The structural properties of single component fluids of hard hyperspheres in odd space dimensionalities $d$ are studied with an analytical approximation method that generalizes the rational function approximation earlier introduced in the study of hard-sphere fluids [S. B. Yuste and A. Santos, Phys. Rev. A 43, 5418 (1991)]. The theory makes use of the exact form of the radial distribution function to first order in density and extends it to finite density by assuming a rational form for a function defined in Laplace space, the coefficients being determined by simple physical requirements. Fourier transform in terms of reverse Bessel polynomials constitute the mathematical framework of this approximation, from which an analytical expression for the static structure factor is obtained. In its most elementary form, the method recovers the solution of the Percus-Yevick closure to the Ornstein-Zernike equation for hyperspheres at odd dimensions. The present formalism allows one to go beyond by yielding solutions with thermodynamic consistency between the virial and compressibility routes to any desired equation of state. Excellent agreement with available computer simulation data at $d=5$ and $d=7$ is obtained.

We use time-resolved x-ray photon correlation spectroscopy to investigate the slow dynamics of colloidal gels made of moderately attractive carbon black particles. We show that the slow dynamics is temporally heterogeneous and quantify its fluctuations by measuring the variance $\chi$ of the instantaneous intensity correlation function. The amplitude of dynamical fluctuations has a nonmonotonic dependence on scattering vector $q$, in stark contrast with recent experiments on strongly attractive colloidal gels [Duri and Cipelletti, Europhys. Lett. 76, 972 (2006)]. We propose a simple scaling argument for the $q$-dependence of fluctuations in glassy systems that rationalizes these findings.

We report, for a nematic liquid crystal with a low conductivity anisotropy, an ac field generated transition from a uniformly planar to a periodically modulated director configuration with the wave vector parallel to the initial director. Significantly, with unblocked electrodes, this instability is not excited by dc fields. Additionally, in very low frequency square wave fields, it occurs transiently after each polarity reversal, vanishing completely during field constancy. The time of occurrence of maximum distortion after polarity reversal decreases exponentially with voltage. The time dependence of optical phase change during transient distortion is nearly Gaussian. The pattern threshold $V_{\mathrm{c}}$ is linear in $\sqrt{f}$, $f$ denoting the frequency; the critical wave number $q_{\mathrm{c}}$ of the modulation scales nearly linearly as $\sqrt{f}$ to a peak at $\sim 50\mathrm{Hz}$ before falling slightly thereafter. The observed $V_{\mathrm{c}}\left(f\right)$ and $q_{\mathrm{c}}\left(f\right)$ characteristics differ from the predictions of the standard model (SM). The instability may be interpreted as a special case of the Carr-Helfrich distortion suppressed in static fields due to weak charge focusing and strong charge injection. Its transient nature in the low frequency regime is suggestive of the possible role of gradient flexoelectric effect in its occurrence. The study includes measurement of certain elastic and viscosity parameters relevant to the application of the SM.

We analyze the dynamics of a star polymer of $F$ arms trapped in a double well potential. Initially the molecule is confined to one of the minima and can cross over the barrier to the other side. We use the continuum version of the Rouse-Ham model and calculate the rate of crossing using the multidimensional approach due to Langer [Ann. Phys. (N.Y.) 54, 258 (1969)]. Finding the transition state for the process is shown to be equivalent to the solution of Newton’s equations for $F$ independent particles, moving in an inverted potential. For each star polymer, there is a critical barrier top curvature, below which the star crosses over in coiled conformation. The value of the critical curvature is determined by the first Rouse mode of the star. If the curvature is greater than this critical value, the saddle point for the crossing is a stretched conformation of the star. For the coiled transition state, the activation energy is proportional to the total arm length of the star. For the stretched transition state, as one increases the length of an arm of the star, the activation energy at first increases and then decreases. This results from the fact that in the stretched state, only one arm of the polymer is stretched across the top of the barrier, while others need not be. We calculate the rate by expanding the energy around the saddle up to second order in the fluctuations. As we use the continuum model, there are infinite modes for the polymer and, consequently, the prefactor has infinite products. We show that these infinite products can be reduced to a simple expression, and evaluated easily. However, the rate diverges near $N_{Tc}$ due to the multifurcation, which results in more than one unstable mode. The cure for this divergence is to keep terms up to fourth order in the expansion of energy for these modes. Performing this, we have calculated the rate as a function of the length of the star. It is found that the rate has a nonmonotonic dependence on the length, suggesting that longer stars may actually cross over the barrier faster.

