We study dynamical scaling of flux fluctuation $\overline{\sigma }\left(t\right)$ from the one-random-walker model on regular lattices and complex networks and compare it to the surface width $W\left(t\right)$ of a corresponding growth model. On the regular lattices, we analytically show that $\overline{\sigma }\left(t\right)$ undergoes a crossover from the nontrivial scaling regime to the trivial one by increasing time $t$, and we verify the results by numerical simulations. In contrast to the results on the regular lattices, $\overline{\sigma }\left(t\right)$ does not show any crossover behavior on complex networks and satisfies the scaling relation $\overline{\sigma }\left(t\right)\sim t^{1∕2}$ for any $t$. On the other hand, we show that $W\left(t\right)$ of the corresponding model on complex networks has two different scaling regimes, $W\sim t^{1∕2}$ for $t⪡N$ and $W\left(t\right)\sim t$ for $t⪢N$.

Phase-field modeling has proven to be a versatile tool for simulating microstructural evolution phenomena, such as grain growth in polycrystalline materials. However, the computing time and computing memory requirements of a phase-field model pose severe limitations on the number of phase-field variables that can be taken into account in a practical implementation. In this paper, a sparse bounding box algorithm is proposed that allows the use of a large number of phase-field variables without excessive memory usage or computational requirements. The algorithm is applied to a three-dimensional model for grain growth in the presence of second-phase particles.

This paper investigates the sequence of morphological transitions in a nearly hard sphere arrangement confined in a wedge cell. A model that shows smooth transitions between the different particle orderings for a small number of layers is proposed. In this model, both the buckling and the (100) hexagonal close packed (hcp) phases are particular cases of a much more general particle arrangement tendency that we call hcp-like ordering. This phase, which does not correspond to any known close packed ordering, is able to adopt packing arrangements commensurate with the cell thickness. More striking, the hcp-like phase adapts itself to the progressive changes of the cell thickness by a smooth change in the interlayer spacing. We present hcp-like orderings up to six layers and a complete sequence of transformations between two and four layers. Finally, a packing model of the transition from two to three layers is also presented.

We have characterized a close-packed structure of confined charged colloidal spheres, which has been recently discovered. Using different microscopy experiments, the vertically arranged hexagonal planes of $n$-$\mathrm{hcp}\perp$ are found to continuously evolve from the horizontally oriented stacks of $n$ hexagonal planes $\left(n\mathrm{\Delta }\right)$ following the maximum packing criterion, but discontinuously transform to a stack of $n+1$ square planes $\left[\right(n+1)◻]$. Large mechanically stable domains with threefold twin structures are regularly observed in the suspended state at packing fractions between 0.4 and 0.58.

Several statistical mechanical theories predict that colloidal suspensions of highly charged macroions and monovalent microions can exhibit unusual thermodynamic phase behavior when strongly deionized. Density-functional, extended Debye-Hückel, and response theories, within mean-field and linearization approximations, predict a spinodal phase instability of charged colloids below a critical salt concentration. Poisson-Boltzmann cell model studies of suspensions in Donnan equilibrium with a salt reservoir demonstrate that effective interactions and osmotic pressures predicted by such theories can be sensitive to the choice of reference system, e.g., whether the microion density profiles are expanded about the average potential of the suspension or about the reservoir potential. By unifying Poisson-Boltzmann and response theories within a common perturbative framework, it is shown here that the choice of reference system is dictated by the constraint of global electroneutrality. On this basis, bulk suspensions are best modeled by density-dependent effective interactions derived from a closed reference system in which the counterions are confined to the same volume as the macroions. Lower-dimensional systems (e.g., monolayers, clusters), depending on the strength of macroion-counterion correlations, may be governed instead by density-independent effective interactions tied to an open reference system with counterions dispersed throughout the reservoir, possibly explaining the observed structural crossover in colloidal monolayers and anomalous metastability of colloidal crystallites.

