The dynamics of vesicles under shear flow are carefully analyzed in the regime of a small vesicle excess area relative to a sphere. This regime corresponds to the quasispherical limit, for which several groups have analytically extracted simple nonlinear differential equations. Under shear flow, vesicles are known to exhibit three types of motion: (i) tank-treading (TT): the vesicle assumes a steady inclination angle with respect to the flow direction, while its membrane undergoes a tank-treading motion, (ii) tumbling (TB), and (iii) vacillating-breathing (VB): the vesicle main axis oscillates about the flow direction, whereas the overall shape undergoes a breathinglike motion. The region of existence for each regime depends on material and control parameters. The whole set of parameters can be cast into three dimensionless control parameters: (i) the viscosity ratio between the internal and external fluid, $\lambda$, (ii) the excess area relative to a sphere (this parameter measures the degree of the vesicle deflation), $\Delta$, and (iii) the capillary number (the ratio between the vesicle relaxation time toward its equilibrium shape after cessation of the flow and the flow time scale, which is the inverse shear rate), Ca. Recent studies [Danker et al., Phys. Rev. E 76, 041905 (2007)] have focused on the shape of the phase diagram (representing the TT, TB, and VB regimes in the $\text{Ca}-\lambda$ plane). In this paper, the physical quantities are analyzed in detail and attention is brought to features that are essential for future experimental studies. It is shown that the boundaries delimiting different dynamical regimes (TT, TB, and VB) in parameter space depend on the three dimensionless control parameters, in contrast with a recent study [V. V. Lebedev et al., Phys. Rev. Lett. 99, 218101 (2007)] where it is claimed that only two parameters are relevant. Consideration of the amplitude of oscillation (of the vesicle orientation angle and its shape deformation) in the VB mode reveals an even more significant dependence on the three parameters. It is also shown that the inclination angle in the TT regime significantly depends on the shear rate (Ca), which runs contrary to common belief. Finally, we show that the TB and VB periods are quite insensitive to Ca, in marked contrast with a recent study [H. Noguchi and G. Gompper, Phys. Rev. Lett. 98, 128103 (2007)].

The solution space of a $K$-satisfiability $\left(K\text{-SAT}\right)$ formula is a collection of solution clusters, each of which contains all the solutions that are mutually reachable through a sequence of single-spin flips. Knowledge of the statistical property of solution clusters is valuable for a complete understanding of the solution space structure and the computational complexity of the random $K\text{-SAT}$ problem. This paper explores single solution clusters of random 3- and 4-SAT formulas through unbiased and biased random-walk processes and the replica-symmetric cavity method of statistical physics. We find that the giant connected component of the solution space has already formed many different communities when the constraint density of the formula is still lower than the solution space clustering transition point. Solutions of the same community are more similar with each other and more densely connected with each other than with the other solutions. The entropy density of a solution community is calculated using belief propagation and is found to be different for different communities of the same cluster. When the constraint density is beyond the clustering transition point, the same behavior is observed for the solution clusters reached by several stochastic search algorithms. Taking together, the results of this work suggest a refined picture on the evolution of the solution space structure of the random $K\text{-SAT}$ problem; they may also be helpful for designing heuristic algorithms.

In the last decades simulation tools for Brownian dynamics of polymers have attracted more and more interest. Such simulation tools have been applied to a large variety of problems and accelerated the scientific progress significantly. However, the currently most frequently used explicit bead models exhibit severe limitations, especially with respect to time step size, the necessity of artificial constraints and the lack of a sound mathematical foundation. Here we present a framework for simulations of Brownian polymer dynamics based on the finite-element method. This approach allows simulating a wide range of physical phenomena at a highly attractive computational cost on the basis of a far-developed mathematical background.

