We give the general solutions of lattices, i.e., velocity sets and weights, for the lattice Bhatanagar-Gross-Krook (LBGK) models on two- and three-dimensional Cartesian grids. The solutions define the necessary and sufficient conditions so that the resulting LBGK model can accurately capture the dynamics of the moments retained in the distribution function. In the parameter space of the weights, the general solutions form low-dimensional linear spaces from which minimal velocity sets are identified for the degrees of precision that are most relevant to the construction of high-order LBGK models. All well-known LBGK lattices are found to be special cases of the given general solutions.

We find that transport on scale-free random networks depends strongly on degree-correlated network topologies whereas transport on Erdös-Rényi networks is insensitive to the degree correlation. An approach for the tuning of scale-free network transport efficiency through assortative or dissortative topology is proposed. We elucidate that the unique transport behavior for scale-free networks results from the heterogeneous distribution of degrees.

A study is made of the random sequential packing of complete lines in a cube of integer lattice points, with side $N$. For $N\le 15$ exact packing fractions are computed. It is found that if line occupation attempts arrive as a spatial Poisson process the packing has two distinct phases; initially where large numbers of potential adsorption sites are blocked, and subsequently where no further blocking occurs so that filling is exponential in time. It is shown that the ratio of the durations of the blocking to the nonblocking phases falls to zero as $N\to \infty$. In this limit, the packing fraction at time $t$ is $\theta \left(t\right)=\frac{3}{4}\left(1-e^{-t}\right)$. The rapid switch between phases in large systems creates a dramatic fall in the packing rate at the start of the process. This becomes a discontinuity as $N\to \infty$ and is a consequence of the high aspect ratio of the packing objects. It provides a physical explanation for the diverging coefficients in expansions of $\theta \left(t\right)$ about $t=0$ for objects with diverging aspect ratio. After considering the three-dimensional case, the analysis is extended to $d$-dimensional cubes, for which it is conjectured that $\theta =d/2^{d-1}$ in the limit $N\to \infty$.

A coupling inertial navigation sensor (INS) system may proven to be beneficial for performance improvement, especially when the manufacturing yield is very low for meeting the specification requirement of various applications. For instance, navigation grade sensors using the current fabrication process would yield one in every few hundreds which would meet the specification requirement after careful selection process and testing. We propose to couple these sensors by putting together the “low grade” sensors in a small array of particular coupling topology to explore their stability properties of known parameter variations produced during the fabrication process. By coupling them in a particular way one may improve the system stability to effect the performance of the INS. Thus in this work we present a coupled inertial navigation sensor (CINS) system consisting of a ring of vibratory gyroscopes coupled through the driving axis of each individual gyroscope. Numerical simulations show that under certain conditions, which depend mainly on the coupling strength, the dynamics of the individual gyroscopes will synchronize with one another. The same simulations also show an optimal network size at which the effects of noise can be minimized, thus yielding a reduction in the phase drift. We quantify the reduction in the phase drift and perform an asymptotic analysis of the motion equations to determine the conditions for the existence of the synchronized state. The analysis yields an analytical expression for a critical coupling strength at which different nonzero mean oscillations merge in a pitchfork bifurcation; passed this critical coupling the synchronized state becomes locally asymptotically stable. The Liapunov-Schmidt (LS) reduction is then applied to determine the stability properties of the synchronized solution and to further show that the pitchfork bifurcation can be subcritical or supercritical, depending on the coefficient of the nonlinear terms in the equations of motion.

We experimentally investigate jamming in a quasi-two-dimensional granular system of automatically swelling particles and show that a maximum in the height of the first peak of the pair correlation function is a structural signature of the jamming transition at zero temperature. The same signature is also found in the second peak of the pair correlation function, but not in the third peak, reflecting the underlying singularity of jamming transition. We also study the development of clusters in this system. A static length scale extracted from the cluster structure reaches the size of the system when the system approaches the jamming point. Finally, we show that in a highly inhomogeneous system, friction causes the system to jam in series of steps. In this case, jamming may be obtained through successive buckling of force chains.

The electrical properties of the cellular membrane are important for ion transport across cells and electrophysiology. Plasma membranes also resist bending and stretching, and mechanical properties of the membrane influence cell shape and forces in membrane tethers pulled from cells. There exists a coupling between the electrical and mechanical properties of the membrane. Previous work has shown that applied voltages can induce forces and movements in the lipid bilayer. We present a theory that computes membrane bending deformations and forces as the applied voltage is changed. We discover that electromechanical coupling in lipid bilayers depends on the voltage-dependent adsorption of ions into the region occupied by the phospholipid head groups. A simple model of counter-ion absorption is investigated. We show that electromechanical coupling can be measured using membrane tethers and we use our model to predict the membrane tether tension as a function of applied voltage. We also discuss how electromechanical coupling in membranes may influence transmembrane protein function.