We study the phase behavior of a nematic liquid crystal confined between a flat substrate with strong anchoring and a patterned substrate whose structure and local anchoring strength we vary. By first evaluating an effective surface free-energy function characterizing the patterned substrate, we derive an expression for the effective free energy of the confined nematic liquid crystal. Then we determine phase diagrams involving a homogeneous state in which the nematic director is almost uniform and a hybrid aligned nematic state in which the orientation of the director varies through the cell. Direct minimizations of the free-energy functional were performed in order to test the predictions of the effective free-energy method. We find remarkably good agreement between the phase boundaries calculated from the two approaches. In addition, the effective free-energy method allows one to determine the energy barriers between two states in a bistable nematic device.

We present results for a lattice model of polymers where the type of $\beta$ sheet formation can be controlled by different types of hydrogen bonds depending on the relative orientation of close segments of the polymer. Tuning these different interaction strengths leads to low-temperature structures with different types of orientational order. We perform simulations of this model and so present the phase diagram, ascertaining the nature of the phases and the order of the transitions between these phases.

This paper summarizes the results of numerical simulations of the interaction of a pair of biofilaments mediated by a molecular motor. The filaments are modeled as flexible rods, and the results are applicable to microtubules, which are relatively stiff, as well as to much softer filaments, such as actin. The results provide insight into the effects of flexibility on cytoskeleton formation and the rheology of semiflexible filament networks. The simulations are based on a nonlinear elasticity equation. The results show that flexibility enhances the tendency of filaments to align. The enhancement in turn favors the formation of large-scale structures in multifilament systems. Simulations for soft filaments show that the action of the motor can result in the formation of multiple loops of the filaments as a result of buckling, which can affect the structure of a cross-linked network and thereby its rheology. The estimate for the minimal buckling length as a function of the motor speed, the viscosity of the solvent, and the bending stiffness of the filament is derived analytically.

In this paper, the investigation is first motivated by showing two examples of simple regular symmetrical graphs, which have the same structural parameters, such as average distance, degree distribution, and node betweenness centrality, but have very different synchronizabilities. For a given network with identical node dynamics, it is further shown that two key factors influencing the network synchronizability are the network inner linking matrix and the eigenvalues of the network topological matrix. Several examples are then provided to show that adding new edges to a network can either increase or decrease the network synchronizability. In searching for conditions under which the network synchronizability may be increased by adding edges, it is found that for networks with disconnected complementary graphs, adding edges never decreases their synchronizability. Moreover, it is found that an unbounded synchronized region is always easier to analyze than a bounded synchronized region. Therefore to effectively enhance the network synchronizability, a design method is finally presented for the inner linking matrix of rank 1 such that the resultant network has an unbounded synchronized region, for the case where the synchronous state is an equilibrium point of the network.

Plasma plumes produced by laser ablation are an established method for manufacturing the high quality stoichiometrically complex thin films used for a variety of optical, photoelectric, and superconducting applications. The state and reproducibility of the plasma close to the surface of the irradiated target plays a critical role in producing high quality thin films. Unfortunately, this dense plasma has historically eluded quantifiable characterization. The difficulty in modeling the plume formation arises in the accounting for the small amount of energy deposited into the target when physical properties of these exotic target materials are not known. In this work we obtain the high density state of the plasma plume through the use of an experimental spectroscopic technique and a custom spectroscopic model. In addition to obtaining detailed temperature and density profiles, issues regarding line broadening and opacity for spectroscopic characterization will be addressed for this unique environment.

We introduce a model of negotiation dynamics whose aim is that of mimicking the mechanisms leading to opinion and convention formation in a population of individuals. The negotiation process, as opposed to “herdinglike” or “bounded confidence” driven processes, is based on a microscopic dynamics where memory and feedback play a central role. Our model displays a nonequilibrium phase transition from an absorbing state in which all agents reach a consensus to an active stationary state characterized either by polarization or fragmentation in clusters of agents with different opinions. We show the existence of at least two different universality classes, one for the case with two possible opinions and one for the case with an unlimited number of opinions. The phase transition is studied analytically and numerically for various topologies of the agents’ interaction network. In both cases the universality classes do not seem to depend on the specific interaction topology, the only relevant feature being the total number of different opinions ever present in the system.

