The anelastic relaxation behavior of amorphous $\mathrm{A}{\mathrm{l}}_{86.8}\mathrm{N}{\mathrm{i}}_{3.7}{\mathrm{Y}}_{9.5}$ was characterized in prolonged, quasistatic measurements, up to $1.1\times {10}^8\mathrm{s}$. The size-density distribution of potential shear transformation zones was determined from the data. We derive an expression for the distribution, based on a free-volume criterion for an atomic cluster being a potential shear transformation zone. The model is shown to be consistent with experiment.

Hard-sphere models exhibit many of the same kinds of supercooled-liquid behavior as more realistic models of liquids, but the highly nonanalytic character of their potentials makes it a challenge to think of that behavior in potential energy landscape terms. We show here that it is possible to calculate an important topological property of hard-sphere landscapes, the geodesic pathways through those landscapes, and to do so without artificially coarse-graining or softening the potential. We show, moreover, that the rapid growth of the lengths of those pathways with increasing packing fraction quantitatively predicts the precipitous decline in diffusion constants in a glass-forming hard-sphere mixture model. The geodesic paths themselves can be considered as defining the intrinsic dynamics of hard spheres, so it is also revealing to find that they (and therefore the features of the underlying potential energy landscape) correctly predict the occurrence of dynamic heterogeneity and nonzero values of the non-Gaussian parameter. The success of these landscape predictions for the dynamics of such a singular model emphasizes that there is more to potential energy landscapes than is revealed by looking at the minima and saddle points.

The nonequilibrium activity taking place in a living cell can be monitored with a tracer embedded in the medium. While microrheology experiments based on optical manipulation of such probes have become increasingly standard, we put forward a number of experiments with alternative protocols that, we claim, will provide insight into the energetics of active fluctuations. These are based on either performing thermodynamiclike cycles in control-parameter space or determining response to external perturbations of the confining trap beyond simple translation. We illustrate our proposals on an active itinerant Brownian oscillator modeling the dynamics of a probe embedded in a living medium.

A class of networks are those with both positive and negative links. In this manuscript, we studied the interplay between positive and negative ties on mesoscopic level of these networks, i.e., their community structure. A community is considered as a tightly interconnected group of actors; therefore, it does not borrow any assumption from balance theory and merely uses the well-known assumption in the community detection literature. We found that if one detects the communities based on only positive relations (by ignoring the negative ones), the majority of negative relations are already placed between the communities. In other words, negative ties do not have a major role in community formation of signed networks. Moreover, regarding the internal negative ties, we proved that most unbalanced communities are maximally balanced, and hence they cannot be partitioned into $k$ nonempty sub-clusters with higher balancedness $\left(k\ge 2\right)$. Furthermore, we showed that although the mediator triad $++-$ (hostile-mediator-hostile) is underrepresented, it constitutes a considerable portion of triadic relations among communities. Hence, mediator triads should not be ignored by community detection and clustering algorithms. As a result, if one uses a clustering algorithm that operates merely based on social balance, mesoscopic structure of signed networks significantly remains hidden.

We propose a model for the formation of patterns in the visual cortex. The dynamical units of the model are Kuramoto phase oscillators that interact through a complex network structure embedded in two dimensions. In this way the strength of the interactions takes into account the geographical distance between units. We show that for different parameters, clustered or striped patterns emerge. Using the structure factor as an order parameter we are able to quantitatively characterize these patterns and present a phase diagram. Finally, we show that the model is able to reproduce patterns with cardinal preference, as observed in ferrets.

The influence of a periodic spatial forcing on the pattern formation in a generalized Cahn-Hilliard model describing Langmuir-Blodgett transfer is studied. The occurring locking effects enable a control mechanism for the pattern formation process. In the one-dimensional case the parameter range in which patterns are created is increased and the patterns' properties can be adjusted in a broader range. In two dimensions, one-dimensional stripe patterns can be destabilized, giving rise to a multitude of complex two-dimensional structures, including oblique and lattice patterns.

We study the soliton-like character of traveling bands in systems of interacting deformable self-propelled particles in two dimensions. The collision dynamics of the model in which migration velocity increases with increasing local density is investigated numerically by changing the relaxation rate of deformations. The bands are unstable upon head-on collisions for larger relaxation rates. This clearly indicates that deformability plays a crucial role of the soliton-like behavior.

