We investigate the spatio-temporal dynamics of coupled chaotic systems with nonlocal interactions, where each element is coupled to its nearest neighbors within a finite range. Depending upon the coupling strength and coupling radius, we find characteristic spatial patterns such as wavelike profiles and study the transition from coherence to incoherence leading to spatial chaos. We analyze the origin of this transition based on numerical simulations and support the results by theoretical derivations, identifying a critical coupling strength and a scaling relation of the coherent profiles. To demonstrate the universality of our findings, we consider time-discrete as well as time-continuous chaotic models realized as a logistic map and a Rössler or Lorenz system, respectively. Thereby, we establish the coherence-incoherence transition in networks of coupled identical oscillators.

We examine numerically vortex families near band edges of the Bloch wave spectrum for the Gross-Pitaevskii equation with two-dimensional periodic potentials and for the discrete nonlinear Schrödinger equation. We show that besides vortex families that terminate at a small distance from the band edges via fold bifurcations, there exist vortex families that are continued all the way to the band edges.

We propose a new approach to split up the velocities of atoms of flexible molecules into translational, rotational, and vibrational components. As a result, the kinetic energy of the system can easily be expressed in terms of only three parts related to the above components. This is distinct from the standard Eckart method, where the cumbersome Coriolis contribution to the kinetic energy appears additionally. The absence of such a contribution within the proposed approach allows us to readily extend the microcanonical multiple-time-step dynamics of flexible molecules to the canonical-isokinetic Nosé-Hoover chain ensemble by explicitly integrating the translational, orientational, and vibrational motion. The previous extensions dealt exclusively with translational degrees of freedom of separate atoms, leading to a limitation on the size of the outer time step of 100 femtoseconds. We show on molecular dynamics simulations of the flexible TIP3P water model that the new canonical-isokinetic formulation gives a possibility to significantly overcome this limitation. In particular, huge outer time steps of order from a few hundred femtoseconds up to several picoseconds can now be employed to study conformational properties without loss of accuracy.

We report computer simulation studies of the kinetics of ordering of a two-dimensional system of particles on a template with a one-dimensional periodic pattern. In equilibrium, one obtains a reentrant liquid-solid-liquid phase transition as the strength of the substrate potential is varied. We show that domains of crystalline order grow as $\sim$$t^{1/z}$, with $z\sim 4$, with a possible crossover to $z\sim 2$ at late times. We argue that the $t^{1/4}$ law originates from single-file motion and annihilation of defect pairs of opposite topological charge along channels created by the template.

The phenomenon of spatial clustering induced by death and reproduction in a population of anomalously diffusing individuals is studied analytically. The possibility of social behaviors affecting the migration strategies has been taken into exam, in the case that anomalous diffusion is produced by means of a continuous time random walk (CTRW). In the case of independently diffusing individuals, the dynamics appears to coincide with that of (dying and reproducing) Brownian walkers. In the strongly social case, the dynamics coincides with that of nonmigrating individuals. In both limits, the growth rate of the fluctuations becomes independent of the Hurst exponent of the CTRW. The social behaviors that arise when transport in a population is induced by a spatial distribution of random traps have been analyzed.

We develop a microscopic theory for reaction-diffusion (RD) processes based on a generalization of Einstein's master equation [Ann. Phys. 17, 549 (1905)] with a reactive term and show how the mean-field formulation leads to a generalized RD equation with nonclassical solutions. For the $n$th-order annihilation reaction $A+A+A+\cdots +A\to 0$, we obtain a nonlinear reaction-diffusion equation for which we discuss scaling and nonscaling formulations. We find steady states with solutions either exhibiting long-range power-law behavior showing the relative dominance of subdiffusion over reaction effects in constrained systems or, conversely, solutions that go to zero a finite distance from the source, i.e., having finite support of the concentration distribution, describing situations in which diffusion is slow and extinction is fast. Theoretical results are compared with experimental data for morphogen gradient formation.

