In this paper a partition line is used in the counterflow system to present the default (conventional) traffic rule: pedestrians prefer to walk on a certain side on the road during movement, e.g., the right-hand side in China or the left-hand side in Japan. Based on the counterflow model of Takimoto (model A), we introduced two modified models, i.e., model B and C, to study the effects of a partition line in the consideration of people who do not obey the default traffic rule. Model B represents that factor in time scale, while model C in space scale. In model B, there are pedestrians who cross the partition line but choose not to obey the default traffic rule with a probability $p_{nor}$, while in model C, if a pedestrian crosses the partition line and goes away from it further than a certain nonobeying-rule threshold distance $d_t$, he will not obey the traffic rule. It is found that the behavior of traffic rule breaking influences much the counterflow when it is at the choking flow state rather than at the free moving or stopped state. Furthermore, it is shown that the default traffic rule is not always positive to the counterflow in all situations. It depends on the game result of these two opposite sides: to use the channel width as much as possible and to avoid the interference from the other group as far as possible.

The rich dynamical behavior stemming from unidirectional coupling in a single array of overdamped nonlinear elements has, recently, been extensively studied. By adjusting control parameters, one obtains regimes of oscillations with a frequency that scales in a characteristic way with the control parameter. With an external time-sinusoidal driving signal, a richness of synchronized (to the drive frequency or its subharmonics depending on the control parameter) dynamical behavior ensues. Including $M⩾2$ arrays with a suitably chosen cross coupling has also been shown to lead to multifrequency patterns in the emergent dynamics. Here, we consider this arrangement and demonstrate that, under the appropriate conditions, the oscillation frequency of each successive array decreases by a rational factor with increasing $M$. This frequency down-conversion, obtainable without a heterodyning signal, affords the promise of very efficient signal processing in a variety of applications wherein, currently, the frequency down-conversion stage typically involves multistep processes with complicated and (often) noisy circuitry.

We examine various recently proposed translationally invariant discretizations of the well-known ${\varphi }^4$ field theory. We compare and contrast the properties of their fundamental solutions including the nature of their kink-type solitary waves and the spectral properties of the linearization around such waves. We study these features as a function of the lattice spacing $h$, as one deviates from the continuum limit of $h\to 0$. We then proceed to a more “stringent” comparison of the models, by discussing the scattering properties of a kink-antikink pair for the different discretizations. These collisions are well known to possess properties that quite sensitively depend on the initial speed even at the continuum limit. We examine how typical model behaviors are modified in the presence (and as a function) of discreteness. One of the surprising trends that we observe is the increasing elasticity of kink collisions with deviation from the continuum limit. Another general feature is that the most inelastic kink collisions are observed in the classical discrete ${\varphi }^4$ model, while they are more elastic in the four studied translationally invariant models.

We present estimations of the accuracy and convergence of the Wang-Landau algorithm. Both accuracy and the related length of the Monte Carlo run depend on the modification parameter $f$ and the density of states. The analytical solution obtained for the two-level system was checked numerically on the two-dimensional Ising model. Although the two-level system is a very simple one, it appears that the proposed solution describes the generic features of the Wang-Landau algorithm. The estimations should prove useful in Monte Carlo calculations of protein folding, first-order transitions, and other systems with a rough energy landscape.

We study the statistical behavior of two out of equilibrium systems. The first one is a quasi-one-dimensional gas with two species of particles under the action of an external field which drives each species in opposite directions. The second one is a one-dimensional spin system with nearest-neighbor interactions also under the influence of an external driving force. Both systems show a dynamical scaling with domain formation. The statistical behavior of these domains is compared with models based on the coalescing random walk and the interacting random walk. We find that the scaling domain size distribution of the gas and the spin systems is well-fitted by the Wigner surmise, which lead us to explore a possible connection between these systems and the circular orthogonal ensemble of random matrices. However, the study of the correlation function of the domain edges shows that the statistical behavior of the domains in both gas and spin systems is not completely well-described by a circular orthogonal ensemble, nor it is by other models proposed such as the coalescing random walk and the interacting random walk. Nevertheless, we find that a simple model of independent intervals describes more closely the statistical behavior of the domains formed in these systems.

