We present numerical evidence that, in the presence of a suitable electric field, an isolated broken plane wave retracting originally in subexcitable media can propagate continuously and eventually evolve into a rotating spiral. Simulations for the FitzHugh-Nagumo, the Barkley, and the Oregonator models are carried out and the same electric-field-sustained spiral phenomena are observed. Semianalytical results in the framework of a kinematic theory are quantitatively consistent with the numerical results.

On the basis of the critical point analysis, we study the reconnection process of vorticity contours associated with coherent vortices in two-dimensional turbulence. After checking topological integrity by the Euler index theorem, we make use of the critical points and their connectivity (so-called surface networks) to characterize topological changes of vorticity contours. We quantify vortex merger by computing the number of centers and saddles of the vorticity field systematically. Surface networks are topological graphs consisting of the critical points and edges connecting them. They can tell in particular which vortices are going to merge in near future. Moreover, we show how this method can remarkably distinguish the dynamics of the vorticity field in the Navier-Stokes equations and that of the Charney-Hasegawa-Mima equation. The relationship between the number of the critical points and hyperpalinstrophy is discussed by deriving the so-called generalized Rice theorem in the spirit of S. Goto and J. C. Vassilicos [Phys. Fluids 21, 035104-1 (2009)]. The Okubo-Weiss' conditional sampling is used to compare reconnection in elliptic and hyperbolic regions. A comparison has been made between topological changes of the vorticity and that of a passive scalar. A study in inviscid flows with different resolutions is also given.

We study numerically the dynamo transition of an incompressible electrically conducting fluid filling the gap between two concentric spheres. In a first series of simulations, the fluid is driven by the rotation of a smooth inner sphere through no-slip boundary conditions, whereas the outer sphere is stationary. In a second series a volume force intended to simulate a rough surface drives the fluid next to the inner sphere within a layer of thickness one-tenth of the gap width. We investigate the effect of the boundary layer thickness on the dynamo threshold in the turbulent regime. The simulations show that the boundary forcing simulating the rough surface lowers the necessary rotation rate, which may help to improve spherical dynamo experiments.

Strong violations of existing fluctuation theorems may arise in nonequilibrium steady states characterized by distributions with power-law tails. The ratio of the probabilities of positive and negative fluctuations of equal magnitude behaves in an anomalous nonmonotonic way [H. Touchette and E. G. D. Cohen, Phys. Rev. E 76, 020101(R) (2007)]. Here, we propose an alternative definition of fluctuation relation (FR) symmetry that, in the power-law regime, is characterized by a monotonic linear behavior. The proposal is consistent with a large deviationlike principle. As an example, we study the fluctuations of the work done on a dragged particle immersed in a complex environment able to induce power-law tails. When the environment is characterized by spatiotemporal temperature fluctuations, distributions arising in nonextensive statistical mechanics define the work statistics. In that situation, we find that the FR symmetry is solely defined by the average bath temperature. The case of a dragged particle subjected to a Lévy noise is also analyzed in detail.

We study a fluctuation-driven ratchet-oscillator system that consists of two ratchet pinions in contact with thermal baths at different temperatures. Coupling between noncontact parts of the system is mediated by the Casimir force through a thin corrugated plate. Due to mutual rectification, the two ratchets achieve directed average motion in opposite directions. We numerically probe the average velocity, the Peclet number, and the thermal efficiency of the system as functions of the effective temperatures of the thermal baths and other important dimensionless control parameters. It is found that optimal parameter values exist which maximize the directed transport rate but with very low efficiency. We expect that the obtained results will help in the design of noncontact mechanical devices in the future.

We obtain the Crooks and the Jarzynski nonequilibrium fluctuation relations using a direct quantum-mechanical approach for a finite system that is either isolated or coupled not too strongly to a heat bath. These results were hitherto derived mostly in the classical limit. The two main ingredients in the picture are the time-reversal symmetry and the application of the first law to the case where an agent performs work on the system. No further assumptions regarding stochastic or Markovian behavior are necessary, neither a master equation or a classical phase-space picture are required. The simplicity and the generality of these nonequilibrium relations are demonstrated, giving very simple insights into the physics.

