The hydrodynamic equations for a model of a confined quasi-two-dimensional gas of smooth inelastic hard spheres are derived from the Boltzmann equation for the model, using a generalization of the Chapman-Enskog method. The heat and momentum fluxes are calculated to Navier-Stokes order, and the associated transport coefficients are explicitly determined as functions of the coefficient of normal restitution and the velocity parameter involved in the definition of the model. Also an Euler transport term contributing to the energy transport equation is considered. This term arises from the gradient expansion of the rate of change of the temperature due to the inelasticity of collisions, and it vanishes for elastic systems. The hydrodynamic equations are particularized for the relevant case of a system in the homogeneous steady state. The relationship with previous works is analyzed.

In this paper we study breakage rate statistics of small colloidal aggregates in nonhomogeneous anisotropic turbulence. We use pseudospectral direct numerical simulation of turbulent channel flow and Lagrangian tracking to follow the motion of the aggregates, modeled as sub-Kolmogorov massless particles. We focus specifically on the effects produced by ductile rupture: This rupture is initially activated when fluctuating hydrodynamic stresses exceed a critical value, $\sigma >{\sigma }_{cr}$, and is brought to completion when the energy absorbed by the aggregate meets the critical breakage value. We show that ductile rupture breakage rates are significantly reduced with respect to the case of instantaneous brittle rupture (i.e., breakage occurs as soon as $\sigma >{\sigma }_{cr}$). These discrepancies are due to the different energy values at play as well as to the statistical features of energy distribution in the anisotropic turbulence case examined.

Channeling experiments were performed that demonstrate the transport of high-intensity $(>10{}^{18}W/{\mathrm{cm}}^2)$, multikilojoule laser light through a millimeter-sized, inhomogeneous ($\sim 300\text{−}\mu \mathrm{m}$ density scale length) laser-produced plasma up to overcritical density, which is an important step forward for the fast-ignition concept. The background plasma density and the density depression inside the channel were characterized with a novel optical probe system. The channel progression velocity was measured, which agrees well with theoretical predictions based on large scale particle-in-cell simulations, confirming scaling laws for the required channeling laser energy and laser pulse duration, which are important parameters for future integrated fast-ignition channeling experiments.

Covariance of physical quantities in fluid-turbulence theory and their governing equations under generalized coordinate transformation is discussed. It is shown that the velocity fluctuation and its governing law have a covariance under far wider group of coordinate transformation than that of conventional Euclidean invariance, and, as a natural consequence, various correlations and their governing laws are shown to be formulated in covariant manners under this wider transformation group. In addition, it is also shown that the covariance of the Reynolds stress is tightly connected to the objectivity of the mean flow.

We analyze the dynamics of small particles vertically confined, by means of a linear restoring force, to move within a horizontal fluid slab in a three-dimensional (3D) homogeneous isotropic turbulent velocity field. The model that we introduce and study is possibly the simplest description for the dynamics of small aquatic organisms that, due to swimming, active regulation of their buoyancy, or any other mechanism, maintain themselves in a shallow horizontal layer below the free surface of oceans or lakes. By varying the strength of the restoring force, we are able to control the thickness of the fluid slab in which the particles can move. This allows us to analyze the statistical features of the system over a wide range of conditions going from a fully 3D incompressible flow (corresponding to the case of no confinement) to the extremely confined case corresponding to a two-dimensional slice. The background 3D turbulent velocity field is evolved by means of fully resolved direct numerical simulations. Whenever some level of vertical confinement is present, the particle trajectories deviate from that of fluid tracers and the particles experience an effectively compressible velocity field. Here, we have quantified the compressibility, the preferential concentration of the particles, and the correlation dimension by changing the strength of the restoring force. The main result is that there exists a particular value of the force constant, corresponding to a mean slab depth approximately equal to a few times the Kolmogorov length scale $\eta$, that maximizes the clustering of the particles.

We consider thermalization of a microscopic quantum system by interaction with a thermal bath. Our interest is the minimal size the bath can have while still being able to thermalize the system. Within a specific thermalization scheme, we show that a single spin 1/2 can be fully thermalized by interaction with a bath that consists of just two other spins 1/2. The two bath spins are initially in a pure entangled state and the thermalizing interaction is a Heisenberg exchange interaction of the system spin with one of the bath spins. The time-dependent coupling strength has to obey a single integral constraint. We also present a simple generalization of this minimal model in which the bath consists of an arbitrary number of spin-1/2 pairs.

