We report noise-controlled electrohydrodynamic pattern formations and threshold shifts in nematic liquid crystals. In the electrohydrodynamic system superposed with noise, experimental results obtained in the dielectric regime are compared to those in the conventional conduction regime. The noise intensity dependences of thresholds and pattern evolution processes are remarkably different for each regime. The pattern formation mechanisms in the presence of noise for both regimes are discussed based on the results. Moreover, it is found that the thresholds and characteristic wavelengths of dissipative structures can be effectively controlled by external multiplicative noises with appropriate intensity and correlation times.

We consider the dynamical degenerate four-wave mixing (FWM) model in a cubic nonlinear medium including both the time relaxation of the induced nonlinearity and the nonlocal coupling. The initial ten-dimensional FWM system can be rewritten as a three-variable intrinsic system (namely, the intensity pattern, the amplitude of the nonlinearity, and the total net gain) which is very close to the pumped Maxwell-Bloch system. In the case of a purely nonlocal response the initial system reduces to a real damped sine-Gordon (SG) equation. We obtain a solution of this equation in the form of a sech function with a time-dependent coefficient. By applying the reductive perturbation method to this damped SG equation, we obtain exactly the cubic complex Ginzburg Landau equation (CGL3) but with a time dependence in the loss or gain coefficient. The CGL3 describes the properties of the spatially localized interference pattern formed by the FWM.

Trajectories of self-sustained laboratory ball lightning, generated by arc discharges with silicon, are investigated for understanding the possibility of buoyant flight. Extremely low apparent densities are found, nearly approaching that of standard air. The freely buoyant balls are observed to survive for about 0.1 s, with significantly buoyant balls surviving for several seconds. These ball lightning objects are found to have a density and size that can easily allow them to be carried by a gentle breeze of a few meters per second. The results are interpreted by a model that is an extension of that first proposed by Abrahamson and Dinniss [J. Abrahamson and J. Dinniss, Nature (London) 403, 519 (2000)]. The buoyant behavior of ball lightning seen in our experiments is believed to arise as a result of the formation of a nanoparticle oxide network growing from a molten silicon core.

From consideration of the order-parameter distribution, we propose an observable which makes a clear distinction between true and quasi-long-range orders in the two-dimensional generalized $q$-state clock model. Measuring this quantity by Monte Carlo simulations for $q=8$, we construct a phase diagram and identify critical properties across the phase-separation lines among the true long-range order, quasi-long-range order, and disorder. Our result supports the theoretical prediction that there appears a discontinuous order-disorder transition as soon as the two phase-separation lines merge.

A substrate coated with a polyimide alignment layer is scribed bidirectionally with the stylus of an atomic force microscope to create an easy axis for liquid-crystal orientation. The resulting noncentrosymmetric topography breaks two-dimensional inversion symmetry and results in a spatial amplitude modulation of an imposed twisted nematic state. This is observed optically as spatially periodic light and dark stripes. When the alignment layer is scribed unidirectionally the centrosymmetric topography maintains inversion symmetry, and no stripes are observed. The appearance of the twist modulation is consistent with a chiral term in the free energy.

Although Hinrichsen in his unpublished work theoretically rebutted the possibility of the discontinuous transition in one-dimensional nonequilibrium systems unless there are additional conservation laws, long-range interactions, macroscopic currents, or special boundary conditions, we have recently observed the resurrection of the claim that the triplet creation (TC) model introduced by Dickman and Tomé [Phys. Rev. A 44, 4833 (1991)] would show the discontinuous transition. By extensive simulations, however, we find that the one-dimensional TC does belong to the directed percolation universality class even for larger diffusion constant than the suggested tricritical point in the literature. Furthermore, we find that the phase boundary is well described by the crossover from the mean field to the directed percolation, which supports the claim that the one-dimensional TC does not exhibit a discontinuous transition.

In this work, we introduce a degree of rationality to the public goods games in which players can determine whether or not to participate, and with it a new mechanism has been established. Existence of the bounded rationality would lead to a new equilibrium which differs from the Nash equilibrium and qualitatively explains the fundamental role of loners’ payoff for maintaining cooperation. Meanwhile, it is shown how the potential strategy influences the players’ decision. Finally, we explicitly demonstrate a rock-scissors-paper dynamics which is a consequence of this model.

