An analytical model of non-Gaussian energy landscape of low-temperature fluids is developed based on the thermodynamics of the fluid of dipolar hard spheres. The entire excitation profile of the liquid, from the high-temperature liquid to the point of ideal-glass transition, has been obtained from Monte Carlo simulations. The fluid of dipolar hard spheres loses stability close to the point of ideal-glass transition transforming via a first-order transition into a columnar liquid phase of dipolar chains locally arranged in a body-centered-tetragonal order. Significant non-Gaussianity of the energy landscape is responsible for narrowing of the distribution of potential energies and energies of inherent structures with decreasing temperature. We suggest that the proposed functionality of the enumeration function is widely applicable to both polar and nonpolar low-temperature liquids.

We study a simple model for metal corrosion controlled by the reaction rate of the metal with an anionic species and the diffusion of that species in the growing passive film between the solution and the metal. A crossover from the reaction-controlled to the diffusion-controlled growth regime with different roughening properties is observed. Scaling arguments provide estimates of the crossover time and film thickness as functions of the reaction and diffusion rates and the concentration of anionic species in the film-solution interface, including a nontrivial square-root dependence on that concentration. At short times, the metal-film interface exhibits Kardar-Parisi-Zhang (KPZ) scaling, which crosses over to a diffusion-limited erosion (Laplacian growth) regime at long times. The roughness of the metal-film interface at long times is obtained as a function of the rates of reaction and diffusion and of the KPZ growth exponent. The predictions have been confirmed by simulations of a lattice version of the model in two dimensions. Relations with other erosion and corrosion models and possible applications are discussed.

In this work we use theory to obtain a mathematical expression for a time correlation function $c(l,t)$ that provides insight into the zipping phenomena along a polymer going through a conformational transition. The polymer is modeled as an Ising-like chain with each segment being in one of two states: bound $(+1)$ or unbound $(-1)$. The time correlation function $c(l,t)$ predicts the correlation between the state of the $j\text{th}$ polymer segment at time 0 and the state of the $(j\pm l)\text{th}$ polymer segment at time $t$. The expressions for $c(0,t)$, $c(1,t)$, and $c(2,t)$ obtained from our theory are dependent on the values of $k_0$ and $k_1$, where $2k_0$ is the rate coefficient for one segment changing from an unbound state to a bound state when both the neighboring segments are in an unbound state, and $2k_1$ is the rate coefficient for one segment changing from an unbound state to a bound state when both the neighboring segments are in a bound state. The ratio $k_1∕k_0$ is an indication of the extent of cooperativity of binding adjacent segments on the polymer. We observe that $c(0,t)$, $c(1,t)$, and $c(2,t)$ decay to 0 (no correlation) more slowly and the maximum values of $c(1,t)$ and $c(2,t)$ are lower for low values of $k_1∕k_0$ as compared to high values of $k_1∕k_0$. This is because at low values of $k_1∕k_0$ the consecutive binding of adjacent segments along the polymer occurs slowly, while at high values of $k_1∕k_0$ the cooperativity of binding adjacent segments is high and the segments along the polymer bind in a fast zipping mechanism.

One of the grand puzzles in neuroscience is establishing the link between cognition and the disparate patterns of spontaneous and task-induced brain activity that can be measured clinically using a wide range of detection modalities such as scalp electrodes and imaging tomography. High-level brain function is not a single-neuron property, yet emerges as a cooperative phenomenon of multiply-interacting populations of neurons. Therefore a fruitful modeling approach is to picture the cerebral cortex as a continuum characterized by parameters that have been averaged over a small volume of cortical tissue. Such mean-field cortical models have been used to investigate gross patterns of brain behavior such as anesthesia, the cycles of natural sleep, memory and erasure in slow-wave sleep, and epilepsy. There is persuasive and accumulating evidence that direct gap-junction connections between inhibitory neurons promote synchronous oscillatory behavior both locally and across distances of some centimeters, but, to date, continuum models have ignored gap-junction connectivity. In this paper we employ simple mean-field arguments to derive an expression for $D_2$, the diffusive coupling strength arising from gap-junction connections between inhibitory neurons. Using recent neurophysiological measurements reported by Fukuda et al. [J. Neurosci. 26, 3434 (2006)], we estimate an upper limit of $D_2\approx 0.6{\mathrm{cm}}^2$. We apply a linear stability analysis to a standard mean-field cortical model, augmented with gap-junction diffusion, and find this value for the diffusive coupling strength to be close to the critical value required to destabilize the homogeneous steady state. Computer simulations demonstrate that larger values of $D_2$ cause the noise-driven model cortex to spontaneously crystalize into random mazelike Turing structures: centimeter-scale spatial patterns in which regions of high-firing activity are intermixed with regions of low-firing activity. These structures are consistent with the spatial variations in brain activity patterns detected with the BOLD (blood oxygen–level–dependent) signal detected with magnetic resonance imaging, and may provide a natural substrate for synchronous gamma-band rhythms observed across separated EEG (electroencephalogram) electrodes.