We present a mean-field theory for the dynamics of driven flow with exclusion in graphenelike structures, and numerically check its predictions. We treat first a specific combination of bond transmissivity rates, where mean field predicts, and numerics to a large extent confirms, that the sublattice structure characteristic of honeycomb networks becomes irrelevant. Dynamics, in the various regions of the phase diagram set by open boundary injection and ejection rates, is then in general identical to that of one-dimensional systems, although some discrepancies remain between mean-field theory and numerical results, in similar ways for both geometries. However, at the critical point for which the characteristic exponent is $z=3/2$ in one dimension, the mean-field value $z=2$ is approached for very large systems with constant (finite) aspect ratio. We also treat a second combination of bond (and boundary) rates where, more typically, sublattice distinction persists. For the two rate combinations, in continuum or late-time limits, respectively, the coupled sets of mean-field dynamical equations become tractable with various techniques and give a two-band spectrum, gapless in the critical phase. While for the second rate combination quantitative discrepancies between mean-field theory and simulations increase for most properties and boundary rates investigated, theory still is qualitatively correct in general, and gives a fairly good quantitative account of features such as the late-time evolution of density profile differences from their steady-state values.

Many shear flows follow a route to turbulence that has striking similarities to bifurcation scenarios in low-dimensional dynamical systems. Among the bifurcations that appear, crisis bifurcations are important because they cause global transitions between open and closed attractors, or indicate drastic increases in the range of the state space that is covered by the dynamics. We here study exterior and interior crisis bifurcations in direct numerical simulations of transitional plane Poiseuille flow in a mirror-symmetric subspace. We trace the state space dynamics from the appearance of the first three-dimensional exact coherent structures to the transition from an attractor to a chaotic saddle in an exterior crisis. For intermediate Reynolds numbers, the attractor undergoes several interior crises, in which new states appear and intermittent behavior can be observed. The bifurcations contribute to increasing the complexity of the dynamics and to a more dense coverage of state space.

We consider a tournament among four equally strong semifinalists. The players have to decide how much stamina to use in the semifinals, provided that the rest is available in the final and the third-place playoff. We investigate optimal strategies for allocating stamina to the successive matches when players' prizes (payoffs) are given according to the tournament results. From the basic assumption that the probability to win a match follows a nondecreasing function of stamina difference, we present symmetric Nash equilibria for general payoff structures. We find three different phases of the Nash equilibria in the payoff space. First, when the champion wins a much bigger payoff than the others, any pure strategy can constitute a Nash equilibrium as long as all four players adopt it in common. Second, when the first two places are much more valuable than the other two, the only Nash equilibrium is such that everyone uses a pure strategy investing all stamina in the semifinal. Third, when the payoff for last place is much smaller than the others, a Nash equilibrium is formed when every player adopts a mixed strategy of using all or none of its stamina in the semifinals. In a limiting case that only last place pays the penalty, this mixed-strategy profile can be proved to be a unique symmetric Nash equilibrium, at least when the winning probability follows a Heaviside step function. Moreover, by using this Heaviside step function, we study the tournament by using evolutionary replicator dynamics to obtain analytic solutions, which reproduces the corresponding Nash equilibria on the population level and gives information on dynamic aspects.

In this paper we present properties of an external colored cross-correlated noise-driven Brownian system which is coupled to a thermal bath. Multiplicative cross-correlated noises can stabilize the transition state. Thus by monitoring the interference between the noises one can understand the mechanism of a chemical reaction. At the same time, we have investigated how the interference affects the barrier-crossing dynamics. In its presence breakdown of the Arrhenius result occurs. The breakdown becomes prominent if the multiplicative noises become additive in nature. We have also investigated how the power law behavior of the rate constant as a function of damping strength is affected by the properties of external colored noises. Furthermore, we have observed that multiplicative colored cross-correlated noises can induce the resonant activation phenomenon.

The electrostatic interaction in ionic fluids is well known to give rise to a characteristic phase behavior and structure. Sometimes its long range is proposed to single out the electrostatic potential over other interactions with shorter ranges. Here the importance of the range for the phase behavior and the structure of ionic fluids is investigated by means of grandcanonical Monte Carlo simulations of the lattice restricted primitive model (LRPM). The long-ranged electrostatic interaction is compared to various types of short-ranged potentials obtained by sharp and/or smooth cutoff schemes. Sharply cutoff electrostatic potentials are found to lead to a strong dependence of the phase behavior and the structure on the cutoff radius. However, when combined with a suitable additional smooth cutoff, the short-ranged LRPM is found to exhibit quantitatively the same phase behavior and structure as the conventional long-ranged LRPM. Moreover, the Stillinger-Lovett perfect screening property, which is well known to be generated by the long-ranged electrostatic potential, is also fulfilled by short-ranged LRPMs with smooth cutoffs. By showing that the characteristic phase behavior and structure of ionic fluids can also be found in systems with short-ranged potentials, one can conclude that the decisive property of the electrostatic potential in ionic fluids is not the long range but rather the valency dependence.

