Oscillatory dynamics of complex networks has recently attracted great attention. In this paper we study pattern formation in oscillatory complex networks consisting of excitable nodes. We find that there exist a few center nodes and small skeletons for most oscillations. Complicated and seemingly random oscillatory patterns can be viewed as well-organized target waves propagating from center nodes along the shortest paths, and the shortest loops passing through both the center nodes and their driver nodes play the role of oscillation sources. Analyzing simple skeletons we are able to understand and predict various essential properties of the oscillations and effectively modulate the oscillations. These methods and results will give insights into pattern formation in complex networks and provide suggestive ideas for studying and controlling oscillations in neural networks.

The excitation of sound vibrations of a cylindrical fine fiber due to the impact of a spherical aerosol particle is investigated. The equations describing the dynamics of impact are derived for an arbitrary shooting parameter. The coefficient of restitution is calculated, and its analytical approximation is obtained. It is shown, for the case of long fibers, that the coefficient of restitution depends upon a single parameter ${\lambda }_c$. The parameter ${\lambda }_c$ depends on the particle radial velocity component near the fiber surface, the mass of the particle, the density of the fiber, the modulus of elasticity, and the geometric parameters of the fiber and the particle. The inertial deposition of submicron aerosol particles on fine fibers in a filter is considered. The efficiency of filtration is studied as a function of the gas flow velocity. The existence of a critical flow velocity $U^{*}$, below which the losses of particle energy during collision have no effect on the efficiency, is demonstrated. For velocities higher than the critical velocity, the filtration efficiency is dependent on the mechanisms of nonelastic losses of the particle's energy. Its value can be significantly lower than that estimated when particle rebound effects are neglected. After they have rebounded, some particles are not able to attain the initial high velocities in the stream, thus depositing on neighboring fibers. The dynamics of these particles is investigated. For this case, it is shown that the filtration efficiency is dependent on the velocity distribution of the rebounded particles and that it increases with the packing density of fibers. A qualitative difference between the asymptotic behavior of a fiber and that of a flat plate is found long after the initial impulse.

A Xenon gas bubble introduced into a vertically suspended steel cylinder is driven to sonoluminescence by impacting the apparatus against a solid steel base. This produces a 150-ns flash of broadband light that exceeds 100-W peak intensity and has a spectral temperature of 10 200 K. This bubble system, which yields light with a single shot, emits very powerful sonoluminescence. A jet is visible following bubble collapse, which demonstrates that spherical symmetry is not necessary to produce sonoluminescence.

When a Nafion tube is immersed in water and a small hole is punched in the tube's wall, an unexpected phenomenon occurs: Water flows continuously into the tube through the hole. The phenomenon has proved repeatable, and dynamic aspects were therefore explored, including the effects of altered pH and introduction of a second hole. It appears that the flow is closely tied to the recently discovered “exclusion zone” that forms as an annulus inside the Nafion tube. These zones generate protons in the core of the tube, which exert pressure on the menisci; once a hole is punched, the pressure is relieved by sucking water through the hole. This hypothesis is consistent with the observed experimental evidence and may be relevant to the mechanism of water transport in trees.

We derive exact solutions of the Ablowitz-Ladik (A-L) equation using a special ansatz that linearly relates the real and imaginary parts of the complex function. This ansatz allows us to derive a family of first-order solutions of the A-L equation with two independent parameters. This novel technique shows that every exact solution of the A-L equation has a direct analog among first-order solutions of the nonlinear Schrödinger equation (NLSE).

The venerable two-dimensional (2D) point-vortex model plays an important role as a simplified version of many disparate physical systems, including superfluids, Bose-Einstein condensates, certain plasma configurations, and inviscid turbulence. This system is also a veritable mathematical playground, touching upon many different disciplines from topology to dynamic systems theory. Point-vortex dynamics are described by a relatively simple system of nonlinear ordinary differential equations which can easily be integrated numerically using an appropriate adaptive time stepping method. As the separation between a pair of vortices relative to all other intervortex length scales decreases, however, the computational time required diverges. Accuracy is usually the most discouraging casualty when trying to account for such vortex motion, though the varying energy of this ostensibly Hamiltonian system is a potentially more serious problem. We solve these problems by a series of coordinate transformations: We first transform to action-angle coordinates, which, to lowest order, treat the close pair as a single vortex amongst all others with an internal degree of freedom. We next, and most importantly, apply Lie transform perturbation theory to remove the higher-order correction terms in succession. The overall transformation drastically increases the numerical efficiency and ensures that the total energy remains constant to high accuracy.

In this work we study the effect of limiting the number of interactions (the associative capacity) that a node can establish per round of a prisoner’s dilemma game. We focus on the way this limitation influences the level of cooperation sustained by scale-free networks. We show that when the game includes cooperation costs, limiting the associative capacity of nodes to a fixed quantity renders in some cases larger values of cooperation than in the unrestricted scenario. This allows one to define an optimum capacity for which cooperation is maximally enhanced. Finally, for the case without cooperation costs, we find that even a tight limitation of the associative capacity of nodes yields the same levels of cooperation as in the original network.

