At high cell concentrations, bacterial suspensions are known to develop a state of collective swimming (the “zooming bionematic phase,” or ZBN) characterized by transient, recurring regions of coordinated motion greatly exceeding the size of individual cells. Recent theoretical studies of semidilute suspensions have suggested that long-range hydrodynamic interactions between swimming cells are responsible for long-wavelength instabilities that lead to these patterns, while models appropriate for higher concentrations have suggested that steric interactions between elongated cells play an important role in the self-organization. Using particle imaging velocimetry in well-defined microgeometries, we examine the statistical properties of the transition to the ZBN in suspensions of Bacillus subtilis, with particular emphasis on the distribution of cell swimming speeds and its correlation with orientational order. This analysis reveals a nonmonotonic relationship between mean cell swimming speed and cell concentration, with a minimum occurring near the transition to the ZBN. Regions of high orientational order in the ZBN phase have locally high swimming speeds, while orientationally disordered regions have lower speeds. A model for steric interactions in concentrated suspensions and previous observations on the kinetics of flagellar rebundling associated with changes in swimming direction are used to explain this observation. The necessity of incorporating steric effects on cell swimming in theoretical models is emphasized.

We propose a method for quantitative characterization of spatial networklike patterns with loops, such as surface fracture patterns, leaf vein networks, and patterns of urban streets. Such patterns are not well characterized by purely topological estimators: also patterns that both look different and result from different morphogenetic processes can have similar topology. A local geometric cue—the angles formed by the different branches at junctions—can complement topological information and allow the quantification of the large scale spatial coherence of the pattern. For patterns that grow over time, such as fracture lines on the surface of ceramics, the rank assigned by our method to each individual segment of the pattern approximates the order of appearance of that segment. We apply the method to various networklike patterns and find a continuous but sharp dichotomy between two classes of spatial networks: hierarchical and homogeneous. The former class results from a sequential growth process and presents large scale organization, and the latter presents local, but not global, organization.

A system of nearest neighbors Kuramoto-like coupled oscillators placed in a ring is studied above the critical synchronization transition. We find a richness of solutions when the coupling increases, which exists only within a solvability region (SR). We also find that the solutions possess different characteristics, depending on the section of the boundary of the SR where they appear. We study the birth of these solutions and how they evolve when the coupling strength increases, and determine the diagram of solutions in phase space.

The magneto-Rayleigh-Taylor instability (MRT) of a finite slab is studied analytically using the ideal MHD model. The slab may be accelerated by an arbitrary combination of magnetic pressure and fluid pressure, thus allowing an arbitrary degree of anisotropy intrinsic to the acceleration mechanism. The effect of feedthrough in the finite slab is also analyzed. The classical feedthrough solution obtained by Taylor in the limit of zero magnetic field, the single interface MRT solution of Chandrasekhar in the limit of infinite slab thickness, and Harris’ stability condition on purely magnetic driven MRT, are all readily recovered in the analytic theory as limiting cases. In general, we find that MRT retains robust growth if it exists. However, feedthrough may be substantially reduced if there are magnetic fields on both sides of the slab, and if the MRT mode invokes bending of the magnetic field lines.

We study the flow of energy between a harmonic oscillator (HO) and an external environment consisting of $N$ two-degrees-of-freedom nonlinear oscillators, ranging from integrable to chaotic according to a control parameter. The coupling between the HO and the environment is bilinear in the coordinates and scales with system size as $1/\sqrt{N}$. We study the conditions for energy dissipation and thermalization as a function of $N$ and of the dynamical regime of the nonlinear oscillators. The study is classical and based on a single realization of the dynamics, as opposed to ensemble averages over many realizations. We find that dissipation occurs in the chaotic regime for fairly small values of $N$, leading to the thermalization of the HO and the environment in a Boltzmann distribution of energies for a well-defined temperature. We develop a simple analytical treatment, based on the linear response theory, that justifies the coupling scaling and reproduces the numerical simulations when the environment is in the chaotic regime.

We consider the one-dimensional totally asymmetric simple exclusion process (TASEP) with position-dependent hopping rates. The problem is solved, in a mean-field adiabatic approximation, for a general (smooth) form of spatial rate variation. Numerical simulations of systems with hopping rates varying linearly against position (constant rate gradient), for both periodic and open-boundary conditions, provide detailed confirmation of theoretical predictions, concerning steady-state average density profiles and currents, as well as open-system phase boundaries, to excellent numerical accuracy.