The stability of sand castles is determined by the structure of wet granulates. Experimental data on the size distribution of fluid pockets are ambiguous with regard to their origin. We discovered that contact-angle hysteresis plays a fundamental role in the equilibrium distribution of bridge volumes, and not geometrical disorder as commonly conjectured. This has substantial consequences on the mechanical properties of wet granular beds, including a history-dependent rheology and lowered strength. Our findings are obtained using a model in which the Laplace pressures, bridge volumes, and contact angles are dynamical variables associated with the contact points. While accounting for contact line pinning, we track the temporal evolution of each bridge. We observe a crossover to a power-law decay of the variance of capillary pressures at late times and a saturation of the variance of bridge volumes to a finite value connected to contact line pinning. Large-scale simulations of liquid transport in the bridge network reveal that the equilibration dynamics at early times is well described by a mean-field model. The spread of final bridge volumes can be directly related to the magnitude of contact-angle hysteresis.

Using a granular-mechanics code, we study the impact of a highly porous granular body on a hard wall. The projectile consists of monodisperse adhesive micrometer-sized silica grains. For the impact velocities studied, $v<0.5\mathrm{m}/\mathrm{s}$, the sample does not fragment, but is compacted. We find that the compaction is proportional to the impact speed. The proportionality constant increases with decreasing porosity. However, the compaction is inhomogeneous and decreases with distance from the target. A compaction wave runs through the aggregate; it slows down while the compaction becomes less efficient.

We used speckle visibility spectroscopy to measure the time-resolved dynamcis of avalanching down the inclined surface of a granular material in a half-full rotating drum operating in the slumping regime. The distribution of the avalanche period, $t_d$, rest time between them, $t_r$, and peak particle velocity fluctuation, $\delta v_p^2$, are all normally distributed. While the distributions of the two times at the top and bottom of the free surface are very similar, the particle velocity fluctuation is greater at the bottom of the free surface than at the top. The rest time is observed to be inversely related to the drum speed. Combining this with the relation of $t_r$ and the difference of the upper and lower angle of repose for the granular material, $\Delta \theta$, we find that the latter decreases linearly with increasing rotational speed. We also observe that $t_d$ increases in a linear fashion with the drum speed. Using the relation of $t_r$ and the distance that particles have to move during an avalanche, we further find that a new scaling relation of the mean number of avalanches required to traverse the free surface with drum speed. We find that the slumping frequency increases with the rotating speed before becoming constant in the slumping-to-rolling transition region. Finally, we find that the average peak of the fluctuation speed of the avalanche, $\delta v_p^2$, increases linearly with the drum speed.

We present here a detailed numerical study of the dynamical behavior of “soft” uncompressed grains in a granular chain where the grains interact via the intrinsically nonlinear Hertz force. It is well known that such a chain supports the formation of solitary waves (SWs). Here, however, the system response to the material properties of the grains and boundaries is explored further. In particular, we examine the details of the transition of the system from a SW phase to an equilibrium-like (or quasiequilibrium) phase, and for this reason we ignore the effects of dissipation in this study. We find that the soft walls slow the reflection of SWs at the boundaries of the system, which in turn slows the journey to quasiequilibrium. Moreover, the increased grain-wall compression as the boundaries are softened results in fewer average grain-grain contacts at any given time in the quasiequilibrium phase. These effects lead to increased kinetic energy fluctuations in the short term in softer systems. We conclude with a toy model that exploits the results of soft-wall systems. This toy model supports the formation of breather-like entities and may therefore be useful for localizing energy in desired places in the granular chain.

Magnetic fluids based on manganese ferrite nanoparticles were studied from the structural point of view through small angle x-rays scattering (SAXS) and from the magnetic point of view through zero-field cooling and field cooling (ZFC-FC) and ac susceptibility measurements (MS). Three different colloids with particles mean diameters of $2.78,3.42$, and $6.15$ nm were investigated. The size distribution obtained from SAXS measurements follows a log-normal behavior. The ZFC-FC and MS results revealed the presence of an important magnetic interaction between the nanoparticles, characterized by a magnetic correlation distance $\mathrm{\Lambda }$. The colloidal medium can be pictures as composed by magnetic cluster constituted by $N$ interacting particles. These magnetic clusters are not characterized by a physical aggregation of particles. The energy barrier energy obtained is consistent with the existence of this magnetic clusters. Besides the magnetic interaction between particles, confinement effects must be included to account for the experimental values of the magnetic energy barrier encountered.

