We present numerical results from a simulation of a granular collider experiment [B. Painter, M. Dutt, and R. P. Behringer, Physica D 175, 43 (2003)] using a numerical model which accounts for substrate frictional effects [M. Dutt and R. P. Behringer, Phys. Rev. E 70, 061304 (2004)]. We find the gradual birth and growth of a central cluster for the final state of the particles that depends on the system size, the substrate frictional dissipation, and the initial average kinetic energy. For systems where a central cluster is observed in the final state, the autocorrelation function $C\left(r\right)$ of the interparticle spacing satisfies a Gaussian functional form $C\left(r\right)=A{e}^{-(r∕\sigma {)}^2}$. We also find that the fluctuation speed distributions adhere to a Maxwell-Boltzmann distribution for times in the vicinity of collapse. Our results strongly indicate that the principal mechanism responsible for the energy and momentum dissipation is the particle-substrate kinetic friction. Our findings reiterate the importance of considering the effects of substrate friction in particle-substrate systems, as shown by the agreement between our numerical results with experimental findings of Painter, Dutt, and Behringer.

Orientation distributions in droplets of liquid crystals with homeotropic anchoring are computed with a simulated annealing algorithm that minimizes the free energy of the Oseen-Frank continuum theory. The droplets exhibit multiple orientational steady states that are separated by finite energy barriers over the entire range of the dimensionless ratio of surface to elastic forces, with maximum transition energy densities of the order of $2000\mathrm{J}∕{\mathrm{m}}^3\left(\mathrm{Pa}\right)$ for a typical liquid crystalline droplet with a spherical radius of $1\mu \mathrm{m}$. The transition energy densities decrease with elongation to spheroidal droplets with aspect ratios of four or more, indicating that droplet elongation is favored to drive surface-induced transitions.

We show that the mechanical properties of a worm-like-chain (WLC) polymer, of contour length $L$ and persistence length $\lambda$ such that $t=L∕\lambda \sim O\left(1\right)$, depend both on the ensemble and the constraint on end orientations. In the Helmholtz ensemble, multiple minima in the free energy near $t=4$ persists for all kinds of orientational boundary conditions. The qualitative features of projected probability distribution of end-to-end vector depend crucially on the embedding dimensions. A mapping of the WLC model, to a quantum particle moving on the surface of a unit sphere, is used to obtain the statistical and mechanical properties of the polymer under various boundary conditions and ensembles. The results show excellent agreement with Monte Carlo simulations.

Narrowband signals have fast and slow time scales. The transmission of narrowband signal features on both times cales, by spiking neurons, is demonstrated experimentally and theoretically. The interaction of the narrowband input and the threshold nonlinearity may create out-of-band interference, hindering the transmission of signals in a low-frequency range. The resultant out-of-band signal is the “envelope,” or time-varying modulation of the narrowband signal. The levels of noise and nonlinearity intrinsic to the neuron gate transmission on the slow “envelope” time scale. When a narrowband and a distinct slow signal drive the neuron, the slow signal may be poorly transmitted. Increasing intrinsic noise in an averaging network removes the envelope in favor of the slow signal, paradoxically increasing the signal-to-noise ratio. These gating effects are generic for threshold and excitable systems.

DNA torsion dynamics is essential in the transcription process; a simple model for it, in reasonable agreement with experimental observations, has been proposed by Yakushevich (Y) and developed by several authors; in this, the nucleotides (the DNA subunits made of a sugar-phosphate group and the attached nitrogen base) are described by a single degree of freedom. In this paper we propose and investigate, both analytically and numerically, a “composite” version of the Y model, in which the sugar-phosphate group and the base are described by separate degrees of freedom. The model proposed here contains as a particular case the Y model and shares with it many features and results, but represents an improvement from both the conceptual and the phenomenological point of view. It provides a more realistic description of DNA and possibly a justification for the use of models which consider the DNA chain as uniform. It shows that the existence of solitons is a generic feature of the underlying nonlinear dynamics and is to a large extent independent of the detailed modeling of DNA. The model we consider supports solitonic solutions, qualitatively and quantitatively very similar to the Y solitons, in a fully realistic range of all the physical parameters characterizing the DNA.

