We study the long-time behavior of an underdamped Brownian particle moving through a viscous medium and in a systematic potential, when it is subjected to a space-dependent high-frequency periodic force. When the frequency is very large, much larger than all other relevant system-frequencies, there is a Kapitsa time window wherein the effect of frequency-dependent forcing can be replaced by a static effective potential. Our analysis includes the case in which the forcing, in addition to being frequency-dependent, is space-dependent as well. The results of our analysis then lead to additional contributions to the effective potential. These are applied to the numerical calculation of the diffusion coefficient $\left(D\right)$ for a Brownian particle moving in a periodic potential. Presented are numerical results, which are in excellent agreement with theoretical predictions and which indicate a significant enhancement of $D$ due to the space-dependent forcing terms. In addition, we study the transport property (current) of an underdamped Brownian particle in a ratchet potential.

Ion transport through narrow water-filled channels is impeded by a high electrostatic barrier. The latter originates from the large ratio of the dielectric constants of the water and the surrounding media. We show that “doping,” i.e., immobile charges attached to the walls of the channel, substantially reduces the barrier. This explains why most of the biological ion channels are “doped.” We show that at rather generic conditions the channels may undergo ion exchange phase transitions (typically of the first order). Upon such a transition a finite latent concentration of ions may either enter or leave the channel, or be exchanged between the ions of different valences. We discuss possible implications of these transitions for the Ca-vs-Na selectivity of biological Ca channels. We also show that transport of divalent Ca ions is assisted by their fractionalization into two separate excitations.

In this work we extend our earlier Voronoi neighbor analysis [J. Chem. Phys. 123, 074502 (2005)] to homogeneously sheared inelastic hard-particle structures, the simplest model for rapid granular matter. The pair distribution function is partitioned into the $n\mathrm{th}$ neighbor coordination number $\left(C_n\right)$, and the $n\mathrm{th}$ neighbor position distribution $\left[f_n\right(\mathbf{r}\left)\right]$. The distribution of the number of Voronoi faces $\left(P_n\right)$ is also considered since $C_1$ is its mean. We report the $C_n$ and $P_n$ for the homogeneously sheared inelastic hard-disk and hard-sphere structures. These statistics are sensitive to shear ordering transition, the nonequilibrium analogue of the freezing transition. In the near-elastic limit, the sheared fluid statistics approach that of the thermodynamic fluid. On shear ordering, due to the onset of order, the $C_n$ for sheared structures approach that of the thermodynamic solid phase. The suppression of nucleation by the homogeneous shear is evident in these statistics. As inelasticity increases, the shear ordering packing fraction increases. Due to the topological instability of the isotropically perturbed face-centered cubic lattice, polyhedra with faces 12 to 18, with a mean at 14, coexist even in the regular close packed limit for the thermodynamic hard-sphere solid. In shear ordered inelastic hard-sphere structures there is a high incidence of 14-faceted polyhedra and a consequent depletion of polyhedra with faces 12, 13, 15–18, due to the formation of body-centered-tetragonal (bct) structures. These bct structures leave a body-centered-cubic-like signature in the $C_n$ and $P_n$ data. On shear ordering, close-packed layers slide past each other. However, with a velocity-dependent coefficient of restitution, at a critical shear rate these layers get disordered or amorphized. We find that the critical shear rate for amorphization is inversely proportional to the particle diameter, as compared to the inverse square scaling observed in dense colloidal suspensions.

Simulations show that sliding bilayers of colloidal particles can exhibit a phase, the “melt-freeze” phase, where the layers stochastically alternate between solidlike and liquidlike states. We introduce a mean field phenomenological model with two order parameters to understand the interplay of two adjacent layers while the system is in this remarkable phase. Predictions from our numerical simulations of a system in the melt-freeze phase include the tendency of two adjacent layers to be in opposite states (solid and liquid) and the difference between the fluctuation of the order parameter in one layer while the other layer is in the same phase compared to the fluctuation while the other layer is in the opposite phase. We expect this behavior to be seen in future simulations and experiments.

We study a class of quadratic Hamiltonians which describe both fully attractive and partly repulsive molecular interactions, characteristic of biaxial liquid crystal molecules. To treat the partly repulsive interactions we establish a minimax principle for the associated mean-field free energy. We show that the phase diagram described by Sonnet et al. [Phys. Rev. E 67, 061701 (2003)] is universal. Our predictions are in good agreement with the recent observations on both V-shaped and tetrapodal molecules.