We report a mesoscale modeling of the liquid-vapor interface of water. A mesoscopic model of water has been established in dissipative particle dynamics (DPD) to reproduce the interfacial properties of water. The surface tension and coexisting densities are compared between atomistic and mesoscopic simulations. Simple scaling relations have been established to link the atomistic and mesoscopic length and time scales. Our study demonstrates the capability of the DPD method to explore the interfacial properties of a planar water liquid-vapor interface and a water nanodroplet. This constitutes an important step toward the calculation of the surface tension of larger and more complex interfacial systems.

We report on a dramatic order-of-magnitude increase in flow velocity within pinned evaporating droplets toward the end of their lifetime. The measurements were performed using high-speed microparticle image velocimetry. The study revealed interesting observations about the spatial and temporal evolution of the velocity field. The profile along the radius of the droplet is found to exhibit a maximum toward the three phase contact line with flow oscillations in time in this region. Additional optical measurements allowed further analysis of the observed trends. Analysis of the potential mechanisms responsible for the flow within the droplet demonstrated that these observations can be satisfactorily explained and accounted for by mass conservation within the droplet to compensate for evaporation.

In a number of experimental situations, single-polymer molecules can be suspended in a vacuum. Here collisions between such molecules are considered. The limit of high collision velocity is investigated numerically for a variety of conditions. The distribution of contact times, scattering angles, and final velocities are analyzed. In this limit, self-avoiding chains are found to become highly stretched as they collide with each other and have a distribution of scattering times that depends on the scattering angle. The velocity of the molecules after the collisions is similar to predictions of a model assuming thermal equilibration of molecules during the collision. The most important difference is a significant subset of molecules that inelastically scatter but do not substantially change direction.

We study a one-dimensional model of microtubule assembly and disassembly in which GTP bound to tubulins within the microtubule undergoes stochastic hydrolysis. In contrast to models that consider only a cap of GTP-bound tubulin, stochastic hydrolysis allows GTP-bound tubulin remnants to exist within the microtubule. We find that these buried GTP remnants enable an alternative mechanism of recovery from shrinkage and enhances fluctuations of filament lengths. Under conditions for which this alternative mechanism dominates, an increasing depolymerization rate leads to a decrease in dissociation rate and thus a net increase in assembly.

Robust synchronized activity is widely observed in real neural systems. However, a mechanism for robust synchronization that can be understood analytically, and has a clear physical meaning, remains elusive. This paper considers such a mechanism by formalizing three synaptic components contributing to robust synchronization in networks with heterogeneous external drive currents and conductance-based synapses. The first component arises from the assumption that the aggregate post-synaptic potential of a neuron decays more if it fires later within a spike volley. The second component results because neurons with smaller drives have reached a lower membrane potential at the time when the volley of inputs arrives than that reached by neurons with larger drives. The third component arises from the assumption that neurons firing later in the previous volley have had less time to integrate their drives than neurons firing earlier have had, again causing a lower membrane potential at the time when the volley of inputs arrives. Because of the voltage-dependent properties of synaptic currents, either of the last two components will cause smaller inhibitions for the later-firing neurons if the synapses are inhibitory. This smaller inhibition causes the later-firing neurons to fire earlier in the next cycle, thereby forcing them toward synchrony. With these three synaptic components, we discuss the relationship between the robustness of the synchrony and the parameters, search for the optimal parameter set for the robust network synchronization of a certain frequency band, and demonstrate the key role of the voltage-dependent properties of synaptic currents in robust or stable synchronization.

In this brief report we explore the energy landscapes of two spin glass models using a greedy single-spin flipping process, Gmax. The ground-state energy density of the random maximum two-satisfiability problem is efficiently approached by Gmax. The achieved energy density $e(t)$ decreases with the evolution time $t$ as $e(t)-e(\infty )=h(\log {}_{10}t){}^{-z}$ with a small prefactor $h$ and a scaling coefficient $z>1$, indicating an energy landscape with deep and rugged funnel-shape regions. For the $\pm J$ Viana-Bray spin glass model, however, the greedy single-spin dynamics quickly gets trapped to a local minimal region of the energy landscape.

The motion of inertial particles is investigated numerically in a time-periodic flow in the presence of gravity. The flow is restricted to a finite (or semi-infinite) vertical column, and the dynamics is therefore transiently chaotic. The long-term motion of the center of mass is a uniform settling. The settling velocity is found to differ from the one that would characterize a still fluid, and the distribution of an ensemble of settling particles spreads with a well-defined diffusion coefficient. The underlying chaotic saddle appears to have a height-dependent fractal dimension. The coarse-grained density of both the natural measure and the conditionally invariant measure (defined along the unstable manifold) of the saddle is smooth, and exhibits a local maximum as a function of the height. The latter density corresponds to the eigenfunction of the first eigenvalue of an effective Fokker–Planck equation subject to an absorbing boundary condition at the bottom. The transport coefficients can be determined as averages taken with respect to the conditionally invariant measure.