The influence of a liquid film on the coefficient of restitution (COR) is investigated experimentally by tracing freely falling particles bouncing on a wet surface. The dependence of the COR on the impact velocity and various properties of the particle and liquid is presented and discussed in terms of dimensionless numbers that characterize the interplay between inertial, viscous, and surface forces. In the Reynolds number regime where lubrication theory does not apply, the ratio of the film thickness to the particle size is found to be a crucial parameter determining the COR.

In colloidal suspensions, self-organization processes can be easily fueled by external fields. Here we consider monolayers of particles with permanent dipole moments that are driven by rotating external fields. In recent experiments, it has been shown that the particles in such systems self-organize into two-dimensional clusters. Here we report results from a computer simulation study of these pattern forming systems. Specifically, we employ Langevin dynamics simulations, Brownian dynamics simulations that include hydrodynamic interactions, and Wang-Landau Monte Carlo simulations of soft spheres interacting via dipolar potentials. We investigate at which field strengths and frequencies clusters form and explore the influence of hydrodynamic interactions. We also examine the phase behavior of the equilibrium system resulting from a time average of the colloidal interactions in the rotating field. In this way we demonstrate that the clustering described in the driven system arises from a first-order phase transition between a vapor and a condensed phase.

We report on the diffusion of purely repulsive and freely rotating colloidal rods in the isotropic, nematic, and smectic liquid crystal phases to probe the agreement between Brownian and Monte Carlo dynamics under the most general conditions. By properly rescaling the Monte Carlo time step, being related to any elementary move via the corresponding self-diffusion coefficient, with the acceptance rate of simultaneous trial displacements and rotations, we demonstrate the existence of a unique Monte Carlo time scale that allows for a direct comparison between Monte Carlo and Brownian dynamics simulations. To estimate the validity of our theoretical approach, we compare the mean square displacement of rods, their orientational autocorrelation function, and the self-intermediate scattering function, as obtained from Brownian dynamics and Monte Carlo simulations. The agreement between the results of these two approaches, even under the condition of heterogeneous dynamics generally observed in liquid crystalline phases, is excellent.

We investigate nematic wetting and filling transitions of crenellated surfaces (rectangular gratings) by numerical minimization of the Landau–de Gennes free energy as a function of the anchoring strength, for a wide range of the surface geometrical parameters: depth, width, and separation of the crenels. We have found a rich phase behavior that depends in detail on the combination of the surface parameters. By comparison to simple fluids, which undergo a continuous filling or unbending transition, where the surface changes from a dry to a filled state, followed by a wetting or unbinding transition, where the thickness of the adsorbed fluid becomes macroscopic and the interface unbinds from the surface, nematics at crenellated surfaces reveal an intriguingly rich behavior: in shallow crenels only wetting is observed, while in deep crenels, only filling transitions occur; for intermediate surface geometrical parameters, a new class of filled states is found, characterized by bent isotropic-nematic interfaces, which persist for surfaces structured on large scales, compared to the nematic correlation length. The global phase diagram displays two wet and four filled states, all separated by first-order transitions. For crenels in the intermediate regime re-entrant filling transitions driven by the anchoring strength are observed.

We investigate the entrainment of a neuron model exhibiting a chaotic spiking-bursting behavior in response to a weak periodic force. This model exhibits two types of oscillations with different characteristic time scales, namely, long and short time scales. Several types of phase synchronization are observed, such as $1:1$ phase locking between a single spike and one period of the force and $1:l$ phase locking between the period of slow oscillation underlying bursts and $l$ periods of the force. Moreover, spiking-bursting oscillations with chaotic firing patterns can be synchronized with the periodic force. Such a type of phase synchronization is detected from the position of a set of points on a unit circle, which is determined by the phase of the periodic force at each spiking time. We show that this detection method is effective for a system with multiple time scales. Owing to the existence of both the short and the long time scales, two characteristic phenomena are found around the transition point to chaotic phase synchronization. One phenomenon shows that the average time interval between successive phase slips exhibits a power-law scaling against the driving force strength and that the scaling exponent has an unsmooth dependence on the changes in the driving force strength. The other phenomenon shows that Kuramoto's order parameter before the transition exhibits stepwise behavior as a function of the driving force strength, contrary to the smooth transition in a model with a single time scale.