We analyze the entropic equation of state for a many-particle interacting system in a scale-free network. The analysis is performed in terms of scaling functions, which are of fundamental interest in the theory of critical phenomena and have previously been theoretically and experimentally explored in the context of various magnetic, fluid, and superconducting systems in two and three dimensions. Here, we obtain general scaling functions for the entropy, the constant-field heat capacity, and the isothermal magnetocaloric coefficient near the critical point in uncorrelated scale-free networks, where the node-degree distribution exponent $\lambda$ appears to be a global variable and plays a crucial role, similar to the dimensionality $d$ for systems on lattices. This extends the principle of universality to systems on scale-free networks and allows quantification of the impact of fluctuations in the network structure on critical behavior.

Using Monte Carlo simulations we examine the diffusive properties of the greedy algorithm in the $d$-dimensional traveling salesman problem. Our results show that for $d=3$ and 4 the average squared distance from the origin $\langle r^2\rangle$ is proportional to the number of steps $t$. In the $d=2$ case such a scaling is modified with some logarithmic corrections, which might suggest that $d=2$ is the critical dimension of the problem. The distribution of lengths also shows marked differences between $d=2$ and $d>2$ versions. A simple strategy adopted by the salesman might resemble strategies chosen by some foraging and hunting animals, for which anomalous diffusive behavior has recently been reported and interpreted in terms of Lévy flights. Our results suggest that broad and Lévy-like distributions in such systems might appear due to dimension-dependent properties of a search space.

We introduce a simple model consisting of two or three coupled one-dimensional channels of particles with Yukawa interactions. For the two-channel system, when an external drive is applied only to the top or primary channel, we find a transition from locked flow, where particles in both channels move together, to decoupled flow, where the particles in the secondary or undriven channel move at a slower velocity than the particles in the primary or driven channel. Pronounced commensurability effects in the decoupling transition occur when the ratio of the number of particles in the top and bottom channels is varied, and the coupling of the two channels is enhanced when this ratio is an integer or a rational fraction. Near the commensurate fillings, we find additional features in the velocity-force curves caused by the slipping of individual vacancies or incommensurations in the secondary channels. For three coupled channels, when only the top channel is driven we find a remarkably rich variety of distinct dynamic phases, including multiple decoupling and recoupling transitions. These transitions produce pronounced signatures in the velocity response of each channel. We also find regimes where a negative drag effect can be induced in one of the nondriven channels. The particles in this channel move in the opposite direction from the particles in the driven channel due to the mixing of the two different periodic frequencies produced by the discrete motion of the particles in the two other channels. In the two-channel system, we also demonstrate a ratchet effect for the particles in the secondary channel when an asymmetric drive is applied to the primary channel. This ratchet effect is similar to that observed in superconducting vortex systems when there is a coupling between two different species of vortices.

Time-dependent isothermal dielectric measurements were carried out deeply in the glassy state on two very important saccharides: sucrose and trehalose. In both compounds two prominent secondary relaxation processes were identified. The faster one is an inherent feature of the whole family of carbohydrates. The slower one can also be detected in oligo- and polysaccharides. It was shown earlier that the $\beta$ process is the Johari-Goldstein (JG) relaxation coupled to motions of the glycosidic linkage, while the $\gamma$ relaxation originates from motions of the exocyclic hydroxymethyl unit. Recently, it was shown that the JG relaxation process can be used to determine structural relaxation times in the glassy state [R. Casalini and C. M. Roland, Phys. Rev. Lett. 102, 035701 (2009)]. In this paper we present the results of an analysis of the data obtained during aging using two independent approaches. The first was proposed by Casalini and Roland, and the second one is based on the variation of the dielectric strength of the secondary relaxation process during aging [J. K. Vij and G. Power, J. Non-Cryst. Solids 357, 783 (2011)]. Surprisingly, we found that the estimated structural relaxation times in the glassy state of both saccharides are almost the same, independent of the type of secondary mode. This finding calls into question the common view that secondary modes of intramolecular origin do not provide information about the dynamics of the glassy state.

Quantum tunneling rates through a barrier separating two-dimensional, symmetric, double-well potentials are shown to depend on the classical dynamics of the billiard trajectories in each well and, hence, on the shape of the wells. For shapes that lead to regular (integrable) classical dynamics the tunneling rates fluctuate greatly with eigenenergies of the states sometimes by over two orders of magnitude. Contrarily, shapes that lead to completely chaotic trajectories lead to tunneling rates whose fluctuations are greatly reduced, a phenomenon we call regularization of tunneling rates. We show that a random-plane-wave theory of tunneling accounts for the mean tunneling rates and the small fluctuation variances for the chaotic systems.