We consider the inverse-folding problem for RNA secondary structures: for a given (pseudo-knot-free) secondary structure we want to find a sequence that has a certain structure as its ground state. If such a sequence exists, the structure is called designable. We have implemented a branch-and-bound algorithm that is able to do an exhaustive search within the sequence space, i.e., gives an exact answer as to whether such a sequence exists. The bounds required by the branch-and-bound algorithm are calculated by a dynamic programming algorithm. We consider different alphabet sizes and an ensemble of random structures, which we want to design. We find that for two letters almost none of these structures are designable. The designability improves for the three-letter case, but still a significant fraction of structures is undesignable. This changes when we look at the natural four-letter case with two pairs of complementary bases: undesignable structures are the exception, although they still exist. Finally, we also study the relation between designability and the algorithmic complexity of the branch-and-bound algorithm. Within the ensemble of structures, a high average degree of undesignability is correlated with a long time to prove that a given structure is (un-)designable. In the four-letter case, where the designability is high everywhere, the algorithmic complexity is highest in the region of naturally occurring RNA.

We study the dynamical and critical behavior of a model for irreversible opinion spreading on Barabási-Albert (BA) scale-free networks by performing extensive Monte Carlo simulations. The opinion spreading within an inhomogeneous society is investigated by means of the magnetic Eden model, a nonequilibrium kinetic model for the growth of binary mixtures in contact with a thermal bath. The deposition dynamics, which is studied as a function of the degree of the occupied sites, shows evidence for the leading role played by hubs in the growth process. Systems of finite size grow either ordered or disordered, depending on the temperature. By means of standard finite-size scaling procedures, the effective order-disorder phase transitions are found to persist in the thermodynamic limit. This critical behavior, however, is absent in related equilibrium spin systems such as the Ising model on BA scale-free networks, which in the thermodynamic limit only displays a ferromagnetic phase. The dependence of these results on the degree exponent is also discussed for the case of uncorrelated scale-free networks.

For many technological networks, the network structures and the traffic taking place on them mutually interact. The demands of traffic increment spur the evolution and growth of the networks to maintain their normal and efficient functioning. In parallel, a change of the network structure leads to redistribution of the traffic. In this paper, we perform an extensive numerical and analytical study, extending results of Wang et al. [Phys. Rev. Lett. 94, 188702 (2005)]. By introducing a general strength-coupling interaction driven by the traffic increment between any pair of vertices, our model generates networks of scale-free distributions of strength, weight, and degree. In particular, the obtained nonlinear correlation between vertex strength and degree, and the disassortative property demonstrate that the model is capable of characterizing weighted technological networks. Moreover, the generated graphs possess both dense clustering structures and an anticorrelation between vertex clustering and degree, which are widely observed in real-world networks. The corresponding theoretical predictions are well consistent with simulation results.

We present an approach which enables one to identify phase synchronization in coupled chaotic oscillators without having to explicitly measure the phase. We show that if one defines a typical event in one oscillator and then observes another one whenever this event occurs, these observations give rise to a localized set. Our result provides a general and easy way to identify PS, which can also be used to oscillators that possess multiple time scales. We illustrate our approach in networks of chemically coupled neurons. We show that clusters of phase synchronous neurons may emerge before the onset of phase synchronization in the whole network, producing a suitable environment for information exchanging. Furthermore, we show the relation between the localized sets and the amount of information that coupled chaotic oscillator can exchange.