A simple model system is introduced for demonstrating how a single photon source might be used to transduce classical analog information. The theoretical scheme results in measurements of analog source samples that are (i) quantized in the sense of analog-to-digital conversion and (ii) corrupted by random noise that is solely due to the quantum uncertainty in detecting the polarization state of each photon. This noise is unavoidable if more than 1 bit per sample is to be transmitted and we show how it may be exploited in a manner inspired by suprathreshold stochastic resonance. The system is analyzed information theoretically, as it can be modeled as a noisy optical communication channel, although unlike classical Poisson channels, the detector’s photon statistics are binomial. Previous results on binomial channels are adapted to demonstrate numerically that the classical information capacity, and thus the accuracy of the transduction, increases logarithmically with the square root of the number of photons, $N$. Although the capacity is shown to be reduced when an additional detector nonideality is present, the logarithmic increase with $N$ remains.

The intensity statistics of random signals in the presence of Gaussian noise is obtained by considering the model of a random signal plus a random phasor sum. The additive Gaussian noise is shown to result in a Bessel transform of the probability density of signal intensity. The transformation of the intensity statistics can generally be applied to mixtures of independent random signals, one of which being a complex-valued Gaussian random process. It is used to retrieve intensity statistics of microwave pulsed transmission from Gaussian noise at long time delays.

An approximate theory is developed to describe the properties of mobile particles with extended charge distributions in the presence of a neutralizing fixed background charge. Long-wavelength fluctuations of the electric potential are handled within a variational perturbation approximation, and the short-wavelength fluctuations are handled within a cumulant (fugacity) expansion. The distinct treatment of these two contributions to the free energy enables the theory to provide quantitative predictions for the properties of these systems from the weak- to the strong-coupling regimes. With this theory, we study three different variations in the classical one-component plasma model: a plasma of point charges, a plasma of particles consisting of 8 linearly bonded point charges (8-mer), and a plasma of line charges. The theory was found to agree well with the available computer simulation data for the electrostatic interaction energy of these systems for all values of the plasma coupling parameter examined ($\Gamma =0$ to 400). In addition, we find that both the 8-mer rod and the line charge systems form a strongly ordered nematic phase, which is entirely driven by electrostatic interactions. The nematic phase only exists within a finite range of lengths of the charged particles. If the particles are too short or too long, the nematic phase does not appear. Finally, we find that the nematic phase is stable over a broader range of conditions for the line charge system than for the 8-mer rod system; consequently, the phase behavior of the one-component plasma is sensitive to the manner in which the charge is distributed on the particles.

We introduce models of generic rigidity percolation in two dimensions on hierarchical networks and solve them exactly by means of a renormalization transformation. We then study how the possibility for the network to self organize in order to avoid stressed bonds may change the phase diagram. In contrast to what happens on random graphs and in some recent numerical studies at zero temperature, we do not find a true intermediate phase separating the usual rigid and floppy ones.

We develop the exact energy spectrum for a two-temperature kinetic Ising spin chain and its dual reaction-diffusion system with spatially alternating pair annihilation and creation rates. We also discuss the symmetries of the system pseudo-Hamiltonian and their role in developing a general solution. The surprisingly simple form for the eigenvalues leads to interesting physical consequences and to a possible numerical analysis of the dynamical properties of the system.

We recently found that crystallization of monodisperse hard spheres from the bulk fluid faces a much higher free-energy barrier in four than in three dimensions at equivalent supersaturation, due to the increased geometrical frustration between the simplex-based fluid order and the crystal [J. A. van Meel, D. Frenkel, and P. Charbonneau, Phys. Rev. E 79, 030201(R) (2009)]. Here, we analyze the microscopic contributions to the fluid-crystal interfacial free energy to understand how the barrier to crystallization changes with dimension. We find the barrier to grow with dimension and we identify the role of polydispersity in preventing crystal formation. The increased fluid stability allows us to study the jamming behavior in four, five, and six dimensions and to compare our observations with two recent theories [C. Song, P. Wang, and H. A. Makse, Nature (London) 453, 629 (2008); G. Parisi and F. Zamponi, Rev. Mod. Phys. (to be published)].

