We investigate some statistical mechanical properties of a system consisting of two hard spheres in a $D$-dimensional rectangular box $(D=1,2,\dots )$. We give a theoretical method for computing a configurational partition function $Z_{c,D}$ of this system and compare the equation of state obtained from $Z_{c,D}$ with molecular dynamics simulations. Especially in $D=3$, we give a fully analytic expression for the pressure which turns out to have one or more negative compressibility regions when the box size is small.

We investigate the stability of the localized stationary solutions of a three-component reaction-diffusion system with one activator and two inhibitors. A change of the time constants of the inhibitors can lead to a destabilization of the stationary solution. The special case we are interested in is that the breathing mode becomes unstable first and the stationary dissipative soliton undergoes a bifurcation from a stationary to a “breathing” state. This situation is analyzed performing a two-time-scale expansion in the vicinity of the bifurcation point thereby obtaining the corresponding amplitude equation. Also numerical simulations are carried out showing good agreement with the analytical predictions.

A local evolution equation for one-dimensional interfaces is derived in the context of erosion by ion beam sputtering. We present numerical simulations of this equation which show interrupted coarsening in which an ordered cell pattern develops with constant wavelength and amplitude at intermediate distances, while the profile is disordered and rough at larger distances. Moreover, for a wide range of parameters the lateral extent of ordered domains ranges up to tens of cells. We also provide analytical estimates for the stationary pattern wavelength and mean growth velocity.

Recent works reported planar and conical azimuthally degenerated nematic anchorings. Here we predict an additional “anticonical” degenerated anchoring. Its energy presents two minima, parallel and perpendicular to the substrate plane, separated by a conical energy barrier. We realize this bistable anchoring on a grafted polymer brush and we observe temperature-driven transitions between the conical, planar, and anticonical degenerated anchorings. Under electric field we break the anticonical anchoring and switch between its bistable states.

We present mathematical and simulation analyses of the below-threshold noisy response of two biophysically motivated models for excitable membrane due to H. R. Wilson: a squid axon (“resonator”) and a human cortical neuron (“integrator”). When stimulated with a low-intensity white noise superimposed on a dc control current, both membrane types generate voltage fluctuations that exhibit critical slowing down—that is, the voltage responsiveness to noisy input currents grows in amplitude while slowing in frequency—as the membrane approaches spiking threshold from below. We define threshold unambiguously as that dc current that renders a zero real eigenvalue for the Jacobian matrix for the integrator neuron, and, for the resonator neuron, as the dc current that gives a complex eigenvalue pair whose real part is zero. Using a linear Ornstein-Uhlenbeck analysis, we give exact small-noise expressions for the variance, power spectrum, and correlation function of the voltage fluctuations, and we derive the scaling laws for the divergence of susceptibility and correlation times for approach to threshold. We compare these predictions with numerical simulations of the nonlinear stochastic equations, and demonstrate that, provided the white-noise perturbations are kept sufficiently small, the linearized theory works well. These predictions should be testable in the laboratory using a current-clamped cell configuration. If confirmed, then the proximity of a neuron to its spike-transition point can be judged by measuring its subthreshold susceptibility to white-noise stimulation. We postulate that such temporally correlated fluctuations could provide a means of subthreshold signaling via gap-junction connections with neighboring neurons.

A theoretical analysis on wave propagation and optical properties of slabs with light-induced free charge carriers within a Fabry-Pérot framework is presented. The key of the analysis is to attack the wave propagation problem in terms of the time-averaged Poynting vector modulus within the medium through an alternative approach. This fact allows coupling the microscopic (free charge rate) and macroscopic (electromagnetic field evolution) equations self-consistently by means of the nonlinear permittivity and conductivity, which, in turn, depend on the time-averaged Poynting vector modulus. Thereby, the transmittance, reflectance, and absorptive power are derived as functions of the pump intensity and medium thickness. Bistable behavior is found at relatively high excitation intensity for positive values of the nonlinear permittivity coefficient. The bistability enhances for increasing values of such coefficient and weakens for increasing values of nonlinear photoconductivity coefficient. On the contrary, for negative nonlinear permittivity coefficient, bistability does not appear possessing these media mirrorlike behavior. Some possible applications are suggested.

$ϵ$-negative (ENG) and $\mu$-negative (MNG) materials are successfully fabricated by using composite right/left-handed transmission line. The ENG and MNG materials are opaque in experiments, but the completely tunneling phenomenon occurs in the ENG-MNG pair, if the wave impedance and the effective phase shift of ENG and MNG materials are under the conditions of match, respectively. We experimentally confirmed that the photonic crystals consisting of ENG and MNG materials can possess left-handed propagation modes and right-handed propagation modes within forbidden gaps. At the same time, the Bragg gaps for the band-gap indices $m=\pm 1$ and the zero effective phase (zero-${\Phi }_{\mathrm{eff}}$) gaps were also observed. The experimental results agree extremely well with the simulations.

