We investigate a driven two-channel system where particles on different lanes mutually obstruct each other’s motion, extending an earlier model by Popkov and Peschel [Phys. Rev. E 64, 026126 (2001)]. This obstruction may occur in biological contexts due to steric hinderance where motor proteins carry cargos by “walking” on microtubules. Similarly, the model serves as a description for classical spin transport where charged particles with internal states move unidirectionally on a lattice. Three regimes of qualitatively different behavior are identified, depending on the strength of coupling between the lanes. For small and large coupling strengths the model can be mapped to a one-channel problem, whereas a rich phase behavior emerges for intermediate ones. We derive an approximate but quantitatively accurate theoretical description in terms of a one-site cluster approximation, and obtain insight into the phase behavior through the current-density relations combined with an extremal-current principle. Our results are confirmed by stochastic simulations.

Water plays a critical role in protein dynamics and functions. However, the most basic property of hydration—the water sorption isotherm—remains inadequately understood. Surface adsorption is the commonly adopted picture of hydration. Since it does not account for changes in the conformational entropy of proteins, it is difficult to explain why protein dynamics and activity change upon hydration. The solution picture of hydration provides an alternative approach to describe the thermodynamics of hydration. Here, the flexibility of proteins could influence the hydration level through the change of elastic energy upon hydration. Using nuclear magnetic resonance to measure the isotherms of lysozyme in situ between 18 and 2 °C, the present work provides evidence that the part of water uptake associated with the onset of protein function is significantly reduced below 8 °C. Quantitative analysis shows that such reduction is directly related to the reduction of protein flexibility and enhanced cost in elastic energy upon hydration at lower temperature. The elastic property derived from the water isotherm agrees with direct mechanical measurements, providing independent support for the solution model. This result also implies that water adsorption at charged and polar groups occurring at low vapor pressure, which is known for softening the protein, is crucial for the later stage of water uptake, leading to the activation of protein dynamics. The present work sheds light on the mutual influence of protein flexibility and hydration, providing the basis for understanding the role of hydration on protein dynamics.

The connection between membrane inhomogeneity and the structural basis of lipid rafts has sparked interest in the lateral organization of model lipid bilayers of two and three components. In an effort to investigate anisotropic lipid distribution in mixed bilayers, a self-consistent mean-field theoretical model is applied to palmitoyloleoylphosphatidylcholine (POPC)–palmitoyl sphingomyelin (PSM)–cholesterol mixtures. The compositional dependence of lateral organization in these mixtures is mapped onto a ternary plot. The model utilizes molecular dynamics simulations to estimate interaction parameters and to construct chain conformation libraries. We find that at some concentration ratios the bilayers separate spatially into regions of higher and lower chain order coinciding with areas enriched with PSM and POPC, respectively. To examine the effect of the asymmetric chain structure of POPC on bilayer lateral inhomogeneity, we consider POPC-lipid interactions with and without angular dependence. Results are compared with experimental data and with results from a similar model for mixtures of dioleoylphosphatidylcholine, steroyl sphingomyelin, and cholesterol.

Fluctuations in the time-averaged mean-square displacement for random walks on hypercubic lattices with static disorder are investigated. It is analytically shown that the diffusion coefficient becomes a random variable as a manifestation of weak ergodicity breaking. For two- and higher- dimensional systems, the distribution function of the diffusion coefficient is found to be the Mittag–Leffler distribution, which is the same as for the continuous-time random walk, whereas for one-dimensional systems a different distribution (a modified Mittag-Leffler distribution) arises. We also present a comparison of these two distributions in terms of an ergodicity-breaking parameter and show that the modified Mittag-Leffler distribution has a larger deviation from ergodicity. Some remarks on similarities between these results and observations in biological experiments are presented.

We present a generally covariant formulation of human arm dynamics and optimization principles in Riemannian configuration space. We extend the one-parameter family of mean-squared-derivative (MSD) cost functionals from Euclidean to Riemannian space, and we show that they are mathematically identical to the corresponding dynamic costs when formulated in a Riemannian space equipped with the kinetic energy metric. In particular, we derive the equivalence of the minimum-jerk and minimum-torque change models in this metric space. Solutions of the one-parameter family of MSD variational problems in Riemannian space are given by (reparametrized) geodesic paths, which correspond to movements with least muscular effort. Finally, movement invariants are derived from symmetries of the Riemannian manifold. We argue that the geometrical structure imposed on the arm’s configuration space may provide insights into the emerging properties of the movements generated by the motor system.

