We study numerically the phases and dynamics of a dense collection of self-propelled particles with soft repulsive interactions in two dimensions. The model is motivated by recent in vitro experiments on confluent monolayers of migratory epithelial and endothelial cells. The phase diagram exhibits a liquid phase with giant number fluctuations at low packing fraction $\phi$ and high self-propulsion speed $v_0$ and a jammed phase at high $\phi$ and low $v_0$. The dynamics of the jammed phase is controlled by the low-frequency modes of the jammed packing.

We study heat generation and transport properties for solids in the presence of arbitrary time-dependent forces. Using a nonequilibrium Green’s function (NEGF) approach we present an exact analytical expression of heat current for the linear system. We found that the current can be expressed in terms of the displacement of the atoms in the center and the self-energy of the heat bath. We carry out the calculation for a periodic driving force and study the dependence of steady state current on frequency and system size for one- and two-dimensional systems. We obtain an explicit solution of current for a one-dimensional linear chain connected with a Rubin bath. We found that the heat current is related to the density of states of the system and is independent of the bath temperature in ballistic transport. The baths can absorb energy only when the external frequency lies within the phonon band frequency. We also discuss the effect due to nonlinear interactions in the center.

We construct a nonperturbative fully analytical approximation for the thermodynamics and the structure of nonadditive hard-sphere fluid mixtures. The method essentially lies in a heuristic extension of the Percus-Yevick solution for additive hard spheres. Extensive comparison with Monte Carlo simulation data shows a generally good agreement, especially in the case of like-like radial distribution functions.

We study the effective interactions between nanoparticles immersed in an athermal polymer solution using Molecular dynamics. The directly measured polymer-induced depletion forces are well described with a scaling model in which the attraction between particles is caused by the depletion of concentration blobs and thus independent of the length of the polymer chains. We find strong evidence for a repulsive barrier which arises when the distance between the particles is of the order of the correlation length of the solution and which can be interpreted as a packing effect of concentration blobs. Interestingly, the scaling picture can be extended into the regime in which higher virial coefficients of the polymer solution become relevant. We derive a universal relation between the attraction force at the particle contact, $f\left(0\right)$, and the osmotic pressure $\Pi$ as $f\left(0\right)\sim {\Pi }^{2/3}$, demonstrating its validity over a wide range of concentrations of the polymer solution.

Analytical solutions of the diffusion equation for a radially $N$-layered cylinder were derived in the steady-state, frequency, and time domains. Solutions for axially infinite and finite cylinders are presented. The derived formulas were compared to a known solution of the diffusion equation for a layered semi-infinite geometry and to Monte Carlo simulations, showing excellent and good agreement, respectively. The analytical solutions were applied to calculate the light propagation in models of the forearm and the finger, demonstrating the improvement in analysis of hemodynamics measurements compared to the formulas used so far.

Starting from an observed single time series, it is shown how to reconstruct a global model in the original phase space by using the ansatz library approach. This model is then compared to the underlying dynamical system that describes the initial time series, and the nonuniqueness of the reconstructed model is discussed. This framework is extended by taking an additional time scaling factor in the reconstructed model class under consideration.

We analyze the synchronization dynamics of a model obtained from the phase reduction of the mean-field complex Ginzburg-Landau equation with heterogeneity. We present exact results that uncover the role of dissipative and reactive couplings on the synchronization transition when shears and natural frequencies are independently distributed. As it occurs in the purely dissipative case, an excess of shear diversity prevents the onset of synchronization, but this does not hold true if coupling is purely reactive. In this case, the synchronization threshold turns out to depend on the mean of the shear distribution, but not on all the other distribution’s moments.

The nonstationary evolution of observable quantities in complex systems can frequently be described as a juxtaposition of quasistationary spells. Given that standard theoretical and data analysis approaches usually rely on the assumption of stationarity, it is important to detect in real time series intervals holding that property. With that aim, we introduce a segmentation algorithm based on a fully nonparametric approach. We illustrate its applicability through the analysis of real time series presenting diverse degrees of nonstationarity, thus showing that this segmentation procedure generalizes and allows one to uncover features unresolved by previous proposals based on the discrepancy of low order statistical moments only.

We numerically investigate the necessary ingredients for reentrant behavior in the phase diagram of physical systems. Studies on the possibly simplest model that exhibits reentrance, the two-dimensional random-bond Ising model, show that reentrant behavior is generic whenever frustration is present in the model. For both discrete and continuous disorder distributions, the phase diagram in the disorder-temperature plane is found to be reentrant, where for some disorder strengths a paramagnetic phase exists at both high and low temperatures, but an ordered ferromagnetic phase exists for intermediate temperatures.

