In the 70s Schelling introduced a multiagent model to describe the segregation dynamics that may occur with individuals having only weak preferences for “similar” neighbors. Recently variants of this model have been discussed, in particular, with emphasis on the links with statistical physics models. Whereas these models consider a fixed number of agents moving on a lattice, here, we present a version allowing for exchanges with an external reservoir of agents. The density of agents is controlled by a parameter which can be viewed as measuring the attractiveness of the city lattice. This model is directly related to the zero-temperature dynamics of the Blume-Emery-Griffiths spin-1 model, with kinetic constraints. With a varying vacancy density, the dynamics with agents making deterministic decisions leads to a variety of “phases” whose main features are the characteristics of the interfaces between clusters of agents of different types. The domains of existence of each type of interface are obtained analytically as well as numerically. These interfaces may completely isolate the agents leading to another type of segregation as compared to what is observed in the original Schelling model, and we discuss its possible socioeconomic correlates.

Chaos synchronization in a ring of diffusively coupled nonlinear oscillators driven by an external identical oscillator is studied. Based on numerical simulations we show that by introducing additional couplings at $\left(m{N}_c+1\right)$-th oscillators in the ring, where $m$ is an integer and $N_c$ is the maximum number of synchronized oscillators in the ring with a single coupling, the maximum number of oscillators that can be synchronized can be increased considerably beyond the limit restricted by size instability. We also demonstrate that there exists an exponential relation between the number of oscillators that can support stable synchronization in the ring with the external drive and the critical coupling strength ${\epsilon }_c$ with a scaling exponent $\gamma$. The critical coupling strength is calculated by numerically estimating the synchronization error and is also confirmed from the conditional Lyapunov exponents of the coupled systems. We find that the same scaling relation exists for $m$ couplings between the drive and the ring. Further, we have examined the robustness of the synchronous states against Gaussian white noise and found that the synchronization error exhibits a power-law decay as a function of the noise intensity indicating the existence of both noise-enhanced and noise-induced synchronizations depending on the value of the coupling strength $\epsilon$. In addition, we have found that ${\epsilon }_c$ shows an exponential decay as a function of the number of additional couplings. These results are demonstrated using the paradigmatic models of Rössler and Lorenz oscillators.

Ideally an embedding of an $N$-dimensional dynamical system is $N$-dimensional. Ideally, an embedding of a dynamical system with symmetry is symmetric. Ideally, the symmetry of the embedding is the same as the symmetry of the original system. This ideal often cannot be achieved. Differential embeddings of the Lorenz system, which possesses a twofold rotation symmetry, are not ideal. While the differential embedding technique happens to yield an embedding of the Lorenz attractor in three dimensions, it does not yield an embedding of the entire flow. An embedding of the flow requires at least four dimensions. The four dimensional embedding produces a flow restricted to a twisted three dimensional manifold in ${\mathbb{R}}^4$. This inversion symmetric three-manifold cannot be projected into any three dimensional Euclidean subspace without singularities.

We address the dynamical behavior of a single polymer chain under nanometric confinement. We show how neutron spin-echo, combined with contrast matching and zero average contrast, makes it possible to, all at once, (i) match the intense porous detrimental elastic small angle neutron scattering contribution to the total intermediate scattering function $I\left(Q,t\right)$ and (ii) measure the $Q$ dependence of the dynamical modes of a single chain under confinement. The method presented here has a general relevance when probing the large scale dynamics of a system of large molecular mass under confinement.

While uniform temperature has no effect on equilibrium properties of hard-core systems, its gradient might substantially change their behavior. In particular, in hard-disk system subject to temperature difference $\Delta T$ disks are repelled from the hot boundary of the system and accumulate at the cold one. Using event-driven molecular dynamics simulations we show that for sufficiently large $\Delta T$ or coverage ratio ${\rho }^{\ast }$, crystal forms at the cold boundary. In this spatially inhomogeneous system a significant decrease of diffusivity of disks clearly marks the stationary interface between liquid and crystal. Such a behavior is also supported through calculation of the radial distribution function and the bond order parameter. Simulations show that for this nonequilibrium system the equipartition of energy holds and velocity obeys the Boltzmann distribution.

We adapt a recent theory for the random close packing of polydisperse spheres in three dimensions [R. S. Farr and R. D. Groot, J. Chem. Phys. 131, 244104 (2009)] in order to predict the Hausdorff dimension $d_A$ of the Apollonian gasket in dimensions 2 and above. Our approximate results agree with published values in two and three dimensions to within 0.05% and 0.6%, respectively, and we provide predictions for dimensions 4–8.