Chromatin-remodeling complexes such as SWI/SNF and RSC of yeast can perturb the structure of nucleosomes in an ATP-dependent manner. Experimental results prove that this chromatin remodeling process involves DNA bending. We simulate the effect of DNA bending, caused by chromatin-remodeling complexes, on directional sliding of histone octamers by Brownian dynamics simulation. The simulation results show that, after a DNA loop being generated at the side of a nucleosome, the histone octamer slides towards this DNA loop until the loop disappears. The DNA loop size is an important factor affecting the process of directional sliding of the histone octamer.

We used the transfer-integral method to compute, with an uncertainty smaller than 5%, the six fundamental characteristic exponents of two dynamical models for DNA thermal denaturation and investigate the validity of the scaling laws. Doubts concerning this point arise because the investigated systems (i) have a divergent internal length, (ii) are described by a divergent order parameter, and (iii) are of dimension 1. We found that the assumption that the free energy can be described by a single homogeneous function is robust, despite the divergence of the order parameter, so that Rushbrooke’s and Widom’s identities are valid relations. Josephson’s identity is instead not satisfied. This is probably due to the divergence of the internal length, which invalidates the assumption that the correlation length is solely responsible for singular contributions to thermodynamic quantities. Fisher’s identity is even more wrong. We showed that this is due to the $d=1$ dimensionality and obtained an alternative law, which is well satisfied at DNA thermal denaturation.

Local field potentials (LFPs) are routinely measured experimentally in brain tissue, and exhibit strong low-pass frequency filtering properties, with high frequencies (such as action potentials) being visible only at very short distances $(\approx 10\mathrm{\mu }\mathrm{m})$ from the recording electrode. Understanding this filtering is crucial to relate LFP signals with neuronal activity, but not much is known about the exact mechanisms underlying this low-pass filtering. In this paper, we investigate a possible biophysical mechanism for the low-pass filtering properties of LFPs. We investigate the propagation of electric fields and its frequency dependence close to the current source, i.e., at length scales in the order of average interneuronal distances. We take into account the presence of a high density of cellular membranes around current sources, such as glial cells. By considering them as passive cells, we show that under the influence of the electric source field, they respond by polarization. Because of the finite velocity of ionic charge movements, this polarization will not be instantaneous. Consequently, the induced electric field will be frequency-dependent, and much reduced for high frequencies. Our model establishes that this situation is analogous to an equivalent RC circuit, or better yet a system of coupled RC circuits. We present a number of numerical simulations of an induced electric field for biologically realistic values of parameters, and show the frequency filtering effect as well as the attenuation of extracellular potentials with distance. We suggest that induced electric fields in passive cells surrounding neurons are the physical origin of frequency filtering properties of LFPs. Experimentally testable predictions are provided allowing us to verify the validity of this model.

We introduce vector soliton complexes in nonlocal Kerr-type nonlinear media. We discover that under proper conditions the combination of nonlocality and vectorial coupling has a remarkable stabilizing action on multihumped solitons. In particular, we find that stable bound states featuring several field oscillations in each soliton component do exist. This affords stabilization of vector soliton trains incorporating a large number of humps, a class of structures known to self-destroy via strong instabilities in scalar settings.

We investigate the $O\left(4\right)$ spin model on the simple-cubic lattice by means of the Wolff cluster algorithm. Using the toroidal boundary condition, we locate the bulk critical point at coupling $K_c=0.935856\left(2\right)$, and determine the bulk thermal magnetic renormalization exponents as $y_t=1.3375\left(15\right)$ and $y_h=2.4820\left(2\right)$, respectively. The universal ratio $Q={⟨m^2⟩}^2∕⟨m^4⟩$ is also determined as 0.9142(1). The precision of these estimates significantly improves over that of the existing results. Then, we simulate the critical $O\left(4\right)$ model with two open surfaces on which the coupling strength $K_1$ can be varied. At the ordinary transitions, the surface magnetic exponent is determined as $y_{h1}^{\left(\mathrm{o}\right)}=1.0202\left(12\right)$. Further, we find a so-called special surface transition at $\kappa =K_1∕K-1=1.258\left(20\right)$. At this point, the surface thermal exponent $y_{t1}^{\left(\mathrm{s}\right)}$ is rather close to zero, and we cannot exclude that the corresponding surface transition is Kosterlitz-Thouless-like. The surface magnetic exponent is $y_{h1}^{\left(\mathrm{s}\right)}=1.816\left(2\right)$.

We obtain exact expressions for the two-time autocorrelation and response functions of the $d$-dimensional linear Glauber model. Although this linear model does not obey detailed balance in dimensions $d⩾2$, we show that the usual form of the fluctuation-dissipation ratio still holds in the stationary regime. In the transient regime, we show the occurrence of aging, with a special limit of the fluctuation-dissipation ratio, $X_{\infty }=1∕2$, for a quench at the critical point.

