Online auctions have expanded rapidly over the last decade and have become a fascinating new type of business or commercial transaction in this digital era. Here we introduce a master equation for the bidding process that takes place in online auctions. We find that the number of distinct bidders who bid $k$ times up to the $t$th bidding progresses, called the $k$-frequent bidder, seems to scale as $n_k\left(t\right)\sim t{k}^{-2.4}$. The successfully transmitted bidding rate by the $k$-frequent bidder is likely to scale as $q_k\left(t\right)\sim k^{-1.4}$, independent of $t$ for large $t$. This theoretical prediction is close to empirical data. These results imply that bidding at the last moment is a rational and effective strategy to win in an eBay auction.

We study analytically the effect of metrically structured connectivity on the behavior of autoassociative networks. The steady state equations are derived for a generic input-output function, and then we focus on their solutions in the case of networks composed of three alternative simple rate-based model neurons: threshold-linear, binary or smoothly saturating units. For a connectivity which is short range enough the threshold-linear network shows localized retrieval states. The saturating and binary models also exhibit spatially modulated retrieval states if the highest activity level that they can achieve is above the maximum activity of the units in the stored patterns. We show that this saturation level together with the linear gain of the transfer function are important parameters that determine the possibility of localized retrieval. If the ratio of the number of stored patterns to the number of connections per unit goes to zero, while the latter goes to infinity, it is possible to derive an analytical formula for the critical value of the connectivity width, below which one observes spatially nonuniform retrieval states. The formula is also shown to offer a good first approximation for higher storage loads. We show that even in the case of localized retrieval the storage capacity remains proportional to the number of connections per neurons, with the proportionality constant lower by a factor of 3–4 compared to uniform retrieval. The approach that we present here is generic in the sense that there are no specific assumptions on the single unit input-output function nor on the exact connectivity structure.

We perform molecular dynamics and Monte Carlo simulations of two-dimensional melting with dipole-dipole interactions. Both static and dynamic behaviors are examined. In the isotropic liquid phase, the bond orientational correlation length ${\xi }_6$ and susceptibility ${\chi }_6$ are measured, and the data are fitted to the theoretical ansatz. An algebraic decay is detected for both spatial and temporal bond orientational correlation functions in an intermediate temperature regime, and it provides an explicit evidence for the existence of the hexatic phase. From the finite-size scaling analysis of the global bond orientational order parameter, the disclination unbinding temperature $T_i$ is estimated. In addition, from dynamic Monte Carlo simulations of the positional order parameter, we extract the critical exponents at the dislocation unbinding temperature $T_m$. All the results are in agreement with those from experiments and support the Kosterlitz-Thouless-Halperin-Nelson-Young (KTHNY) theory.

We show that a planar medium, locally modeled by a simple one-dimensional excitable system with a piece-wise linear potential, can serve as a minimal model for spatial coherence resonance. Via an analytical treatment of the spatially extended system, we derive the dependence of the resonant wave number on several crucial system parameters, ranging from the diffusion coefficient to the local excursion time of constitutive excitable units. Thus, we provide vital insights into mechanisms that enable the emergence of exclusively noise-induced spatial periodicity in excitable media.

We develop a numerical scheme for solving the time-dependent Kohn-Sham equation in semiconductor heterostructures. Based on the efficient and accurate method recently proposed by Watanabe and Tsukada [Phys. Rev. E 65, 036705 (2002)], an extension is made for treating effective-mass mismatch between different semiconductor materials. A demonstrative calculation shows that the energy of the quantum-well state is accurately conserved during the time-evolution calculation with the present method. Examples under the existence of Hartree and exchange-correlation interactions are also shown as demonstrations of nonlinear electron dynamics in quantum wells. The present method is particularly useful for analyzing nonlinear coherent charge oscillations in semiconductor quantum wells, taking into account many-body effects.

In order to address the selection mechanism that is responsible for the unique lamellar orientation observed in block copolymers under oscillatory shears, we use a constitutive law for the dissipative part of the stress tensor that respects the uniaxial symmetry of a lamellar phase. An interface separating two domains oriented parallel and perpendicular to the shear is shown to be hydrodynamically unstable, a situation analogous to the thin layer instability of stratified fluids under shears. The resulting secondary flows break the degeneracy between the parallel and perpendicular lamellar orientation, leading to a preferred perpendicular orientation in certain ranges of parameters of the polymer and of the shear.

