Approximate analytical chirped solitary pulse (chirped dissipative soliton) solutions of the one-dimensional complex cubic-quintic nonlinear Ginzburg-Landau equation are obtained. These solutions are stable and highly accurate under condition of domination of a normal dispersion over a spectral dissipation. The parametric space of the solitons is three-dimensional, that makes theirs to be easily traceable within a whole range of the equation parameters. Scaling properties of the chirped dissipative solitons are highly interesting for applications in the field of high-energy ultrafast laser physics.

The structural properties of static, jammed packings of monodisperse spheres in the vicinity of the jamming transition are investigated using large-scale computer simulations. At small wave number $k$, we argue that the anomalous behavior in the static structure factor, $S\left(k\right)\sim k$, is consequential of an excess of low-frequency, collective excitations seen in the vibrational spectrum. This anomalous feature becomes more pronounced closest to the jamming transition, such that $S\left(0\right)\to 0$ at the transition point. We introduce an appropriate dispersion relation that accounts for these phenomena that leads us to relate these structural features to characteristic length scales associated with the low-frequency vibrational modes of these systems. When the particles are frictional, this anomalous behavior is suppressed providing yet more evidence that the jamming transitions for frictional spheres lie at lower packing fractions than for frictionless spheres. These results suggest that the mechanical properties of jammed and glassy media may therefore be inferred from measurements of both the static and dynamical structure factors.

A disordered network of bonds with a fixed configuration can relax via a variety of unconstrained motions. These motions can be directly inferred from the topological arrangement of constraints without any geometrical information. We use the pebble game algorithm of Jacobs and Thorpe [D. J. Jacobs and M. F. Thorpe, Phys. Rev. Lett. 75, 4051 (1995)] to decompose the system into separate rigid clusters and identify the remaining degrees of freedom. Unconstrained motions can then be resolved in the form of translations and rotations of isolated groups of bonds and the internal motion within bond groups. We show that each motion can be assigned a characteristic thermal velocity and hence a relaxation time scale. We use this information to construct a relaxation function and also examine the spatial distribution of relaxation time scales. We investigate the sensitivity of the relaxation time scales and their spatial distribution when making individual bond changes in the system, and we consider the dependence of these time scales on the underlying structure.

We solve a model of polymers represented by self-avoiding walks on a lattice, which may visit the same site up to three times in the grand-canonical formalism on the Bethe lattice. This may be a model for the collapse transition of polymers where only interactions between monomers at the same site are considered. The phase diagram of the model is very rich, displaying coexistence and critical surfaces, critical, critical end point, and tricritical lines, as well as a multicritical point. From the grand-canonical results, we present an argument to obtain the properties of the model in the canonical ensemble, and compare our results with simulations in the literature. We do actually find extended and collapsed phases, but the transition between them, composed by a line of critical end points and a line of tricritical points, separated by the multicritical point, is always continuous. This result is at variance with the simulations for the model, which suggest that part of the line should be a discontinuous transition. Finally, we discuss the connection of the present model with the standard model for the collapse of polymers (self-avoiding, self-attracting walks), where the transition between the extended and collapsed phases is a tricritical point.

By means of time-of-flight neutron scattering, we have characterized the dynamic structure factor and the hydrogen motions of polyethylene above its melting point. As signatures of simple-liquid dynamics, we observe that (i) in the explored dynamic window, the intermediate scattering functions display a single-step decay, without reminiscence of cage effects, and (ii) the structural relaxation as observed at the intermolecular structure factor peak shows a weak temperature dependence, indicating a low degree of interchain cooperativity. However, stretched functional forms are observed for all length scales and temperatures investigated. An apparent direct crossover from the microscopic regime to Rouse-like dynamics suggests an essential role of connectivity in the observed stretching. Finally, while at momentum-transfer values above the structure factor peak the relation between coherent and incoherent characteristic times is reasonably described by the de Gennes narrowing, at larger length scales it is not reproduced by any existing approach.