We investigate the evolutionary dynamics of an idealized model for the robust self-assembly of two-dimensional structures called polyominoes. The model includes rules that encode interactions between sets of square tiles that drive the self-assembly process. The relationship between the model’s rule set and its resulting self-assembled structure can be viewed as a genotype-phenotype map and incorporated into a genetic algorithm. The rule sets evolve under selection for specified target structures. The corresponding complex fitness landscape generates rich evolutionary dynamics as a function of parameters such as the population size, search space size, mutation rate, and method of recombination. Furthermore, these systems are simple enough that in some cases the associated model genome space can be completely characterized, shedding light on how the evolutionary dynamics depends on the detailed structure of the fitness landscape. Finally, we apply the model to study the emergence of the preference for dihedral over cyclic symmetry observed for homomeric protein tetramers.

The influence of linear time-delayed feedback on vibrational resonance is investigated in underdamped and overdamped Duffing oscillators with double-well and single-well potentials driven by both low frequency and high frequency periodic forces. This task is performed through both theoretical approach and numerical simulation. Theoretically determined values of the amplitude of the high frequency force and the delay time at which resonance occurs are in very good agreement with the numerical simulation. A major consequence of time-delayed feedback is that it gives rise to a periodic or quasiperiodic pattern of vibrational resonance profile with respect to the time-delayed parameter. An appropriate time delay is shown to induce a resonance in an overdamped single-well system which is otherwise not possible. For a range of values of the time-delayed parameters, the response amplitude is found to be larger than in delay-time feedback-free systems.

A dissipative-particle-dynamics model for the quantitative simulation of biofilm growth controlled by substrate (nutrient) consumption, advective and diffusive substrate transport, and hydrodynamic interactions with fluid flow (including fragmentation and reattachment) is described. The model was used to simulate biomass growth, decay, and spreading. It predicts how the biofilm morphology depends on flow conditions, biofilm growth kinetics, the rheomechanical properties of the biofilm, and adhesion to solid surfaces. The morphology of the model biofilm depends strongly on its rigidity and the magnitude of the body force that drives the fluid over the biofilm.

We analyze the (large) deformation and energy of a thin elastic cylindrical tube compressed between two plates parallel to the tube axis. The deformation is studied theoretically using a numerical calculation and the variational approach. The results are used to interpret the experimental data obtained by pressing tubes made from plastic-foil transparencies. We obtain a universal scaling relation that characterizes the response of the tube. Our results may serve as a benchmark for the application of variational methods to thin-walled nanoscale systems in order to obtain functional relations between the energy and the deformation.

We study excitability phenomena for the stochastically forced FitzHugh-Nagumo system modeling a neural activity. Noise-induced changes in the dynamics of this model can be explained by the high stochastic sensitivity of its attractors. Computational methods based on the stochastic sensitivity functions technique are suggested for the analysis of these attractors. Our method allows us to construct confidence ellipses and estimate a threshold value of a noise intensity corresponding to the neuron excitement. On the basis of the proposed technique, a supersensitive limit cycle is found for the FitzHugh-Nagumo model.

An exact expression for the finite frequency response of open classical systems coupled to reservoirs is obtained. The result is valid for any conserved current. No assumption is made about the reservoirs apart from thermodynamic equilibrium. At nonzero frequencies, the expression involves correlation functions of boundary currents and cannot be put in the standard Green-Kubo form involving currents inside the system.

We extend the stochastic energetics to a relativistic system. The thermodynamic laws and equipartition theorem are discussed for a relativistic Brownian particle and the first and the second law of thermodynamics in this formalism are derived. The relation between the relativistic equipartition relation and the rate of heat transfer is discussed in the relativistic case together with the nature of the noise term.

Thermally driven colloidal transport is, to a large extent, due to the thermoelectric or Seebeck effect of the charged solution. We show that, contrary to the generally adopted single-particle picture, the transport coefficient depends on the colloidal concentration. For solutions that are dilute in the hydrodynamic sense, collective effects may significantly affect the thermophoretic mobility. Our results provide an explanation for recent experimental observations on polyelectrolytes and charged particles and suggest that for charged colloids collective behavior is the rule rather than the exception.