The turbulent flow of a ferrofluid in channel flow is studied using direct numerical simulation. The method of analysis is an extension of that used for Newtonian fluids, with additional features necessary to model the ferrofluid. The analysis is applied to low Reynolds number turbulence in the range of existing experimental data in a capillary. For steady and oscillating magnetic fields, comparisons are made between a Newtonian fluid and a ferrofluid by comparing the pressure drop, turbulent Reynolds number, turbulent kinetic energy ($k$), Reynolds stress, velocity, and spin profiles. The results are also compared with predictions of a $k-\varepsilon$ model to show the accuracy of that model when applied to ferrofluids, where $\varepsilon$ is the rate of viscous dissipation of turbulent kinetic energy.

The location of the plasma sheath edge, where quasineutrality is broken, is rigorously derived by using a kinetic description of the plasma. It is shown that sheaths can exist with arbitrarily small ion velocity at the sheath edge, thus violating the Bohm criterion, $V_i=c_s$ at the sheath edge. Bohm’s criterion is recovered in the case of large enough ion current through the wall, and it is found to be a reasonable approximation in floating potential conditions. However, in the case of a predominant electron current through the wall, Bohm’s criterion is not able to describe the sheath-edge transition. The analytical results are supported by numerical simulations performed with a fully kinetic particle-in-cell code modeling a source-driven, weakly collisional plasma, bound between two absorbing walls.

The procedure to obtain gas temperature in plasmas is to fit the experimental rotational spectrum to a theoretical one based on the Boltzmann distribution. For many systems a single distribution fails to account for the occupation of the levels. Researchers have improved the fitting by coupling two distributions and obtaining two distinct temperatures. They assigned the lowest temperature to the gas. Here, we show that these systems should be described by Tsallis nonextensive statistics and its unique associated temperature. Experimental and simulated spectra are tested and excellent agreement is obtained.

We study polymer translocation through a nanopore subject to conformational differences created by putting two different solvents at the $\mathit{cis}$ and $\mathit{trans}$ compartments using Langevin dynamics in three dimensions (3D). Initially a fraction of the chain is placed in a good solvent at the $\mathit{cis}$ side and the rest of the chain at the $\mathit{trans}$ side is immersed in a bad solvent where it forms a globule. We study several aspects of the translocating chain as a function of the strength of the interaction $\varepsilon /k_{B}T$ for the bad solvent, where the temperature $T$ is kept below the $\Theta$ temperature for the specific bead-spring model that we have used to describe the chain. For $\varepsilon /k_{B}T⩾1$ we find the mean first passage time $\langle \tau \rangle ~(\frac{\varepsilon }{k_{B}T}){}^{-1}$ and $\langle \tau \rangle ~N^{1.1\pm 0.05}$. In that regard, translocation under solvent asymmetry is similar to the case of driven translocation under a bias inside the pore. However, the globule formed at the $\mathit{trans}$ in the immediate vicinity of the pore readily absorbs the incoming particles making the translocation process faster than the driven translocation. Our simulation results for long chains and $\varepsilon /k_{B}T⩾1$ agree well with a theoretical prediction by Muthukumar [M. Muthukumar, J. Chem. Phys. 111, 10371 (1999).].

A dipolar flow structure is experimentally studied in a layer of salt solution driven by time-independent electromagnetic forcing. In particular, the response of the flow to the forcing is quantified by measuring the Reynolds number Re as a function of the Chandrasekhar number Ch (the ratio of Lorentz forces to viscous forces) and $\delta$ (the ratio of vertical to horizontal length scales of the flow domain). In agreement with theoretical predictions, two scaling regimes are found: $\mathrm{Re}~\mathrm{Ch}/{\mathrm{\pi }}^2$ (viscous regime) and $\mathrm{Re}~{\mathrm{Ch}}^{1/2}{\mathrm{\delta }}^{-1}$ (advective regime). The transition between the two regimes at ${\mathrm{Ch}}^{1/2}\mathrm{\delta }~{\mathrm{\pi }}^2$ is reflected in the flow geometry in the form of an asymmetry of the dipolar flow structure.