The spin-bath induced decay of a quantum system out of a metastable state, which can tunnel and undergo thermal activation, is considered. The treatment is based on the $c$-number description of bath degrees of freedom and a canonical thermal distribution of the associated $c$-number variables. We show that, apart from the usual frequency prefactor and its dynamical modification in the spatial diffusion-limited regime, i.e., the Grote-Hynes factor, the rate coefficient contains two other factors. One is a quantum correction to the dynamical factor resulting from quantum transmission and reflection of the particle at the finite barrier. This term exhibits exponential rate enhancement at low temperature. The other one is a quantum corrected Arrhenius factor, which incorporates the effect of thermal saturation. At 0 K, dissipation due to tunneling multiplies the tunneling probability by a factor that gets exponentially damped by friction, implying that, at this temperature, the behavior of spin bath is almost identical to that of a harmonic bath.

We investigate by means of computer simulations the effect of structural disorder on the statistics of cracking for a thin layer of material under uniform and isotropic drying. For this purpose, the layer is discretized into a triangular lattice of springs with a slightly randomized arrangement. The drying process is captured by reducing the natural length of all springs by the same factor, and the amount of quenched disorder is controlled by varying the width $\xi$ of the distribution of the random breaking thresholds for the springs. Once a spring breaks, the redistribution of the load may trigger an avalanche of breaks, not necessarily as part of the same crack. Our computer simulations revealed that the system exhibits a phase transition with the amount of disorder as control parameter: at low disorders, the breaking process is dominated by a macroscopic crack at the beginning, and the size distribution of the subsequent breaking avalanches shows an exponential form. At high disorders, the fracturing proceeds in small-sized avalanches with an exponential distribution, generating a large number of microcracks, which eventually merge and break the layer. Between both phases, a sharp transition occurs at a critical amount of disorder ${\xi }_c=0.40\pm 0.01$, where the avalanche size distribution becomes a power law with exponent $\tau =2.6\pm 0.08$, in agreement with the mean-field value $\tau =5/2$ of the fiber bundle model. Moreover, good quality data collapses from the finite-size scaling analysis show that the average value of the largest burst $\langle {\Delta }_{\text{max}}\rangle$ can be identified as the order parameter, with $\beta /\nu =1.4$ and $1/\nu \simeq 1.0$, and that the average ratio $\langle m_2/m_1\rangle$ of the second $m_2$ and first moments $m_1$ of the avalanche size distribution shows similar behavior to the susceptibility of a continuous transition, with $\gamma /\nu =1$, $1/\nu \simeq 0.9$. These results suggest that the disorder-induced transition of the breakup of thin layers is analogous to a continuous phase transition.

We study the formation of crystalline clusters for a two-dimensional (2D) sinusoidally vibrated granular gas, with maximum vertical acceleration smaller than gravity, using fully 3D simulations. It is found that this phenomenon arises from the spontaneous segregation of the granulate into two dynamical modes: one of grains that bounce in synchrony with the motion of the sustaining plate (“bouncers”) and another of grains that cease to bounce and simply rolls on the plate, without ever loosing contact with it (“rollers”). These two dynamical categories are quite robust with respect to perturbations. The populations for bouncers and rollers depend on the preparation of the granulate and can be made to take arbitrary values in all the range of accelerations where both dynamical modes are present. It is found that the dynamical mode with the largest population coalesces in clusters under the influence of the other mode, whose grains act as a higher pressure gas that compresses the clusters. In this way it is possible to produce clusters of rollers or clusters of bouncers. A gas made of grains from only one dynamical class shows only weak density fluctuations. When the occupation fractions for both modes are similar, one observes segregation and clusters of both types. The clustering of the gas is monitored using both the average coordination number and the local hexatic order parameter ${\psi }_6$. Energy flows in the plane are monitored, and it is shown that roller-bouncer collisions increase horizontal kinetic energy, while all other types of collisions reduce this energy. We find that friction with the substrate is the main sink of horizontal energy for these granular gases.

Experiments with nematic liquid crystals have proved that an ultrasonic wave exerts a torque on the liquid-crystal molecules, causing a change in its optical properties (acousto-optic effect). In this work we report a theoretical study on the theory proposed by Selinger et al. [Phys. Rev. E 66, 051708 (2002).] and, independently, by Boneto et al. [Chem. Phys. Lett. 361, 237 (2002).] for this effect. We solved exactly the Euler-Lagrange equation, which determines the equilibrium configuration of the director profile. The liquid-crystal director is also calculated in powers of the acoustic intensity and a comparison of this expansion with the solution in a closed form is given. We show the existence of minimizers that does not satisfy the Euler-Lagrange equation and report the possibility of observing a Fréedericksz-type transition. Finally, a possibility of controlling light by ultrasonic wave is also discussed in the limit of low acoustic intensity.