We study the statistical properties of the potential energy landscape of a system of particles interacting via a very short-range square-well potential (of depth $-u_0$) as a function of the range of attraction $\Delta$ to provide thermodynamic insights of the Noro and Frenkel [M. G. Noro and D. Frenkel, J. Chem. Phys. 113, 2941 (2000)] scaling. We exactly evaluate the basin free energy and show that it can be separated into a vibrational ($\Delta$ dependent) and a floppy ($\Delta$ independent) component. We also show that the partition function is a function of $\mathrm{\Delta }{e}^{\beta u_o}$, explaining the equivalence of the thermodynamics for systems characterized by the same second virial coefficient. An outcome of our approach is the possibility of counting the number of floppy modes (and their entropy).

In this paper, random walks with independent steps distributed according to a $Q$-power-law probability distribution function with $Q=1∕(1-q)$ are studied. In the case $q>1$, we show that (i) a stochastic representation of the location of the walk after $n$ steps can be explicitly given (for both finite and infinite variance) and (ii) a clear connection with the superstatistics framework can be established (including the anomalous diffusion case). In the case $q<1$, we prove that this random walk can be considered as the projection of an isotropic random walk, i.e., a random walk with fixed length steps and uniformly distributed directions. These results provide a natural extension of (i) the usual Gaussian framework and (ii) the infinite-covariance case of the superstatistics treatments.

The two-letter hydrophobic-polar (HP) model of Lau and Dill [Macromolecules 22, 3986 (1989)] has been widely used in theoretical studies of protein folding due to its conceptual and computational simplicity. Despite its success in elucidating various aspects of the sequence-structure relationship, thermodynamic behavior of the model is not in agreement with a sharp two-state folding transition of many single-domain proteins. To gain a better understanding of this discrepancy, we consider an extension of the HP model by including an “antiferromagnetic” (AF) interaction in the contact potential that favors amino acid residues with complementary attributes. With an enlarged four-letter alphabet, the density of states on the low energy side can be significantly decreased. Computational studies of the four-letter HP model are performed on 36-mer sequences on a square lattice. It is found that the designability of folded structures in the extended model exhibits strong correlation with that of the two-letter HP model, while the AF interaction alone selects a very different class of structures that resembles the Greek key motif for beta sheets. A procedure is introduced to select sequences which have the largest energy gap to the native state. Based on density of states and specific heat calculations in the full configuration space, we show that the optimized sequence is able to fold nearly as cooperatively as a corresponding Gō model.

Within the framework of the random replicator model of ecosystems, we use equilibrium statistical mechanics tools to study the effect of manipulating the ecosystem so as to guarantee that a fixed fraction of the surviving species at equilibrium display a predefined set of characters (e.g., characters of economic value). Provided that the intraspecies competition is not too weak, we find that the consequence of such intervention on the ecosystem composition is a significant increase on the number of species that become extinct, and so the impoverishment of the ecosystem.

The threshold model can be used to generate random networks of arbitrary size with given local properties such as the degree distribution, clustering, and degree correlation. We summarize the properties of networks created using the threshold model and present an alternative deterministic construction. These networks are threshold graphs and therefore contain a highly compressible layered structure and allow computation of important network properties in linear time. We show how to construct arbitrarily large, sparse, threshold networks with (approximately) any prescribed degree distribution or Laplacian spectrum. Control of the spectrum allows careful study of the synchronization properties of threshold networks including the relationship between heterogeneous degrees and resistance to synchrony.

By using a four-hot-wire probe and an eight-hot-wire probe, different approximations to energy dissipation rate have been made in the far field of a cylinder wake. The appropriateness of the various approximations is evaluated by examining their mean values, spectra, conditional analysis, and scaling range exponents. It is found that there are significant differences between the instantaneous values of ${ϵ}_{iso}$, the isotropic dissipation rate, and other approximations. The present measurements also allow the examination of the spatial correlation between the energy dissipation rate and the enstrophy $\Omega$. While the correlation between ${ϵ}_{iso}$ and $\Omega$ is low, there is a strong correlation between the other approximations to energy dissipation rate $ϵ$ and the enstrophy $\Omega$. The scaling range exponents show that the substitutes to the energy dissipation rate and enstrophy based on isotropy are more intermittent than their corresponding true values. The present results suggest that using ${ϵ}_{iso}$ as a substitute of $ϵ$ should be re-examined, especially for the instantaneous values.