The paper investigates the effects of surface stiffness on the slip process aiming to obtain a better insight of the momentum transfer at nanoscale. The surface stiffness is modeled through the stiffness, $\kappa$, of spring potentials, which are employed to construct the thermal walls. It is shown that variations of stiffness, $\kappa$, influence the slip mechanism either toward slip or stick conditions. Increasing the values of $\kappa$ alters the oscillation frequency and the mean displacement of the wall particles toward higher and lower values, respectively. Our results suggest that the amount of slip produced as a function of stiffness follows a common pattern that can be modeled through a fifth-order polynomial function.

Jagla ramp particles, interacting through a ramp potential with two characteristic length scales, are known to show in their bulk phase thermodynamic and dynamic anomalies, similar to what is found in water. Jagla particles also exhibit a line of phase transitions separating a low density liquid phase and a high density liquid phase, terminating in a liquid-liquid critical point in a region of the phase diagram that can be studied by simulations. Employing molecular dynamics computer simulations, we study the thermodynamics and the dynamics of solutions of hard spheres (HS) in a solvent formed by Jagla ramp particles. We consider the cases of HS mole fraction $x_{\text{HS}}=0.10$, 0.15, and 0.20, and also the case $x_{\text{HS}}=0.50$ (a 1:1 mixture of HS and Jagla particles). We find a liquid-liquid critical point, up to the highest HS mole fraction; its position shifts to higher pressures and lower temperatures upon increasing $x_{\text{HS}}$. We also find that the diffusion coefficient anomalies appear to be preserved for all the mole fractions studied.

We show that the sequence of distorted commensurate phases observed in tilted chiral smectics is explained by the gain in electrostatic and elastic energies due to the lock-in of the unit cell to a number of layers which is the integer closest to the ratio of the helix pitch over the smectic layer thickness of the subjacent ${\text{Sm-}C}_{\alpha }^{\ast }$ phase. We also explain the sign change of the helicity in the middle of the sequence by a balance between two twist sources one intrinsic and another due to the distortion of the ${\text{Sm-}C}_{\alpha }^{\ast }$.

In order to search for nontrivial properties of the thermal conductivity with possible applications in the mechanism of heat flow control, we address the detailed analytical study of simple microscopic models. We investigate harmonic chains of oscillators with alternate masses and thermal baths at the boundaries only, and show that the heat flow decays as the inverse of the square of the mass difference, in contrast with the homogeneous chain, where it decays with the inverse of the mass. We recall some results for the chain with self-consistent inner reservoirs, another model with similar behavior, in order to show that it may be a general property.

In this paper, we present an approach in which synchronization of chaos is used to address identification problems. In particular, we are able to identify (i) the discontinuity points of systems described by piecewise dynamical equations and (ii) the delays of systems described by delay differential equations. Delays and discontinuities are widespread features of the dynamics of both natural and manmade systems. The foremost goal of the paper is to present a general and flexible methodology that can be used in a broad variety of identification problems.

Light irradiation can induce the vectorial motion of an aerosol particle. This phenomenon is often explained in terms of inelastic collision between gas molecules and the aerosol particle under a temperature gradient. We considered the photophoresis of a micron-sized liquid droplet in a rarefied gas atmosphere based on the Boltzmann equation for the atmosphere coupled with the Navier-Stokes equation for the droplet. Two features attributable to induced internal flow in the droplet are analyzed: the contribution of homogeneous energy inflow to the motion of the droplet and the nonlinear scaling of the photophoretic velocity depending on the irradiated light intensity.

We study the case in which the nonlinear Schrödinger equation (NLSE) on simple networks consisting of vertices and bonds has an infinite number of constants of motion and becomes completely integrable just as in the case of a simple one-dimensional (1D) chain. Here the strength of cubic nonlinearity is different from bond to bond, and networks are assumed to have at least two semi-infinite bonds with one of them working as an incoming bond. The connection formula at vertices obtained from norm and energy conservation rules shows (1) the solution on each bond is a part of the universal (bond-independent) soliton solution of the completely integrable NLSE on the 1D chain, but is multiplied by the inverse of square root of bond-dependent nonlinearity; (2) nonlinearities at individual bonds around each vertex must satisfy a sum rule. Under these conditions, we also showed an infinite number of constants of motion. The argument on a branched chain or a primary star graph is generalized to other graphs, i.e., general star graphs, tree graphs, loop graphs and their combinations. As a relevant issue, with use of reflectionless propagation of Zakharov-Shabat’s soliton through networks we have obtained the transmission probabilities on the outgoing bonds, which are inversely proportional to the bond-dependent strength of nonlinearity. Numerical evidence is also given to verify the prediction.