We have investigated the effect of the phase response curve on the dynamics of oscillators driven by noise in two limit cases that are especially relevant for neuroscience. Using the finite element method to solve the Fokker-Planck equation we have studied (i) the impact of noise on the regularity of the oscillations quantified as the coefficient of variation, (ii) stochastic synchronization of two uncoupled phase oscillators driven by correlated noise, and (iii) their cross-correlation function. We show that, in general, the limit of type II oscillators is more robust to noise and more efficient at synchronizing by correlated noise than type I.

We analyze the effect of disorder and notches on crack roughness in two dimensions. Our simulation results based on large system sizes and extensive statistical sampling indicate that the crack surface exhibits a universal local roughness of ${\zeta }_{\mathit{loc}}=0.71$ and is independent of the initial notch size and disorder in breaking thresholds. The global roughness exponent scales as $\zeta =0.87$ and is also independent of material disorder. Furthermore, we note that the statistical distribution of crack profile height fluctuations is also independent of material disorder and is described by a Gaussian distribution, albeit deviations are observed in the tails.

We consider $n$ reactive species involved in unimolecular reactions and submitted to a temperature modulation of small amplitude. We determine the conditions on the rate constants for which the deviations from the equilibrium concentrations of each species can be optimized and find the analytical expression of the frequency associated with an extremum of concentration shift in the case $n=3$. We prove that the frequency dependence of the displacement of equilibrium gives access to the number $n$ of species involved in the mechanism. We apply the results to the case of the transformation of a reactant into a product through a possible reactive intermediate and find the order relation obeyed by the activation energies of the different barriers. The results typically apply to enzymatic catalysis with kinetics of Michaelis-Menten type.

We consider the targeted manipulation of reaction-diffusion waves by optimization of an external forcing parameter. As an example, we present numerical results for the FitzHugh-Nagumo system exploiting model-based optimization capable of targeting characteristic wave properties such as wavelength, shape, and propagation speed by spatiotemporally controlling electric current. The conceptual basis of our approach is optimal control of periodic orbits in a wave-variable coordinate system. The results are transferred back to the partial differential equation context and validated in numerical simulations. The whole procedure is applicable to any reaction-diffusion model.

When a droplet is gently laid onto the surface of the same liquid, it stays at rest for a moment before coalescence. The coalescence can be delayed and sometimes inhibited by injecting fresh air under the droplet. This can happen when the surface of the bath oscillates vertically. In this case the droplet basically bounces on the interface. The lifetime of the droplet has been studied with respect to the amplitude and the frequency of the excitation. The lifetime decreases when the acceleration increases. The thickness of the air film between the droplet and the bath has been investigated using interference fringes obtained when the system is illuminated by low-pressure sodium lamps. Moreover, both the shape evolution and the motion of the droplet center of mass have been recorded in order to evidence the phase offset between the deformation and the trajectory. A short lifetime is correlated to a small air-film thickness and to a large phase offset between the maximum of deformation and the minimum of the vertical position of the center of mass.

The lattice Boltzmann equation (LBE) has shown its promise in the simulation of microscale gas flows. One of the critical issues with this advanced method is to specify suitable slip boundary conditions to ensure simulation accuracy. In this paper we study two widely used kinetic boundary conditions in the LBE: the combination of the bounce-back and specular-reflection scheme and the discrete Maxwell’s scheme. We show that (i) both schemes are virtually equivalent in principle, and (ii) there exist discrete effects in both schemes. A strategy is then proposed to adjust the parameters in the two kinetic boundary conditions such that an accurate slip boundary condition can be implemented. The numerical results demonstrate that the corrected boundary conditions are robust and reliable.

We sketch the statistical physics framework of the replica exchange technique when applied to molecular dynamics simulations. In particular, we draw attention to generalized move sets that allow a variety of optimizations as well as new applications of the method.