Pattern formation in reaction-diffusion systems is of great importance in surface micropatterning [Grzybowski et al., Soft Matter 1, 114 (2005)], self-organization of cellular micro-organisms [Schulz et al., Annu. Rev. Microbiol. 55, 105 (2001)], and in developmental biology [Barkai et al., FEBS Journal 276, 1196 (2009)]. In this work, we apply the lattice Boltzmann method to study pattern formation in reaction-diffusion systems. As a first methodological step, we consider the case of a single species undergoing transformation reaction and diffusion. In this case, we perform a third-order Chapman-Enskog multiscale expansion and study the dependence of the lattice Boltzmann truncation error on the diffusion coefficient and the reaction rate. These findings are in good agreement with numerical simulations. Furthermore, taking the Gray-Scott model as a prominent example, we provide evidence for the maturity of the lattice Boltzmann method in studying pattern formation in nonlinear reaction-diffusion systems. For this purpose, we perform linear stability analysis of the Gray-Scott model and determine the relevant parameter range for pattern formation. Lattice Boltzmann simulations allow us not only to test the validity of the linear stability phase diagram including Turing and Hopf instabilities, but also permit going beyond the linear stability regime, where large perturbations give rise to interesting dynamical behavior such as the so-called self-replicating spots. We also show that the length scale of the patterns may be tuned by rescaling all relevant diffusion coefficients in the system with the same factor while leaving all the reaction constants unchanged.

We study a percolation problem on a substrate formed by two-dimensional $\mathit{XY}$ spin configurations using Monte Carlo methods. For a given spin configuration, we construct percolation clusters by randomly choosing a direction $x$ in the spin vector space, and then placing a percolation bond between nearest-neighbor sites $i$ and $j$with probability $p_{\mathit{ij}}=max(0,1-e^{-2K{s}_i^x{s}_j^x})$, where $K>0$ governs the percolation process. A line of percolation thresholds $K_c(J)$ is found in the low-temperature range $J⩾J_c$, where $J>0$ is the $\mathit{XY}$ coupling strength. Analysis of the correlation function $g_p(r)$, defined as the probability that two sites separated by a distance $r$ belong to the same percolation cluster, yields algebraic decay for $K⩾K_c(J)$, and the associated critical exponent depends on $J$ and $K$. Along the threshold line $K_c(J)$, the scaling dimension for $g_p$ is, within numerical uncertainties, equal to $1/8$. On this basis, we conjecture that the percolation transition along the $K_c(J)$ line is of the Berezinskii-Kosterlitz-Thouless type.

The forest-fire model with immune trees (FFMIT) is a cellular automaton early proposed by Drossel and Schwabl [Physica A 199, 183 (1993)], in which each site of a lattice can be in three possible states: occupied by a tree, empty, or occupied by a burning tree (fire). The trees grow at empty sites with probability $p$, healthy trees catch fire from adjacent burning trees with probability $(1-g)$, where $g$ is the immunity, and a burning tree becomes an empty site spontaneously. In this paper we study the FFMIT by means of the recently proposed gradient method (GM), considering the immunity as a uniform gradient along the horizontal axis of the lattice. The GM allows the simultaneous treatment of both the active and the inactive phases of the model in the same simulation. In this way, the study of a single-valued interface gives the critical point of the active-absorbing transition, whereas the study of a multivalued interface brings the percolation threshold into the active phase. Therefore we present a complete phase diagram for the FFMIT, for all range of $p$, where, besides the usual active-absorbing transition of the model, we locate a transition between the active percolating and the active nonpercolating phases. The average location and the width of both interfaces, as well as the absorbing and percolating cluster densities, obey a scaling behavior that is governed by the exponent $\alpha =1/(1+\nu )$, where $\nu$ is the suitable correlation length exponent (${\nu }_{\perp }$ for the directed percolation transition and $\nu$ for the standard percolation transition). We also show that the GM allows us to calculate the critical exponents associated with both the order parameter of the absorbing transition and the number of particles in the multivalued interface. Besides, we show that by using the gradient method, the collapse in a single curve of cluster densities obtained for samples of different side is a very sensitive method in order to obtain the critical points and the percolation thresholds.