We analyze the memory in volatility by studying volatility return intervals, defined as the time between two consecutive fluctuations larger than a given threshold, in time periods following stock market crashes. Such an aftercrash period is characterized by the Omori law, which describes the decay in the rate of aftershocks of a given size with time $t$ by a power law with exponent close to 1. A shock followed by such a power law decay in the rate is here called Omori process. We find self-similar features in the volatility. Specifically, within the aftercrash period there are smaller shocks that themselves constitute Omori processes on smaller scales, similar to the Omori process after the large crash. We call these smaller shocks subcrashes, which are followed by their own aftershocks. We also show that the Omori law holds not only after significant market crashes as shown by Lillo and Mantegna [Phys. Rev. E 68, 016119 (2003)], but also after “intermediate shocks.” By appropriate detrending we remove the influence of the crashes and subcrashes from the data, and find that this procedure significantly reduces the memory in the records. Moreover, when studying long-term correlated fractional Brownian motion and autoregressive fractionally integrated moving average artificial models for volatilities, we find Omori-type behavior after high volatilities. Thus, our results support the hypothesis that the memory in the volatility is related to the Omori processes present on different time scales.

We present a detailed numerical and analytical study of the stability properties of the $N∕4$ ($\pi ∕2$-mode) one-mode nonlinear solution of the Fermi-Pasta-Ulam-$\beta$ system. The numerical analysis is made as a function of the number $N$ of the particles of the system and of the product $\lambda =\epsilon \beta$, where $\epsilon$ is the energy density and $\beta$ is the parameter characterizing the nonlinearity. It is shown that, both for $\beta >0$ and $\beta <0$, the instability threshold value $\left|{\lambda }_t\left(N\right)\right|$ converges, with increasing $N$, to the same value $2{\pi }^2∕\left(3N^2\right)$, that for $\beta >0$ $\left|{\lambda }_t{N}^2\right|$ is a decreasing function of $N$ as in the $\pi$-mode, whereas, for $\beta <0$, it is an increasing one. The asymptotic behavior of $\left|{\lambda }_t\right|$ for large values of $N$ is analytically obtained in both cases with a Floquet analysis of the stability.

We investigate axisymmetric spin coating of power law and Ellis fluids. The flow is driven by centrifugal force, gravity and surface tension. For power law and Ellis models a single equation for the fluid film height is obtained. For a Newtonian fluid the flux only involves linear derivative terms which allows the flux to be easily split for a numerical scheme. For power law and Ellis models the derivatives appear as nonlinear terms. To overcome this we develop an alternative numerical scheme to solve for the film height. Neglecting surface tension and gravity the power law model shows a central spike which is reduced by the introduction of surface tension and gravity. In certain cases the shear thinning power law model predicts slower spreading than the Newtonian model. The Ellis fluid shows no central spike, even for zero surface tension and the film always spreads further than the Newtonian fluid.

