We investigate the long time dynamics of a strong glass former, SiO${}_2$, below the glass transition temperature by averaging single-particle trajectories over time windows which comprise roughly 100 particle oscillations. The structure on this coarse-grained time scale is very well defined in terms of coordination numbers, allowing us to identify ill-coordinated atoms, which are called defects in the following. The most numerous defects are O-O neighbors, whose lifetimes are comparable to the equilibration time at low temperature. On the other hand, SiO and OSi defects are very rare and short lived. The lifetime of defects is found to be strongly temperature dependent, consistent with activated processes. Single-particle jumps give rise to local structural rearrangements. We show that in SiO${}_2$ these structural rearrangements are coupled to the creation or annihilation of defects, giving rise to very strong correlations of jumping atoms and defects.

We present an alternative finite-size approach to a set of parity-conserving interfaces involving attachment, dissociation, and detachment of extended objects in 1+1 dimensions. With the aid of a nonlocal construct introduced by Barma and Dhar in related systems [Phys. Rev. Lett. 73, 2135 (1994)], we circumvent the subdiffusive dynamics and examine close-to-equilibrium aspects of these interfaces by assembling states of much smaller, numerically accessible scales. As a result, roughening exponents, height correlations, and width distributions exhibiting universal scaling functions are evaluated for interfaces virtually grown out of dimers and trimers on large-scale substrates. Dynamic exponents are also studied by finite-size scaling of the spectrum gaps of evolution operators.

In the present article, we introduce a phase-field model for thin-film growth with anisotropic step energy, attachment kinetics, and diffusion, with second-order (thin-interface) corrections. We are mainly interested in the limit in which kinetic anisotropy dominates, and hence we study how the expected shape of a crystallite, which in the long-time limit is the kinetic Wulff shape, is modified by anisotropic diffusion. We present results that prove that anisotropic diffusion plays an important, counterintuitive role in the evolving crystal shape, and we add second-order corrections to the model that provide a significant increase in accuracy for small supersaturations. We also study the effect of different crystal symmetries and discuss the influence of the deposition rate.

Chromatin inside the cell nucleus consists of the DNA and its hierarchy of interacting molecules, which can be modeled as a complex polymer. To describe the chromatin dynamic, we develop and analyze here a polymer model that accounts for long-range interactions and not just those between the closest neighbors as in the Rouse polymer model. Our construction of the polymer model allows us to recover the local interaction between monomers from the anomalous diffusion exponent, which can be directly measured experimentally. We compute asymptotically for this polymer model the cross-correlation function for a given monomer and the mean time for a loop to be formed. Finally, we discuss some possible applications for interpretation of chromosome capture data.

We investigate the mechanism of the phenomenon called the “faster-is-slower”effect in pedestrian flow studies analytically with a simplified phenomenological model. It is well known that the flow rate is maximized at a certain strength of the driving force in simulations using the social force model when we consider the discharge of self-driven particles through a bottleneck. In this study, we propose a phenomenological and analytical model based on a mechanics-based modeling to reveal the mechanism of the phenomenon. We show that our reduced system, with only a few degrees of freedom, still has similar properties to the original many-particle system and that the effect comes from the competition between the driving force and the nonlinear friction from the model. Moreover, we predict the parameter dependences on the effect from our model qualitatively, and they are confirmed numerically by using the social force model.

Three-dimensional excitation vortices exist in systems such as chemical reactions and the human heart. Their one-dimensional rotation backbone can pin to unexcitable heterogeneities, which greatly affect the structure, dynamics, and lifetime of the vortex. In experiments with the Belousov-Zhabotinsky reaction, we demonstrate vortex unpinning from a pair of inert and impermeable spheres using externally applied electric fields. Unpinning occurs abruptly but is preceded by a slow reorientation and deformation of the initially circular vortex loop. Our experimental findings are reproduced by numerical simulations of an excitable reaction-diffusion-advection model.

Long-lasting exponential quantum spreading was recently found in a simple but very rich dynamical model, namely, an on-resonance double-kicked rotor model [J. Wang, I. Guarneri, G. Casati, and J. B. Gong, Phys. Rev. Lett. 107, 234104 (2011)]. The underlying mechanism, unrelated to the chaotic motion in the classical limit but resting on quasi-integrable motion in a pseudoclassical limit, is identified for one special case. By presenting a detailed study of the same model, this work offers a framework to explain long-lasting exponential quantum spreading under much more general conditions. In particular, we adopt the so-called “spinor” representation to treat the kicked-rotor dynamics under high-order resonance conditions and then exploit the Born-Oppenheimer approximation to understand the dynamical evolution. It is found that the existence of a flat band (or an effectively flat band) is one important feature behind why and how the exponential dynamics emerges. It is also found that a quantitative prediction of the exponential spreading rate based on an interesting and simple pseudoclassical map may be inaccurate. In addition to general interests regarding the question of how exponential behavior in quantum systems may persist for a long time scale, our results should motivate further studies toward a better understanding of high-order resonance behavior in $\delta$-kicked quantum systems.