We present a numerical Monte Carlo analysis of the phase structure in a continuous spin Ising chain that describes chiral homopolymers. We find that depending on the value of the Metropolis temperature, the model displays the three known nontrivial phases of polymers: At low temperatures the model is in a collapsed phase, at medium temperatures it is in a random walk phase, and at high temperatures it enters the self-avoiding random walk phase. By investigating the temperature dependence of the specific energy we confirm that the transition between the collapsed phase and the random walk phase is a phase transition, while the random walk phase and self-avoiding random walk phase are separated from each other by a crossover transition. We propose that the model can be applied to characterize the statistical properties of protein folding. For this we compare the predictions of the model to a phenomenological elastic energy formula, proposed by J. Lei and K. Huang [e-print arXiv:1002.5013; Europhys. Lett. 88, 68004 (2009)] to describe folded proteins.

Video microscopy is employed to study the melting behaviors of multilayer colloidal crystals composed of diameter-tunable microgel spheres confined between two walls. We systematically explore film thickness effects on the melting process and on the phase behaviors of single crystal and polycrystalline films. Thick films ($>4$ layers) are observed to melt heterogeneously, while thin films ($⩽4$ layers) melt homogeneously, even for polycrystalline films. Grain-boundary melting dominates other types of melting processes in polycrystalline films thicker than 12 layers. The heterogeneous melting from dislocations is found to coexist with grain-boundary melting in films bewteen 5- and 12-layers. In dislocation melting, liquid nucleates at dislocations and forms lakelike domains embedded in the larger crystalline matrix; the “lakes” are observed to diffuse, interact, merge with each other, and eventually merge with large strips of liquid melted from grain boundaries. Thin film melting is qualitatively different: thin films homogeneously melt by generating many small defects which need not nucleate at grain boundaries or dislocations. For three- and four-layer thin films, different layers are observed to have the same melting point, but surface layers melt faster than bulk layers. Within our resolution, two- to four-layer films appear to melt in one step, while monolayers melt in two steps with an intermediate hexatic phase.

Tension in lipid membranes is often controlled externally, by pulling on the boundary of the membrane or changing osmotic pressure across a curved membrane. But modifications of the tension can also be induced in an internal fashion, for instance as a byproduct of changing a membrane’s electric potential or, as observed experimentally, by activity of membrane proteins. Here we develop a theory that demonstrates how such internal contributions to the tension are moderated through elastic stretching of the membrane when the membrane is initially in a low-tension floppy state.

We propose a simple thermal transistor, a device to control heat current. In order to effectively change the current, we utilize the gas-liquid transition of the heat-conducting medium (fluid) because the gas region can act as a good thermal insulator. The three terminals of the transistor are located at both ends and the center of the system, and are put into contact with distinct heat baths. The key idea is a special arrangement of the three terminals. The temperature at one end (the gate temperature) is used as an input signal to control the heat current between the center (source, hot) and another end (drain, cold). Simulating the nanoscale systems of this transistor, control of heat current is demonstrated. The heat current is effectively cut off when the gate temperature is cold and it flows normally when it is hot. By using an extended version of this transistor, we also simulate a primitive application for an inverter.

Recently, a model of opinion formation with kinetic exchanges has been proposed in which a spontaneous symmetry-breaking transition was reported [M. Lallouache, A. S. Chakrabarti, A. Chakraborti, and B. K. Chakrabarti, Phys. Rev. E 82, 056112 (2010)]. We generalize the model to incorporate two parameters: $\lambda$, to represent conviction, and $\mu$, to represent the influencing ability of individuals. A phase boundary given by $\lambda =1-\mu /2$ is obtained separating the symmetric and symmetry broken phases: The effect of the influencing term enhances the possibility of reaching a consensus in the society. The time scale diverges near the phase boundary in a power-law manner. The order parameter and the condensate also show power-law growth close to the phase boundary albeit with different exponents. The exponents in general change along the phase boundary, indicating a nonuniversality. The relaxation times, however, become constant with increasing system size near the phase boundary, indicating the absence of any diverging length scale. Consistently, the fluctuations remain finite but show strong dependence on the trajectory along which it is estimated.