The asymptotic survival probability of a spherical target in the presence of a single subdiffusive trap or surrounded by a sea of subdiffusive traps in a continuous Euclidean medium is calculated. In one and two dimensions the survival probability of the target in the presence of a single trap decays to zero as a power law and as a power law with logarithmic correction, respectively. The target is thus reached with certainty, but it takes the trap an infinite time on average to do so. In dimensions higher than two a single trap may never reach the target and so the survival probability is finite and, in fact, does not depend on whether the traps move diffusively or subdiffusively. When the target is surrounded by a sea of traps, on the other hand, its survival probability decays as a stretched exponential in all dimensions (with a logarithmic correction in the exponent for $d=2$). A trap will therefore reach the target with certainty, and will do so in a finite time. These results may be directly related to enzyme binding kinetics on DNA in the crowded cellular environment.

We perform simulations of continuum gradient percolation to measure the percolation threshold of systems of fully penetrable disks of two different radii. As a function of volumetric proportion $v$, the percolation threshold ${\varphi }_c(v,\lambda )$ is approximately symmetric about $v=0.5$ for a fixed ratio $\lambda$ of the radii. However, the difference from symmetry is strongly statistically significant. We also improve, by an order of magnitude, the measurement of the percolation threshold for disks of equal radius: ${\varphi }_c^{*}=0.6763475\left(6\right)$.

We experimentally investigate the response to perturbations of circular symmetry for dense granular flow inside a three-dimensional right-conical hopper. These experiments consist of particle tracking velocimetry for the flow at the outer boundary of the hopper. We are able to test commonly used constitutive relations and observe granular flow phenomena that we can model numerically. Unperturbed conical hopper flow has been described as a radial velocity field with no azimuthal component. Guided by numerical models based upon continuum descriptions, we find experimental evidence for secondary, azimuthal circulation in response to perturbation of the symmetry with respect to gravity by tilting. For small perturbations we can discriminate between constitutive relations, based upon the agreement between the numerical predictions they produce and our experimental results. We find that the secondary circulation can be suppressed as wall friction is varied, also in agreement with numerical predictions. For large tilt angles we observe the abrupt onset of circulation for parameters where circulation was previously suppressed. Finally, we observe that for large tilt angles the fluctuations in velocity grow, independent of the onset of circulation.

The long-time behavior of the current autocorrelation functions for the velocity, the shear stress, and the heat flux is investigated in freely cooling granular gases. It is found that the correlation functions for the velocity and the shear stress have the long-time tails obeying ${\tau }^{-d∕2}$, while the correlation function for heat flux decays as ${\tau }^{-(d+2)∕2}\exp (-{\zeta }^{*}\tau )$ with the dimensionless cooling rate ${\zeta }^{*}$, the spatial dimension $d$, and the scaled time $\tau$ in terms of the collision frequency. The result of our numerical simulation of the freely cooling granular gases is consistent with the theoretical prediction.

Aqueous gelatin solutions when spread on hydrophilic substrates form self-organized structures where the gelatin molecules and clusters are arranged as self-similar objects giving a mass fractal dimension $d_f=1.67$ and 1.72 for solutions made with $\mathrm{KCl}$ and $\mathrm{NaCl}$ salts as estimated from atomic force microscopic studies. The dehydration driven self-organization of particles changed the $d_f$ values to 1.78 and 1.81, respectively, after $24\mathrm{h}$. This further changed to 1.83 and 1.85 after a time lapse of 10 days. The dynamics of formation of these structures are modeled through spin-exchange kinetics in the nonequilibrium steady state regime in order to understand their complex behavior. Kawasaki spin exchange dynamics has been applied to a diffusion limited aggregation type fractal object, and the growth of the domains was observed by minimizing the free energy. The fractal dimension of such a system changed from 1.70 to 1.82 which inferred the loss of fractal behavior and the generation of a more compact object. The experimentally observed temporal evolution of these complex structures could be adequately described through the results obtained from the computer simulation data.

Photon propagation in biological tissue is commonly described by the radiative transfer equation, while the phase function in the equation represents the scattering characteristics of the medium and has significant influence on the precision of solution and the efficiency of computation. In this work, we present a generalized Delta-Eddington phase function to simplify the radiative transfer equation to an integral equation with respect to photon fluence rate. Comparing to the popular diffusion approximation model, the solution of the integral equation is highly accurate to model photon propagation in the biological tissue over a broad range of optical parameters. This methodology is validated by Monte Carlo simulation.