We study level-number variance in a two-dimensional random matrix model characterized by a power-law decay of the matrix elements. The amplitude of the decay is controlled by the parameter $b$. We find analytically that at small values of $b$ the level number variance behaves linearly, with the compressibility $\chi$ between 0 and 1, which is typical for critical systems. For large values of $b$, we derive that $\chi =0$, as one would normally expect in the metallic phase. Using numerical simulations we determine the critical value of $b$ at which the transition between these two phases occurs.

We present a modified master equation for a homogeneous gaseous reactive system which includes nonequilibrium corrections due to the reaction-induced perturbation of the particle velocity distribution function. For the Schlögl model, the modified stochastic approach predicts nonequilibrium-induced transitions between different dynamical regimes, including the transformation of a monostable system into a bistable one, and vice versa. These predictions are confirmed by the comparison with microscopic simulations using the direct simulation Monte Carlo method. Compared to microscopic simulations of the particle dynamics, the modified master equation approach proves to be much more efficient.

Several recent theories address the efficiency of a macroscopic thermodynamic motor at maximum power and question the so-called Curzon-Ahlborn (CA) efficiency. Considering the entropy exchanges and productions in an n-sources motor, we study the maximization of its power and show that the controversies are partly due to some imprecision in the maximization variables. When power is maximized with respect to the system temperatures, these temperatures are proportional to the square root of the corresponding source temperatures, which leads to the CA formula for a bithermal motor. On the other hand, when power is maximized with respect to the transition durations, the Carnot efficiency of a bithermal motor admits the CA efficiency as a lower bound, which is attained if the duration of the adiabatic transitions can be neglected. Additionally, we compute the energetic efficiency, or “sustainable efficiency,” which can be defined for n sources, and we show that it has no other universal upper bound than 1, but that in certain situations, which are favorable for power production, it does not exceed ½.

Recently the Brownian dynamics of self-propelled (active) rodlike particles was explored to model the motion of colloidal microswimmers, catalytically driven nanorods, and bacteria. Here we generalize this description to biaxial particles with arbitrary shape and derive the corresponding Langevin equation for a self-propelled Brownian spinning top. The biaxial swimmer is exposed to a hydrodynamic Stokes friction force at low Reynolds numbers, to fluctuating random forces and torques as well as to an external and an internal (effective) force and torque. The latter quantities control its self-propulsion. Due to biaxiality and hydrodynamic translational-rotational coupling, the Langevin equation can only be solved numerically. In the special case of an orthotropic particle in the absence of external forces and torques, the noise-free (zero-temperature) trajectory is analytically found to be a circular helix. This trajectory is confirmed numerically to be more complex in the general case of an arbitrarily shaped particle under the influence of arbitrary forces and torques involving a transient irregular motion before ending up in a simple periodic motion. By contrast, if the external force vanishes, no transient regime is found, and the particle moves on a superhelical trajectory. For orthotropic particles, the noise-averaged trajectory is a generalized concho-spiral. We furthermore study the reduction of the model to two spatial dimensions and classify the noise-free trajectories completely finding circles, straight lines with and without transients, as well as cycloids and arbitrary periodic trajectories.

Confinement can have a dramatic effect on the behavior of all sorts of particulate systems, and it therefore is an important phenomenon in many different areas of physics and technology. Here, we investigate the role played by the softness of the confining potential. Using grand canonical Monte Carlo simulations, we determine the phase diagram of three-dimensional hard spheres that in one dimension are constrained to a plane by a harmonic potential. The phase behavior depends strongly on the density and on the stiffness of the harmonic confinement. While we find the familiar sequence of confined hexagonal and square-symmetric packings, we do not observe any of the usual intervening ordered phases. Instead, the system phase separates under strong confinement, or forms a layered re-entrant liquid phase under weaker confinement. It is plausible that this behavior is due to the larger positional freedom in a soft confining potential and to the contribution that the confinement energy makes to the total free energy. The fact that specific structures can be induced or suppressed by simply changing the confinement conditions (e.g., in a dielectrophoretic trap) is important for applications that involve self-assembled structures of colloidal particles.