In this paper, we study shocks and related transitions in asymmetric simple exclusion processes of particles with nearest-neighbor interactions. We consider two kinds of interparticle interactions. In one case, the particle-hole symmetry is broken due to the interaction. In the other case, particles have an effective repulsion due to which the particle current density drops down near one-half filling. These interacting particles move on a one-dimensional lattice which is open at both the ends with injection of particles at one end and withdrawal of particles at the other. In addition to this, there are possibilities of attachments or detachments of particles to or from the lattice with certain rates. The hydrodynamic equation that involves the exact particle current density of the particle conserving system and additional terms taking care of the attachment-detachment kinetics is studied using the techniques of boundary layer analysis.

Competitive random sequential adsorption on a line from a binary mix of incident particles is studied using both an analytic recursive approach and Monte Carlo simulations. We find a strong correlation between the small and the large particle distributions so that while both partial contributions to the fill factor fluctuate widely, the variance of the total fill factor remains relatively small. The variances of partial contributions themselves are quite different between the smaller and the larger particles, with the larger particle distribution being more correlated. The disparity in fluctuations of partial fill factors increases with the particle size ratio. The additional variance in the partial contribution of a smaller particle originates from the fluctuations in the size of gaps between larger particles. We discuss the implications of our results to semiconductor high-energy gamma detectors where the detector energy resolution is controlled by correlations in the cascade energy branching process.

This paper investigates the flow induced disaggregation, deformation and orientation of several modified human red blood cells suspended in concentrated, physiological like conditions (volume fraction in erythrocytes of 0.4). The aim is to determine simultaneously, and under flow, the aggregate sizes as well as the deformation and orientation of the cells. The measurement method uses steady, incoherent, unpolarized light transport while the sample is sheared in a flow cell controlled by a rheometer. Several blood samples were prepared to alter the erythrocyte’s aggregating, deformability and shape properties. The measurements using these samples show a clear relationship between the intrinsic properties of the cells and the evolution of aggregate sizes, average cell orientation and anisotropy as a function of the applied shear, which may lead to clinical applications. In other words, the careful analysis of the incoherent light transport in concentrated media provides quantitative insight into their microscopic details. In particular, the topological properties (average anisotropy and orientation) and size of the suspended objects can be determined.

We present a scheme for coarse-graining hydrodynamic interactions in an isolated flexible homopolymer molecule in solution. In contrast to the conventional bead-spring model that employs spherical beads of fixed radii to represent the hydrodynamic characteristics of coarse-grained segments, we show that our procedure leads naturally to a discrete model of a polymer molecule as a chain of orientable and stretchable Gaussian blobs. This model accounts for both intrablob and interblob hydrodynamic interactions, which depend on the instantaneous shapes of the blobs. In Brownian dynamics simulations of initially stretched chains relaxing under quiescent conditions, the transient evolution of the mean-square end-to-end distance and first normal stress difference obtained with the Gaussian-blob model are found to be less sensitive to the degree of coarse graining, in comparison with the conventional bead-spring model with Rotne-Prager-Yamakawa hydrodynamic interactions.

