We present a further development of an inhomogeneous scaled particle theory (I-SPT) for hard particle fluids confined by hard walls, such that the reversible work of cavity insertion can now be determined for all cavities that intersect one of the walls. Building upon a previous version of I-SPT [D. W. Siderius and D. S. Corti, Phys. Rev. E, 71, 036141 (2005)], a new function, $\overline{F}$, is introduced, which is proportional to the net force on the surface of the cavity in the direction normal to the wall. The reversible work of cavity insertion is then determined by an integral over the force required to “push” the cavity of fixed size into the fluid starting from a position behind the wall. An exact relation for $\overline{F}$ at certain cavity locations and radii is derived and an accurate interpolation scheme is proposed for the computation of $\overline{F}$ beyond these exact limits. The chosen interpolation incorporates a large number of exact and nearly exact conditions, several of which follow from the surface thermodynamics of macroscopic cavities. Work predictions using $\overline{F}$ are highly accurate as compared to simulation results at low to moderate fluid densities. Good agreement still persists at densities near the hard-sphere freezing transition. The interpolation of $\overline{F}$ is also used to estimate the depletion force between a hard sphere solute and the wall. The I-SPT entropic force predictions are in good agreement with simulation results presented in the literature. Due to its reliance upon physical and geometric arguments, I-SPT provides important insights into the origin of various depletion effects such as how the interplay between geometry and the varying local density at the cavity surface gives rise to the appearance of multiple attractive regions at intermediate solute sizes and a universal repulsive region, both within solute to wall separations that are less than the diameter of a solvent particle. Finally, all of the scaled particle theory-based methods presented here can, in principle, be extended to describe hard particle fluids confined by nonplanar surfaces, thereby providing estimates of the depletion force between a solute and a variety of surfaces of interest.

A random fiber bundle model with a mixed Weibull distribution is studied under the global load sharing scheme. The mixed model consists of two sets of fibers. The threshold strength of one set of fibers is randomly chosen from a Weibull distribution with a particular Weibull index, and another set of fibers with a different index. The mixing tunes the critical stress of the bundle and the variation of critical stress with the amount of mixing is determined using a probabilistic method where the external load is increased quasistatically. In a special case which we illustrate, the critical stress is found to vary linearly with the mixing parameter. The critical exponents and power-law behavior of burst avalanche size distribution is found to remain unaltered due to mixing.

We develop a series of molecular dynamics computer simulations of liquid water, performed with a polarizable potential model, to calculate the spinodal line and the curve of maximum density inside the metastable supercooled region. After analyzing the structural properties, the liquid spinodal line is followed down to $T=210\mathrm{K}$. A monotonic decrease is found in the explored region. The curve of maximum density bends on approaching the spinodal line. These results, in agreement with similar studies on nonpolarizable models of water, are consistent with the existence of a second critical point for water.

This work investigates phase separation of a monodisperse gas of inelastically colliding hard disks confined in a two-dimensional annulus, the inner circle of which represents a “thermal wall.” When described by granular hydrodynamic equations, the basic steady state of this system is an azimuthally symmetric state of increased particle density at the exterior circle of the annulus. When the inelastic energy loss is sufficiently large, hydrodynamics predicts spontaneous symmetry breaking of the annular state, analogous to the van der Waals–like phase separation phenomenon previously found in a driven granular gas in rectangular geometry. At a fixed aspect ratio of the annulus, the phase separation involves a “spinodal interval" of particle area fractions, where the gas has negative compressibility in the azimuthal direction. The heat conduction in the azimuthal direction tends to suppress the instability, as corroborated by a marginal stability analysis of the basic steady state with respect to small perturbations. To test and complement our theoretical predictions we performed event-driven molecular dynamics (MD) simulations of this system. We clearly identify the transition to phase separated states in the MD simulations, despite large fluctuations present, by measuring the probability distribution of the amplitude of the fundamental Fourier mode of the azimuthal spectrum of the particle density. We find that the instability region, predicted from hydrodynamics, is always located within the phase separation region observed in the MD simulations. This implies the presence of a binodal (coexistence) region, where the annular state is metastable. The phase separation persists when the driving and elastic walls are interchanged, and also when the elastic wall is replaced by weakly inelastic one.

We study the topological configurations and dynamics of individual point defect vacancies and interstitials in a two-dimensional crystal of colloids interacting via a repulsive Yukawa potential. Our Brownian dynamics simulations show that the diffusion mechanism for vacancy defects occurs in two phases. The defect can glide along the crystal lattice directions, and it can rotate during an excited topological transition configuration to assume a different direction for the next period of gliding. The results for the vacancy defects are in good agreement with recent experiments. For interstitial point defects, which were not studied in the experiments, we find several of the same modes of motion as in the vacancy defect case along with two additional diffusion pathways. The interstitial defects are more mobile than the vacancy defects due to the more two-dimensional nature of the diffusion of the interstitial defects.