In this work, using molecular dynamics simulation, the viscosity (dynamic property) and the pressure (static property) of spherical fluid particles interacting through Lennard-Jones $\alpha$-6 and exponential $\alpha$-6 potentials are computed. Simulations are performed for $\alpha$ going from 10 to 20 for the Lennard-Jones potential and from 12 to 22 for the exponential one. Six different thermodynamic states are tested that cover a large range of conditions, from sub- to supercritical temperature and from low to high density. To compare in a consistent manner the results for the various potentials tested, the simulations are carried out for the same set of reduced thermodynamic conditions (using the critical point). It is found that a perfect corresponding-states formulation is not possible between these potentials. Then, these potentials are applied on real simple fluids (argon, oxygen, nitrogen, methane, ethane, and one mixture, air) and the calculated viscosity and pressure values are compared with reference values. It appears that, using the appropriate $\alpha$, both potential families lead to a good accuracy in pressure and viscosity using the same set of molecular parameters for both properties, the average absolute deviations being always lower than 5% for the studied states. In addition, it is shown that the exponential potential results do not outperform the Lennard-Jones ones. Furthermore, for all compounds except for methane, the best results are obtained for the Lennard-Jones 12-6 and the exponential 14-6 potentials. This result partly explains why, despite no theoretical background, the Lennard-Jones 12-6 potential is so widely used. Finally, it is shown that a van der Waals one-fluid model performs extremely well for the studied mixture (air).

We simulate a model of repulsively interacting colloids on a commensurate two-dimensional triangular pinning substrate where the amount of heterogeneous motion that appears at melting can be controlled systematically by turning off a fraction of the pinning sites. We correlate the amount of heterogeneous motion with the average topological defect number, time-dependent defect fluctuations, colloid diffusion, and the form of the van Hove correlation function. When the pinning sites are all off or all on, the melting occurs in a single step. When a fraction of the sites are turned off, the melting becomes considerably broadened and signatures of a two-step melting process appear. The noise power associated with fluctuations in the number of topological defects reaches a maximum when half of the pinning sites are removed and the noise spectrum has a pronounced $1∕f^{\alpha }$ structure in the heterogeneous regime. We find that regions of high mobility are associated with regions of high dislocation densities.

The Brownian motions of microscopic particles in viscous or viscoelastic fluids can be used to measure rheological properties. This is the basis of recently developed one- and two-particle microrheology techniques. For increased temporal and spatial resolution, some microrheology techniques employ optical traps, which introduce additional forces on the particles. We have systematically studied the effect that confinement of particles by optical traps has on their auto- and cross-correlated fluctuations. We show that trapping causes anticorrelations in the motion of two particles at low frequencies. We demonstrate how these anticorrelations depend on trap strength and the shear modulus of viscoelastic media. We present a method to account for the effects of optical traps, which permits the quantitative measurement of viscoelastic properties in one- and two-particle microrheology over an extended frequency range in a variety of viscous and viscoelastic media.

Three-dimensional phase coarsening at various volume fractions is simulated by employing multiparticle diffusion methods. The dynamic process of phase coarsening is visualized through a three-dimensional movie. The present study also characterizes interparticle spacings in polydispersed particle systems and clarifies the controversial mathematical expressions for interparticle spacings used in the literature for 30 years. Consequently, this study reveals spatial, temporal, and nearest-neighbor correlations in polydispersed particle systems. A new three-dimensional movie of a Voronoi network demonstrating these correlations is provided. Our simulation and experiments show that growth rates of individual particles deviate from those of the mean-field theory, which is caused by their differing local environments. Multiplicative noise provides a good basis to describe the stochastic nature of fluctuations during phase coarsening.

Because electrostatic forces are crucial in biological systems, molecular dynamics simulations of biological systems require a method of computing electrostatic forces that is accurate and rapid. We propose a surface charge method, apply it to a system of arbitrary number of charged dielectric spheres, and obtain an exact solution for an arbitrary configuration of the spheres. The precision depends only on the number of terms kept in a series expansion and can therefore be controlled at will. It appears that the first few terms are usually adequate. The exact result exhibits a phenomenon that we call asymmetric screening. Namely, the magnitude of attractive interactions is decreased (relative to point charges in an infinite solvent) while the magnitude of repulsive interactions is increased (again, relative to point charges in an infinite solvent). This effect might aid in the adoption of correct conformations and in intermolecular recognition. Evaluation of the energy involves only matrix inversion. The surface charge method can be transformed easily to a numerical method for use with arbitrary surfaces. With modest additions, the model also describes an electrorheological fluid. Such a system provides the cleanest opportunity to apply the model.

An approach to protein design is proposed based on the relative entropy and a reduced amino acid alphabet. In this approach, the relative entropy is used as a minimization object function. The method has been tested on a real protein’s off-lattice model successfully, and the results are similar to those obtained from other design studies. It can be applied as a uniform frame for both folding and inverse folding of protein. An iterative calculation method of the ensemble average of the contact strength is proposed at the same time.

We study the effects of the environment on tunneling in an open system described by a static double-well potential. We describe the evolution of a quantum state localized in one of the minima of the potential at $t=0$, in both the limits of high and zero environment temperature. We show that the evolution of the system can be summarized in terms of three main physical phenomena—namely, decoherence, quantum tunneling, and noise-induced activation—and we obtain analytical estimates for the corresponding time scales. These analytical predictions are confirmed by large-scale numerical simulations, providing a detailed picture of the main stages of the evolution and of the relevant dynamical processes.