Around 300 bat species are known to emit their ultrasonic biosonar pulses through the nostrils. This nasal emission coincides with the presence of intricately shaped baffle structures surrounding the nostrils. Some prior experimental evidence indicates that these “noseleaves” have an effect on the shape of the animals’ radiation patterns. Here, we present a numerical acoustical analysis of the noseleaf of a horseshoe bat species. We show that all three distinctive parts of its noseleaf (“lancet," “sella," “anterior leaf”) have an effect on the acoustic near field as well as on the directivity pattern. Furthermore, we show that furrows in one of the parts (the lancet) also exert such an influence. The underlying physical mechanisms suggested by the properties of the estimated near field are cavity resonance, as well as reflection and shadowing of the sound waves emitted by the nostrils. In their effects on the near field, the noseleaf parts showed a tendency toward spatial partitioning with the effects due to each part dominating a certain region. However, interactions between the acoustic effects of the parts were also evident, most notably, a synergism between two frequency-dependent effects (cavity resonance and shadowing) to produce an even stronger frequency selectivity.

Much effort has been devoted to developing analysis methods of subdural electroencephalogram and depth electrode recordings of epileptic patients being evaluated for surgical resection. The general approach is to investigate the brain activity at different locations as recorded by the different electrodes in an attempt to localize the epileptogenic focus or foci. Currently, most of the methods are based on the notion that epileptogenic brain activity is associated with changes in synchronization and in complexity. Here we present a method that is based on the temporal dynamics combined with the spectral distribution of energy in terms of frequency-entropy (FE) templates. The FE templates are based upon maximum information partitioning into a set of frequency bands. The FE template is calculated by wavelet packet decomposition followed by an application of the best basis algorithm minimizing the entropy cost function. A comparison between two FE templates is performed by a special quantitative similarity measure according to the overlap in the partitioning into frequency bands and weighted by the bands’ entropy. For localization of the epileptogenic foci, the templates of each electrode during the interictal period are compared with a representative template evaluated from the ensemble of all electrodes during the ictal period. We suggest associating the locations that reveal high template similarity to the ictal template with the epileptogenic foci. To test the method and the underlying assumptions, we perform retrospective analysis of the recorded brain activity, from both grid and depth electrodes, from 11 patients suffering from medically intractable epilepsy. Application of the ictal-interictal FE template similarity analysis revealed regions in the epileptic brain in which the interictal characteristics are highly similar to those of the ictal period. To asses the foci we compared the interictal templates of the different electrodes to each other, forming interelectrode similarity matrices. Investigation of these similarity matrices revealed the existence of a single distinct subcluster of electrodes with high interelectrode similarity in the brain activity of seven patients (type-I activity), and the existence of multiple high interelectrode similarity subclusters in the activity of four patients (type-II activity). Comparisons of the analysis results to the medical presurgical evaluations and the outcomes of the surgical resections suggest that the method may be helpful in the chronic evaluation of the epileptogenic zone before operation, and in some cases (type-I activity) without the need to wait for seizures to occur.

An improved method for the description of hierarchical complex systems by means of a Fokker-Planck equation is presented. In particular the limited-memory Broyden-Fletcher-Goldfarb-Shanno algorithm for constraint problems is used to minimize the distance between the numerical solutions of the Fokker-Planck equation and the empirical probability density functions and thus to estimate properly the drift and diffusion term of the Fokker-Planck equation. The optimization routine is applied to a time series of velocity measurements obtained from a turbulent helium gas jet in order to demonstrate the benefits and to quantify the improvements of this optimization routine.

We consider the Kuramoto model of phase oscillators with natural frequencies distributed according to a unimodal function with the plateau section in the middle representing the maximum and symmetric tails falling off predominantly as $\mid \omega -{\omega }_0{\mid }^m$, $m>0$, in the vicinity of the flat region. It is found that the phase transition is of first order as long as there is a finite flat region and that in the vicinity of the critical coupling the following scaling law holds $r-r_c\propto (K-K_c{)}^{2∕(2m+3)}$, where $r$ is the order parameter and $K$ is the coupling strength of the interacting oscillators.