We present a comprehensive analysis of salt transport and overlimiting currents in a microchannel during concentration polarization. We have carried out full numerical simulations of the coupled Poisson-Nernst-Planck-Stokes problem governing the transport and rationalized the behavior of the system. A remarkable outcome of the investigations is the discovery of strong couplings between bulk advection and the surface current; without a surface current, bulk advection is strongly suppressed. The numerical simulations are supplemented by analytical models valid in the long channel limit as well as in the limit of negligible surface charge. By including the effects of diffusion and advection in the diffuse part of the electric double layers, we extend a recently published analytical model of overlimiting current due to surface conduction.

We study the quantum critical behavior of networks consisting of Lipkin-Meshkov-Glick models with an anisotropic ferromagnetic coupling. We focus on the low-energy properties of the system within a mean-field approach and the quantum corrections around the mean-field solution. Our results show that the weak-coupling regime corresponds to the paramagnetic phase when the local field dominates the dynamics, but the local anisotropy leads to the existence of an exponentially degenerate ground state. In the strong-coupling regime, the ground state is twofold degenerate and possesses long-range magnetic ordering. Analytical results for a network with the ring topology are obtained.

A lyotropic chromonic liquid crystal (LCLC) is an orientationally ordered system made by self-assembled aggregates of charged organic molecules in water, bound by weak noncovalent attractive forces and stabilized by electrostatic repulsions. We determine how the ionic content of the LCLC, namely, the presence of mono- and divalent salts and $p\mathrm{H}$ enhancing agent, alter the viscoelastic properties of the LCLC. Aqueous solutions of the dye sunset yellow with a uniaxial nematic order are used as an example. By applying a magnetic field to impose orientational deformations, we measure the splay $K_1$, twist $K_2$, and bend $K_3$ elastic constants and rotation viscosity ${\gamma }_1$ as a function of concentration of additives. The data indicate that the viscoelastic parameters are influenced by ionic content in dramatic and versatile ways. For example, the monovalent salt NaCl decreases $K_3$ and $K_2$ and increases ${\gamma }_1$, while an elevated $p\mathrm{H}$ decreases all the parameters. We attribute these features to the ion-induced changes in length and flexibility of building units of LCLC, the chromonic aggregates, a property not found in conventional thermotropic and lyotropic liquid crystals formed by covalently bound units of fixed length.

Neurons generate magnetic fields which can be recorded with macroscopic techniques such as magnetoencephalography. The theory that accounts for the genesis of neuronal magnetic fields involves dendritic cable structures in homogeneous resistive extracellular media. Here we generalize this model by considering dendritic cables in extracellular media with arbitrarily complex electric properties. This method is based on a multiscale mean-field theory where the neuron is considered in interaction with a “mean” extracellular medium (characterized by a specific impedance). We first show that, as expected, the generalized cable equation and the standard cable generate magnetic fields that mostly depend on the axial current in the cable, with a moderate contribution of extracellular currents. Less expected, we also show that the nature of the extracellular and intracellular media influence the axial current, and thus also influence neuronal magnetic fields. We illustrate these properties by numerical simulations and suggest experiments to test these findings.

With the growth in world population, the density of crowds in public places has been increasing steadily, leading to a higher incidence of crowd disasters at high densities. Recent research suggests that emergent chaotic behavior at high densities—known collectively as crowd turbulence—is to blame. Thus, a deeper understanding of crowd turbulence is needed to facilitate efforts to prevent and plan for chaotic conditions in high-density crowds. However, it has been noted that existing algorithms modeling collision avoidance cannot faithfully simulate crowd turbulence. We hypothesize that simulation of crowd turbulence requires modeling of both collision avoidance and frictional forces arising from pedestrian interactions. Accordingly, we propose a model for turbulent crowd simulation, which incorporates a model for interpersonal stress and acceleration constraints similar to real-world pedestrians. Our simulated results demonstrate a close correspondence with observed metrics for crowd turbulence as measured in known crowd disasters.