Recent progress in bottom-up tissue engineering has demonstrated that three-dimensional tissue constructs with predefined architectures may be obtained by assembling shape-controlled hydrogels in multiphase reactor systems. Driven by the hydrophobic force between gel unit and liquid media, highly ordered hydrogel clusters can be formed. Many complex factors occurring at microscale (i.e., gel unit collisions, hydrophobic forces, and gel unit movement) are involved in the self-assembly process. In this paper a two-dimensional off-lattice Monte Carlo model with Lennard-Jones-type potential describing unit-unit interactions is introduced for studying this process. Simulations are shown to agree well with the experimental results for hydrogel assembly in mineral oil. The simulation method is demonstrated for rectangular hydrogel units of different aspect ratios as well as extended to the case of more complex hydrogel unit geometries.

We study the effect of advection on the aggregation and pattern formation in chemotactic systems described by Keller-Segel-type models. The evolution of small perturbations is studied analytically in the linear regime complemented by numerical simulations. We show that a uniform differential flow can significantly alter the spatial structure and dynamics of the chemotactic system. The flow leads to the formation of anisotropic aggregates that move following the direction of the flow, even when the chemotactic organisms are not directly advected by the flow. Sufficiently strong advection can stop the aggregation and coarsening process that is then restricted to the direction perpendicular to the flow.

Exploiting nanoscopically tunable composite gold–alkanethiol–ionic-liquid/ferrocene self-assembled systems with tunable electron transfer distance, we discovered in the case of thinner alkanethiol films a thermally activated electron transfer pattern totally controlled by the viscosity-related slow relaxation mode(s) of the ionic liquid acting as the reactant’s fluctuating environment. This pattern manifested through the activation enthalpy and volume parameters that are identical to those for viscous flow was explained in terms of the extreme adiabatic mechanism with a vanishing Marcus barrier (via the exponential Franck-Condon-like term approaching unity).

Effects of excitability and coupling strength on plane and spiral waves in two-dimensional excitable lattices modeled by phase-coupled elements are investigated. The corresponding phase diagrams for stable plane waves and spiral waves are obtained by simulations. The parameters capable of supporting stable spiral waves are sorted out together with the spiral rotation frequencies. This discrete model corresponds to an excitable medium with zero refractoriness and in the continuum limit supports zero-core spiral waves. The associated wave propagating behaviors are also discussed analytically and verified.

The magnetorotational instability (MRI) is thought to play a key role in the formation of stars and black holes by sustaining the turbulence in hydrodynamically stable Keplerian accretion disks. In previous experiments the MRI was observed in a liquid metal Taylor-Couette flow at moderate Reynolds numbers by applying a helical magnetic field. The observation of this helical MRI (HMRI) was interfered with a significant Ekman pumping driven by solid end caps that confined the instability only to a part of the Taylor-Couette cell. This paper describes the observation of the HMRI in an improved Taylor-Couette setup with the Ekman pumping significantly reduced by using split end caps. The HMRI, which now spreads over the whole height of the cell, appears much sharper and in better agreement with numerical predictions. By analyzing various parameter dependencies we conclude that the observed HMRI represents a self-sustained global instability rather than a noise-sustained convective one.

The excitation of plasma waves over a length of up to 8 cm is demonstrated using laser guiding of intense laser pulses through hydrogen-filled glass capillary tubes. The plasma waves are diagnosed by spectral analysis of the transmitted laser radiation. The dependence of the spectral redshift—measured as a function of filling pressure, capillary tube length, and incident laser energy—is in excellent agreement with simulation results. The longitudinal accelerating field inferred from the simulations is in the range of 1–10 GV/m.

