We investigate the dynamics of a realization of the stochastic Fermi acceleration mechanism. The model consists of test particles moving between two oscillating magnetic clouds and differs from the usual Fermi-Ulam model in two ways. (i) Particles can penetrate inside clouds before being reflected. (ii) Particles can radiate a fraction of their energy during the process. Since the Fermi mechanism is at work, particles are stochastically accelerated, even in the presence of the radiated energy. Furthermore, due to a kind of resonance between particles and oscillating clouds, the probability density function of particles is strongly modified, thus generating beams of accelerated particles rather than a translation of the whole distribution function to higher energy. This simple mechanism could account for the presence of beamlets in some space plasma physics situations.

Spontaneous spin-up, i.e., the significant increase of the total angular momentum of a flow that initially has no net angular momentum, is very characteristic for decaying two-dimensional turbulence in square domains bounded by rigid no-slip walls. In contrast, spontaneous spin-up is virtually absent for such flows in a circular domain with a no-slip boundary. In order to acquire an understanding of this strikingly different behavior observed on the square and the circle, we consider a set of elliptic geometries with a gradual increase of the eccentricity. It is shown that a variation of the eccentricity can be used as a control parameter to tune the relative contribution of the pressure and viscous stresses in the angular momentum balance. Direct numerical simulations demonstrate that the magnitude of the torque can be related to the relative contribution of the pressure. As a consequence, the number of spin-up events in an ensemble of slightly different initial conditions depends strongly on the eccentricity. For small eccentricities, strong and rapid spin-up events are observed occasionally, whereas the majority of the runs do not show significant spin-up. Small differences in the initial condition can result in a completely different evolution of the flow and an appearance of the end state of the decay process. For sufficiently large eccentricities, all the runs in the ensemble demonstrate strong and rapid spin-up, which is consistent with the flow development on the square. It is verified that the number of spin-up events for a given eccentricity does not depend on the Reynolds number of the flow. This observation is consistent with the conjecture that it is the pressure on the domain boundaries that drives the spin-up processes.

A theoretical model is proposed to describe narrowband pulse dynamics in two-dimensional systems with arbitrary correlated disorder. In anisotropic systems with elongated cigarlike inhomogeneities, fast propagation is predicted in the direction across the structure where the wave is exponentially localized and tunneling of evanescent modes plays a dominant role in typical realizations. Along the structure, where the wave is channeled as in a waveguide, the motion of the wave energy is relatively slow. Numerical simulations performed for ultra-wide-band pulses show that even at the initial stage of wave evolution, the radiation diffuses predominantly in the direction along the major axis of the correlation ellipse. Spectral analysis of the results relates the long tail of the wave observed in the transverse direction to a number of frequency domain “lucky shots” associated with the long-living resonant modes localized inside the sample.

We show the existence of natural subsurface channels that guide acoustic waves for periodic arrays of spherical grains under the influence of gravity. Downward propagation of acoustic rays can be stopped altogether as a result of a caustic whose origin lies in the continuous bending of rays as a result of a gravitationally induced increase of rigidity with depth. Upward propagation of acoustic rays, on the other hand, is attenuated by Bragg reflection arising from the continuous diminishing of rigidity in the direction of the surface, resulting in a vertical propagation constant that approaches a limited allowed value. Waves with different frequencies are shown to travel at different depths below the surface. The key conditions for the manifestation of the predicted wave modes are microscopic periodicity and macroscopic inhomogeneity of the medium.

It was recently found that neuronal (and many other) networks contain some significantly recurring wiring patterns, termed “network motifs,” which are believed to be basic building blocks of these networks and to perform important functional roles in them. We study the functions of neuronal network motifs by computational modeling. We use both the firing-rate and integrate-and-fire models to model the neuronal network motifs. Several interesting functions and dynamics are found in the neuronal network motifs, such as the acceleration and delay of response and long- and short-term memory.

We study a quasibound state of a $\delta$-kicked rotor with absorbing boundaries focusing on the nature of the dynamical localization in open quantum systems. The localization lengths $\xi$ of lossy quasibound states located near the absorbing boundaries decrease as they approach the boundary while the corresponding decay rates $\Gamma$ are dramatically enhanced. We find the relation $\xi \sim {\Gamma }^{-1∕2}$ and explain it based upon the finite time diffusion, which can also be applied to a random unitary operator model. We conjecture that this idea is valid for the system exhibiting both the diffusion in classical dynamics and the exponential localization in quantum mechanics.