In general, the power-law degree distribution has profound influence on various dynamical processes defined on scale-free networks. In this paper, we will show that power-law degree distribution alone does not suffice to characterize the behavior of trapping problems on scale-free networks, which is an integral major theme of interest for random walks in the presence of an immobile perfect absorber. In order to achieve this goal, we study random walks on a family of one-parameter (denoted by $q$) scale-free networks with identical degree sequence for the full range of parameter $q$, in which a trap is located at a fixed site. We obtain analytically or numerically the mean first-passage time (MFPT) for the trapping issue. In the limit of large network order (number of nodes), for the whole class of networks, the MFPT increases asymptotically as a power-law function of network order with the exponent obviously different for different parameter $q$, which suggests that power-law degree distribution itself is not sufficient to characterize the scaling behavior of MFPT for random walks at least trapping problem, performed on scale-free networks.

Clipping a Gaussian random field at a level that is position-dependent yields statistically inhomogeneous morphologies, relevant to many ordered nanostructured materials. The one-point and two-point probability functions of the morphology are derived, as well as a general relation between the specific surface area and the gradient of the clipping function. The general results are particularized for the comprehensive analysis of small-angle x-ray scattering and nitrogen adsorption of SBA-15 ordered mesoporous silica.

We show that spiral vortices in oscillatory systems can lose stability to secondary modes to form dual-mode spiral vortices. The secondary modes grow at the vortex core where the oscillation amplitude vanishes but are nonlinearly damped by the oscillatory mode away from the core. Gradients of the oscillation phase, induced by the hosted secondary mode, can lead to additional hosting events that culminate in periodic core oscillations or in a novel form of spatiotemporal chaos. The results of this study apply to physical, chemical, and biological systems that go through cusp-Hopf, fold-Hopf, and Hopf-Turing bifurcations.

Since both attractive and repulsive effects among agents are important in social systems, we present simulations of two models based on Axelrod’s homogenization mechanism that includes repulsion. These models are the repulsive model, where all individuals can repel, and the partially repulsive model where only a fraction of repelling agents are considered. In these two models, attractive dynamics is implemented for agents with the ability to repel each other only if the number of features shared by them is greater than a threshold parameter. Otherwise, repelling dynamics is used. In the repulsive model, the transition from a monocultural state to a fragmented one often occurs abruptly from one cultural-variability value to the next one and a second transition emerges. For the partially repulsive model, there are also two different transitions present: the initial one being as abrupt as the one found for the repulsive model, whereas the second one follows a less abrupt behavior and resembles that of the original Axelrod model. However, the second transition for this model occurrs from a partially fragmented state and not from a monocultural one.

We consider a network of deterministic and stochastic locally coupled oscillators with positive or negative dissipation and local time-delayed feedback. (i) For a deterministic system, we study propagation of waves through the network. We show that time delay leads to a coexistence of several neutral modes with different wave numbers and group velocities, which we compute analytically. (ii) For noisy system, we study the response of the network to external random forcing correlated in space and uncorrelated in time. Below the threshold of spatial instability, noise induces spatiotemporal fluctuations, which can be characterized by the structure function. We give an analytical expression for the structure function and demonstrate the effect of the time delay and of the correlation length of noise on the wave number of the most excited mode.

Colloidal probe atomic force microscopy is used to study the slip behavior of 18 Newtonian liquids from two homologous series, the $n$-alkanes and $n$-alcohols, at molecularly smooth hydrophobic $n$-hexadecyltrichlorosilane coated surfaces. We find that the slip behavior is governed by the bulk viscosity $\eta$ of the liquid, specifically, the slip length $b\sim {\eta }^x$ with $x\sim 0.33$. Additionally, the slip length was found to be shear rate independent, validating the use of Vinogradova slip theory in this work.