We perform molecular dynamics simulations to characterize the occurrence of inhomogeneous shear flows in soft jammed materials. We use rough walls to impose a simple shear flow and study the athermal motion of jammed assemblies of soft particles in two spatial dimensions, both for purely repulsive interactions and in the presence of an additional short-range attraction of varying strength. In steady state, pronounced flow inhomogeneities emerge for all systems when the shear rate becomes small. Deviations from linear flow are stronger in magnitude and become very long lived when the strength of the attraction increases, but differ from permanent shear bands. Flow inhomogeneities occur in a stress window bounded by the dynamic and static yield stress values. Attractive forces enhance the flow heterogeneities because they accelerate stress relaxation, thus effectively moving the system closer to the yield stress regime where inhomogeneities are most pronounced. The present scenario for understanding the effect of particle adhesion on shear localization, which is based on detailed molecular dynamics simulations with realistic particle interactions, differs qualitatively from previous qualitative explanations and ad hoc theoretical modeling.

A recently introduced capillary-wave description of binary-alloy solidification is generalized to include the procedure of directional solidification. For a class of model systems a universal dispersion relation of the unstable eigenmodes of a planar steady-state solidification front is derived, which readjusts previously known stability considerations. We moreover establish a differential equation for oscillatory motions of a planar interface that offers a limit-cycle scenario for the formation of solute bands and, taking into account the Mullins-Sekerka instability, of banded structures.

In the present paper we investigated the optical properties of a stack of right- and left- hand chiral photonic crystal layers. The problem is solved by Ambartsumian's layer addition modified method. We investigated the reflection spectra peculiarities of this system and showed that in contrast to a single cholesteric liquid crystal (CLC) layer this system has multiple photonic band gaps (PBGs) (at light normal incidence). We showed that this system has unique polarization properties, particularly the eigenpolarizations (EPs) of the system are degenerated (i.e., the two EPs coincide) for an even number of layers and, in contrast to ordinary gyrotropic systems, the polarization plane rotation decreases if the system thickness is increased, the rotation sign depends on the first sublayer chirality sign, the system is very sensitive to the change of the sublayer number in the system, etc. We also investigated the influence of sublayer thicknesses, incidence angle, the sublayer local dielectric anisotropies, the sublayer helix pitches on the reflection peculiarities, and other optical parameters of the system.

By dynamic light scattering we studied the temperature dependence of scattered intensities and relaxation rates for pure twist and pure bend modes in a colloidal system of BaTiO${}_3$ single domain nanoparticles and liquid crystal octylcyanobiphenyl (8CB) close to the nematic to smectic-$A$ phase transition. From the experiments we obtained the critical exponents for the smectic correlation lengths, which in suspensions differ from the values for pure 8CB. The phase transition temperatures from isotropic to nematic phase ($T_{NI}$) and from nematic to smectic-$A$ phase ($T_{NA}$) are both affected by the presence of the particles in two ways. The electric field around the ferroelectric particles increases the transition temperatures, whereas the disorder and probably also the excess of the surfactant cause a decrease of the transition temperatures compared to pure 8CB. The net effect is lower $T_{NI}$ and almost unchanged $T_{NA}$ in suspensions. After prolonged exposure to the external field the ferroelectric particles irreversibly aggregate, which results in the decrease of the internal electric field and, consequently, in the decrease of both transition temperatures.

The electric-field-driven entry process of flexible charged polymers such as single-stranded DNA (ssDNA) into asymmetric nanoscale channels such as the $\alpha$-hemolysin protein channel is studied theoretically and using molecular dynamics simulations. Dependence of the height of the free-energy barrier on the polymer length, the strength of the applied electric field, and the channel entrance geometry is investigated. It is shown that the squeezing effect of the driving field on the polymer and the lateral confinement of the polymer before its entry to the channel crucially affect the barrier height and its dependence on the system parameters. The attempt frequency of the polymer for passing the channel is also discussed. Our theoretical and simulation results support each other and describe related data sets of polymer translocation experiments through the $\alpha$-hemolysin protein channel reasonably well.