The well-known van Kampen system size expansion, while of rather general applicability, is shown to fail to reproduce some qualitative features of the time evolution for systems with an absorbing state, apart from a transient initial time interval. We generalize the van Kampen ansatz by introducing a new prescription leading to non-Gaussian fluctuations around the absorbing state. The two expansion predictions are explicitly compared for the infinite range voter model with speciation as a paradigmatic model with an absorbing state. The new expansion, both for a finite size system in the large time limit and at finite time in the large size limit, converges to the exact solution as obtained in a numerical implementation using the Gillespie algorithm. Furthermore, the predicted lifetime distribution is shown to have the correct asymptotic behavior.

Motivated by the classification of nonequilibrium steady states suggested by R. K. P. Zia and B. Schmittmann, in J. Stat. Mech. (2007) P07012, we propose to measure the violation of the detailed balance criterion by the $p$ norm ($\left|\right|K^{*}\left|\right|{}_p$) of the matrix formed by the probability currents. Its asymptotic analysis, for the totally asymmetric simple exclusion process, motivates the definition of a “distance” from equilibrium $K^{*}$ obtained for $p=1$. In addition, we show that the latter quantity and the average activity $\langle {\mathcal{A}}^{*}\rangle$ are both related to the probability distribution of the entropy production. Finally, considering the open asymmetric simple exclusion process and open zero-range process, we show that the current of particles gives an exact measure of the violation of detailed balance.

A general random walk theory for diffusion in the presence of nanoscale confinement is developed and applied. The random-walk theory contains two parameters describing confinement: a cage size and a cage-to-cage hopping probability. The theory captures the correct nonlinear dependence of the mean square displacement (MSD) on observation time for intermediate times. Because of its simplicity, the theory also requires modest computational requirements and is thus able to simulate systems with very low diffusivities for sufficiently long time to reach the infinite-time-limit regime where the Einstein relation can be used to extract the self-diffusivity. The theory is applied to three practical cases in which the degree of order in confinement varies. The three systems include diffusion of (i) polyatomic molecules in metal organic frameworks, (ii) water in proton exchange membranes, and (iii) liquid and glassy iron. For all three cases, the comparison between theory and the results of molecular dynamics (MD) simulations indicates that the theory can describe the observed diffusion behavior with a small fraction of the computational expense. The confined-random-walk theory fit to the MSDs of very short MD simulations is capable of accurately reproducing the MSDs of much longer MD simulations. Furthermore, the values of the parameter for cage size correspond to the physical dimensions of the systems and the cage-to-cage hopping probability corresponds to the activation barrier for diffusion, indicating that the two parameters in the theory are not simply fitted values but correspond to real properties of the physical system.

We study zero-temperature hysteresis in random-field $\mathit{XY}$ and Heisenberg models in the zero-frequency limit of a cyclic driving field. We consider three distributions of the random field and present exact solutions in the mean-field limit. The results show a strong effect of the form of disorder on critical hysteresis as well as the shape of hysteresis loops. A discrepancy with an earlier study based on the renormalization group is resolved.

The one-dimensional Lévy flight in a composite medium consisting of two layers in contact, with arbitrary Lévy indices, is investigated. Such systems are of much interest in the field of organic electronics, where diffusional transport between two materials profoundly influences the device performance. Using the jump-length probability density function for a particular Lévy index as a starting point, equations are derived that describe anomalous diffusion in a composite two-layer medium. Moreover, expressions for the current density are given, and the steady-state distribution for the special case of one dominating diffusion coefficient is illustrated.

We consider a tiling model of the two-dimensional square lattice, where each site is tiled with one of the 16 Wang tiles. The ground states of this model are all quasiperiodic. The systems undergoes a disorder to quasiperiodicity phase transition at finite temperature. Introducing a proper order parameter, we study the system at criticality and extract the critical exponents characterizing the transition. The exponents obtained are consistent with hyperscaling.

The viscous stress in nonideal fluid lattice Boltzmann methods is investigated theoretically and by simulations. Three representative liquid-gas models are compared in a steady-state situation, where an analytical expression for the viscous stress is available. It is shown that, in the presence of nonideal fluid interactions or strong body forces, the accuracy of the computed viscous stress depends strongly on the underlying model.