d$ dimensions, which is strongly supported by identical free-energy distributions. This shows that pair interactions in the replicated Hamiltonian determine the nature of directed line localization transitions with consequences for the critical behavior of the Kardar-Parisi-Zhang equation. We support the proposed relation to directed lines via multifractal analysis, revealing an analogous Anderson transition-like scenario and a matching correlation length exponent. Furthermore, we quantify how the persistence length of the stiff directed line is reduced by disorder.

We investigate a Brownian pump which, being powered by a flashing ratchet mechanism, produces net particle transport through a membrane. The extension of the Parrondo's approach developed for reversible Brownian motors [Parrondo, Phys. Rev. E 57, 7297 (1998)] to adiabatically driven pumps is given. We demonstrate that the pumping mechanism becomes especially efficient when the time variation of the potential occurs adiabatically fast or adiabatically slow, in perfect analogy with adiabatically driven Brownian motors which exhibit high efficiency [Rozenbaum et al., Phys. Rev. E 85, 041116 (2012)]. At the same time, the efficiency of the pumping mechanism is shown to be less than that of Brownian motors due to fluctuations of the number of particles in the membrane.

Evolutionary graph theory is an extension of evolutionary game theory in which each individual agent, represented by a node, interacts only with a subset of the entire population to which it belongs (i.e., those to which it is connected by edges). In the context of the evolution of cooperation, in which individuals playing the cooperator strategy interact with individuals playing the defector strategy and game payoffs are equated with fitness, evolutionary games on graphs lead to global standoffs (i.e., static patterns) when all cooperators in a population have the same payoff as any defectors with which they share an edge. I consider the simplest type of regular-connected graph, the cycle graph, in which every node has exactly two edges ($k$ $=$ 2), for the prisoner's dilemma game and the snowdrift game, the two most important pairwise games in cooperation theory. I show that for simplified payoff structures associated with these games, standoffs are only possible for two valid cost-benefit ratios in the snowdrift game. I further show that only the greater of these two cost-benefit ratios is likely to be attracting in most situations (i.e., likely to spontaneously result in a global standoff when starting from nonstandoff conditions). Numerical simulations confirm this prediction. This work contributes to our understanding of the evolution of pattern formation in games played in finite, sparsely connected populations.

Flows at the nanoscale are subject to thermal fluctuations. In this work, we explore the consequences for a fluid confined within a channel of nanometric size. First, the phenomenon is illustrated on the basis of molecular dynamics simulations. The center of mass of the confined fluid is shown to perform a stochastic, non-Markovian motion, whose diffusion coefficient satisfies Einstein's relation, and which can be further characterized by the fluctuation relation. Next, we develop an analytical description of the thermally induced fluid motion. We compute the time- and space-dependent velocity correlation function, and characterize its dependence on the nanopore shape, size, and boundary slip at the surface. The experimental implications for mass and charge transports are discussed for two situations. For a particle confined within the nanopore, we show that the fluid fluctuating motion results in an enhanced diffusion. The second situation involves a charged nanopore in which fluid motion within the double layer induces a fluctuating electric current. We compute the corresponding contribution to the current power spectrum.

We investigate the synchronization of stochastic oscillations in biochemical models by calculating the complex coherence function within the linear noise approximation. The method is illustrated on a simple example and then applied to study the synchronization of chemical concentrations in social amoeba. The degree to which variation of rate constants in different cells and the volume of the cells affects synchronization of the oscillations is explored and the phase lag calculated. In all cases the analytical results are shown to be in good agreement with those obtained through numerical simulations.

The standard Fermi-Hubbard chain becomes nonintegrable by adding to the nearest neighbor hopping additional longer range hopping amplitudes. We assume that the quartic interaction is weak and investigate numerically the dynamics of the chain on the level of the Boltzmann type kinetic equation. Only the spatially homogeneous case is considered. We observe that the huge degeneracy of stationary states in the case of nearest neighbor hopping is lost and the convergence to the thermal Fermi-Dirac distribution is restored. The convergence to equilibrium is exponentially fast. However for small next-nearest neighbor hopping amplitudes one has a rapid relaxation towards the manifold of quasistationary states and slow relaxation to the final equilibrium state.