We study the evolution under their self-gravity of particles evolving from infinite “shuffled lattice” initial conditions. We focus here specifically on the comparison between the evolution of such a system and that of “daughter” coarse-grained particle distributions. These are sparser (i.e., lower density) particle distributions, defined by a simple coarse-graining procedure, which share the same large-scale mass fluctuations. We consider both the case that such coarse-grainings are performed (i) on the initial conditions, and (ii) at a finite time with a specific additional prescription. In numerical simulations we observe that, to a first approximation, these coarse-grainings represent well the evolution of the two-point correlation properties over a significant range of scales. We note, in particular, that the form of the two-point correlation function in the original system, when it is evolving in the asymptotic “self-similar” regime, may be reproduced well in a daughter coarse-grained system in which the dynamics are still dominated by two-body (nearest neighbor) interactions. This provides a simple physical description of the origin of the form of part of the asymptotic nonlinear correlation function. Using analytical results on the early time evolution of these systems, however, we show that small observed differences between the evolved system and its coarse-grainings at the initial time will in fact diverge as the ratio of the coarse-graining scale to the original interparticle distance increases. The second coarse-graining studied, performed at a finite time in a specified manner, circumvents this problem. It also makes it more physically transparent why gravitational dynamics from these initial conditions tends toward a self-similar evolution. We finally discuss the precise definition of a limit in which a continuum (specifically Vlasov-type) description of the observed linear and nonlinear evolution should be applicable. This requires the introduction of an additional intrinsic length scale (e.g., a physical smoothing in the force at small scales), which is kept fixed as the particle density diverges. In this limit the different coarse-grainings are equivalent and leave the evolution of the “mother” system invariant.

We study transition matrices for projected dynamics in the energy-magnetization, magnetization, and energy spaces. Several single-spin-flip dynamics are considered, such as the Glauber and Metropolis canonical ensemble dynamics, and the Metropolis dynamics for three multicanonical ensembles: the flat energy-magnetization, the flat energy, and the flat magnetization histograms. From the numerical diagonalization of the matrices for the projected dynamics we obtain the subdominant eigenvalues and the largest relaxation times for systems of varying size. Although the projected dynamics is an approximation to the full state space dynamics, comparison with some available results, obtained by other authors, shows that projection in the magnetization space is a reasonably accurate method to study the scaling of relaxation times with system size. For each system size, the transition matrices for arbitrary single-spin-flip dynamics are obtained from a single Monte Carlo estimate of the infinite-temperature transition matrix. This makes the method an efficient tool for evaluating the relative performance of any arbitrary local spin-flip dynamics. We also present results for appropriately defined average tunneling times of magnetization and compare their finite-size scaling exponents with results of energy tunneling exponents available for the flat energy histogram multicanonical ensemble.

Nearly thirty years ago, Daoud and de Gennes derived the scaling predictions for the linear polymer chains trapped in a slit with dimension close to the Kuhn length; however, these predictions have yet to be compared with experiments. We have fabricated nanoslits with vertical dimension similar to the Kuhn length of ds-DNA $\left(110\mathrm{nm}\right)$ using standard photolithography techniques. Fluorescently labeled single DNA molecules with contour lengths $L$ ranging from $4\text{to}75\mu \mathrm{m}$ were successfully injected into the slits and the chain molecules undergoing Brownian motions were imaged by fluorescence microscopy. The distributions of the chain radius of gyration and the two-dimensional asphericity were measured. It is found that the DNA molecules exhibit highly anisotropic shape and the mean asphericity is chain length independence. The shape anisotropy of DNA in our measurements is between two and three dimensions (2D and 3D). The static scaling law of the chain extension and the radius of gyration $⟨R_{\parallel }⟩,⟨R_g⟩\sim L^{\nu }$ were observed with ${\nu }_{R\Vert }=0.65\pm 0.02$ and ${\nu }_{\mathrm{Rg}}=0.68\pm 0.05$. These results are close to the average value between two $({\nu }_{R\Vert ,\mathrm{Rg}}=0.75)$ and three $({\nu }_{R\Vert ,\mathrm{Rg}}=0.6)$ -dimensional theoretical value. The scaling of the extensional and rotational relaxation time are between Rouse model in nanoslits and Zimm model in the bulk solution, respectively. We show that the conformation and chain relaxation of DNA confined in a slit close to Kuhn length exhibit the quasi-two-dimensional behavior.

We show that, even when the eigenmodes of an optical cavity are wave chaotic, degenerate eigenfrequencies of those modes split into different frequencies due to the rotation of the cavity. The frequency difference is proportional to the angular velocity, although the splitting eigenmodes are still wave chaotic and do not correspond to any unidirectionally rotating waves.

We study the different coherence resonance (CR) phenomena induced when an excitable FitzHugh-Nagumo-type system is forced using diverse deterministic and/or stochastic time series. The possible implications of this comparative study involving these different CR’s are also discussed. The main result of the present work suggests that for appropriate forcing and system parameters the generated CR curves reflect the correlations of the superimposed time series.