The article [Phys. Rev. E 73, 031111 (2006)] by Horowitz and Albano reports on simulations of competitive surface-growth models $\text{RD}+\text{X}$ that combine random deposition (RD) with another deposition X that occurs with probability $p$. The claim is made that at saturation the surface width $w\left(p\right)$ obeys a power-law scaling $w\left(p\right)\propto 1/p^{\delta }$, where $\delta$ is only either $\delta =1/2$ or $\delta =1$, which is illustrated by the models where X is ballistic deposition and where X is RD with surface relaxation. Another claim is that in the limit $p\to 0^{+}$, for any lattice size $L$, the time evolution of $w\left(t\right)$ generally obeys the scaling $w\left(p,t\right)\propto \left(L^{\alpha }/p^{\delta }\right)F\left(p^{2\delta }t/L^z\right)$, where $F$ is Family-Vicsek universal scaling function. We show that these claims are incorrect.

In an early paper [C. M. Horowitz and E. V. Albano, Phys. Rev. E 73, 031111 (2006)], we studied growing models, generically called $X/RD$, such that a particle is attached to the aggregate with probability $p$ following the mechanisms of a generic model $X$ and at random (random deposition) with probability $\left(1-p\right)$. We also formulated scaling relationships that are expected to hold in the limits $p\to 0$ and $L\to \infty$, where $L$ is the sample side. In the previous comment, Kolakowska and Novotny (KN) state that our scaling hypothesis does not hold. Here, we show that the criticisms of KN are outlined by analyzing data out of the proper scaling regime and consequently they are groundless and can be disregarded.

A demanding task, for successful fluid dynamic design in many industrial applications, is being able to predict the transition to turbulence location in boundary layer flows. The focus of the present experimental study is on the late stage of transition scenarios where turbulent spots are borne. We report on a natural stabilizing mechanism on the growth rate of turbulent spots, which takes place in a specific bypass transition scenario, and show that there is a palpable history effect of the origin of the turbulent spot on the streamwise evolution. Furthermore, experimental evidence on Reynolds number effects on the spot evolution in boundary layers is put forward. This has been made possible by setting up an idealized experiment, which usually only is considered as a schoolbook example.

We present a method to start electrospinning from a polymeric drop. This method uses a pulsed laser which is focused inside the drop close to the liquid surface. The pulse cavitates the liquid and produces a protrusion from the tip of the drop. The protrusion narrows by drainage and vertical stretching, thus concentrating the electric field and increasing the charge density until it overcomes the surface tension and produces the electrified jet. This approach can reduce the required value of applied electric field to half of its value required to start convectional electrospinning from a stationary drop.

The quantum ratchet effect in fully chaotic systems is approached by studying statistical properties of the ratchet current over well-defined sets of initial states. Natural initial states in a semiclassical regime are those that are phase-space uniform with the maximal possible resolution of one Planck cell. General arguments in this regime, for quantum-resonance values of a scaled Planck constant $\hslash$, predict that the distribution of the current over all such states is a zero-mean Gaussian with variance $\sim D{\hslash }^2/\left(2{\pi }^2\right)$, where $D$ is the chaotic-diffusion coefficient. This prediction is well supported by extensive numerical evidence. The average strength of the effect, measured by the variance above, is significantly larger than that for the usual momentum states and other states. Such strong effects should be experimentally observable.

A numerical simulation and a theoretical model of the two-dimensional flow produced by the harmonic oscillation of a localized magnetic field (magnetic obstacle) in a quiescent viscous, electrically conducting fluid are presented. Nonuniform Lorentz forces produced by induced currents interacting with the oscillating magnetic field create periodic laminar flow patterns that can be characterized by three parameters: the oscillation Reynolds number, ${\text{Re}}_{\omega }$, the Hartmann number, Ha, and the dimensionless amplitude of the magnetic obstacle oscillation, $D$. The analysis is restricted to oscillations of small amplitude and $\text{Ha}=100$. The resulting flow patterns are described and interpreted in terms of position and evolution of the critical points of the instantaneous streamlines. It is found that in most of the cycle, the flow is dominated by a pair of counter rotating vortices that switch their direction of rotation twice per cycle. The transformation of the flow field present in the first part of the cycle into the pattern displayed in the second half occurs via the generation of hyperbolic and elliptic critical points. The numerical solution of the flow indicates that for low frequencies (v.e. ${\text{Re}}_{\omega }=1$), two elliptic and two hyperbolic points are generated, while for high frequencies (v.e. ${\text{Re}}_{\omega }=100$), a more complex topology involving four elliptic and two hyperbolic points appear. The bifurcation map for critical points of the instantaneous streamline is obtained numerically and a theoretical model based on a local analysis that predicts most of the qualitative properties calculated numerically is proposed.