We give an explicit formula for the change of speed of pushed and bistable fronts of the reaction-diffusion equation when a small cutoff is applied to the reaction term at the unstable or metastable equilibrium point. The results are valid for arbitrary reaction terms and include the case of density-dependent diffusion.

A microscopic theory for coarse graining diblock copolymers into dumbbells of interacting soft colloidal particles has been developed based on the solution of liquid-state integral equations. The Ornstein-Zernike equation is solved to provide a mesoscopic description of the diblock copolymer system at the level of block centers of mass, and at the level of polymer centers of mass. Analytical forms of the total correlation functions for block-block, block-monomer, and center-of-mass pairs are obtained for a liquid of structurally symmetric diblock copolymers as a function of temperature, density, chain length, and chain composition. The theory correctly predicts thermodynamically driven segregation of diblocks into microdomains as a function of temperature ($\chi$ parameter). The coarse-grained description contains contributions from density and concentration fluctuations, with the latter becoming dominant as temperature decreases. Numerical calculations for the block coarse-grained total correlation functions, as a function of the proximity of the system to its phase transition, are presented. Comparison with united atom molecular dynamics simulations are carried out in the athermal regime, where simulations and theory quantitatively agree with no need of adjustable parameters.

We study the public goods game in the noisy case by considering the players with inhomogeneous activity of teaching on a square lattice. It is shown that the introduction of the inhomogeneous activity of teaching the players can remarkably promote cooperation. By investigating the effects of noise on cooperative behavior in detail, we find that the variation of cooperator density ${\rho }_C$ with the noise parameter $\kappa$ displays several different behaviors: ${\rho }_C$ monotonically increases (decreases) with $\kappa$; ${\rho }_C$ first increases (decreases) with $\kappa$ and then it decreases (increases) monotonically after reaching its maximum (minimum) value, which depends on the amount of the multiplication factor $r$, on whether the system is homogeneous or inhomogeneous, and on whether the adopted updating is synchronous or asynchronous. These results imply that the noise plays an important and nontrivial role in the evolution of cooperation.

The Nikolaevskiy equation has been proposed as a model for seismic waves, electroconvection, and weak turbulence; we show that it can also be used to model transverse instabilities of fronts. This equation possesses a large-scale “Goldstone” mode that significantly influences the stability of spatially periodic steady solutions; indeed, all such solutions are unstable at onset, and the equation exhibits spatiotemporal chaos. In many applications, a weak damping of this neutral mode will be present, and we study the influence of this damping on solutions to the Nikolaevskiy equation. We examine the transition to the usual Eckhaus instability as the damping of the large-scale mode is increased, through numerical calculation and weakly nonlinear analysis. The latter is accomplished using asymptotically consistent systems of coupled amplitude equations. We find that there is a critical value of the damping below which (for a given value of the supercriticality parameter) all periodic steady states are unstable. The last solutions to lose stability lie in a cusp close to the left-hand side of the marginal stability curve.

The emergence of chaotic motion is discussed for hard-point like and soft collisions between two particles in a one-dimensional box. It is known that ergodicity may be obtained in hard-point like collisions for specific mass ratios $\gamma =m_2∕m_1$ of the two particles and that Lyapunov exponents are zero. However, if a Yukawa interaction between the particles is introduced, we show analytically that positive Lyapunov exponents are generated due to double collisions close to the walls. While the largest finite-time Lyapunov exponent changes smoothly with $\gamma$, the number of occurrences of the most probable one, extracted from the distribution of finite-time Lyapunov exponents over initial conditions, reveals details about the phase-space dynamics. In particular, the influence of the integrable and pseudointegrable dynamics without Yukawa interaction for specific mass ratios can be clearly identified and demonstrates the sensitivity of the finite-time Lyapunov exponents as a phase-space probe. Being not restricted to two-dimensional problems such as Poincaré sections, the number of occurrences of the most probable Lyapunov exponents suggests itself as a suitable tool to characterize phase-space dynamics in higher dimensions. This is shown for the problem of two interacting particles in a circular billiard.