We study a modified version of the stochastic susceptible-infected-refractory-susceptible (SIRS) model by employing a nonlinear (exponential) reinforcement in the contagion rate and no diffusion. We run simulations for complete and random graphs as well as $d$-dimensional hypercubic lattices (for $d=3,2,1$). For weak nonlinearity, a continuous nonequilibrium phase transition between an absorbing and an active phase is obtained, such as in the usual stochastic SIRS model [Joo and Lebowitz, Phys. Rev. E 70, 036114 (2004)]. However, for strong nonlinearity, the nonequilibrium transition between the two phases can be discontinuous for $d\ge 2$, which is confirmed by well-characterized hysteresis cycles and bistability. Analytical mean-field results correctly predict the overall structure of the phase diagram. Furthermore, contrary to what was observed in a model of phase-coupled stochastic oscillators with a similar nonlinearity in the coupling [Wood et al., Phys. Rev. Lett. 96, 145701 (2006)], we did not find a transition to a stable (partially) synchronized state in our nonlinearly pulse-coupled excitable elements. For long enough refractory times and high enough nonlinearity, however, the system can exhibit collective excitability and unstable stochastic oscillations.

Recently, dispersionless (coherent) motion of (noninteracting) massive Brownian particles, at intermediate time scales, was reported in a sinusoidal potential with a constant tilt. The coherent motion persists for a finite length of time before the motion becomes diffusive. We show that such coherent motion can be obtained repeatedly by applying an external zero-mean square-wave drive of appropriate period and amplitude instead of a constant tilt. Thus, the cumulative duration of coherent motion of particles is prolonged. Moreover, by taking an appropriate combination of periods of the external field, one can postpone the beginning of the coherent motion and can even have coherent motion at a lower value of position dispersion than in the constant tilt case.

A rank-dependent deactivation mechanism is introduced to network evolution. The growth dynamics of the network is based on a finite memory of individuals, which is implemented by deactivating one site at each time step. The model shows striking features of a wide range of real-world networks: power-law degree distribution, high clustering coefficient, and disassortative degree correlation.

To model biochemical systems in which both noise in the chemical reaction process and spatial movement of molecules is important, both the reaction-diffusion master equation (RDME) and Smoluchowski diffusion-limited reaction (SDLR) partial differential equation (PDE) models have been used. In previous work we showed that the solution to the RDME may be interpreted as an asymptotic approximation in the reaction radius to the solution of the SDLR PDE [S. A. Isaacson, SIAM J. Appl. Math. 70, 77 (2009)]. The approximation was shown to be divergent in the limit that the lattice spacing in the RDME approached zero. In this work we expand upon these results for the special case of the two-molecule annihilation reaction, $\text{A}+\text{B}\to \varnothing$. We first introduce a third stochastic reaction-diffusion PDE model that incorporates a pseudopotential based bimolecular reaction mechanism. The solution to the pseudopotential model is then shown to be an asymptotic approximation to the solution of the SDLR PDE for small reaction radii. We next illustrate how the RDME may be obtained by a formal discretization of the pseudopotential model, motivating why the RDME is itself an asymptotic approximation of the SDLR PDE. Finally, we give a more detailed numerical analysis of the difference between solutions to the RDME and SDLR PDE models as a function of both the reaction-radius and the lattice spacing (in the RDME).

Considering the fact that signal transmission time delays between different pairs of synaptically coupled neurons in the brain are different, we study the effects of distributed time delays on phase synchronization of bursting neurons. We consider the case of inhibitory coupled bursting Hindmarsh-Rose neurons and find that distributed time delays in chemical coupling can induce a variety of phase-coherent dynamic behaviors. The critical mean time delay for the emergence of coherent behaviors is inversely proportional to both the coupling strength and the average degree. This phenomenon is robust to nonidentical external inputs and is independent of network topology. A physical theory is formulated to explain the emergence of coherent neuronal activity.