In this work we characterize in detail the bifurcation leading to an excitable regime mediated by localized structures in a dissipative nonlinear Kerr cavity with a homogeneous pump. Here we show how the route can be understood through a planar dynamical system in which a limit cycle becomes the homoclinic orbit of a saddle point (saddle-loop bifurcation). The whole picture is unveiled, and the mechanism by which this reduction occurs from the full infinite-dimensional dynamical system is studied. Finally, it is shown that the bifurcation leads to an excitability regime, under the application of suitable perturbations. Excitability is an emergent property for this system, as it emerges from the spatial dependence since the system does not exhibit any excitable behavior locally.

Nonlinear effects of acoustic wave propagation and dispersion are observed in a one-dimensional lattice made of Helmholtz resonators connected to a tube. These regularly spaced scatterers exhibit individually a wave frequency dependence, which induces a strong velocity dispersion. In addition, they exhibit a wave amplitude dependence (acoustic nonlinearity), which induces nonlinear effects on the dispersion relation of waves in the lattice. The usually observed forbidden frequency band gaps for the transmission coefficient through the lattice are shown to be amplitude dependent. Experimental results are compared to a developed model taking into account the nonlinear behavior of the Helmholtz resonator.

We investigate kinetics of the uniformly driven bosonic $A+B\to 0$ reaction with on-site attractive interaction in one dimension. In this model, $n_i^{\lambda }$ particles from a site with $n_i$ particles are driven to the right. When particles of opposite species occupy the same site, the reaction takes place instantaneously. Since $n_i^{\lambda }<n_i$ for $\lambda <1$, $\lambda$ controls the on-site attractive interaction between like particles. The $\lambda =0$ case corresponds to the hard-core (HC) particle model. With equal initial densities of both species, we numerically confirm that the scaling behaviors of density and lengths are the same as those of the uniformly driven HC particle system. Especially the domain length $l$ satisfies the power law $l\sim t^{2∕3}$. The kinetics of the reaction is independent of $\lambda$ as long as $\lambda <1$. The $\lambda$-independent kinetics results from the $\lambda$-independent collective motions of single species domains.

Several studies on colloidal depletion systems have reported the existence of a fluid phase consisting of clusters of particles above a critical polymer concentration that acts as a precursor regime to the gel phase at low colloid volume fractions $(\varphi \le 0.20)$. The clusters are found to be stable against further aggregation suggesting that individual particles are localized within a cluster. However the clusters themselves behave as distinct entities in an equilibrium fluid phase. In this study, we probe the internal microstructure of the cluster entities by ultrasmall angle x-ray scattering (USAXS) techniques. These studies reveal that over the accessible length scales, the microstructure of the particle clusters are similar to that observed in dense space-spanning depletion gels. The origin of these clusters is unclear but the scattering patterns as they settle with time reveal that the percolation of the clusters to form space-spanning gels does not influence their internal microstructure. These observations lend support to the hypothesis that the formation of space-spanning depletion gels at a given volume fraction is driven by the percolation of the particle clusters. Settling experiments at $\varphi =0.08$ also provide rough estimates of the cluster sizes that appear consistent with the observations from the USAXS experiments.

Suspensions containing rigid monodisperse spherical particles in a Newtonian carrier liquid are investigated experimentally, providing evidence for solid and liquid states in a transient shear rate from rest. Between these two states a transition takes place; the transition pathways from solid to liquid and from liquid to solid being different. The dynamics of the transition are shown, with the material in this regime reacting as a highly nonlinear system. This involves inverting the input to output and vice versa and comparing them. A key feature of the transition regime is a material instability caused by the collapse of the particle network structure.

Collective behaviors of biological swarms have attracted significant interest in recent years, but much attention and efforts have been focused on constant speed models in which all agents are assumed to move with the same constant speed. One limitation of the constant speed assumption without attraction function is that global convergence is quite difficult or even practically impossible to achieve if the speed is relatively fast. In this paper, we propose an adaptive velocity model in which each agent not only adjusts its moving direction but also adjusts its speed according to the degree of direction consensus among its local neighbors. One important feature of the adaptive velocity model is that the speeds of all agents are adaptively tuned to the same maximum constant speed after a short transient process. The adaptive velocity strategy can greatly enhance the global convergence probability, and thus provides a powerful mechanism for coordinated motion in biological and technological multiagent systems.