Pumps with step microelectrodes subjected to an ac voltage are known to have faster pumping rates than those with planar asymmetric microelectrodes. The driving force for pumping in these systems is ac electro-osmosis. This paper aims to understand the flow behaviors of pumps with step microelectrodes by using a realistic model applicable to high external voltages. This model takes the steric effect due to the finite sizes of ions into account and copes with the exponential sensitivity of the counterion concentration to voltage. The effects on the pumping flow rate of varying the pump parameters were investigated. The geometrical parameters were optimized, and the effects of varying the ac frequency and amplitude were examined. The electrical potential of the fluid and the electrical charge at the electrode surface were solved simultaneously, and the Stokes equation was used to describe the fluid flow.

Under investigation is a generalized variable-coefficient forced Korteweg–de Vries equation in fluids and other fields. From the bilinear form of such equation, the $N$-soliton solution and a type of analytic solution are constructed with symbolic computation. Analytic analysis indicates that: (1) dispersive and dissipative coefficients affect the solitonic velocity; (2) external-force term affects the solitonic velocity and background; (3) line-damping coefficient and some parameters affect the solitonic velocity, background, and amplitude. Solitonic propagation and interaction can be regarded as the combination of the effects of various variable coefficients. According to a constraint among the nonlinear, dispersive, and line-damping coefficients in this paper, the possible applications of our results in the real world are also discussed in three aspects, i.e., solution with the constraint, solution without the constraint, and approximate solution.

We consider the three-dimensional Ising model in a $L_{\perp }\times L_{\parallel }\times L_{\parallel }$ cuboid geometry with a finite aspect ratio $\rho =L_{\perp }/L_{\parallel }$ and periodic boundary conditions along all directions. For this model the finite-size scaling functions of the excess free energy and thermodynamic Casimir force are evaluated numerically by means of Monte Carlo simulations. The Monte Carlo results compare well with recent field theoretical results for the Ising universality class at temperatures above and slightly below the bulk critical temperature $T_{\mathrm{c}}$. Furthermore, the excess free energy and Casimir force scaling functions of the two-dimensional Ising model are calculated exactly for arbitrary $\rho$ and compared to the three-dimensional case. We give a general argument that the Casimir force vanishes at the critical point for $\rho =1$ and becomes repulsive in periodic systems for $\rho >1$.

We present dielectric spectroscopy data obtained for gallium-doped Cd${}_{0.99}$Mn${}_{0.01}$Te:Ga mixed crystals, which exhibit a very special case of the two-power-law relaxation pattern with the high-frequency power-law exponent equal to 1. We explain this behavior, which cannot be fitted by any of the well-known empirical relaxation functions, in a subordinated diffusive framework. We propose a diffusion scenario based on a renormalized clustering of a random number of spatio-temporal steps in the continuous-time random walk. Such a construction substitutes the renewal counting process, which is used in the classical continuous time random walk methodology, with a compound counting one. As a result, we obtain an appropriate relaxation function governing the observed nonstandard pattern, and we show the importance of the compound counting processes in studying fractional dynamics of complex systems.

The two- and three-dimensional transverse-field Ising models with ferromagnetic exchange interactions are analyzed by means of the real-space renormalization-group method. The basic strategy is a generalization of a method developed for the one-dimensional case, which exploits the exact invariance of the model under renormalization and is known to give the exact values of the critical point and critical exponent $\nu$. The resulting values of the critical exponent $\nu$ in two and three dimensions are in good agreement with those for the classical Ising model in three and four dimensions. To the best of our knowledge, this is the first example in which a real-space renormalization group on ($2+1$)- and ($3+1$)-dimensional Bravais lattices yields accurate estimates of the critical exponents.

We investigate the properties of the Ising-Glauber model on a periodic cubic lattice of linear dimension $L$ after a quench to zero temperature. The resulting evolution is extremely slow, with long periods of wandering on constant energy plateaus, punctuated by occasional energy-decreasing spin-flip events. The characteristic time scale $\tau$ for this relaxation grows exponentially with the system size; we provide a heuristic and numerical evidence that $\tau ~\exp (L^2)$. For all but the smallest-size systems, the long-time state is almost never static. Instead, the system contains a small number of “blinker” spins that continue to flip forever with no energy cost. Thus, the system wanders ad infinitum on a connected set of equal-energy blinker states. These states are composed of two topologically complex interwoven domains of opposite phases. The average genus $g_L$ of the domains scales as $L^{\gamma }$, with $\gamma \approx 1.7$; thus, domains typically have many holes, leading to a “plumber’s nightmare” geometry.