Several experiments have reported that ferroelectric nanoparticles have drastic effects on nematic liquid crystals—increasing the isotropic-nematic transition temperature by about 5 K, and greatly increasing the sensitivity to applied electric fields. In a recent paper [Lopatina and Selinger, Phys. Rev. Lett. 102, 197802 (2009)], we modeled these effects through a Landau theory, based on coupled orientational order parameters for the liquid crystal and the nanoparticles. This model has one important limitation: Like all Landau theories, it involves an expansion of the free energy in powers of the order parameters, and hence it overestimates the order parameters that occur in the low-temperature phase. For that reason, we now develop a new Maier-Saupe-type model, which explicitly shows the low-temperature saturation of the order parameters. This model reduces to the Landau theory in the limit of high temperature or weak coupling, but shows different behavior in the opposite limit. We compare these calculations with experimental results on ferroelectric nanoparticles in liquid crystals.

We propose an adaptive multiscale approach to data analysis based on synchronization. The approach is nonlinear, data driven in the sense that it does not rely on a priori chosen basis, and automatically determines the data scale. Numerical results for one- and two-dimensional cases illustrate that the method works effectively for the usual modulated signals such as chirps, etc., as well as for more complicated data with multiple scales. The method extends straightforwardly to functions defined on weighted graphs and grids in high dimensions. Connections with some other recent approaches to multiscale analysis are briefly discussed.

This numerical study of the axisymmetric motion of a viscous incompressible fluid in an elongated cylindrical container explains how colliding counterflows develop. Two swirling flows enter the container through peripheral inlets and leave it through central exhausts symmetrically from both ends. Different flow rates, characterized by the Reynolds number Re, are studied for a fixed swirl number. For small Re, the throughflow (TF) is limited to the inlet-exhaust vicinities and a few circulation cells occupy the rest of the interior. As Re grows, (i) the circulation cells disappear while the TF reaches the container's midsection and becomes U shaped, moving near the sidewall inward and going back near the container axis; elongated circulation regions develop separating the TF branches; (ii) the flow convergence to the axis focuses near the container's midsection, resulting in the vortex breakdown development; (iii) the swirl-induced low pressure causes suction of the ambient fluid through the central parts of the exhausts; (iv) the suction flow reaches the container's midsection, turns around, mixes with the driving TF, forms an annular outflow, and leaves through the exhaust periphery. The two factors, (a) swirl decay due to friction at the sidewall and (b) the focused flow convergence to the axis, constitute the physical mechanism of the colliding counterflows. Such flow pattern is favorable for a vortex solid-fuel combustor.

The stability of liquid films flowing down a vertical porous cylinder is investigated in this paper. Fluids in the porous medium are assumed to be governed by Darcy's law. The Beaver-Joseph conditions on the liquid-porous surface are applied, and the influence of the porous medium reduces as a slip condition on the cylinder, which leads to the one-sided model. A Benney-type equation governing the interfacial shape is derived to study the nonlinear behavior of liquid films. Linear stability analysis shows that the film flow system on a porous vertical cylinder is more unstable than that on a solid impermeable vertical cylinder and that increasing the permeability of the porous medium enhances the destabilizing effect. Nonlinear studies examine our linear stability analysis. We find that, for Reynolds number $\text{Re}=0$, as the permeability parameter increases, the rupture time of film decreases; for $\text{Re}>0$, Rayleigh-Plateau instability is suppressed, and disturbances evolve to saturated traveling waves. By increasing the permeability parameter, the amplitude of traveling wave increases, and the wave speed increases too. Aside from that, the wave speed increases with increasing Re.

We present numerical calculations of the linearized Navier-Stokes equations for axially extended and axially localized spiral structures in the Taylor-Couette system. The eigenvalue surface for spiral vortices with azimuthal wave number $M=2$ shows significantly more structure than that for vortices with $M=0$ and 1. Islands are found in parameter space where axially periodic vortex perturbations can grow. Bicriticality of different axial wave numbers is observed. Furthermore, parameter islands of absolute instability are found where wave packets consisting of near-critical extended perturbations can grow and expand via oppositely moving fronts. Some results are compared with those of the Ginzburg-Landau approximation.

We study the mechanical buckling of a freestanding superfluid layer. A topological defect in the phase of the quantum order parameter distorts the underlying metric into a surface of negative Gaussian curvature, irrespective of the sign of the defect charge. The resulting instability is in striking contrast with classical buckling, where the in-plane strain induced by positive (negative) disclinations is screened by positive (negative) curvature. We derive the conditions under which the quantum buckling instability occurs in terms of the dimensionless ratio between superfluid stiffness and bending modulus. An ansatz for the resulting shape of the buckled surface is analytically and numerically confirmed.

The interaction of a Zeldovich-Frank-Kamenetsky reaction-diffusion front with a localized defect is studied numerically and analytically. For the analysis, we start from conservation laws and develop simple, collective variable, ordinary differential equations for the front position and width. Their solutions are in good agreement with the solutions of the full problem. Finally, using this reduced model, we explain the pinning of the front on a large defect and obtain a quantitative criterion.