A collective coordinate theory is developed for soliton ratchets in the damped discrete sine-Gordon model driven by a biharmonic force. An ansatz with two collective coordinates, namely the center and the width of the soliton, is assumed as an approximated solution of the discrete nonlinear equation. The dynamical equations of these two collective coordinates, obtained by means of the generalized travelling wave method, explain the mechanism underlying the soliton ratchet and capture qualitatively all the main features of this phenomenon. The numerical simulation of these equations accounts for the existence of a nonzero depinning threshold, the nonsinusoidal behavior of the average velocity as a function of the relative phase between the harmonics of the driver, the nonmonotonic dependence of the average velocity on the damping, and the existence of nontransporting regimes beyond the depinning threshold. In particular, it provides a good description of the intriguing and complex pattern of subspaces corresponding to different dynamical regimes in parameter space.

We carry out theoretical and experimental studies of cross-frequency synchronization of two pulse oscillators with time-delayed coupling. In the theoretical part of the paper we utilize the concept of phase resetting curves and analyze the system dynamics in the case of weak coupling. We construct a Poincaré map and obtain the synchronization zones in the parameter space for $m:n$ synchronization. To challenge the theoretical results we designed an electronic circuit implementing the coupled oscillators and studied its dynamics experimentally. We show that the developed theory predicts dynamical properties of the realistic system, including location of the synchronization zones and bifurcations inside them.

Experimental evidence of vibrational higher-order resonances in a bistable vertical-cavity surface-emitting laser driven by two harmonic signals with very different frequencies is reported. The phenomenon shows up in a parameter space (the dc current, the amplitude of the high-frequency signal) as well-defined structures with multiple local maxima at higher harmonics of the low-frequency signal. Such structures appear due to a strong suppression of higher harmonics for certain values of the high-frequency amplitude and the dc current. Complexity of the structures and the total number of the local maxima depend on the harmonic order $k$. The behavior of nonlinear distortion factor is also studied. The experimental results are in a good agreement with the numerical results which were obtained in the model of the bistable overdamped oscillator with biharmonic excitation.

We study interface and vortex motion in the two-component dissipative Ginzburg-Landau equation in two-dimensional space. We consider cases where the whole system is divided into several domains, and we assume that these domains are separated by interfaces and each domain contains quantized vortices. The equations for interface and vortex motion will be derived by means of a variational approach by Kawasaki. These equations indicate that, along an interface, the phase gradient fields of the complex order parameters is parallel to the interface. They also indicate that the interface motion is driven by the curvature and the phase gradient fields along the interface, and vortex motion is driven by the phase gradient field around the vortex. With respect to the static interactions between defects, we find an analogy between quantized vortices in a domain and electric charges in a vacuum domain surrounded by a metallic object in electrostatic. This analogy indicates that there is an attractive interaction between an interface and a quantized vortex with any charge. We also discuss several examples of interface and vortex motion.

The depolarization coefficients are calculated for multiply scattered linearly and circularly polarized light. For a number of media (aqueous suspension of polystyrene particles, water droplets in air), the calculations are carried out both numerically, with solving the vector radiative transfer equation and analytically, within the polarization mode approximation. In the latter case the depolarization coefficients are expressed explicitly in terms of the scattering and absorption coefficients, and the scattering matrix elements of the medium. The range of applicability of the polarization mode approximation is established. For most practically important cases, this method is shown to provide a satisfactory degree of accuracy. We also find the fundamental values of the depolarization coefficients for a Rayleigh medium.

After recognizing that point particles moving inside the extended version of the rippled billiard perform Lévy flights characterized by a Lévy-type distribution $P\left(l\right)\sim l^{-(1+\alpha )}$ with $\alpha =1$, we derive a generalized two-dimensional nonlinear map $M_{\alpha }$ able to produce Lévy flights described by $P\left(l\right)$ with $0<\alpha <2$. Due to this property, we call $M_{\alpha }$ the Lévy map. Then, by applying Chirikov's overlapping resonance criteria, we are able to identify the onset of global chaos as a function of the parameters of the map. With this, we state the conditions under which the Lévy map could be used as a Lévy pseudorandom number generator and furthermore confirm its applicability by computing scattering properties of disordered wires.