Fermi acceleration of an ensemble of noninteracting particles evolving in a stochastic two-moving wall variant of the Fermi-Ulam model (FUM) and the phase randomized harmonically driven periodic Lorentz gas is investigated. As shown in [A. K. Karlis, P. K. Papachristou, F. K. Diakonos, V. Constantoudis, and P. Schmelcher, Phys. Rev. Lett. 97, 194102 (2006)], the static wall approximation, which ignores scatterer displacement upon collision, leads to a substantial underestimation of the mean energy gain per collision. In this paper, we clarify the mechanism leading to the increased acceleration. Furthermore, the recently introduced hopping wall approximation is generalized for application in the randomized driven Lorentz gas. Utilizing the hopping approximation the asymptotic probability distribution function of the particle velocity is derived. Moreover, it is shown that, for harmonic driving, scatterer displacement upon collision increases the acceleration in both the driven Lorentz gas and the FUM by the same amount. On the other hand, the investigation of a randomized FUM, comprising one fixed and one moving wall driven by a sawtooth force function, reveals that the presence of a particular asymmetry of the driving function leads to an increase of acceleration that is different from that gained when symmetrical force functions are considered, for all finite number of collisions. This fact helps open up the prospect of designing accelerator devices by combining driving laws with specific symmetries to acquire a desired acceleration behavior for the ensemble of particles.

We present a method to compute the smooth part of the density of states in a semiclassical expansion when the Hamiltonian contains a Coulomb potential and non-Cartesian coordinates are appropriate. We apply this method to the case of the hydrogen atom in a magnetic field with fixed $z$ component of the angular momentum. This is then compared with numerical results obtained by a high precision finite element approach. The agreement is excellent, especially in the chaotic region of the spectrum. The need to go beyond the Thomas-Fermi model is clearly established.

We suggest a mechanism by which vorticity structuring and velocity rolls can form in complex fluids, triggered by the linear instability of one-dimensional gradient shear banded flow. We support this with a numerical study of the diffusive Johnson-Segalman model. In the steady vorticity structured state, the thickness of the interface between the bands remains finite in the limit of zero stress diffusivity, presenting a possible challenge to the accepted theory of shear banding.

Surface plasmon excitations and the associated optical transmission properties in perforated metal/dielectric/metal trilayer structures are numerically investigated. Pronounced magnetic modes are observed in the antisymmetric and asymmetric modes of surface plasmon polaritons (SPPs). The influence of substrates on the magnetic response is studied in detail. Quite different from the conventional LC-circuit resonance, these magnetic excitations arise from the nonlocalized SPPs in the perforated layered structure, which may considerably enrich the electromagnetic properties of such metamaterials, especially the artificial magnetism at optical frequency.

It is true that the Knudsen number that characterizes gas flows in microchannels increases to a finite value as the geometric dimension is reduced. However, since the gas in such a flow may retain a small mean free path and a small mean molecular spacing, the gas can still be rather dense in microdevices. Gas flows in microchannels have mainly been studied by molecular dynamics and direct simulation Monte Carlo methods. However, both methods are computationally expensive. In this work, we study dense gas flows in microchannels using an Enskog equation-based lattice Boltzmann Bhatnagar-Gross-Krook model. It is found that a dense gas flowing through a microchannel behaves different than a dilute gas under the same flow conditions.

We study spatiotemporal chaos in the complex Ginzburg-Landau equation in parameter regions of weak amplification and viscosity. Turbulent states involving many solitonlike pulses appear in the parameter range, because the complex Ginzburg-Landau equation is close to the nonlinear Schrödinger equation. We find that the distributions of amplitude and wave number of pulses depend only on the ratio of the two parameters of the amplification and the viscosity. This implies that a one-parameter family of soliton turbulence states characterized by different distributions of the soliton parameters exists continuously around the completely integrable system.

Inference and optimization of real-value edge variables in sparse graphs are studied using the Bethe approximation and replica method of statistical physics. Equilibrium states of general energy functions involving a large set of real edge variables that interact at the network nodes are obtained in various cases. When applied to the representative problem of network resource allocation, efficient distributed algorithms are also devised. Scaling properties with respect to the network connectivity and the resource availability are found, and links to probabilistic Bayesian approximation methods are established. Different cost measures are considered and algorithmic solutions in the various cases are devised and examined numerically. Simulation results are in full agreement with the theory.