Continuous transitions between different periodic orbits in a one-dimensional inelastic particle system are investigated. We show that continuous transitions that occur when adding or subtracting a single collision are, generically, of co-dimension 2. We give a full mechanical description of the system and explain why this is the case. Surprisingly, we also show that there are an infinite set of degenerate transitions of co-dimension 1. We provide a theoretical analysis that gives a simple criteria to classify which transitions are degenerate purely using the discrete set of collisions that occur in the orbits. Our analysis allows us to understand the nature of the degeneracy. We also show that higher degrees of degeneracy can occur, and provide an explanation.

We investigate the dynamics of colloids at a fluid interface driven by attractive capillary interactions. At submillimeter length scales, the capillary attraction is formally analogous to two-dimensional gravity. In particular it is a nonintegrable interaction and it can be actually relevant for collective phenomena in spite of its weakness at the level of the pair potential. We introduce a mean-field model for the dynamical evolution of the particle number density at the interface. For generic values of the physical parameters the homogeneous distribution is found to be unstable against large-scale clustering driven by the capillary attraction. We also show that for the instability to be observable, the appropriate values for the relevant parameters (colloid radius, surface charge, external electric field, etc.) are experimentally well accessible. Our analysis contributes to current studies of the structure and dynamics of systems governed by long-ranged interactions and points toward their experimental realizations via colloidal suspensions.

The classical nucleation theory (CNT) is tested systematically by computer simulations of the two-dimensional (2D) and three-dimensional (3D) Ising models with a Glauber-type spin flip dynamics. While previous studies suggested potential problems with CNT, our numerical results show that the fundamental assumption of CNT is correct. In particular, the Becker-Döring theory accurately predicts the nucleation rate if the correct droplet free energy function is provided as input. This validates the coarse graining of the system into a one dimensional Markov chain with the largest droplet size as the reaction coordinate. Furthermore, in the 2D Ising model, the droplet free energy predicted by CNT matches numerical results very well, after a logarithmic correction term from Langer’s field theory and a constant correction term are added. But significant discrepancies are found between the numerical results and existing theories on the magnitude of the logarithmic correction term in the 3D Ising model. Our analysis underscores the importance of correctly accounting for the temperature dependence of surface energy when comparing numerical results and nucleation theories.

We study the smectic director structure of the rodlike liquid crystal $4\text{−}n$-dodecyl-$4^{\prime }$-cyanobiphenyl (12CB) confined in cylindrical cavities of 200 nm diameter in porous alumina templates by means of combined broadband dielectric spectroscopy, optical birefringence, and neutron scattering measurements. We show that the collective molecular orientation differs between entering the smectic A phase upon cooling from the isotropic state and entering the same phase upon heating while melting the confined crystal. We discuss this collective molecular realignment in terms of a competition between weak planar anchoring at the $p{\text{-Al}}_2{\text{O}}_3/12\text{CB}$ interface and a preferred texture typical of the crystallization of rodlike molecules in nanochannels (Bridgman growth).

A Green’s function method is developed to approach the spatiotemporal equations describing the cAMP production in Dictyostelium discoideum, markedly reducing numerical calculations times: cAMP concentrations and gradients are calculated just at the amoeba locations. A single set of parameters is capable of reproducing the different observed behaviors, from cAMP synchronization, spiral waves and reaction-diffusion patterns to streaming and mound formation. After aggregation, the emergence of a circular motion of amoebas, breaking the radial cAMP field symmetry, is observed.

The response behavior of binary fluid convection to low-frequency temporal modulation of the heating is studied for the case of a negative Soret coupling between temperature and concentration gradients. Numerical simulations using a finite difference method are carried out for ethanol-water mixtures subject to realistic boundary conditions. We study in particular the response when the Rayleigh number periodically drops below the saddle node in the bifurcation diagram of convective solutions under stationary heating, i.e., into a regime where convection would die out in the absence of modulation. Quasiperiodic traveling waves, several different periodic traveling waves, and synchronously modulated patterns with fixed spatial phase are found as stable solutions depending on parameters. The symmetry properties of the different periodic traveling waves are discussed. Anomalous variations of the mixing behavior relative to advection are observed and explained. Lateral and temporal Fourier decompositions are used together with other diagnostic tools to analyze the complex bifurcation and spatiotemporal properties that are caused by the interplay of modulated heating, nonlinear advection, Soret induced gradients, and mixing of the fluid.

A rigorous theoretical investigation has been made of fully nonlinear ion-acoustic waves in nonrelativistic and ultrarelativistic, collisionless, unmagnetized plasma containing of degenerate electrons and positrons, and classical cold ions. In both (nonrelativistic and ultrarelativistic) regimes the electrons and positrons are assumed to follow the corresponding Fermi distribution while the ions are described by the hydrodynamic equations. An energy balancelike equation involving a Sagdeev-type pseudopotential is derived separately for both the regimes. In addition, stationary periodic and solitary waves are also investigated for the two cases. The present work would be helpful to understand the excitation of nonlinear ion-acoustic waves in a degenerate plasma such as in superdense white dwarfs.