Extensive molecular dynamics (MD) simulations were carried out to compute the solubilities and self-diffusivities of $\mathrm{C}{\mathrm{O}}_2$ and $\mathrm{C}{\mathrm{H}}_4$ in amorphous polyetherimide (PEI) and mixed-matrix PEI generated by inserting single-walled carbon nanotubes into the polymer. Atomistic models of PEI and its composites were generated using energy minimizations, MD simulations, and the polymer-consistent force field. Two types of polymer composite were generated by inserting (7,0) and (12,0) zigzag carbon nanotubes into the PEI structure. The morphologies of PEI and its composites were characterized by their densities, radial distribution functions, and the accessible free volumes, which were computed with probe molecules of different sizes. The distributions of the cavity volumes were computed using the Voronoi tessellation method. The computed self-diffusivities of the gases in the polymer composites are much larger than those in pure PEI. We find, however, that the increase is not due to diffusion of the gases through the nanotubes which have smooth energy surfaces and, therefore, provide fast transport paths. Instead, the MD simulations indicate a squeezing effect of the nanotubes on the polymer matrix that changes the composite polymers’ free-volume distributions and makes them more sharply peaked. The presence of nanotubes also creates several cavities with large volumes that give rise to larger diffusivities in the polymer composites. This effect is due to the repulsive interactions between the polymer and the nanotubes. The solubilities of the gases in the polymer composites are also larger than those in pure PEI, hence indicating larger gas permeabilities for mixed-matrix PEI than PEI itself.

In this paper we use a simple model to explore the function of the gene Osteosarcoma-9 (OS-9). We are particularly interested in understanding the role of this gene as a potent anti-apoptotic factor. The theoretical description is constrained by experimental data from induction of apoptosis in cells where OS-9 is overexpressed. The data available suggest that OS-9 promotes cell viability and confers resistance to apoptosis, potentially implicating OS-9 in the survival of cancer cells. Three different apoptosis-inducing mechanisms were tested and are modeled here. A more complex and realistic model is also discussed.

In this work, we evaluate the probability distribution function of the order parameter for the two-dimensional site-diluted Ising model. Extensive Monte Carlo simulations have been performed for different spin concentrations $p$ $(0.70\le p\le 1)$ on square lattices with linear sizes $L$ $(20\le L\le 100)$. The results indicate that the universality class of the diluted Ising model seems to be independent of the amount of dilution. Logarithmic corrections of the finite-size critical temperature behavior of the model can also be inferred even for such small lattices.

Autonomous nonlinear systems commonly exhibit simultaneous coexistence, in the phase space, of chaos and stable steady states, created by subcritical Hopf bifurcation. We show that such chaotic instability can be destroyed by small-amplitude modulation of any system parameters. The chaotic attractor undergoes boundary crisis due to a modulation-induced collision with an unstable periodic orbit (UPO). Such a boundary crisis exhibits a new resonance that we refer to as “crisis resonance” in the control parameter space. Crisis resonance implies that crisis occurs at minimum modulation depth due to resonant evolutions of the UPOs and the chaotic attractor. Crisis resonance occurs close to some critical frequency (we refer to it as “crisis resonance frequency”) or its multiples. The UPO frequency is a good estimate of the crisis resonance frequency. The small-amplitude parameter modulation destroys chaos in the presence of noise as well. These features are observed theoretically with the paradigm of autonomous systems, namely, Lorenz equations of thermal hydraulics and are in excellent agreement with the experimental results, obtained with an analog circuit of Lorenz equations.

Time-frequency analysis is performed for chaotic flow with a power spectrum estimator based on the phase-space neighborhood. The relation between the reference phase point and its nearest neighbors is demonstrated. The nearest neighbors, representing the state recurrences in the phase space reconstructed by time delay embedding, actually cover data segments with similar wave forms and thus possess redundant information, but recur with no obvious temporal regularity. To utilize this redundant recurrence information, a neighborhood-based spectrum estimator is devised. Then time-frequency analysis with this estimator is performed for the Lorenz time series, the Rössler time series, experimental laser data, and colored noise. Features revealed by the spectrogram can be used to distinguish noisy chaotic flow from colored noise.

This paper presents a two-dimensional pore-scale network model of a rough-walled fracture whose inner structure had been mapped using x-ray microtomography. The model consists of a rectangular lattice of conceptual pores and throats representing local aperture variations. It is a two-phase model that takes into account capillary, viscous, and gravity forces. Mapping of fluids and fracture topology was done at a voxel resolution of $0.027\times 0.027\times 0.032{\mathrm{mm}}^3$, which allowed the construction of realistic fracture representations for modeling purposes. This paper describes the necessary data conditioning for network modeling, a different approach to determine advancing and receding contact angles from direct x-ray microtomography scans, and the network model formulation and methods used in the determination of saturation, absolute and relative permeabilities, capillary pressures, and fluid distributions. Direct comparison of modeled results and experimental observations, for both drainage and imbibition processes, is presented in the companion paper [M. Piri and Z. T. Karpyn, following paper, Phys. Rev. E 76, 016316 (2007)].