The intracellular environment imposes a variety of constraints on biochemical reaction systems that can substantially change reaction rates and equilibria relative to an ideal solution-based environment. One of the most notable features of the intracellular environment is its dense macromolecular crowding, which, among many other effects, tends to strongly enhance binding and assembly reactions. Despite extensive study of biochemistry in crowded media, it remains extremely difficult to predict how crowding will quantitatively affect any given reaction system due to the dependence of the crowding effect on numerous assumptions about the reactants and crowding agents involved. We previously developed a two dimensional stochastic off-lattice model of binding reactions based on the Green’s function reaction dynamics method in order to create a versatile simulation environment in which one can explore interactions among many parameters of a crowded assembly system. In the present work, we examine interactions among several critical parameters for a model dimerization system: the total concentration of reactants and inert particles, the binding probability upon a collision between two reactant monomers, the mean time of dissociation reactions, and the diffusion coefficient of the system. Applying regression models to equilibrium constants across parameter ranges shows that the effect of the total concentration is approximately captured by a low-order nonlinear polynomial model, while the other three parameter effects are each accurately captured by a linear model. Furthermore, validation on tests with multi-parameter variations reveals that the effects of these parameters are separable from one another over a broad range of variation in all four parameters. The simulation work suggests that predictive models of crowding effects can accommodate a wider variety of parameter variations than prior theoretical models have so far achieved.

The Earth’s magnetic field provides an important source of directional information for many living organisms, especially birds, but the sensory receptor responsible for magnetic field detection still has to be identified. Recently, magnetic iron oxide particles were detected in dendritic endings of the ophthalmic nerves in the skin of the upper beak of homing pigeons and were shown to fulfill the special prerequisites of a biological receptor. Here we study the proposed receptor theoretically and formulate the criteria for which it becomes operational and can be used for registering the weak magnetic fields as, e.g., the geomagnetic field, by a bird.

We determine the elastic-mediated interaction between colloidal nanoparticles adsorbed on the surface of free-standing smectic films. In contrast with the short-range character of the elastic-mediated force between particles adsorbed on smectic films supported by a solid substrate, the effective force acquires a long-range character in free-standing films, decaying with the particles distance $R$ as slow as $1/R$. We also discuss the dependence of the effective interaction potential on the surface tension $\gamma$ and film thickness. We show that it decays as $1/\gamma$ in the regime of large surface tensions and becomes independent of the film thickness at a characteristic surface tension.

We propose a variant of the voter model by introducing the social diversity in the evolution process. Each individual is assigned a weight that is proportional to the power of its degree, where the power exponent $\alpha$ is an adjustable parameter that controls the level of diversity among individuals in the network. At each time step, a pair of connected individuals, say $i$ and $j$, are randomly selected to update their opinions. The probability $p_i$ of choosing $i$s opinion as their common opinion is proportional to $i$s weight. We consider the scale-free topology and concentrate on the efficiency of reaching the final consensus, which is significant in characterizing the self-organized systems. Interestingly, it is found that there exists an optimal value of $\alpha$, leading to the shortest consensus time. This phenomenon indicates that, although a strong influence of high-degree individuals is helpful for quick consensus achievement, over strong influence inhibits the convergence process. Other quantities, such as the probability of an individual’s initial opinion becomes the final opinion as a function of degree, the evolution of the number of opinion clusters, as well as the relationship between average consensus time and the network size, are also studied. Our results are helpful for better understanding the role of degree heterogeneity of the individuals in the opinion dynamics.

We present a mode of myopically selective interaction to study the evolutionary prisoner’s dilemma game in scale-free networks. Each individual has a reputation-based tolerance range and only tends to interact with the neighbors whose reputation is within its tolerance range. Moreover, its reputation is assessed in response to the interactions in the neighborhood. Interestingly, we show that moderate values of tolerance range can result in the best promotion of cooperation due to the emergence of group selection mechanism. Furthermore, we study the effects of weighting factor in the assessment rule of reputation on the evolution of cooperation. We also show how cooperation evolves in some extended situations, where an interaction stimulus payment is considered for individuals, and where the strategy and reputation of individuals can spread simultaneously. Our results may enhance the understanding of evolutionary dynamics in graph-structured populations where individuals conditionally play with their neighbors according to some myopic selection criteria.