We examine the quantum dynamics of cold atoms subjected to pairs of closely spaced $\delta$ kicks from standing waves of light and find behavior quite unlike the well-studied quantum kicked rotor (QKR). We show that the quantum phase space has a periodic, cellular structure arising from a unitary matrix with oscillating bandwidth. The corresponding eigenstates are exponentially localized, but scale with a fractional power $L\sim {\hslash }^{-0.75}$, in contrast to the QKR for which $L\sim {\hslash }^{-1}$. The effect of intercell (and intracell) transport is investigated by studying the spectral fluctuations with both periodic as well as “open” boundary conditions.

Pomeau-Manneville intermittency in nonstationary systems is investigated. If one of the parameters characterizing a dynamical system is changed periodically, periodic orbits may appear even when the value of this parameter remains in a range which, in the stationary case, yields chaotic behavior. This property may be used for the control of systems exhibiting intermittency. If the parameter change is not large enough, a periodic orbit does not appear but the distribution of the laminar phases is modified. In the case of type I intermittency, this means a broadening of such a distribution or, alternatively, a splitting of its right peak. We present a theory of these phenomena. Numerical simulations both for one-dimensional maps and for flows support our predictions. Some of the phenomena discussed here were observed earlier in time series of heart rate variability.

This paper is motivated by giving the detailed proofs and some interesting remarks on the results the author obtained in a series of papers [Phys. Rev. Lett. 93, 214101 (2004); Phys. Rev. E 71, 037203 (2005); 69, 067201 (2004)], where an adaptive-feedback algorithm was proposed to effectively stabilize and synchronize chaotic systems. This note proves in detail the strictness of this algorithm from the viewpoint of mathematics, and gives some interesting remarks for its potential applications to chaos control $\&$ synchronization. In addition, a significant comment on synchronization-based parameter estimation is given, which shows some techniques proposed in literature less strict and ineffective in some cases.

Above-threshold ionization (ATI) ionization by linearly polarized light has been proposed by several authors as a means of driving recombination lasers in the soft x-ray spectral region. The pump radiation generates a cold electron plasma with ions in a single ionization stage, which is an ideal starting condition for strong recombination. Population inversions form during the recombination cascade to the ground state of the next ionization stage. In the absence of any relaxation the electron distribution is strongly peaked near zero energy. However, a number of different processes all heat the cold electrons towards Maxwellian, and may thereby reduce the recombination rate in the higher levels. Using numerical models we investigate these relaxation processes and their effect on recombination. We show that the recombination can be well described by the standard cascade model, provided an appropriate temperature is used. We examine two cases in detail, hydrogen-like lithium where the inversion is with respect to the ground state, and lithium-like nitrogen where it is with the first excited state. The two cases differ markedly in the degree of relaxation achieved, and in the duration of the population inversion.

Superluminal group velocities, defined as group velocities exceeding the speed of light in vacuum, $c$, have been theoretically predicted and experimentally observed in various types of dispersive media, such as passive and active Lorentzian media, one-dimensional photonic crystals, and undersized waveguides. Though superluminal group velocities have been found in these media, it has been suggested that the pulse “front” and associated transient field oscillations, known as the precursors or forerunners, will never travel faster than $c$, and hence relativistic causality is always preserved. Until now, few rigorous studies of these transient fields in structures exhibiting superluminal group velocities have been performed. In this paper, we present the dynamic evolution of these earliest field oscillations in one-dimensional photonic crystals (1DPC), using finite-difference time-domain (FDTD) techniques in conjunction with joint time-frequency analysis (JTFA). Our study clearly shows that the precursor fields associated with superluminal pulse propagation travel at subluminal speeds, and thus, the arrival of these precursor fields must be associated with the arrival of “genuine information.” Our study demonstrates the expected result that abnormal group velocities do not contradict Einstein causality. This work also shows that FDTD analysis and JTFA can be combined to study the dynamic evolution of the transient and steady state pulse propagation in dispersive media.

We discuss the existence and stability of two-dimensional solitons in media with spatially nonlocal nonlinear response. We show that such systems, which include thermal nonlinearity and dipolar Bose-Einstein condensates, may support a variety of stationary localized structures, including rotating dipole solitons. We also demonstrate that the stability of these structures critically depends on the spatial profile of the nonlocal response function.

Using the generalized coherent-potential-approximation approach, we present the dispersion relation of the two-dimensional dispersed random media. In the intermediate-frequency regime, two acoustic modes are found in colloidal suspensions including cylindrical plastic rod in water background. The scattering cross section offers a good explanation for the two modes and the observed frequency gaps in the excitation spectra.