We investigate the snaking of localized patterns, seen in numerous physical applications, using a variational approximation. This method naturally introduces the exponentially small terms responsible for the snaking structure, which are not accessible via standard multiple-scales asymptotic techniques. We obtain the symmetric snaking solutions and the asymmetric “ladder” states, and also predict the stability of the localized states. The resulting approximate formulas for the width of the snaking region show good agreement with numerical results.

We consider the classical dynamics of a two-electron system subjected to an intense bichromatic linearly polarized laser pulse. By varying the parameters of the field, such as the phase lag and the relative amplitude between the two colors of the field, we observe several trends from the statistical analysis of a large ensemble of trajectories initially in the ground-state energy of the helium atom: high sensitivity of the sequential double-ionization component, low sensitivity of the intensities where nonsequential double ionization occurs, while the corresponding yields can vary drastically. All these trends hold irrespective of which parameter is varied: the phase lag or the relative amplitude. We rationalize these observations by an analysis of the phase-space structures that drive the dynamics of this system and determine the extent of double ionization. These trends turn out to be mainly regulated by the dynamics of the inner electron.

The survival probability of the open stadium billiard with one hole on its boundary is well known to decay asymptotically as a power law. We investigate the transmission and reflection survival probabilities for the case of two holes placed asymmetrically. Classically, these distributions are shown to lose their algebraic decay tails depending on the choice of injecting hole, therefore exhibiting asymmetric transport. The mechanism behind this is explained while exact expressions are given and confirmed numerically. We propose a model for experimental observation of this effect using semiconductor nanostructures and comment on the relevant quantum time scales.

Liquid slip is essential in nanofluidic systems, as shrinking channel size leads to a dramatic increase in flow resistance and thus high-energy consumption for driving nonslip flow. Using large-scale nonequilibrium molecular dynamics simulation of water flowing in carbon nanotubes (CNT’s), we show that the relationship between the CNT wall-water interfacial friction stress and slip velocity follows a transition-state-theory-based inverse hyperbolic sine function, which remains universally valid regardless of wetting properties, CNT chiralities, and CNT sizes, and holds for all slip velocities from 0 to 1400 m/s. The finding could benefit the research in desalination and other chemical purification techniques.

The growth rates of scalar gradients are studied numerically and analytically in a family of two-dimensional (2D) incompressible fluid equations related to the surface quasigeostrophic (SQG) equation. The active scalar is related to the stream function $\psi$ by $\theta =(-△){}^{\alpha /2}\psi \hspace{0.5em}(0⩽\alpha ⩽2)$. A notable difference is observed in a comparison of the instantaneous growth rates in $L^p$ and in $L^{\infty }$ norms, depending on the stage of the time evolution. The crux is the phase-shift effect of singular integral operators, which displaces the peak location of the scalar gradient from that of the strain rate. On this basis, a method of detecting such a dislocation is proposed in view of the importance of their coalescence needed for a possible blow-up. Moreover, it is found in the long-time evolution that a solution of the SQG equation (whose regularity is not known) is less singular than that of the 2D Euler equations (known to be regular) on the time interval covered by this computation. This consistently expands an earlier observation by Majda and Tabak [Physica D 98, 515 (1996).] in some detail. A 1D model problem is discussed to illustrate the present method, and extensions to the 3D case are also are briefly discussed.

The aim of the present study is to elucidate how simulated annealing (SA) works in its finite-time implementation by starting from the verification of its conventional optimization scenario based on equilibrium statistical mechanics. Two and one supplementary experiments, the design of which is inspired by concepts and methods developed for studies on liquid and glass, are performed on two types of random traveling salesman problems. In the first experiment, a newly parameterized temperature schedule is introduced to simulate a quasistatic process along the scenario and a parametric study is conducted to investigate the optimization characteristics of this adaptive cooling. In the second experiment, the search trajectory of the Metropolis algorithm (constant-temperature SA) is analyzed in the landscape paradigm in the hope of drawing a precise physical analogy by comparison with the corresponding dynamics of glass-forming molecular systems. These two experiments indicate that the effectiveness of finite-time SA comes not from equilibrium sampling at low temperature but from downward interbasin dynamics occurring before equilibrium. These dynamics work most effectively at an intermediate temperature varying with the total search time and thus this effective temperature is identified using the Deborah number. To test directly the role of these relaxation dynamics in the process of cooling, a supplementary experiment is performed using another parameterized temperature schedule with a piecewise variable cooling rate and the effect of this biased cooling is examined systematically. The results show that the optimization performance is not only dependent on but also sensitive to cooling in the vicinity of the above effec-tive temperature and that this feature is interpreted as a consequence of the presence or absence of the workable interbasin dynamics. It is confirmed for the present instances that the effectiveness of finite-time SA derives from the glassy relaxation dynamics occurring in the “landscape-influenced” temperature regime and that its naive optimization scenario should be rectified by considering the analogy with vitrification phenomena. A comprehensive guideline for the design of finite-time SA and SA-related algorithms is discussed on the basis of this rectified analogy.