Together with attractive couplings, repulsive couplings play crucial roles in determining important evolutions in natural systems, such as in learning and oscillatory processes of neural networks. The complex interactions between them have great influence on the systems. A detailed understanding of the dynamical properties under this type of couplings is of practical significance. In this paper, we propose a model to investigate the dynamics of attractive and repulsive couplings, which give rise to rich phenomena, especially for amplitude death (AD). The relationship among various dynamics and possible transitions to AD are illustrated. When the system is in the maximally stable AD, we observe the transient behavior of in-phase (high frequency) and out-of-phase (low frequency) motions. The mechanism behind the phenomenon is given.

The main characteristics of the linear Darrieus-Landau instability in the laser ablation flow are investigated. The dispersion relation of the instability is found numerically as a solution to an eigenvalue stability problem, taking into account the continuous structure of the flow. The results are compared to the classical Darrieus-Landau instability of a usual slow flame. The difference between the two cases is due to the specific features of laser ablation: sonic velocities of hot plasma and strong temperature dependence of thermal conduction. It is demonstrated that the Darrieus-Landau instability in laser ablation is much stronger than in the classical case. In particular, the maximum growth rate in the case of laser ablation is about three times larger than that for slow flames. The characteristic length scale of the Darrieus-Landau instability in the ablation flow is comparable to the total distance from the ablation zone to the critical zone of laser light absorption. The possibility of experimental observations of the Darrieus-Landau instability in laser ablation is discussed.

We apply the gas-kinetic scheme (GKS) for the direct numerical simulations (DNSs) of compressible decaying homogeneous isotropic turbulence (DHIT). We intend to study the accuracy, stability, and efficiency of the gas-kinetic scheme for DNS of compressible homogeneous turbulence depending on both flow conditions and numerics. In particular, we study the GKS with multidimensional, quasi-one-dimensional, dimensional-splitting, and smooth-flow approximations. We simulate the compressible DHIT with the Taylor microscale Reynolds number ${\text{Re}}_{\lambda }=72.0$ and the turbulence Mach number ${\text{Ma}}_{\text{t}}$ between 0.1 and 0.6. We compute the low-order statistical quantities including the total kinetic energy $K\left(t\right)$, the dissipation rate $\epsilon \left(t\right)$, the skewness $S_u\left(t\right)$, and the flatness $F_u\left(t\right)$ of the velocity field $\mathit{u}\left(\mathit{x},t\right)$. We assess the effects on the turbulence statistics due to the approximations made in the treatment of fluxes, the flux limiter, the accuracy of the interpolation, and the bulk viscosity. Our results show that the GKS is adequate for DNS of compressible homogeneous turbulence as far as the low-order turbulence statistics are concerned.

The bond-percolation properties of the recently introduced Hanoi networks are analyzed with the renormalization group. Unlike scale-free networks, these networks are meant to provide an analytically tractable interpolation between finite-dimensional, lattice-based models and their mean-field limits. In percolation, the hierarchical small-world bonds in the Hanoi networks impose order by uniting otherwise disconnected, local clusters. This “patchy” order results in merely a finite probability to obtain a spanning cluster for certain ranges of the bond probability, unlike the usual 0–1 transition found on ordinary lattices. The various networks studied here exhibit a range of phase behaviors, depending on the prevalence of those long-range bonds. Fixed points in general exhibit nonuniversal behavior.

Results from molecular dynamics simulations of two viscous molecular model liquids—the Lewis-Wahnström model of orthoterphenyl and an asymmetric dumbbell model—are reported. We demonstrate that the liquids have a “hidden” approximate scale invariance: equilibrium potential energy fluctuations are accurately described by inverse power-law (IPL) potentials, the radial distribution functions are accurately reproduced by the IPL’s, and the radial distribution functions obey the IPL predicted scaling properties to a good approximation. IPL scaling of the dynamics also applies—with the scaling exponent predicted by the equilibrium fluctuations. In contrast, the equation of state does not obey the IPL scaling. We argue that our results are general for van der Waals liquids, but do not apply, e.g., for hydrogen-bonded liquids.