We consider the fracture of a free-standing two-dimensional (2D) elastic-brittle network to be used as protective coating subject to constant tensile stress applied on its rim. Using a molecular-dynamics simulation with a Langevin thermostat, we investigate the scission and recombination of bonds, and the formation of cracks in the 2D graphenelike hexagonal sheet for different pulling force $f$ and temperature $T$. We find that bond rupture occurs almost always at the sheet periphery, and the first mean breakage time $\langle \tau \rangle$ of bonds decays with membrane size as $\langle \tau \rangle \propto N^{-\beta }$, where $\beta \approx 0.50\pm 0.03$ and $N$ denotes the number of atoms in the membrane. The probability distribution of bond scission times $t$ is given by a Poisson function $W\left(t\right)\propto t^{1/3}\exp (-t/\langle \tau \rangle )$. The mean failure time $\langle {\tau }_r\rangle$ necessary to rip off the sheet declines with growing size $N$ as a power law $\langle {\tau }_r\rangle \propto N^{-\phi \left(f\right)}$. We also find $\langle {\tau }_r\rangle \propto \exp (\Delta U_0/k_{B}T)$, where the nucleation barrier for crack formation $\Delta U_0\propto f^{-2}$, in agreement with Griffith's theory. $\langle {\tau }_r\rangle$ displays an Arrhenian dependence of $\langle {\tau }_r\rangle$ on temperature $T$. Our results indicate a rapid increase in crack spreading velocity with growing external tension $f$.

We present a detailed account of a recently proposed phenomenological theory for noncatenated ring polymer melts [Sakaue, Phys. Rev. Lett. 106, 167802 (2011)]. A basic assumption lies in the implementation of the noncatenation constraint via the effective excluded-volume effect, from which a geometrical picture of melts emerges. The result captures many of the salient features observed so far, including (i) the overall spatial size of rings, (ii) the coordinate number, i.e., the number of rings surrounding a given ring, (iii) the topological length scale as a function of the molecular weight, and (iv) the effect of the chain stiffness and concentration. We also suggest a geometrical interpretation of the topological length scale, which may shed some light on the entanglement concept in polymeric systems.

The knowledge of mechanical properties of root cell walls is vital to understand how these properties interact with relevant genetic and physiological processes to bring about growth. Expansion of cell walls is an essential component of growth, and the regulation of cell wall expansion is one of the ways in which the mechanics of growth is controlled, managed and directed. In this study, the inherent surface mechanical properties of living Arabidopsis thaliana whole-root epidermal cells were studied at the nanoscale using the technique of atomic force microscopy (AFM). A novel methodology was successfully developed to adapt AFM to live plant roots. Force-Indentation (F-I) experiments were conducted to investigate the mechanical properties along the length of the root. F-I curves for epidermal cells of roots were also generated by varying turgor pressure. The F-I curves displayed a variety of features due to the heterogeneity of the surface. Hysteresis is observed. Application of conventional models to living biological systems such as cell walls in nanometer regimes tends to increase error margins to a large extent. Hence information from the F-I curves were used in a preliminary semiquantitative analysis to infer material properties and calculate two parameters. The work done in the loading and unloading phases (hysteresis) of the force measurements were determined separately and were expressed in terms of “Index of Plasticity” ($\eta$), which characterized the elasticity properties of roots as a viscoelastic response. Scaling approaches were used to find the ratio of hardness to reduced modulus ($\frac{H}{E^{*}}$).

A recurrent loop consisting of a single Hodgkin-Huxley neuron influenced by a chemical excitatory delayed synaptic feedback is considered. We show that the behavior of the system depends on the duration of the activity of the synapse, which is determined by the activation and deactivation time constants of the synapse. For the fast synapses, those for which the effect of the synaptic activity is small compared to the period of firing, depending on the delay time, spiking with single and multiple interspike intervals is possible and the average firing rate can be smaller or larger than that of the open loop neuron. For slow synapses for which the synaptic time constants are of order of the period of the firing, the self-excitation increases the firing rate for all values of the delay time. We also show that for a chain consisting of few similar oscillators, if the synapses are chosen from different time constants, the system will follow the dynamics imposed by the fastest element, which is the oscillator that receives excitations via a slow synapse. The generalization of the results to other types of relaxation oscillators is discussed and the results are compared to those of the loops with inhibitory synapses as well as with gap junctions.