Recent studies have established that, in addition to the well-known kicked-Harper model (KHM), an on-resonance double-kicked rotor (ORDKR) model also has Hofstadter's butterfly Floquet spectrum, with strong resemblance to the standard Hofstadter spectrum that is a paradigm in studies of the integer quantum Hall effect. Earlier it was shown that the quasienergy spectra of these two dynamical models (i) can exactly overlap with each other if an effective Planck constant takes irrational multiples of $2\pi$ and (ii) will be different if the same parameter takes rational multiples of $2\pi$. This work makes detailed comparisons between these two models, with an effective Planck constant given by $2\pi M/N$, where $M$ and $N$ are coprime and odd integers. It is found that the ORDKR spectrum (with two periodic kicking sequences having the same kick strength) has one flat band and $N-1$ nonflat bands with the largest bandwidth decaying in a power law as $\sim K^{N+2}$, where $K$ is a kick strength parameter. The existence of a flat band is strictly proven and the power-law scaling, numerically checked for a number of cases, is also analytically proven for a three-band case. By contrast, the KHM does not have any flat band and its bandwidths scale linearly with $K$. This is shown to result in dramatic differences in dynamical behavior, such as transient (but extremely long) dynamical localization in ORDKR, which is absent in the KHM. Finally, we show that despite these differences, there exist simple extensions of the KHM and ORDKR model (upon introducing an additional periodic phase parameter) such that the resulting extended KHM and ORDKR model are actually topologically equivalent, i.e., they yield exactly the same Floquet-band Chern numbers and display topological phase transitions at the same kick strengths. A theoretical derivation of this topological equivalence is provided. These results are also of interest to our current understanding of quantum-classical correspondence considering that the KHM and ORDKR model have exactly the same classical limit after a simple canonical transformation.

In this Rapid Communication we show that the interplay between the deformation geometric-nonlinearity and distributions of external charges and dipoles lead to the renormalization of the membrane's native flexoelectric response. Our work provides a framework for a mesoscopic interpretation of flexoelectricity and if necessary, artificially “design” tailored flexoelectricity in membranes. Comparisons with experiments indicate reasonable quantitative agreement.

We studied the transport process of overdamped Brownian particles, in a chain of asymmetric cavities, interacting through a hard-core potential. When a force is applied in opposite directions a difference in the drift velocity of the particles inside the cavity can be observed. Previous works on similar systems deal with the low-concentration regime, in which the interaction is irrelevant. In this case it was found that large particles show a stronger asymmetry in the drift velocity when a small force is applied, allowing for the separation of different size particles [Reguera et al., Phys. Rev. Lett. 108, 020604 (2012)]. We found that when the interaction between particles is considered, the behavior of the system is substantially different. For example, as concentration is increased, the small particles are the ones that show a stronger asymmetry. For the case where all the particles in the system are of the same size we took advantage of the particle-vacancy analogy to predict that the left and right currents are almost equal in a region around the concentration $0.5$ despite the asymmetry of the cavity.

We consider a long-range interacting system of $N$ particles moving on a spherical surface under an attractive Heisenberg-like interaction of infinite range and evolving under deterministic Hamilton dynamics. The system may also be viewed as one of globally coupled Heisenberg spins. In equilibrium, the system has a continuous phase transition from a low-energy magnetized phase, in which the particles are clustered on the spherical surface, to a high-energy homogeneous phase. The dynamical behavior of the model is studied analytically by analyzing the Vlasov equation for the evolution of the single-particle distribution and numerically by direct simulations. The model is found to exhibit long-lived nonmagnetized quasistationary states (QSSs) which in the thermodynamic limit are dynamically stable within an energy range where the equilibrium state is magnetized. For finite $N$, these states relax to equilibrium over a time that increases algebraically with $N$. In the dynamically unstable regime, nonmagnetized states relax fast to equilibrium over a time that scales as $\ln N$. These features are retained in presence of a global anisotropy in the magnetization.

We study the phase transition behavior of a frustrated Heisenberg model on a stacked triangular lattice by Monte Carlo simulations. The model has three types of interactions: the ferromagnetic nearest-neighbor interaction $J_1$ and antiferromagnetic third nearest-neighbor interaction $J_3$ in each triangular layer and the ferromagnetic interlayer interaction $J_{\perp }$. Frustration comes from the intralayer interactions $J_1$ and $J_3$. We focus on the case that the order parameter space is SO(3)$\times C_3$. We find that the model exhibits a first-order phase transition with breaking of the SO(3) and $C_3$ symmetries at finite temperature. We also discover that the transition temperature increases but the latent heat decreases as $J_{\perp }/J_1$ increases, which is opposite to the behavior observed in typical unfrustrated three-dimensional systems.

We present exact, analytic results for the mean time to trapping of a random walker on the class of deterministic Sierpinski graphs embedded in $d\ge 2$ Euclidean dimensions, when both nearest-neighbor (NN) and next-nearest-neighbor (NNN) jumps are included. Mean first-passage times are shown to be modified significantly as a consequence of the fact that NNN transitions connect fractals of two consecutive generations.