Free energies of dissipative media are reviewed. Then we use free-energy-optimal excitation and de-excitation fields to generate a dielectric’s time-reversal spectrum, with several properties: a) The spectrum generalizes the time-reversal parity from “even” and “odd” of conservative systems to an interval $\left[-1,+1\right]$ of “time-reversal eigenvalues” $\lambda$ in dissipative media. b) It yields eigenmodes that are complete: any state of the medium is optimally excitable or de-excitable by them. c) These excitations are orthogonal with respect to the work function of the medium and, so, d) characterize field excitations for the given medium that, when superimposed, only do work on the medium, not on each other via the medium-field interaction mechanism. Notions of en masse potential and kinetic energy in the dissipative medium arise through even $\left(\lambda =+1\right)$ and odd $\left(\lambda =-1\right)$ parity, but also other energy notions via alternative parity $\left(\left|\lambda \right|<1\right)$ under time reversal.

The Gibbs entropy of a microcanonical network ensemble is the logarithm of the number of network configurations compatible with a set of hard constraints. This quantity characterizes the level of order and randomness encoded in features of a given real network. Here, we show how to relate this entropy to large deviations of conjugated canonical ensembles. We derive exact expression for this correspondence using the cavity methods for the configuration model, for the ensembles with constraint degree sequence and community structure and for the ensemble with constraint degree sequence and number of links at a given distance.

In this paper we introduce a Langevin-type model of subdiffusion with tempered $\alpha$-stable waiting times. We consider the case of space-dependent external force fields. The model displays subdiffusive behavior for small times and it converges to standard Gaussian diffusion for large time scales. We derive general properties of tempered anomalous diffusion from the theory of tempered $\alpha$-stable processes, in particular we find the form of the fractional Fokker-Planck equation corresponding to the tempered subdiffusion. We also construct an algorithm of simulation of sample paths of the introduced process. We apply the algorithm to approximate solutions of the fractional Fokker-Planck equation and to study statistical properties of the tempered subdiffusion via Monte Carlo methods.

We study the random-walk problem on a deterministic scale-free network, in the presence of a set of static, identical targets; due to the strong inhomogeneity of the underlying structure the mean first-passage time (MFPT), meant as a measure of transport efficiency, is expected to depend sensitively on the position of targets. We consider several spatial arrangements for targets and we calculate, mainly rigorously, the related MFPT, where the average is taken over all possible starting points and over all possible paths. For all the cases studied, the MFPT asymptotically scales like $\sim N^{\theta }$, being $N$ the volume of the substrate and $\theta$ ranging from $1-\text{log}2/\text{log}3$, for central target(s), to 1, for a single peripheral target.

We consider the problem of diffusion-controlled evolution of the $A$-particle island—$B$-particle island system in a semi-infinite medium at propagation of the sharp annihilation front $A+B\to 0$. We present an exact asymptotic solution of this problem for the general case of an arbitrary ratio of species diffusivities $D$. This elegant analytic solution describes self-similar evolution of the island-island system at equal particle numbers of $A$ and $B$ species that decay by the law $N\propto t^{-\beta \left(D\right)}$ with a nonuniversal exponent $\beta \left(D\right)$, which is determined by a self-consistent condition of the front velocity selection and varies from $\beta \left(D\to 0\right)\propto D^{-1/2}\to \infty$ to $\beta \left(D\to \infty \right)=1/2$. In the quasistatic approximation, we derive nontrivial laws of the front width growth, which define the applicability limits of the presented solution for the cases of mean field and fluctuation fronts.

Gene regulatory networks typically have low in-degrees, whereby any given gene is regulated by few of the genes in the network. They also tend to have broad distributions for the out-degree. What mechanisms might be responsible for these degree distributions? Starting with an accepted framework of the binding of transcription factors to DNA, we consider a simple model of gene regulatory dynamics. There, we show that selection for a target expression pattern leads to the emergence of minimum connectivities compatible with the selective constraint. As a consequence, these gene networks have low in-degree and “functionality” is parsimonious, i.e., is concentrated on a sparse number of interactions as measured for instance by their essentiality. Furthermore, we find that mutations of the transcription factors drive the networks to have broad out-degrees. Finally, these classes of models are evolvable, i.e., significantly different genotypes can emerge gradually under mutation-selection balance.

The possibility of microscopic swimming by extraction of energy from an external flow is discussed, focusing on the migration of a simple trimer across a linear shear flow. The geometric properties of swimming, together with the possible generalization to the case of a vesicle, are analyzed. The mechanism of energy extraction from the flow appears to be the generalization to a discrete swimmer of the tank-treading regime of a vesicle. The swimmer takes advantage of the external flow by both extracting energy for swimming and “sailing” through it. The migration velocity is found to scale linearly in the stroke amplitude, and not quadratically as in a quiescent fluid. This effect turns out to be connected with the nonapplicability of the scallop theorem in the presence of external flow fields.