This paper presents the implementation of the pore-scale network model described in paper I [see preceding paper, Z. T. Karpyn and M. Piri, Phys. Rev. E 76, 016315 (2007)]. The model is used to estimate flow properties and predict fluid occupancy during two-phase flow displacements in a rough-walled fracture. The fracture’s inner structure is available from the reconstruction of x-ray microtomography images of a fractured sandstone core. The model is able to represent mechanisms such as pistonlike displacement, cooperative pore filling, and snapoff. We study the effects of aperture map scales, rate of injection, and gravity on the distribution of phases inside the fracture and present successful predictions of fluid occupancy during primary drainage, imbibition, and secondary drainage. Results were validated rigorously against x-ray microtomography scans obtained from two-phase flow experiments [see Z. T. Karpyn, A. S. Grader, and P. M. Halleck, J. Colloid Interface Sci. 307, 181 (2007)] and showed two-phase fluid structures in agreement with experimental observations.

We consider a Brownian particle which is driven by a harmonically oscillating force, the motion of which is restricted by two reflecting boundaries. We solve the Fokker-Planck equation using the finite-element method and focus on the dynamics of the mean position of the particle in the time-asymptotic regime. As a function of the strength of the external force, the response of the system, i.e., the amplitude of the mean position and the dynamical shift, in the stationary limit shows a resonancelike behavior as a function of the diffusion coefficient for certain parameter regimes. We explain these numerical results heuristically and give some qualitative estimates.

A study of the fractal dimension of the aggregation of three different types of large unilamellar vesicles, formed by egg yolk phosphatidylcholine (EYPC), dimyristoyl-phosphocholine (DMPC), and dipalmitoyl-phosphocholine (DPPC), in the presence of ${\mathrm{La}}^{3+}$, is presented. Aggregate liposome fractal dimensions were calculated by two methods, aggregation kinetics, using the approaches diffusion-limited cluster aggregation (DLCA) and reaction-limited cluster aggregation (RLCA) and angle-scattering light dispersion. Electrophoretic measurements show a similar variation of the zeta potential ($\zeta$ potential) for EYPC and DPPC, with a small increase of initial positive values. However, the $\zeta$ potential of DMPC changes from a initial negative value to near zero with increasing ${\mathrm{La}}^{3+}$ concentration. The evolution of the aggregate sizes was followed by light scattering. DPPC and DMPC show a RLCA regimen growth at low ${\mathrm{La}}^{3+}$ concentrations and a DLCA regimen at higher concentrations. In the case of EYPC, the final size of aggregation strongly depends on ${\mathrm{La}}^{3+}$ concentration. The calculated fractal dimension is in the range 1.8 to 2.1.

The surface of a soft elastic film becomes unstable and forms a self-organized undulating pattern because of adhesive interactions when it comes in contact proximity with a rigid surface. For a single film, the pattern length scale $\lambda$, which is governed by the minimization of the elastic stored energy, gives $\lambda \sim 3h$, where $h$ is the film thickness. Based on a linear stability analysis and simulations of adhesion and debonding, we consider the contact instability of an elastic bilayer, which provides greater flexibility in the morphological control of interfacial instability. Unlike the case of a single film, the morphology of the contact instability patterns, debonding distance, and debonding force in a bilayer can be controlled in a nonlinear way by varying the thicknesses and shear moduli of the films. Interestingly, the pattern wavelength in a bilayer can be greatly increased or decreased compared to a single film when the adhesive contact is formed by the stiffer or the softer of the two films, respectively. In particular, $\lambda$ as small as $0.5h$ can be obtained. This indicates a new strategy for pattern miniaturization in elastic contact lithography.