We analyze the dynamics of a classical particle in a spatially periodic potential under the influence of a periodic in time uniform force. It was shown by S. Flach and coworkers [Phys. Rev. Lett. 84, 2358 (2000)] that despite zero average force, directed transport is possible in the system. Asymptotic description of this phenomenon for the case of slow driving was developed by X. Leoncini and coworkers [Phys. Rev. E 79, 026213 (2009)]. Here we consider the case of fast driving using the canonical perturbation theory. An asymptotic formula is derived for the average drift velocity as a function of the system parameters and the driving law. We show that directed transport arises in an effective Hamiltonian that does not possess chaotic dynamics, thereby clarifying the relation between chaos and transport in the system. Sufficient conditions for transport are derived.

We study the scattering of waves in systems with losses or gains simulated by imaginary potentials. This is done for a complex delta potential that corresponds to a spatially localized absorption or amplification. In the Argand plane the scattering matrix moves on a circle $C$ centered on the real axis, but not at the origin, that is tangent to the unit circle. From the numerical simulations it is concluded that the distribution of the scattering matrix, when measured from the center of the circle $C$, agrees with the nonunitary Poisson kernel. This result is also obtained analytically by extending the analyticity condition, of unitary scattering matrices, to the no-unitary ones. We use this nonunitary Poisson kernel to obtain the distribution of nonunitary scattering matrices when measured from the origin of the Argand plane. The obtained marginal distributions have excellent agreement with the numerical results.

The anomalous dynamics of capillary rise in a porous medium discovered experimentally more than a decade ago [T. Delker et al., Phys. Rev. Lett. 76, 2902 (1996)] is described. The developed theory is based on considering the principal modes of motion of the menisci that collectively form the wetting front on the Darcy scale. These modes, which include (i) dynamic wetting mode, (ii) threshold mode, and (iii) interface depinning process, are incorporated into the boundary conditions for the bulk equations formulated in the regular framework of continuum mechanics of porous media, thus allowing one to consider a general case of three-dimensional flows. The developed theory makes it possible to describe all regimes observed in the experiment, with the time spanning more than four orders of magnitude, and highlights the dominant physical mechanisms at different stages of the process.

Using readily available experimental thermophoretic particle-velocity data it is shown, contrary to current teachings, that for the case of compressible flows independent dye- and particle-tracer velocity measurements of the local fluid velocity at a point in a flowing fluid do not generally result in the same fluid velocity measure. Rather, tracer-velocity equality holds only for incompressible flows. For compressible fluids, each type of tracer is shown to monitor a fundamentally different fluid velocity, with (i) a dye (or any other such molecular-tagging scheme) measuring the fluid's mass velocity $\mathbf{v}$ appearing in the continuity equation and (ii) a small, physicochemically and thermally inert, macroscopic (i.e., non-Brownian), solid particle measuring the fluid's volume velocity ${\mathbf{v}}_v$. The term “compressibility” as used here includes not only pressure effects on density, but also temperature effects thereon. (For example, owing to a liquid's generally nonzero isobaric coefficient of thermal expansion, nonisothermal liquid flows are to be regarded as compressible despite the general perception of liquids as being incompressible.) Recognition of the fact that two independent fluid velocities, mass- and volume-based, are formally required to model continuum fluid behavior impacts on the foundations of contemporary (monovelocity) fluid mechanics. Included therein are the Navier-Stokes-Fourier equations, which are now seen to apply only to incompressible fluids (a fact well-known, empirically, to experimental gas kineticists). The findings of a difference in tracer velocities heralds the introduction into fluid mechanics of a general bipartite theory of fluid mechanics, bivelocity hydrodynamics [Brenner, Int. J. Eng. Sci. 54, 67 (2012)], differing from conventional hydrodynamics in situations entailing compressible flows and reducing to conventional hydrodynamics when the flow is incompressible, while being applicable to both liquids and gases.