The response of shear stress to a weak ac electric field as a probe is measured in a nematic liquid crystal under shear flow and dc electric fields. Two states with different responses are clearly observed when the dc electric field is changed at a constant shear rate: the flow aligning and non–flow aligning states. The director lies in the shear plane in the flow aligning state and out of the plane in the non–flow aligning state. Through application of dc electric field, the non–flow aligning state can be changed to the flow aligning state. In the transition from the flow aligning state to the non–flow aligning state, it is found that the response increases and the relaxation time becomes longer. Here, the experimental results in the flow aligning state are discussed on the basis of the Ericksen-Leslie theory.

Density of photonic states $\rho \left(\omega \right)$, group $v_g$, and phase $v_{\mathrm{ph}}$ velocity of light, and the dispersion relation between wave vector $k$, and frequency $\omega \left(k\right)$ were determined in a cholesteric photonic crystal. A highly sensitive method (measurement of rotation of the plane of polarization of light) was used to determine $\rho \left(\omega \right)$ in samples of different quality. In high-quality samples a drastic increase in $\rho \left(\omega \right)$ near the boundaries of the stop band and oscillations related to Pendellösung beatings are observed. In low-quality samples photonic properties are strongly modified. The maximal value of $\rho \left(\omega \right)$ is substantially smaller, and density of photonic states increases near the selective reflection band without oscillations in $\rho \left(\omega \right)$. Peculiarities of $\rho \left(\omega \right), v_g$, and $\omega \left(k\right)$ are discussed. Comparison of the experimental results with theory was performed.

We develop a formalism for the dynamics of a flexible branched polymer with arbitrary topology in the presence of random flows. This is achieved by employing the generalized Gaussian structure (GGS) approach and the Matheron–de Marsily model for the random layered flow. The expression for the average square displacement (ASD) of the center of mass of the GGS is obtained in such flow. The averaging is done over both the thermal noise and the external random flow. Although the formalism is valid for branched polymers with various complex topologies, we mainly focus here on the dynamics of the flexible star and dendrimer. We analyze the effect of the topology (the number and length of branches for stars and the number of generations for dendrimers) on the dynamics under the influence of external flow, which is characterized by their root-mean-square velocity, persistence flow length, and flow exponent $\alpha$. Our analysis shows two anomalous power-law regimes, viz., subdiffusive (intermediate-time polymer stretching and flow-induced diffusion) and superdiffusive (long-time flow-induced diffusion). The influence of the topology of the GGS is unraveled in the intermediate-time regime, while the long-time regime is only weakly dependent on the topology of the polymer. With the decrease in the value of $\alpha$, the magnitude of the ASD decreases, while the temporal exponent of the ASD increases in both the time regimes. Also there is an increase in both the magnitude of the ASD and the crossover time (from the subdiffusive to the superdiffusive regime) with an increase in the total mass of the polymeric structure.

It is well known that a variety of cardiac arrhythmias are initiated by a focal excitation in heart tissue. At the single cell level these currents are typically induced by intracellular processes such as spontaneous calcium release (SCR). However, it is not understood how the size and morphology of these focal excitations are related to the electrophysiological properties of cardiac cells. In this paper a detailed physiologically based ionic model is analyzed by projecting the excitation dynamics to a reduced one-dimensional parameter space. Based on this analysis we show that the inward current required for an excitation to occur is largely dictated by the voltage dependence of the inward rectifier potassium current $\left(I_{\mathrm{K}1}\right)$, and is insensitive to the detailed properties of the sodium current. We derive an analytical expression relating the size of a stimulus and the critical current required to induce a propagating action potential (AP), and argue that this relationship determines the necessary number of cells that must undergo SCR in order to induce ectopic activity in cardiac tissue. Finally, we show that, once a focal excitation begins to propagate, its propagation characteristics, such as the conduction velocity and the critical radius for propagation, are largely determined by the sodium and gap junction currents with a substantially lesser effect due to repolarizing potassium currents. These results reveal the relationship between ion channel properties and important tissue scale processes such as excitation and propagation.