We investigate the influence of confinement on phase separation in colloid-polymer mixtures. To describe the particle interactions, the colloid-polymer model of Asakura and Oosawa [J. Chem. Phys. 22, 1255 (1954)] is used. Grand canonical Monte Carlo simulations are then applied to this model confined between two parallel hard walls, separated by a distance $D=5$ colloid diameters. We focus on the critical regime of the phase separation and look for signs of crossover from three-dimensional (3D) Ising to two-dimensional (2D) Ising universality. To extract the critical behavior, finite size scaling techniques are used, including the recently proposed algorithm of Kim et al. [Phys. Rev. Lett. 91, 065701 (2003)]. Our results point to “effective” critical exponents that differ profoundly from 3D Ising values, and that are already very close to 2D Ising values. In particular, we observe that the critical exponent $\beta$ of the order parameter in the confined system is smaller than in 3D bulk, yielding a “flatter” binodal. Our results also show an increase in the critical colloid packing fraction in the confined system with respect to the bulk. The latter seems consistent with theoretical expectations, although subtleties due to singularities in the critical behavior of the coexistence diameter cannot be ruled out.

We study the fluctuation properties of transition intensities applying a recently proposed generalization of the random matrix theory, which is based on Beck and Cohen’s superstatistics. We obtain an analytic expression for the distribution of the reduced transition probabilities that applies to systems undergoing a transition out of chaos. The obtained distribution fits the results of a previous nuclear shell model calculations for some electromagnetic transitions that deviate from the Porter–Thomas distribution. It agrees with the experimental reduced transition probabilities for the ${}^{26}\mathrm{Al}$ nucleus better than the commonly used ${\chi }^2$ distribution.

In this work we consider the problem of flow turbulence control in a two-dimensional Navier-Stokes equation. We suggest a control strategy which sporadically applies global feedback to a single velocity component of the velocity field. It is found that this control strategy can significantly enhance the control efficiency when the optimal fraction for the control period is suitably chosen, both larger and smaller control time fractions may reduce the control precision. The physical mechanism underlying this interesting and strange behavior is heuristically analyzed, based on mode-mode interactions.

We present a large family of exact solitary wave solutions of the one-dimensional Gross-Pitaevskii equation, with time-varying scattering length and gain or loss, in both expulsive and regular parabolic confinement regimes. The consistency condition governing the soliton profiles is shown to map onto a linear Schrödinger eigenvalue problem, thereby enabling one to find analytically the effect of a wide variety of temporal variations in the control parameters, which are experimentally realizable. Corresponding to each solvable quantum mechanical system, one can identify a soliton configuration. These include soliton trains in close analogy to experimental observations of Strecker et al. [Nature (London) 417, 150 (2002)], spatiotemporal dynamics, solitons undergoing rapid amplification, collapse and revival of condensates, and analytical expression of two-soliton bound states, to name a few.

Formulas are derived to compute the mean number of times a site has been visited during symmetric Levy flights. Unrestricted Levy flights are considered first, for lattices of any dimension: conditions for the existence of finite asymptotic maps of the visits over the lattice are analyzed and a connection is made with the transience of the flight. In particular it is shown that flights on lattices of dimension greater than 1 are always transient. For an interval with absorbing boundaries the mean number of visits reaches stationary values, which are computed by means of numerical and analytical methods; comparisons with Monte Carlo simulations are also presented.

Chaos control by simple limiters is an easy-to-implement and effective method of stabilizing irregular fluctuations. Here we show that applying limiter control to a state variable can significantly shift its mean value. In many situations, this is a countereffective as well as unexpected result, when the aim of control is also to restrict the dynamics. We discuss this effect on the basis of a model of population dynamics and conclude that it can have severe implications for the management of pest species and epidemic spread.

The exact closed forms of the partition functions of a two-dimensional Ising model on square lattices with twisted boundary conditions are given. The constructions of helical tori are unambiguously related to the twisted boundary conditions by virtue of the $SL(2,Z)$ transforms. The numerical analyses on the deviations of the specific-heat peaks away from the bulk critical temperature reveal that the finite-size effect of herical tori is independent of the chirality.

A numerical algorithm is presented in order to determine all coefficients of the Mori-Zwanzig equation from a given finite time series. The algorithm is applicable to observables of arbitrary complex systems. Meteorological and financial systems are investigated. By analyzing directional variables and amplitudes we are able to observe and discuss memory effects on different time scales. We show that analyzing the memory kernel provides important insights into the dynamics of a complex system.