From the underlying master equations we derive one-dimensional stochastic processes that describe generalized ensemble simulations as well as tempering (simulated and parallel) simulations. The representations obtained are either in the form of a one-dimensional Fokker-Planck equation or a hopping process on a one-dimensional chain. In particular, we discuss the conditions under which these representations are valid approximate Markovian descriptions of the random walk in order parameter or control parameter space. They allow a unified discussion of the stationary distribution on, as well as of the stationary flow across, each space. We demonstrate that optimizing the flow is equivalent to minimizing the first passage time for crossing the space and discuss the consequences of our results for optimizing simulations. Finally, we point out the limitations of these representations under conditions of broken ergodicity.

We study the spatiotemporal dynamics of a network of coupled chaotic maps modelling neuronal activity, under variation of coupling strength $ϵ$ and degree of randomness in coupling $p$. We find that at high coupling strengths $(ϵ>{ϵ}_{\text{fixed}})$ the unstable saddle point solution of the local chaotic maps gets stabilized. The range of coupling where this spatiotemporal fixed point gains stability is unchanged in the presence of randomness in the connections, namely ${ϵ}_{\text{fixed}}$ is invariant under changes in $p$. As coupling gets weaker $(ϵ<{ϵ}_{\text{fixed}})$, the spatiotemporal fixed point loses stability, and one obtains chaos. In this regime, when the coupling connections are completely regular $(p=0)$, the network becomes spatiotemporally chaotic. Interestingly however, in the presence of random links $(p>0)$ one obtains spatial synchronization in the network. We find that this range of synchronized chaos increases exponentially with the fraction of random links in the network. Further, in the space of fixed coupling strengths, the synchronization transition occurs at a finite value of $p$, a scenario quite distinct from the many examples of synchronization transitions at $p\to 0$. Further we show that the synchronization here is robust in the presence of parametric noise, namely in a network of nonidentical neuronal maps. Finally we check the generality of our observations in networks of neurons displaying both spiking and bursting dynamics.

Binary convection in large-aspect-ratio annular containers heated from below is studied numerically for a water-ethanol mixture. High-resolution numerical tools based on spectral methods are used to solve the hydrodynamic equations in the two-dimensional approximation. The weakly nonlinear states arising very close to the onset of convection, the strongly nonlinear bursts of amplitude that precede the small-amplitude states, and the dispersive chaotic states encountered further above onset in experiments for mixtures with a weak negative Soret coupling are analyzed in detail in extended domains of aspect ratio 80. Steady localized states surrounded either by quiescent fluid or by small-amplitude waves are also obtained, and the role they play in the dynamics is elucidated.

We use a high-level isotropic laser with off-axis focused and on-axis circular pumping to generate the high order polarization-entangled transverse modes. The main finding is that the complex transverse modes can be categorized into four types: square pattern, hyperbolic pattern, elliptic pattern, and circular pattern. Importantly, all types of the polarization-entangled modes can be well analyzed with the generalized coherent states. With the connection between theoretical analysis and experimental results, the formation of complex singularities can be clearly represented.

Coarsening subsequent to phase separations occurs in many two-phase mixtures. While unique scaled particle size distributions have been determined for highly asymmetric mixtures in which spherical particles form in a matrix, it is not known if a unique scaled structure exists for symmetric mixtures, which yield bicontinuous structures having intricately interpenetrating phase domains. Using large-scale simulations, we have established that unique scaled microstructures exist in symmetric mixtures evolving via nonconserved and conserved dynamics. We characterize their morphologies by the interfacial shape distribution, a counterpart to the particle size distribution, and their topologies by the genus. We find that the two dynamics result in unique, but different, scaled interfacial shape distributions, with conserved dynamics yielding a narrower distribution around zero mean curvature. In contrast, the two scaled structures are topologically similar, having nearly equal values of the scaled genus.