We rigorously establish a physical time scale for a general class of kinetic Monte Carlo algorithms for the simulation of continuous-time Markov chains. This class of algorithms encompasses rejection-free (or BKL) and rejection (or “standard”) algorithms. For rejection algorithms, it was formerly considered that the availability of a physical time scale (instead of Monte Carlo steps) was empirical, at best. Use of Monte Carlo steps as a time unit now becomes completely unnecessary.

We study a model granular suspension driven down a channel by an embedding fluid via computer simulations. We characterize the different system flow regimes and the stochastic nature of the transitions between them. For packing fractions below a threshold ${\varphi }_m$, granular flow is disordered and exhibits an Ostwald–de Waele–type power-law shear-stress constitutive relation. Above ${\varphi }_m$, two asymptotic states exist; disordered flow can persist indefinitely, yet, in a fraction of samples, the system self-organizes in an ordered form of flow where grains move in parallel ordered layers. In the latter regime, the Ostwald–de Waele relationship breaks down and a nearly solid plug appears in the center, with linear shear regions at the boundaries. Above a higher threshold ${\varphi }_g$, an abrupt jamming transition is observed if ordering is avoided.

In this work we experimentally study the behavior of a freely rotating asymmetric probe immersed in a vibrated granular medium. For a wide variety of vibration conditions the probe exhibits a steady rotation whose direction is constant with respect to the asymmetry. By changing the vibration amplitude and by filtering the noise in different frequency bands we show that the velocity of rotation depends not only on the RMS acceleration $\Gamma$, but also on the amount of energy provided to two separate frequency bands, which are revealed to be important for the dynamics of the granular medium: The first band governs the transfer of energy from the grains to the probe, and the second affects the dynamics by altering the viscosity of the vibro-fluidized material.

The study of vesicles under flow, a model system for red blood cells (RBCs), is an essential step in understanding various intricate dynamics exhibited by RBCs in vivo and in vitro. Quantitative three-dimensional analyses of vesicles under flow are presented. The regions of parameters to produce tumbling (TB), tank-treating, vacillating-breathing (VB), and even kayaking (or spinning) modes are determined. New qualitative features are found: (i) a significant widening of the VB mode region in parameter space upon increasing shear rate $\mathrm{\gamma ̇}$ and (ii) a robustness of normalized period of TB and VB with $\mathrm{\gamma ̇}$. Analytical support is also provided. We make a comparison with existing experimental results. In particular, we find that the phase diagram of the various dynamics depends on three dimensionless control parameters, while a recent experimental work reported that only two are sufficient.

Uncovering the mechanism leading to the scaling law in human trajectories is of fundamental importance in understanding many spatiotemporal phenomena. We propose a hierarchical geographical model to mimic the real traffic system, upon which a random walker will generate a power-law-like travel displacement distribution with tunable exponent, and display a scaling behavior in the probability density of having traveled a certain distance at a certain time. The simulation results, analytical results, and empirical observations reported in D. Brockmann et al. [Nature (London) 439, 462 (2006)] agree very well with each other.

We determine analytical extended traveling-wave and spatiotemporal solitary solutions to the generalized (3$+$1)-dimensional Gross-Pitaevskii equation with time-dependent coefficients, for the sinusoidally time-varying diffraction and quadratic potential strength. A number of periodic and localized solutions are obtained whose intensity does not decrease in time in the absence of externally induced gain or loss. Stability analysis of our solitary solutions is carried out, to display their modulational stability.

Potts glasses are prototype models that have been used to understand the structural glass transition. However, in finite space dimensions a glass transition remains to be detected in the 10-state Potts glass. Using a one-dimensional model with long-range power-law interactions we present evidence that a glass transition below the upper critical dimension can exist for short-range systems at low enough temperatures. Gaining insights into the structural glass transition for short-range systems using spin models is thus potentially possible, yet difficult.

We study the one-dimensional isotropic Heisenberg model of two spin-1/2 systems as a quantum heat engine. The engine undergoes a four-step Otto cycle where the two adiabatic branches involve changing the external magnetic field at a fixed value of the coupling constant. We find conditions for the engine efficiency to be higher than in the uncoupled model; in particular, we find an upper bound which is tighter than the Carnot bound. A domain of parameter values is pointed out which was not feasible in the interaction-free model. Locally, each spin seems to cause a flow of heat in a direction opposite to the global temperature gradient. This feature is explained by an analysis of the local effective temperature of the spins.