The recent idea of logical stochastic resonance is verified in synthetic gene networks induced by non-Gaussian noise. We realize the switching between two kinds of logic gates under optimal moderate noise intensity by varying two different tunable parameters in a single gene network. Furthermore, in order to obtain more logic operations, thus providing additional information processing capacity, we obtain in a two-dimensional toggle switch model two complementary logic gates and realize the transformation between two logic gates via the methods of changing different parameters. These simulated results contribute to improve the computational power and functionality of the networks.

Neuronal membrane potentials fluctuate stochastically due to conductance changes caused by random transitions between the open and closed states of ion channels. Although it has previously been shown that channel noise can nontrivially affect neuronal dynamics, it is unknown whether ion-channel noise is strong enough to act as a noise source for hypothesized noise-enhanced information processing in real neuronal systems, i.e., “stochastic facilitation”. Here we demonstrate that biophysical models of channel noise can give rise to two kinds of recently discovered stochastic facilitation effects in a Hodgkin-Huxley-like model of auditory brainstem neurons. The first, known as slope-based stochastic resonance (SBSR), enables phasic neurons to emit action potentials that can encode the slope of inputs that vary slowly relative to key time constants in the model. The second, known as inverse stochastic resonance (ISR), occurs in tonically firing neurons when small levels of noise inhibit tonic firing and replace it with burstlike dynamics. Consistent with previous work, we conclude that channel noise can provide significant variability in firing dynamics, even for large numbers of channels. Moreover, our results show that possible associated computational benefits may occur due to channel noise in neurons of the auditory brainstem. This holds whether the firing dynamics in the model are phasic (SBSR can occur due to channel noise) or tonic (ISR can occur due to channel noise).

A wide spectrum of electrokinetic studies is modeled as isothermal ones to expedite analysis even when such conditions may be extremely difficult to realize in practice. Going beyond the isothermal paradigm, we address here the case of flow induced electrohydrodynamics, commonly streaming potential flows, in a situation where finite temperature gradients do exist. By way of analyzing a model problem of flow through a narrow parallel-plate channel, we show that the temperature gradients applied at the channel walls may have a significant effect on the streaming potential, and, consequently, on the flow itself. Our model takes into consideration all the pertinent phenomenological aspects stemming from the imposed thermal gradients, such as the Soret effect, the thermoelectric effect, and the electrothermal effect, by a full-fledged coupling among the electric potential, the ionic species distribution, the fluid velocity and the local fluid temperature fields, without resorting to ad hoc simplifications. We expect this expository study to contribute significantly towards more sophisticated future endeavors in actual development of micro- and nano-devices for applications simultaneously involving thermal management and electrokinetic effects.

We study computationally the dynamics of oblate and prolate spheroidal capsules in simple shear flow with small inertia for a range of dimensionless shear rates. The capsule is modelled as a liquid droplet enclosed by a hyperelastic membrane, and its equatorial plane is initially tilted out of the plane of shear. We find, at low shear rates, the well-accepted tumbling motion is not always stable for both oblate and prolate capsules. For an oblate capsule, the dominant stable modes for increasing dimensionless shear rate are as follows: rolling with the equatorial plane staying in the plane of shear, precessing following Jeffery's orbit [Proc. R. Soc. London A 102, 161 (1922)], and tumbling. Interestingly, the order of modes is reversed for a prolate capsule: tumbling, precessing, and rolling with increasing dimensionless shear rate. At transitional regimes, we find the stable motion of a capsule can depend on its initial titled angle, even at the same shear rate. At high dimensionless shear rates, a spheroidal capsule undergoes a complicated oscillating-swinging motion: Its major axis oscillates about the plane of shear in addition to the swinging about a mean angle with flow direction found previously, and the amplitudes of both oscillations decrease when increasing the dimensionless shear rate towards a steady tank treading motion asymptotically. We summarize the results in phase diagrams and discuss the reorientation of both oblate and prolate capsules in a wide range of dimensionless shear rates.

The efficacy of the common practice of tracking brain dynamics using a few key regions of interest is explained via the fact that these regions are sensitive to underlying extended modes of activity, not just local dynamics. This underlines the inseparable interplay between modes and regions and reflects the reality that brain functions range from highly localized to highly extended.

The dynamics of two- and five-disk systems confined in a square has been studied using molecular dynamics simulations and compared with the predictions of transition state theory. We determine the partition functions $Z$ and $Z^{‡}$ of transition state theory using a procedure first used by Salsburg and Wood for the pressure. Our simulations show this procedure and transition state theory are in excellent agreement with the simulations. A generalization of the transition state theory to the case of a large number of disks $N$ is made and shown to be in full agreement with simulations of disks moving in a narrow channel. The same procedure for hard spheres in three dimensions leads to the Vogel-Fulcher-Tammann formula for their alpha relaxation time.