One-dimensional intermittent maps with stretched exponential $\delta x_t\sim \delta x_0{e}^{{\lambda }_{\alpha }{t}^{\alpha }}$ separation of nearby trajectories are considered. When $t\to \infty$ the standard Lyapunov exponent $\lambda ={\sum }_{i=0}^{t-1}\text{ln}\left|M^{\prime }\left(x_i\right)\right|/t$ is zero ($M^{\prime }$ is a Jacobian of the map). We investigate the distribution of ${\lambda }_{\alpha }={\sum }_{i=0}^{t-1}\text{ln}\left|M^{\prime }\left(x_i\right)\right|/t^{\alpha }$, where $\alpha$ is determined by the nonlinearity of the map in the vicinity of marginally unstable fixed points. The mean of ${\lambda }_{\alpha }$ is determined by the infinite invariant density. Using semianalytical arguments we calculate the infinite invariant density for the Pomeau-Manneville map, and with it we obtain excellent agreement between numerical simulation and theory. We show that $\alpha ⟨{\lambda }_{\alpha }⟩$ is equal to Krengel’s entropy and to the complexity calculated by the Lempel-Ziv compression algorithm. This generalized Pesin’s identity shows that $⟨{\lambda }_{\alpha }⟩$ and Krengel’s entropy are the natural generalizations of usual Lyapunov exponent and entropy for these systems.

It is known that impinging droplets can rebound off superhydrophobic while tend to wet hydrophilic and hydrophobic surfaces. In this work, we show that water droplets can bounce off nonsuperhydrophobic soft surfaces between lower and upper impact velocity limits. The cause for the rebound of the droplet is hypothesized as the formation of an air film at the interface due to the deformability of the surface when the impact velocity is larger than the lower limit. At large impact velocity, an air bubble is entrapped from the cavity formed during the spreading of the droplet on the surface. This air bubble coalesces with and releases the air film beneath the droplet when the impact velocity is larger than the upper limit, beyond which the surface becomes wetting and the rebound of droplets is not observed.

In this work, the dynamics and transport of a polarly driven filament is examined using a continuum slender-body model. Immersed in a viscous fluid, the filament gains polar propulsion from the motor proteins (anchored on the motility assay) while experiencing a viscous drag from the bottom wall. Results from the linear analysis on a straight polar filament illustrate the necessity of spatial inhomogeneity in the polar forcing for the buckling instability. The ensuing buckling leads to filament deformation, undulation, and change of its direction of motion in the numerical simulations. Repeated filament buckling in two types of motor protein concentration landscape results in diffusive transport of a polar filament on scales much larger than the mean-free path and the average duration between filament buckling events.

This paper presents a lattice Boltzmann method for laser interaction with weakly ionized plasmas considering electron impact ionization and three-body recombination. To simulate with physical properties of plasmas, the authors’ previous work on the rescaling of variables is employed and the electromagnetic fields are calculated from the Maxwell equations by using the finite-difference time-domain method. To calculate temperature fields, energy equations are derived separately from the Boltzmann equations. In this way, we attempt to solve the full governing equations for plasma dynamics. With the developed model, the continuous-wave ${\text{CO}}_2$ laser interaction with helium is simulated successfully.

Nonequilibrium molecular-dynamics simulations are presented for the shear rheology of suspensions of extended “jack”-shaped nanoparticles in an explicit solvent. The shear viscosity is measured for two jack-shaped nanoparticle suspensions for volume fractions from 0.01 to 0.15 and compared to spherical nanoparticles of the same mass. Large differences, in some cases, orders of magnitude, are observed for both the equilibrium viscosity and diffusion constant as the shape of the nanoparticle is varied. The source of enhanced viscosity is the very large effective volume swept out by these extended nanoparticles which allows them to become highly entangled even at low volume fraction.

Percolation for a planar lattice has a single percolation threshold, whereas percolation for a negatively curved lattice displays two separate thresholds. The enhanced binary tree (EBT) can be viewed as a prototype model displaying two separate percolation thresholds. We present an analytic result for the EBT model which gives two critical percolation threshold probabilities, $p_{c1}=\frac{1}{2}\sqrt{13}-\frac{3}{2}$ and $p_{c2}=1/2$, and yields a size-scaling exponent $\Phi =\text{ln}\left[\frac{p\left(1+p\right)}{1-p\left(1-p\right)}\right]/\text{ln}2$. It is inferred that the two threshold values give exact upper limits and that $p_{c1}$ is furthermore exact. In addition, we argue that $p_{c2}$ is also exact. The physics of the model and the results are described within the midpoint-percolation concept: Monte Carlo simulations are presented for the number of boundary points which are reached from the midpoint, and the results are compared to the number of routes from the midpoint to the boundary given by the analytic solution. These comparisons provide a more precise physical picture of what happens at the transitions. Finally, the results are compared to related works, in particular, the Cayley tree and Monte Carlo results for hyperbolic lattices as well as earlier results for the EBT model. It disproves a conjecture that the EBT has an exact relation to the thresholds of its dual lattice.