The integrate-and-fire (IF) neuron model and the piecewise-linear version of FitzHugh-Nagumo (PL) neuron model with a time scale parameter $\mu$ are frequently being used in the study of synchronization phenomena. Although the two models are regarded to be different type, we show a certain equivalence between them by deriving the coupled IF model of an improved version with a firing duration from the recovery variable coupled system of the PL model, under taking the limit of $\mu \to 0$ without a loss of any coupling properties. In the coupled IF model with the duration time, the synchronization behavior of a pair of neurons with excitatory or inhibitory synaptic coupling can be systematically explored in terms of three parameters in the model (synaptic strength, decaying relaxation rate of the synaptic coupling, and the parameter exhibiting the firing duration). We find some irregularly synchronous behavior with or without constant firing order alternations. We show that the duration of an impulse plays an important role in synchronization phenomena.

Sequence retrieval has a fundamental importance in information processing by the brain, and has extensively been studied in neural network models. Most of the previous sequential associative memory embedded sequences of memory patterns have nearly equal sizes. It was recently shown that local cortical networks display many diverse yet repeatable precise temporal sequences of neuronal activities, termed “neuronal avalanches.” Interestingly, these avalanches displayed size and lifetime distributions that obey power laws. Inspired by these experimental findings, here we consider an associative memory model of binary neurons that stores sequences of memory patterns with highly variable sizes. Our analysis includes the case where the statistics of these size variations obey the above-mentioned power laws. We study the retrieval dynamics of such memory systems by analytically deriving the equations that govern the time evolution of macroscopic order parameters. We calculate the critical sequence length beyond which the network cannot retrieve memory sequences correctly. As an application of the analysis, we show how the present variability in sequential memory patterns degrades the power-law lifetime distribution of retrieved neural activities.

Efficiency of time evolution of quantum observables, and thermal states of quenched Hamiltonians, is studied using time-dependent density-matrix renormalization group method in a family of generic quantum spin chains which undergo a transition from integrable to nonintegrable-quantum chaotic case as control parameters are varied. Quantum states (observables) are represented in terms of matrix-product operators with rank $D_{ϵ}\left(t\right)$, such that evolution of a long chain is accurate within fidelity error $ϵ$ up to time $t$. We found that the rank generally increases exponentially $D_{ϵ}\left(t\right)\propto \exp \left(\mathrm{const}t\right)$, unless the model system was integrable in which case we found polynomial increase.

Three-dimensional gridless particle simulations of proton acceleration via irradiation of a very thin foil by a short-pulse, high-intensity laser have been performed to evaluate recently proposed microstructured target configurations. It is found that a pure proton microdot target does not by itself result in a quasimonoenergetic proton beam. Such a beam can only be produced with a very lightly doped target, in qualitative agreement with one-dimensional theory. The simulations suggest that beam quality in current experiments could be dramatically improved by choosing microdot compositions with a 5–10 times lower proton fraction.

Most real complex networks—such as protein interactions, social contacts, and the Internet—are only partially known and available to us. While the process of exploring such networks in many cases resembles a random walk, it becomes a key issue to investigate and characterize how effectively the nodes and edges of such networks can be covered by different strategies. At the same time, it is critically important to infer how well can topological measurements such as the average node degree and average clustering coefficient be estimated during such network explorations. The present article addresses these problems by considering random, Barabási-Albert (BA), and geographical network models with varying connectivity explored by three types of random walks: traditional, preferential to untracked edges, and preferential to unvisited nodes. A series of relevant results are obtained, including the fact that networks of the three studied models with the same size and average node degree allow similar node and edge coverage efficiency, the identification of linear scaling with the size of the network of the random walk step at which a given percentage of the nodes/edges is covered, and the critical result that the estimation of the averaged node degree and clustering coefficient by random walks on BA networks often leads to heavily biased results. Many are the theoretical and practical implications of such results.

Dynamics with a threshold input-output relation commonly exist in gene, signal-transduction, and neural networks. Coupled dynamical systems of such threshold elements are investigated, in an effort to find differentiation of elements induced by the interaction. Through global diffusive coupling, novel states are found to be generated that are not the original attractor of single-element threshold dynamics, but are sustained through the interaction with the elements located at the original attractor. This stabilization of the novel state(s) is not related to symmetry breaking, but is explained as the truncation of transient trajectories to the original attractor due to the coupling. Single-element dynamics with winding transient trajectories located at a low-dimensional manifold and having turning points are shown to be essential to the generation of such novel state(s) in a coupled system. The universality of this mechanism for the novel state generation and its relevance to biological cell differentiation are briefly discussed.

European options on coupon bonds are studied in a quantum field theory model of forward interest rates. Swaptions are briefly reviewed. An approximation scheme for the coupon bond option price is developed based on the fact that the volatility of the forward interest rates is a small quantity. The field theory for the forward interest rates is Gaussian, but when the payoff function for the coupon bond option is included it makes the field theory nonlocal and nonlinear. A perturbation expansion using Feynman diagrams gives a closed form approximation for the price of coupon bond option. A special case of the approximate bond option is shown to yield the industry standard one-factor HJM formula with exponential volatility.