The efficiency of total energy utilization and its optimization for long-distance migration of fish have attracted much attention in the past. This paper presents theoretical and computational research, clarifying the above well-known classic questions. Here, we specify the energy-utilization ratio ($f_{\eta }$) as a scale of cruising efficiency, which consists of the swimming speed over the sum of the standard metabolic rate and the energy consumption rate of muscle activities per unit mass. Theoretical formulation of the function $f_{\eta }$ is made and it is shown that based on a basic dimensional analysis, the main dimensionless parameters for our simplified model are the Reynolds number (Re) and the dimensionless quantity of the standard metabolic rate per unit mass ($R_{pm}$). The swimming speed and the hydrodynamic power output in various conditions can be computed by solving the coupled Navier-Stokes equations and the fish locomotion dynamic equations. Again, the energy consumption rate of muscle activities can be estimated by the quotient of dividing the hydrodynamic power by the muscle efficiency studied by previous researchers. The present results show the following: (1) When the value of $f_{\eta }$ attains a maximum, the dimensionless parameter $R_{pm}$ keeps almost constant for the same fish species in different sizes. (2) In the above cases, the tail beat period is an exponential function of the fish body length when cruising is optimal, e.g., the optimal tail beat period of Sockeye salmon is approximately proportional to the body length to the power of 0.78. Again, the larger fish's ability of long-distance cruising is more excellent than that of smaller fish. (3) The optimal swimming speed we obtained is consistent with previous researchers’ estimations.

Subsonic motion of a large particle moving through the bulk of a dust crystal formed by negatively charged small particles is investigated using the PK-3 Plus laboratory onboard the International Space Station. Tracing the particle trajectories shows that the large particle moves almost freely through the bulk of the plasma crystal, while dust particles move along characteristic $\alpha$-shaped pathways near the large particle. In the hydrodynamic approximation, we develop a theory of nonviscous dust particle motion about a large particle and calculate particle trajectories. Good agreement with experiment validates our approach.

On the basis of a quantum mechanical analog of the famous Feynman-Kac formula, we present a method to derive nonequilibrium work equalities for isolated quantum systems, which include the Jarzynski equality and Bochkov-Kuzovlev equality. Compared with other methods in the literature, our method shows a higher similarity in form to the method deriving the fluctuation relations in the classical systems.

We introduce finite ramified self-affine substrates in two dimensions with a set of appropriate hopping rates between nearest-neighbor sites where the diffusion of a single random walk presents an anomalous anisotropic behavior modulated by log-periodic oscillations. The anisotropy is revealed by two different random-walk exponents ${\nu }_x$ and ${\nu }_y$ in the $x$ and $y$ directions, respectively. The values of these exponents as well as the periods of the oscillations are obtained analytically and confirmed by Monte Carlo simulations.

It has been observed that discrete earthquake events possess memory, i.e., that events occurring in a particular location are dependent on the history of that location. We conduct an analysis to see whether continuous real-time data also display a similar memory and, if so, whether such autocorrelations depend on the size of earthquakes within close spatiotemporal proximity. We analyze the seismic wave form database recorded by 64 stations in Japan, including the 2011 “Great East Japan Earthquake,” one of the five most powerful earthquakes ever recorded, which resulted in a tsunami and devastating nuclear accidents. We explore the question of seismic memory through use of mean conditional intervals and detrended fluctuation analysis (DFA). We find that the wave form sign series show power-law anticorrelations while the interval series show power-law correlations. We find size dependence in earthquake autocorrelations: as the earthquake size increases, both of these correlation behaviors strengthen. We also find that the DFA scaling exponent $\alpha$ has no dependence on the earthquake hypocenter depth or epicentral distance.