A phenomenology of isotropic magnetohydrodynamic (MHD) turbulence subject to both rotation and applied magnetic field is presented. It is assumed that the triple correlation decay time is the shortest between the eddy turn-over time and the ones associated to the rotating frequency and the Alfvén wave period. For $\text{Pm}=1$ it leads to four kinds of piecewise spectra, depending on four parameters: injection rate of energy, magnetic diffusivity, rotation rate, and applied field. With a shell model of MHD turbulence (including rotation and applied magnetic field), spectra for $\text{Pm}\le 1$ are presented, together with the ratio between magnetic and viscous dissipations.

We analyze a volumetric formulation of lattice Boltzmann for compressible thermal fluid flows. The velocity set is chosen with the desired accuracy, based on the Gauss-Hermite quadrature procedure, and tested against controlled problems in bounded and unbounded fluids. The method allows the simulation of thermohydrodyamical problems without the need to preserve the exact space-filling nature of the velocity set, but still ensuring the exact conservation laws for density, momentum, and energy. Issues related to boundary condition problems and improvements based on grid refinement are also investigated.

We present results from extensive three-dimensional molecular dynamics (MD) simulations of phase separation kinetics in fluids. A coarse-graining procedure is used to obtain state-of-the-art MD results. We observe an extended period of temporally linear growth in the viscous hydrodynamic regime. The morphological similarity of coarsening in fluids and solids is also quantified. The velocity field is characterized by the presence of monopolelike defects, which yield a generalized Porod tail in the corresponding structure factor.

We have experimentally investigated the influence of a magnetic interaction between the grains on the flow of a granular material in a rotating drum. The magnetic cohesion is induced by applying a homogeneous external magnetic field $\vec{B}$ oriented either parallel or perpendicular to the gravity $\vec{g}$. The drum rotating speed has been selected to obtain a continuous flow when the magnetic field is switched off. We show that, for both magnetic field orientations, the cohesion is able to induce a transition between the continuous flow regime to the discrete avalanche regime. The avalanche dynamics is periodic when $\vec{B}\perp \vec{g}$ and irregular when $\vec{B}\parallel \vec{g}$. Moreover, the maximal angle of stability ${\theta }_m$ increases strongly with the cohesion strength and could be higher than $90°$ when $\vec{B}\perp \vec{g}$. A toy model based on the stability of a magnetic block on a magnetic inclined plane is proposed to explain this behavior.

Recently Wang et al. [Phys. Rev. Lett. 104, 027801 (2010)] discovered a novel smectic-$C^{\ast }$ liquid-crystal commensurate structure with six-layer period. Challenged by this discovery, we show that the observed novel structure and the unusual sequence of polar phases can be explained in the framework of the discrete Landau model of phase transitions with a two-component order parameter. Peculiarities of the six-layer phase and the influence of short-range and long-range interactions on the formation of different phases and phase sequences are discussed.

Finite-size effects in certain critical systems can be understood as universal Casimir forces. Here, we compare the Casimir force for free, fixed, periodic, and antiperiodic boundary conditions in the exactly calculable case of the ferromagnetic Ising model in one and two dimensions. We employ a procedure which allows us to calculate the Casimir force with the aforementioned boundary conditions analytically in a transparent manner. Among other results, we find an attractive Casimir force for the case of periodic boundary conditions and a repulsive Casimir force in the antiperiodic case.

We explore a reaction-dispersal mechanism for the generation of wave fronts which consists of a set of particles traveling with random velocities (chosen from arbitrary distributions) which experience an autocatalytic reaction. The differences found between this mechanism and approaches based on the continuous-time random walks, where the particles are assumed to perform discrete jumps from one position to another, are analyzed and discussed. A complete analytical treatment of our velocity model is achieved, which allows us to predict the constant speed of traveling fronts or their time dependence in case they are accelerated. Also, a general criterion to distinguish the situations of fronts with constant speed from those accelerated is provided. From it, we conclude that accelerated fronts should be expected in different situations easily achievable in nature.

We report on an experimental and numerical study of the collapse under gravity of a rectangular well in a quasi-two-dimensional granular bed. For comparison, we also perform experiments on the collapse of a single vertical step. Experiments are conducted in a vertical Hele-Shaw cell, which allows the flow to be recorded from the side using high-speed video. If the rectangular well is sufficiently narrow, the collapsing sidewalls collide at the center of the well and the dynamics of the collapse are dependant on the aspect ratio of the initial well. We follow the evolution of the free surface from the video images, and use particle image velocimetry to determine the subsurface velocity field. From these data, the potential and kinetic energy of the system are calculated. We observe two stages to the collapse flow: an initial gravity-dominated stage, during which the kinetic energy increases, and a later dissipation-dominated phase during which the kinetic energy decreases. We find that although both the width and depth of the depression that remains after the well has collapsed depend on the initial aspect ratio, the surface profiles are self-similar; that is, the shape of the final profile is independent of the aspect ratio of the initial well. We model the collapse of the well using a depth-averaged continuum model with basal friction and with a discrete element model. Both models give results which agree well with experiment. The discrete element model indicates that friction between the particles is the most important source of dissipation over the course of the collapse.