We discuss quite surprising properties of the one-parameter family of modular nonlinear Schrödinger equations [G. Auberson and P. G. Sabatier, J. Math. Phys. 35, 4028 (1994)]. We develop a unified theoretical framework for this family. Special attention is paid to the emergent dual time evolution scenarios which, albeit running in the real time parameter of the pertinent nonlinear equation, in each considered case may be mapped among each other by means of a suitable analytic continuation-in-time procedure. This dynamical duality is characteristic for nondissipative quantum motions and their dissipative (diffusion-type processes) partners, and naturally extends to classical motions in confining and scattering potentials.

We present an effective field theory to analyze, in a very general way, models defined over small-world networks. Even if the exactness of the method is limited to the paramagnetic regions and to some special limits, it provides, yielding a clear and immediate (also in terms of calculation) physical insight, the exact critical behavior and the exact critical surfaces and percolation thresholds. The underlying structure of the nonrandom part of the model—i.e., the set of spins filling up a given lattice ${\mathcal{L}}_0$ of dimension $d_0$ and interacting through a fixed coupling $J_0$—is exactly taken into account. When $J_0⩾0$, the small-world effect gives rise, as is known, to a second-order phase transition that takes place independently of the dimension $d_0$ and of the added random connectivity $c$. When $J_0<0$, a different and novel scenario emerges in which, besides a spin-glass transition, multiple first- and second-order phase transitions may take place. As immediate analytical applications we analyze the Viana-Bray model $(d_0=0)$, the one-dimensional chain $(d_0=1)$, and the spherical model for arbitrary $d_0$.

We formulate a Swendsen-Wang-like version of the geometric cluster algorithm. As an application, we study the hard-core lattice gas on the triangular lattice with the first- and second-neighbor exclusions. The data were first analyzed by finite-size scaling without including logarithmic corrections. We determine the critical chemical potential as ${\mu }_c=1.75682\left(2\right)$ and the critical particle density as ${\rho }_c=0.180\left(4\right)$. From the Binder ratio $Q$ and susceptibility $\chi$, the thermal and magnetic exponents are estimated as $y_t=1.51\left(1\right)\approx 3∕2$ and $y_h=1.8748\left(8\right)\approx 15∕8$, respectively, while the analyses of energylike quantities yield $y_t$ ranging from 1.440(5) to 1.470(5). Nevertheless, the data for energylike quantities are also well described by theoretically predicted scaling formulas with logarithmic corrections and with exponent $y_t=3∕2$. These results are very similar to the earlier study for the four-state Potts model on the square lattice [J. Stat. Phys. 88, 567 (1997)], and strongly support the general belief that the model is in the four-state Potts universality class. The dynamic scaling behavior of the Metropolis simulation and the combined method of the Metropolis and the geometric cluster algorithm is also studied; the former has a dynamic exponent $z_{\mathrm{int}}\approx 2.21$ and the latter has $z_{\mathrm{int}}\approx 1.60$.

Using molecular dynamics we study the behavior of a large particle immersed in a bed of smaller ones. The system is bidimensional, consisting of many rough inelastic hard disks of equal size plus a larger one: the intruder. All possible parameters of the system are kept fixed except for two dimensionless parameters determining the frequency and amplitude of the vibrating base. A systematic exploration of this parameter space leads to determining a transition line separating a zone in which the Brazil nut effect is observed and one in which it is not. The results strongly suggest that, in the region of the parameter space in which the study is made, there is a minimum amplitude and a maximum frequency for the Brazil nut effect to take place. These results compare well with isolated results from other authors.

We use numerical simulations to examine two-dimensional particle mixtures that strongly phase separate in equilibrium. When the system is externally driven in the presence of quenched disorder, plastic flow occurs in the form of meandering and strongly mixing channels. In some cases, this can produce a fast and complete mixing of previously segregated particle species, as well as an enhancement of transverse diffusion even in the absence of thermal fluctuations. We map the mixing phase diagram as a function of external driving and quenched disorder parameters.

Using the Landau–de Gennes phenomenological approach, we study the fine biaxial core structure of a boojum residing on the surface of a nematic liquid crystal phase. The core is formed by a negatively uniaxial finger, surrounded by a shell with maximal biaxiality. The characteristic finger’s length and the shell’s width are comparable to the biaxial correlation length. The finger tip is melted for topological reasons. Upon decreasing the surface anchoring strength below a critical value, the finger gradually leaves the bulk and it is expelled through the surface.