A generalized nonlinear Maxwell model which had previously been analyzed for plane Couette geometry is here applied to a lid-driven cavity flow. The full three-dimensional hydrodynamical problem is treated numerically. Depending on the relevant model parameters, both smooth laminar and low Reynolds number turbulent flows are found, strikingly similar to the experimentally observed elastic turbulence phenomena in polymer solutions. Representative results of the calculated flow patterns, as well as measures for the turbulent nature of the flow are presented graphically.

Motivated by a diversity of the shape instability phenomena in condensed-matter physics, we study the formation of elastic ribbon structures and transformation into helicoidal structures. Using the multipulse laser-matter interaction with the Co-coated surface, a one-dimensional high-density vortex-filament array has been created. Increasing the number of pulses, the oscillatory strain field causes the cascade of the shape transformations into structures of increasing topological complexity: vortex filaments into ribbons, into ribbon helicoids and tubular-ribbon helicoids, and then into short ribbon structures with the complex Scherk surface being identified. The cascade of transformations follows the scenario in which the topological complexity of the new structure increases with the number of pulses, thus, realizing configurations with more efficient energy relaxation. Above a critical number of pulses, the system is catastrophically disintegrated into small-scale wrinkled and crumpled surfaces. We show that the critical parameter for the ribbon transformations is the number of laser pulses which is equivalent to some critical oscillatory frequency.

Spatial shift produced in scattering process of lattice soliton is studied in the Fermi-Pasta-Ulam model with anharmonic-limit potential. Kink-shaped and antikink-shaped lattice solitons are excited by kicking one single particle. Different behaviors are discovered in two types of head-on collision: kink-kink-shaped collision and kink-antikink-shaped collision. In both cases, the spatial shift not only depends on the scattering pair of lattice solitons but also depends on their collision configuration, i.e., their phase difference. To make a comparison between integrable and nonintegrable lattices, and also to check our method, the Toda model is revisited.

We consider a class of nonlinear stochastic differential equations, giving the power-law behavior of the power spectral density in any desirably wide range of frequency. Such equations were obtained starting from the point process models of $1/f^{\beta }$ noise. In this article the power-law behavior of spectrum is derived directly from the stochastic differential equations, without using the point process models. The analysis reveals that the power spectrum may be represented as a sum of the Lorentzian spectra. Such a derivation provides additional justification of equations, expands the class of equations generating $1/f^{\beta }$ noise, and provides further insights into the origin of $1/f^{\beta }$ noise.

We examine zero-temperature hysteresis in random-field $XY$ and Heisenberg models in the zero-frequency limit of a cyclic driving field. Exact expressions for hysteresis loops are obtained in the mean-field approximation. These show rather unusual features. We also perform simulations of the two models on a simple-cubic lattice and compare them with the predictions of the mean-field theory.

The structure of void space in two- and three-dimensional (3D) polymer solutions is studied using Voronoi tessellation and percolation theory. The polymer molecules are modeled as freely jointed chains of $N$ tangent hard disks (two dimensions) or spheres (three dimensions). Polymer chains are equilibrated via Monte Carlo simulations and the pore space in configurations of equilibrated chains is mapped using Voronoi tessellation. In $d$ dimensions a Voronoi vertex is the center of the sphere tangent to the $d+1$ nearest monomers. An edge of the Voronoi diagram is the shortest route between two neighboring vertices. The edge is considered connected if a monomer can pass through and disconnected otherwise. The Voronoi construction is used to calculate the percolation threshold of the void space. The most interesting result is that the polymer area fraction at the percolation threshold is a nonmonotonic function of $N$ in two dimensions but monotonically reaches a constant value in three dimensions. The crossover behavior of the percolation threshold is also observed in pseudo-3D. The pore size distribution decreases monotonically with increasing pore size. This is markedly different from that in configurations of hard disks (monomeric fluid) where the pore size distribution is peaked at finite size.

Eukaryotic cells are capable of detecting small chemical gradients for a wide range of background concentrations. Ultimately, fluctuations place a limit on gradient sensing and recent work has focused on the role of stochastic receptor occupancy as one possible limiting factor. Here, we use a phenomenological approach to add spontaneous motility fluctuations to receptor noise and predict the directional statistics of eukaryotic chemotaxis. Specifically, an Itô diffusion equation with direction-dependent multiplicative noise is developed and analytically studied. We show that our approach can naturally accommodate recent experimental data for the chemotaxis of the social amoeba Dictyostelium.

We present a modeling framework for dynamical and bursty contact networks made of agents in social interaction. We consider agents’ behavior at short time scales in which the contact network is formed by disconnected cliques of different sizes. At each time a random agent can make a transition from being isolated to being part of a group or vice versa. Different distributions of contact times and intercontact times between individuals are obtained by considering transition probabilities with memory effects, i.e., the transition probabilities for each agent depend both on its state (isolated or interacting) and on the time elapsed since the last change in state. The model lends itself to analytical and numerical investigations. The modeling framework can be easily extended and paves the way for systematic investigations of dynamical processes occurring on rapidly evolving dynamical networks, such as the propagation of an information or spreading of diseases.