We study computationally the local structure of aggregated systems of patchy particles. By calculating the probability distribution functions of various rotational invariants we can identify the precursors of orientation order in amorphous phase. Surprisingly, the strongest signature of local order is observed for four-patch particles with tetrahedral symmetry, not for six-patch particles with the cubic one. This trend is exactly opposite to their known ability to crystallize. We relate this anomaly to the observation that a generic aggregate of patchy systems has a coordination number close to 4. Our results also suggest a significant correlation between rotational order in the studied liquids with the corresponding crystalline phases, making this approach potentially useful for a broader range of patchy systems.

We report a numerical study of a simple, modified Asakura-Oosawa model for nanoparticles that are isotropically grafted with polymer chains. We perform canonical and grand-canonical Monte Carlo simulations to establish a qualitative morphology diagram, as well as quantitative phase diagrams. The morphology diagram qualitatively reproduces experimental observations and theoretical approaches employing more complex models. In addition, we establish the transition lines for a microphase separation and show that the phase behavior saturates for larger polymer sizes. An analytical treatment on the level of the second virial coefficient indicates that this saturation effect is caused by less effective shielding of nanoparticles by longer polymers. Our simple model enables large-scale particle-based simulations of self-assembly of polymer-coated particles.

We have studied the influence of two structurally isomeric organic salts, namely, 2-sodium-3-hydroxy naphthoate (SHN) and 1-sodium-2-hydroxy naphthoate (SHN1), on the phase behavior of concentrated aqueous solutions of the cationic surfactant cetylpyridinium chloride (CPC). Partial phase diagrams of the two systems have been constructed using polarizing optical microscopy and x-ray diffraction techniques. A variety of intermediate phases is seen in both systems for a range of salt concentrations. The CPC-SHN-water system exhibits the rhombohedral and tetragonal mesh phases in addition to the random mesh phase, whereas the CPC-SHN1-water system shows only the tetragonal and random mesh phases. The CPC-SHN-water system also exhibits two nematic phases consisting of cylindrical and disk-like micelles at relatively low and high salt concentrations, respectively. These results show that the concentration of the strongly bound counterion provided by the organic salt can be used as a control parameter to tune the stability of different intermediate phases in amphiphile-water systems.

The large strain behavior of filled rubbers is characterized by the strong Mullins effect, permanent set, and induced anisotropy. Strain controlled cyclic tests also exhibit a pronounced hysteresis as a strain rate independent phenomenon. Prediction of these inelastic features in elastomers is an important challenge with immense industrial and technological relevance. In the present paper, a micromechanical model is proposed to describe the inelastic features in the behavior of filled elastomers. To this end, the previously developed network decomposition concept [Dargazany and Itskov, Int. J. Solids Struct. 46, 2967 (2009)] is extended and an additional network (CP network) is added to the classical elastic rubber (CC) and polymer-filler (PP) networks. The new network is considered to account for the damage of filler aggregates in the cyclic deformation as the source of hysteresis energy loss. The accuracy of the resulting model is evaluated in comparison to a new set of experimental data.

We analyze the force-extension curve for a general class of systems, which are described at the mesoscopic level by a free energy depending on the extension of its components. Similarly to what is done in real experiments, the total length of the system is the controlled parameter. This imposes a global constraint in the minimization procedure leading to the equilibrium values of the extensions. As a consequence, the force-extension curve has multiple branches in a certain range of forces. The stability of these branches is governed by the free energy: there are a series of first-order phase transitions at certain values of the total length, in which the free energy itself is continuous but its first derivative, the force, has a finite jump. This behavior is completely similar to that observed in real experiments with biomolecules like proteins and with other complex systems.