We discuss quantum entanglement in the context of the thermodynamic arrow of time. We review the role of correlations in entropy-decreasing events and prove that the occurrence of a transformation between two thermodynamic states constitutes a new type of entanglement witness, one not defined as a separating plane in state space between separable and entangled states, but as a physical process dependent on the local initial properties of the states. Extending work by Partovi, we consider a general entangled multipartite system that allows large reversals of the thermodynamic arrow of time. We describe a hierarchy of arrows that arises from the different correlations allowed in a quantum state and examine these features in the context of Maxwell’s Demon. We examine in detail the case of three qubits, and also propose some simple experimental demonstrations possible with small numbers of qubits.

A double-stranded system, modeled by a Frenkel-Kontorova lattice, is studied through nonequilibrium molecular dynamics simulations. We have investigated the thermal conductance influenced by the intrachain interaction as well as by the interchain interaction. It is found that the intrachain interaction always enhance the thermal conductance. The interchain interaction, however, has a positive effect on the thermal conductance in the case of strong nonlinear potential, and has a negative effect on the thermal conductance in the case of weak nonlinear potential. This phenomenon can be explained by the transition of thermal transport mode and the phonon band shift of the particles. It is suggested that the inter- and intrachain interactions present different thermal properties in double-stranded lattices.

We study the dynamics of the static-to-flow transition in a model material made of elastic particles immersed in a viscous fluid. The interaction between particle surfaces includes their viscous lubrication, a sharp repulsion when they get closer than a tuned steric length, and their elastic deflection induced by those two forces. We use soft dynamics to simulate the dynamics of this material when it experiences a step increase in the shear stress and a constant normal stress. We observe a long creep phase before a substantial flow eventually establishes. We measure the change in volume (dilatancy) and find that during the creep phase, it does not change significantly. We find that the typical creep time relies on an internal relaxation process, namely, the separation of two particles driven by the applied stress and resisted by the viscous friction. The present mechanism should be relevant for granular pastes, living cells, emulsions, and wet foams.

We develop and analyze a two-mode phase-field-crystal model to describe fcc ordering. The model is formulated by coupling two different sets of crystal density waves corresponding to $⟨111⟩$ and $⟨200⟩$ reciprocal lattice vectors, which are chosen to form triads so as to produce a simple free-energy landscape with coexistence of crystal and liquid phases. The feasibility of the approach is demonstrated with numerical examples of polycrystalline and (111) twin growth. We use a two-mode amplitude expansion to characterize analytically the free-energy landscape of the model, identifying parameter ranges where fcc is stable or metastable with respect to bcc. In addition, we derive analytical expressions for the elastic constants for both fcc and bcc. Those expressions show that a nonvanishing amplitude of [200] density waves is essential to obtain mechanically stable fcc crystals with a nonvanishing tetragonal shear modulus $\left(C_{11}-C_{12}\right)/2$. We determine the model parameters for specific materials by fitting the peak liquid structure factor properties and solid-density wave amplitudes following the approach developed for bcc [K.-A. Wu and A. Karma, Phys. Rev. B 76, 184107 (2007)]. This procedure yields reasonable predictions of elastic constants for both bcc Fe and fcc Ni using input parameters from molecular dynamics simulations. The application of the model to two-dimensional square lattices is also briefly examined.

Confinement is a versatile and well-established tool to study the properties of polymers either to understand biological processes or to develop new nanobiomaterials. We investigate the conformations of a semiflexible polymer ring in weak spherical confinement imposed by an impenetrable shell. We develop an analytic argument for the dominating polymer trajectory depending on polymer flexibility considering elastic and entropic contributions. Monte Carlo simulations are performed to assess polymer ring conformations in probability densities and by the shape measures asphericity and nature of asphericity. Comparison of the analytic argument with the mean asphericity and the mean nature of asphericity confirm our reasoning to explain polymer ring conformations in the stiff regime, where elastic response prevails.