The authors develop a transverse dielectric matrix and from it they calculate the shear mode dispersion in strongly coupled charged-particle bilayer liquids in the $T=0$ quantum domain. The formulation is based on the classical quasilocalized charge approximation (QLCA) and extends the QLCA formalism into the quantum domain. Its development parallels and complements the development of a similarly extended longitudinal dielectric matrix formalism reported in a recent companion work [K. I. Golden, H. Mahassen, G. J. Kalman, G. Senatore, and F. Rapisarda, Phys. Rev. E 71, 036401 (2005)]. Using pair correlation function data generated from diffusion Monte Carlo simulations, the authors calculate the dispersion of the in-phase and out-of-phase shear modes over a wide range of high-$r_s$ values and layer separations. Over the coupling range $10\le r_s\le 30$ and for layer separations $0.2∕\sqrt{\pi n}\le d\le 0.5∕\sqrt{\pi n}$, the present study predicts the existence of a robust out-of-phase gapped shear mode dispersion in the domain of the $q,\omega$-plane above the left boundary of the RPA single-pair excitation region; under these conditions, the out-of-phase collective excitation is entirely immune to Landau damping and can be safely considered to be mostly unaffected by diffusive-migrational damping.

Three-dimensional monochromatic optical beams of uniform polarization interacting with a planar boundary between two homogeneous, isotropic, and lossless media are analyzed. Generalized Fresnel transmission and reflection coefficients for beam spectra are given. Interrelations induced by cross-polarization coupling between beam profile and phase and beam polarization, or between spin and orbital angular momentum of beams are derived. Beam transmission for normal incidence is discussed in detail. It is shown that elegant Hermite-Gaussian beams of linear polarization and Laguerre-Gaussian beams of circular polarization, all projected on the interface, are normal modes at this interface. Creation and annihilation of these modes at the interface are shown with total angular momentum being conserved on a single photon level.

We address the generic problem of extracting the scaling exponents of a stationary, self-affine process realized by a time series of finite length, where information about the process is not known a priori. Estimating the scaling exponents relies upon estimating the moments, or more typically structure functions, of the probability density of the differenced time series. If the probability density is heavy tailed, outliers strongly influence the scaling behavior of the moments. From an operational point of view, we wish to recover the scaling exponents of the underlying process by excluding a minimal population of these outliers. We test these ideas on a synthetically generated symmetric $\alpha$-stable Lévy process and show that the Lévy exponent is recovered in up to the 6th order moment after only $\sim 0.1–0.5\%$ of the data are excluded. The scaling properties of the excluded outliers can then be tested to provide additional information about the system.

We consider the critical short-time evolution of magnetic and droplet-percolation order parameters for the Ising model in two and three dimensions, through Monte Carlo simulations with the (local) heat-bath method. We find qualitatively different dynamic behaviors for the two types of order parameters. More precisely, we find that the percolation order parameter does not have a power-law behavior as encountered for the magnetization, but develops a scale (related to the relaxation time to equilibrium) in the Monte Carlo time. We argue that this difference is due to the difficulty in forming large clusters at the early stages of the evolution. Our results show that, although the descriptions in terms of magnetic and percolation order parameters may be equivalent in the equilibrium regime, greater care must be taken to interpret percolation observables at short times. In particular, this concerns the attempts to describe the dynamics of the deconfinement phase transition in QCD using cluster observables.

We present experimental measurements of a granular slope under horizontal vibration. We use optical particle tracking to measure the motion of surface beads as the slope fails. We find that for all but the largest inclination angles, initial bead motion leads to strengthening rather than an avalanche. The initial motion of the beads is usually intermittent and evolves differently for different preparations, slope angles, and rates of increase in the vibration amplitude. When a specific criterion is chosen to define failure, the Coulomb friction model adequately describes the average acceleration required to produce failure, as long as slope preparation and experimental protocol are constant. However, the observed intermittent motion and rate dependence indicate that strengthening microrearrangements are important features that affect failure of slopes under external perturbations.

We study macroion correlation effects on the thermodynamics of highly charged colloidal suspensions using a mean-field theory and primitive model computer simulations. We suggest a simple way to include the macroion correlations into the mean-field theory as an extension of the renormalized jellium model of Trizac and Levin [Phys. Rev. E 69, 031403 (2004)]. The effective screening parameters extracted from our mean-field approach are then used in a one-component model with macroions interacting via a Yukawa-like potential to predict macroion distributions. We find that inclusion of macroion correlations leads to a weaker screening and hence smaller effective macroion charge and lower osmotic pressure of the colloidal dispersion as compared to other mean-field models. This result is supported by comparison to primitive model simulations and experiments for charged macroions in the low-salt regime, where the macroion correlations are expected to be significant.