Flexoelectricity is a unique property of liquid crystals; it is a linear coupling between electric polarizations and bend and/or splay distortions of the direction of average molecular orientation. Recently it was shown [J. Harden et al., Phys. Rev. Lett. 97, 157802 (2006)] that the bend flexoelectric coefficient in bent-core nematic liquid crystals can be three orders of magnitude higher than the effect with calamitic (rod-shaped) molecular shape. Here we report the converse of the flexoelectric effect: An electric field applied across a bent-core liquid crystal sandwiched between thin flexible substrates produces a director distortion which is manifested as a polarity-dependent flexing of the substrates. The flex magnitude is shown to be consistent with predictions based upon both the measured value of the bend flexoelectric constant and the elastic properties of the substrates. Converse flexoelectricity makes possible a new class of microactuators with no internal moving parts, which offers applications as diverse as optical beam steering to artificial muscles.

An ensemble of stochastic genetic relaxation oscillators via phase-attractive or repulsive cell-to-cell communication are investigated. In the phase-attractive coupling case, it is found that cellular communication can enhance self-induced stochastic resonance as well as collective rhythms, and that different intensities of noise resulting from the fluctuation of intrinsic chemical reactions or the extrinsic environment can induce stochastic limit cycles with different amplitudes for a large cell density. In contrast, in the phase-repulsive coupling case, the distribution of phase differences among the stochastic oscillators can display such characteristic as unimodality, bimodality or polymodality, depending on both noise intensity and cell number, but the modality of phase difference distribution almost keeps invariant for an arbitrary noise intensity as the cell number is beyond a threshold.

The effects of quenched disorder on nonequilibrium phase transitions in the directed percolation universality class are revisited. Using a strong-disorder energy-space renormalization-group method, it is shown that for any amount of disorder the critical behavior is controlled by an infinite-randomness fixed point in the same universality class of the random transverse-field Ising models.

A nonadiabatic two-scale quantum-classical dynamics method is developed to allow for dynamical simulation of photoinduced processes and reactions in chemically complex condensed-matter systems such as photosensitive liquid crystals. A first application to photoswitching of azobenzene in the bulk reveals not only valuable insights into the excited-state dynamics underlying the cis to trans transformation, but also into the influence of the condensed phase environment on mechanism and relaxation time scales compared to vacuum.

Nonequilibrium molecular dynamics (NEMD) calculations of the bulk viscosity of the triple point Lennard-Jones fluid are performed with the aim of investigating the origin of the observed disagreement between Green-Kubo estimates and previous NEMD data. We show that a careful application of the Doll’s perturbation field, the dynamical NEMD method, the instantaneous form of the perturbation and the “subtraction technique” provides a NEMD estimate of the bulk viscosity at zero field in full agreement with the value obtained by the Green-Kubo formula. As previously reported for the shear viscosity, we find that the bulk viscosity exhibits a large linear regime with the field intensity.

A perspective on systems containing many action potential waves that, individually, are prone to spiral wave breakup is proposed. The perspective is based on two quantities, “predator” and “prey,” which we define as the fraction of the system in the excited state and in the excitable but unexcited state, respectively. These quantities exhibited a number of properties in both simulations and fibrillating canine cardiac tissue that were found to be consistent with a proposed theory that assumes the existence of regions we call “domains of influence,” each of which is associated with the activity of one action potential wave. The properties include (i) a propensity to rotate in phase space in the same sense as would be predicted by the standard Volterra-Lotka predator-prey equations, (ii) temporal behavior ranging from near periodic oscillation at a frequency close to the spiral wave rotation frequency (“type-1” behavior) to more complex oscillatory behavior whose power spectrum is composed of a range of frequencies both above and, especially, below the spiral wave rotation frequency (“type-2” behavior), and (iii) a strong positive correlation between the periods and amplitudes of the oscillations of these quantities. In particular, a rapid measure of the amplitude was found to scale consistently as the square root of the period in data taken from both simulations and optical mapping experiments. Global quantities such as predator and prey thus appear to be useful in the study of multiple spiral wave systems, facilitating the posing of new questions, which in turn may help to provide greater understanding of clinically important phenomena such as ventricular fibrillation.

Mechanical events within the thickness of the vessel wall caused by pulsatile blood flow are considered, with focus on axial dynamics of the wall, driven by the oscillatory drag force exerted by the fluid on the endothelial layer of the wall. It is shown that the focus on the axial direction makes it possible to derive simplified equations of motion which, combined with a viscoelastic model of the wall material, makes it possible in turn to obtain solutions in closed form for the displacement and stress of material elements within the wall. The viscoelastic model allows a study of the dynamics of the wall with different ratios of viscosity to elasticity of the wall material, to mimic changes in the properties of the arterial wall caused by disease or aging. It is found that when the wall is highly viscous the displacements and stresses caused by the flow are confined to a thin layer close to the inner boundary of the wall, while as the wall material becomes less viscous and more rigid the displacements and stresses spread deeper into the thickness of the wall to affect most of its elements.