We investigate the standard susceptible-infected-susceptible model on a random network to study the effects of preference and geography on diseases spreading. The network grows by introducing one random node with $m$ links on a Euclidean space at unit time. The probability of a new node $i$ linking to a node $j$ with degree $k_j$ at distance $d_{ij}$ from node $i$ is proportional to $k_j^A∕d_{ij}^B$, where $A$ and $B$ are positive constants governing preferential attachment and the cost of the node-node distance. In the case of $A=0$, we recover the usual epidemic behavior with a critical threshold below which diseases eventually die out. Whereas for $B=0$, the critical behavior is absent only in the condition $A=1$. While both ingredients are proposed simultaneously, the network becomes robust to infection for larger $A$ and smaller $B$.

We consider the linear stability of dissipative magnetic Taylor-Couette flow with imposed toroidal magnetic fields. The inner and outer cylinders can be either insulating or conducting; the inner one rotates, the outer one is stationary. The magnetic Prandtl number can be as small as ${10}^{-5}$, approaching realistic liquid-metal values. The magnetic field destabilizes the flow, except for radial profiles of $B_{\varphi }\left(R\right)$ close to the current-free solution. The profile with $B_{\text{in}}=B_{\text{out}}$ (the most uniform field) is considered in detail. For weak fields the Taylor-Couette flow is stabilized, until for moderately strong fields the $m=1$ azimuthal mode dramatically destabilizes the flow again so that a maximum value for the critical Reynolds number exists. For sufficiently strong fields (as measured by the Hartmann number) the toroidal field is always unstable, even for the nonrotating case with $\text{Re}=0$. The electric currents needed to generate the required toroidal fields in laboratory experiments are a few kA if liquid sodium is used, somewhat more if gallium is used. Weaker currents are needed for wider gaps, so a wide-gap apparatus could succeed even with gallium. The critical Reynolds numbers are only somewhat larger than the nonmagnetic values; hence such experiments would work with only modest rotation rates.

We compute solutions of the Lagrangian-averaged Navier-Stokes $\alpha$- (LANS $\alpha$) model for significantly higher Reynolds numbers (up to $\mathrm{Re}\approx 8300$) than have previously been accomplished. This allows sufficient separation of scales to observe a Navier-Stokes inertial range followed by a second inertial range specific to the LANS $\alpha$ model. Both fully helical and nonhelical flows are examined, up to Reynolds numbers of $\sim 1300$. Analysis of the third-order structure function scaling supports the predicted $l^3$ scaling; it corresponds to a $k^{-1}$ scaling of the energy spectrum for scales smaller than $\alpha$. The energy spectrum itself shows a different scaling, which goes as $k^1$. This latter spectrum is consistent with the absence of stretching in the subfilter scales due to the Taylor frozen-in hypothesis employed as a closure in the derivation of the LANS $\alpha$ model. These two scalings are conjectured to coexist in different spatial portions of the flow. The $l^3$ $\left[E\right(k)\sim k^{-1}]$ scaling is subdominant to $k^1$ in the energy spectrum, but the $l^3$ scaling is responsible for the direct energy cascade, as no cascade can result from motions with no internal degrees of freedom. We demonstrate verification of the prediction for the size of the LANS $\alpha$ attractor resulting from this scaling. From this, we give a methodology either for arriving at grid-independent solutions for the LANS $\alpha$ model, or for obtaining a formulation of the large eddy simulation optimal in the context of the $\alpha$ models. The fully converged grid-independent LANS $\alpha$ model may not be the best approximation to a direct numerical simulation of the Navier-Stokes equations, since the minimum error is a balance between truncation errors and the approximation error due to using the LANS $\alpha$ instead of the primitive equations. Furthermore, the small-scale behavior of the LANS $\alpha$ model contributes to a reduction of flux at constant energy, leading to a shallower energy spectrum for large $\alpha$. These small-scale features, however, do not preclude the LANS $\alpha$ model from reproducing correctly the intermittency properties of the high-Reynolds-number flow.