The scaling of the monomer and island densities, island-size distribution (ISD), and capture-number distribution (CND) as a function of the fraction of occupied sites (coverage) and ratio $D_h/F$ of the monomer hopping rate $D_h$ to the (per site) monomer creation rate $F$ are studied for the case of irreversible nucleation and growth of fractal islands in three dimensions $\left(d=3\right)$. We note that our model is a three-dimensional analog of submonolayer growth in the absence of island relaxation and may also be viewed as a simplified model of the early stages of vacancy cluster nucleation and growth under irradiation. In contrast to results previously obtained for point-islands in $d=3$, for which mean-field behavior corresponding to a CND which is independent of island size was observed, our results indicate that for fractal islands the scaled CND increases approximately linearly with island size in the asymptotic limit of large $D_h/F$. In addition, while the peak height of the scaled ISD for fractal islands appears to diverge with increasing $D_h/F$, the dependence on $D_h/F$ is much weaker than for point-islands in $d=3$. The results of a self-consistent rate-equation calculation for the coverage and $D_h/F$ dependence of the average island and monomer densities are also presented and good agreement with simulation results is obtained. For the case of point-islands, the value of the exponent $\chi$ describing the $D_h/F$ dependence of the island density at fixed coverage, e.g., $N_{sat}\sim {\left(D_h/F\right)}^{-\chi }$, is in good agreement with the value $\left(\chi =1/3\right)$ expected for irreversible growth. However, for both compact and fractal islands in $d=3$, our results indicate that the value of $\chi$ $\left(\chi \simeq 0.42\right)$ is significantly larger. In order to explain this behavior, an analytical expression [e.g., $\chi =d_f/\left(3d_f-2\right)$] for the dependence of $\chi$ on island fractal dimension $d_f$ in $d=3$ is derived and found to give reasonable agreement with our simulation and rate-equation results for the case of point-islands $\left(d_f=\infty \right)$, compact islands $\left(d_f=3\right)$, and fractal islands $\left(d_f\simeq 2.5\right)$. A general expression for the exponent $\chi$, valid for $d\ge 2$, as a function of the critical island size $i$ and $d_f$ is also derived.

DNA rigidity is an important physical property originating from the DNA three-dimensional structure. Although the general DNA rigidity patterns in human promoters have been investigated, their distinct roles in transcription are largely unknown. In this paper, we discover four highly distinct human promoter groups based on similarity of their rigidity profiles. First, we find that all promoter groups conserve relatively rigid DNAs at the canonical $TATA$ box [a consensus $TATA\left(A/T\right)A\left(A/T\right)$ sequence] position, which are important physical signals in binding transcription factors. Second, we find that the genes activated by each group of promoters share significant biological functions based on their gene ontology annotations. Finally, we find that these human promoter groups correlate with the tissue-specific gene expression.

The quantification of the complexity of networks is, today, a fundamental problem in the physics of complex systems. A possible roadmap to solve the problem is via extending key concepts of information theory to networks. In this Rapid Communication we propose how to define the Shannon entropy of a network ensemble and how it relates to the Gibbs and von Neumann entropies of network ensembles. The quantities we introduce here will play a crucial role for the formulation of null models of networks through maximum-entropy arguments and will contribute to inference problems emerging in the field of complex networks.

We introduce a modified phase field crystal (MPFC) technique that self-consistently incorporates rapid strain relaxation alongside the usual plastic deformation and multiple crystal orientations featured by the traditional phase field crystal (PFC) technique. Our MPFC formalism can be used to study a host of important phase transformation phenomena in material processing that require rapid strain relaxation. We apply the MPFC model to study elastic and plastic deformations in nanocrystalline materials, focusing on the “reverse” Hall-Petch effect. Finally, we introduce a multigrid algorithm for efficient numerical simulations of the MPFC model.

Thermal creep flow (TCF) is a flow of gas driven by a temperature gradient along a solid boundary. Here, TCF is demonstrated experimentally in a dusty plasma. Stripes on a glass box are heated by laser beam absorption, leading to both TCF and a thermophoretic force. The design of the experiment allows isolating the effect of TCF. A stirring motion of the dust particle suspension is observed. By eliminating all other explanations for this motion, we conclude that TCF at the boundary couples by drag to the bulk gas, causing the bulk gas to flow, thereby stirring the suspension of dust particles. This result provides an experimental verification, for the field of fluid mechanics, that TCF in the slip-flow regime causes steady-state gas flow in a confined volume.