We present an algorithm for performing rigid-body Brownian dynamics that can take into account the hydrodynamic properties (translational and rotational friction tensors and the coupling between them) of each rigid body. In the zero temperature limit, the error term scales as ${\Delta }^4$ for time step $\Delta$, while at nonzero temperatures the error scaling is ${\Delta }^{5/2}$. We test the algorithm by applying it to a molecule of four-aminopyridine in water. We intend to use the algorithm to model the interaction between biological ion channels and other channel blocker molecules, but it may also have applicability to modeling other small particles such as colloids or nanoparticles.

Thermodiffusion in associating mixtures is a complex phenomenon, owing to the strong dependence of the molecular structure of such mixtures on concentration. In this paper, we attempt to elucidate this phenomenon and propose a qualitative mechanism for the separation of species in binary associating mixtures. A correlation between the sign change in the thermal diffusion factor and a change in the molecular structure, mixture viscosity, and the excess entropy of mixing in such mixtures is established. To quantify this correlation, we modify our recently developed dynamic model based on the Drickamer nonequilibrium thermodynamic approach [M. Eslamian and M. Z. Saghir, Phys. Rev. E 80, 011201 (2009)] and propose expressions for the estimation of thermal diffusion factor in binary associating mixtures. The prediction power of the proposed expressions, as well as other widely used models, are examined against the experimental data. The proposed theoretical expressions are self-contained and only rely on the viscosity data as input and predict a sign change in the thermal diffusion factor in associating mixtures.

In this Brief Report we discuss the effectiveness of the Kozachenko-Leonenko entropy estimator when generalized to cope with entropic forms customarily applied to study systems evincing asymptotic scale invariance and dependence (either of linear or nonlinear kind). We show that when the variables are independently and identically distributed the estimator is only valuable along the whole domain if the data follow the uniform distribution, whereas for other distributions the estimator is only effectual in the limit of the Boltzmann-Gibbs-Shanon entropic form. We also analyze the influence of the dependence (linear and nonlinear) between variables on the accuracy of the estimator between variables. As expected in the last case the estimator loses efficiency for the Boltzmann-Gibbs-Shanon entropic form as well.

We use the idea of a Wigner surmise to compute approximate distributions of the first eigenvalue in chiral random matrix theory, for both real and complex eigenvalues. Testing against known results for zero and maximal non-Hermiticity in the microscopic large-$N$ limit, we find an excellent agreement valid for a small number of exact zero eigenvalues. Compact expressions are derived for real eigenvalues in the orthogonal and symplectic classes and at intermediate non-Hermiticity for the unitary and symplectic classes. Such individual Dirac eigenvalue distributions are a useful tool in lattice gauge theory, and we illustrate this by showing that our results can describe data from two-color quantum chromodynamics simulations with chemical potential in the symplectic class.

Phase transition has been found in many complex interactivity systems. Complex networks are not exception either but there are quite few real systems where we can directly understand the emergence of this nontrivial behavior from the microscopic view. In this paper, we present the emergence of the phase transition between the congested and uncongested phases of a network link. We demonstrate a method to infer the background traffic arrival process, which is one of the key state parameters of the Internet traffic. The traffic arrival process in the Internet has been investigated in several studies, since the recognition of its self-similar nature. The statistical properties of the traffic arrival process are very important since they are fundamental in modeling the dynamical behavior. Here, we demonstrate how the widely used packet train technique can be used to determine the main properties of the traffic arrival process. We show that the packet train dispersion is sensitive to the congestion on the network path. We introduce the packet train stretch as an order parameter to describe the phase transition between the congested and uncongested phases of the bottleneck link in the path. We find that the distribution of the background traffic arrival process can be determined from the average packet train dispersion at the critical point of the system.

A method for systematically deriving simple nonlinear dynamical models from ice-core data is proposed. It offers a tool to integrate models and theories with paleoclimatic data. The method is based on the unscented Kalman filter, a nonlinear extension of the conventional Kalman filter. Here, we adopt the abstract conceptual model of stochastically driven motion in a potential that allows for two distinctly different states. The parameters of the model—the shape of the potential and the noise level—are estimated from a North Greenland ice-core record. For the glacial period from 70 to 20 ky before present, a potential is derived that is asymmetric and almost degenerate. There is a deep well corresponding to a cold stadial state and a very shallow well corresponding to a warm interstadial state.