An existence of a single master curve for the long-time self-diffusion coefficients $D_S^L\left(T\right)$ in diversely different glass-forming liquids is predicted over wide temperature $T$ ranges above the glass transition point $T_g$ by analyzing various experimental and simulation data consistently from a unified point of view based on the mean-field theory recently developed. In order to scale those data appropriately, the power-law dependence of the $\alpha$- and the $\beta$-relaxation times on $D_S^L$ is used. Then, it is shown that any equilibrium data for self-diffusion of atom in different systems are all collapsed onto a singular function $f\left(T_f^{\left(\alpha \right)}/T\right)$, where $T_f^{\left(\alpha \right)}$ is a fictive singular temperature of atom $\alpha$. Thus, we emphasize that any equilibrium self-diffusion data can be described by a single master curve $f\left(x\right)$ above $T_g\left(>T_f\right)$, while the data out of equilibrium start to deviate from $f\left(x\right)$ around $T_g$.

In this paper, we describe the dielectric properties of a biological cell suspension of shelled ellipsoidal cells with a layer of localized charges at the membrane interfaces. In so doing, we are dealing with two different problems encountered in finding an analytical solution of the dielectric problem. The first one concerns the calculation of the electrical polarizability of a shelled ellipsoidal cell in the presence of a localized layer of charges. We will show that what we call the dipolar approximation is good enough to ensure a meaningful behavior of the dielectric spectra, whatever the cell parameters are, contrarily to what happens if one estimates the polarizability without taking into account the appropriate correction term deriving from the localized charge distribution. The second problem we face concerns the fact that the interfaces of the different adjacent media should be surfaces of constant coordinates, within a certain set of coordinate types. This implies, for ellipsoidal geometries, the requirement of a confocal condition which leads to a cell membrane of nonconstant thickness. Even if the membrane thickness is at least two orders of magnitude lower than the typical cell size, its nonconstancy leads to serious discrepancies in the shape of the dielectric spectra, which are heavier the larger the membrane conductivity is or larger as the value of the conductivity of the surface charge layers is. As far as this latter problem is concerned, we propose a compromise that saves the confocality condition and, at the same time, reduces significantly the effects of the nonuniform membrane thickness. We present here some dielectric spectra of shelled ellipsoidal cells (both prolate and oblate in shape) over an extended frequency range, showing their main characteristics, arising from the combined presence of localized charge distributions and polarization charge distributions. Finally, we compare some of these results with the ones obtained using different approximations.

Self-consistent normal mode analysis (SCNMA) is applied to heme c type cytochrome f to study temperature-dependent protein motion. Classical normal mode analysis assumes harmonic behavior and the protein mean-square displacement has a linear dependence on temperature. This is only consistent with low-temperature experimental results. To connect the protein vibrational motions between low and physiological temperatures, we have incorporated a fitted set of anharmonic potentials into SCNMA. In addition, quantum harmonic-oscillator theory has been used to calculate the displacement distribution for individual vibrational modes. We find that the modes involving soft bonds exhibit significant non-Gaussian dynamics at physiological temperature, which suggests that it may be the cause of the non-Gaussian behavior of the protein motions probed by elastic incoherent neutron scattering. The combined theory displays a dynamical transition caused by the softening of few “torsional” modes in the low-frequency regime ($<50{\text{cm}}^{-1}$ or $<6\text{meV}$ or $>0.6\text{ps}$). These modes change from Gaussian to a classical distribution upon heating. Our theory provides an alternative way to understand the microscopic origin of the protein dynamical transition.

We study the dynamics and trapping of excitations for a dimer with an energy off-set $\Delta$ coupled to an external environment. Using a Lindblad quantum master equation approach, we calculate the survival probability $\Pi \left(t\right)$ of the excitation and define different lifetimes ${\tau }_s$ of the excitation, corresponding to the duration of the decay of $\Pi \left(t\right)$ in between two predefined values. We show that it is not possible to always enhance the overall decay to the trap. However, it is possible, even for not too small environmental couplings and for values of $\Delta$ of the order $\mathcal{O}\left(1\right)$, to decrease certain lifetimes ${\tau }_s$, leading to faster decay of $\Pi \left(t\right)$ in these time intervals: there is an optimal environmental coupling, leading to a maximal decay for fixed $\Delta$.