The quantum finance pricing formulas for coupon bond options and swaptions derived by Baaquie [Phys. Rev. E 75, 016703 (2006)] are reviewed. We empirically study the swaption market and propose an efficient computational procedure for analyzing the data. Empirical results of the swaption price, volatility, and swaption correlation are compared with the predictions of quantum finance. The quantum finance model generates the market swaption price to over 90% accuracy.

We extend the Monte Carlo methods developed in our previous papers [J. Phys. A 37, 1573 (2004); Macromol. Theory-Simul. 14, 491 (2005)] and based on entropic sampling within the Wang-Landau algorithm to simulation of a lattice model of flexible polyelectrolytes. We consider a strongly charged polyelectrolyte chain accompanied by neutralizing counterions on a simple cubic lattice with periodic boundary conditions. The Coulomb potential and the excluded volume condition between different ions or beads are taken into account. The obtained energy distributions make possible the calculation of canonical properties such as conformational energy, heat capacity, entropy, free energy, and mean-square end-to-end distance over a wide temperature range in a single simulation.

We investigate the synchronization transition of the modified Kuramoto model where the oscillators form a scale-free network with degree exponent $\lambda$. An oscillator of degree $k_i$ is coupled to its neighboring oscillators with asymmetric and degree-dependent coupling in the form of $J{k}_i^{\eta -1}$. By invoking the mean-field approach, we find eight different synchronization transition behaviors depending on the values of $\eta$ and $\lambda$, and derive the critical exponents associated with the order parameter and the finite-size scaling in each case. The synchronization transition point $J_c$ is determined as being zero (finite) when $\eta >\lambda -2$ $(\eta <\lambda -2)$. The synchronization transition is also studied from the perspective of cluster formation of synchronized vertices. The cluster-size distribution and the largest cluster size as a function of the system size are derived for each case using the generating function technique. Our analytic results are confirmed by numerical simulations.

The fluctuation-dissipation relation is well known for a quantum open system with energy dissipation. In this paper a similar underlying relation is found between the bath fluctuation and the dephasing of the quantum open system, for which energy is conserved, but the information is leaking into the bath. To obtain this relation we revisit the universal, but simple dephasing model with a quantum nondemolition interaction between the bath and the open system. Then we show that the decoherence factor describing the dephasing process is factorized into two parts, to indicate the two sources of dephasing, the vacuum quantum fluctuation, and the thermal excitations defined in the initial state of finite temperature.

Finite-size scaling (FSS) of the five-dimensional $(d=5)$ Ising model is investigated numerically. Because of the hyperscaling violation in $d>4$, FSS of the $d=5$ Ising model no longer obeys the conventional scaling relation. Rather, it is expected that the FSS behavior depends on the geometry of the embedding space (boundary condition). In this paper, we consider a cylindrical geometry and explore its influence on the correlation length $\xi =L^{\Omega }f(ϵL^{y_t^{*}},H{L}^{y_h^{*}})$ with system size $L$, reduced temperature $ϵ$, and magnetic field $H$; the indices $y_{t,h}^{*}$ and $\Omega$ characterize FSS. For that purpose, we employed the transfer-matrix method with Novotny’s technique, which enables us to treat an arbitrary (integral) number of spins, $N=8,10,\dots ,28$; note that, conventionally, $N$ is restricted in $N(=L^{d-1})=16,81,256,\dots$. As a result, we estimate the scaling indices as $\Omega =1.40\left(15\right)$, $y_t^{*}=2.8\left(2\right)$, and $y_h^{*}=4.3\left(1\right)$. Additionally, postulating $\Omega =4∕3$, we arrive at $y_t^{*}=2.67\left(10\right)$ and $y_h^{*}=4.0\left(2\right)$. These indices differ from the naively expected ones $\Omega =1$, $y_t^{*}=2$ and $y_h^{*}=3$. Rather, our data support the generic formulas $\Omega =(d-1)∕3$, $y_t^{*}=2(d-1)∕3$, and $y_h^{*}=d-1$, advocated for a cylindrical geometry in $d⩾4$.

Inverse melting is the phenomenon, observed in both helium isotopes, by which a crystal melts when cooled at constant pressure. I investigate discrete-space analogs of inverse melting by means of two instances of a triangular-lattice-gas system endowed with a soft-core repulsion and a short-ranged attraction. To reconstruct the phase diagram, I use both transfer-matrix and Monte Carlo methods, as well as low-temperature series expansions. In one case, a phase behavior reminiscent of helium emerges, with a loose-packed phase (which is solidlike for low temperatures and liquidlike for high temperatures) extending down to zero temperature for low pressures and the possibility of melting the close-packed solid by isobaric cooling. At variance with previous model studies of inverse melting, the driving mechanism of the present phenomenon is mainly geometrical, related to the larger free-energy cost of a “vacancy” in the loose-packed solid than in the close-packed one.