We study numerically the Kuramoto-Sivashinsky equation forced by external white noise in two space dimensions, that is a generic model for, e.g., surface kinetic roughening in the presence of morphological instabilities. Large scale simulations using a pseudospectral numerical scheme allow us to retrieve Kardar-Parisi-Zhang (KPZ) scaling as the asymptotic state of the system, as in the one-dimensional (1D) case. However, this is only the case for sufficiently large values of the coupling and/or system size, so that previous conclusions on non-KPZ asymptotics are demonstrated as finite size effects. Crossover effects are comparatively stronger for the two-dimensional case than for the 1D system.

Finding modules, or clusters, in networks currently attracts much attention in several domains. The most studied criterion for doing so, due to Newman and Girvan [Phys. Rev. E 69, 026113 (2004)], is modularity maximization. Many heuristics have been proposed for maximizing modularity and yield rapidly near optimal solution or sometimes optimal ones but without a guarantee of optimality. There are few exact algorithms, prominent among which is a paper by Xu et al. [Eur. Phys. J. B 60, 231 (2007)]. Modularity maximization can also be expressed as a clique partitioning problem and the row generation algorithm of Grötschel and Wakabayashi [Math. Program. 45, 59 (1989)] applied. We propose to extend both of these algorithms using the powerful column generation methods for linear and non linear integer programming. Performance of the four resulting algorithms is compared on problems from the literature. Instances with up to 512 entities are solved exactly. Moreover, the computing time of previously solved problems are reduced substantially.

We study the dynamics of time-delay coupled limit-cycle oscillators in the amplitude death regime. Through a detailed analysis of the Jacobian at the fixed point, we show that the phase-flip transition, namely, the abrupt change from in-phase synchronized dynamics to antiphase synchronized dynamics, is associated with an interchange of the imaginary parts of complex pairs of eigenvalues at an “avoided crossing” of Lyapunov exponents as a parameter is varied. An order parameter for the transition is constructed through the eigenvectors of the Jacobian.

Laboratory and numerical experiments are reported on dye advection processes in geostrophic turbulence. The experimental setup is the classical rotating annulus with differential heating which mimics the most essential features of midlatitude atmospheric flow. The main control parameter is the temperature contrast. Fluorescent dye is used as passive tracer, and dispersion is evaluated by digital image processing. The results are compared with tracer dispersion computations which are performed by means of global reanalysis wind fields at the pressure height of 500 hPa covering a time interval of one year. Apart from initial transient periods, the characteristic behavior for intermediate time scales is ballistic dispersion in both systems, where the zonal extent of the tracer cloud increases linearly in time (Batchelor scaling). The long-time evolution cannot be followed by the experimental technique, however, the numerical tests suggest a slower diffusive dispersion (Taylor regime) after 70–80 revolutions (days), in agreement with expectations. Richardson-Obukhov scaling (superdiffusion with an exponent value of 3/2) is neither observed in the laboratory nor in the numerical tests. Our findings confirm recent experimental results on the classic prediction by Batchelor that the initial pair separation is an essential parameter of the subsequent time evolution of tracers.

The modeling of buoyancy driven turbulent flows is considered in conjunction with an advanced statistical turbulence model referred to as the BHR (Besnard-Harlow-Rauenzahn) $k\text{−}S\text{−}a$ model. The BHR $k\text{−}S\text{−}a$ model is focused on variable-density and compressible flows such as Rayleigh-Taylor (RT), Richtmyer-Meshkov (RM), and Kelvin-Helmholtz (KH) driven mixing. The BHR $k\text{−}S\text{−}a$ turbulence mix model has been implemented in the RAGE hydro-code, and model constants are evaluated based on analytical self-similar solutions of the model equations. The results are then compared with a large test database available from experiments and direct numerical simulations (DNS) of RT, RM, and KH driven mixing. Furthermore, we describe research to understand how the BHR $k\text{−}S\text{−}a$ turbulence model operates over a range of moderate to high Reynolds number buoyancy driven flows, with a goal of placing the modeling of buoyancy driven turbulent flows at the same level of development as that of single phase shear flows.

A totally asymmetric exclusion process on a ring with $\nu$ nonconserved internal degrees of freedom, where particles hop forward with a rate that depends on their internal state, has been studied. We show, using a mapping of the model to a zero range process with $\nu$ different kinds of boxes, that steady-state weights can be written in a matrix product form and calculate the spatial correlations exactly. A comparison of the model with an equivalent conserved system reveals that unequal hopping rates of particles belonging to different internal states are responsible for the nontrivial correlations.