By means of a unique probe array, the interaction between zonal flows and broad-band drift-wave turbulence has been investigated experimentally in a magnetized toroidal plasma. Homogeneous potential fluctuations on a magnetic flux surface, previously reported as long range correlations, could be traced back to a predator-prey-like interaction between the turbulence and the zonal flow. At higher frequency the nonlocal transfer of energy to the zonal flow is dominant and the low-frequency oscillations are shown to result from the reduced turbulence activity due to this energy loss. This self-regulation process turns out to be enhanced with increased background shear flows.

The solution-space structure of the three-satisfiability problem (3-SAT) is studied as a function of the control parameter $\alpha$ (ratio of the number of clauses to the number of variables) using numerical simulations. For this purpose one has to sample the solution space with uniform weight. It is shown here that standard stochastic local-search (SLS) algorithms like average satisfiability (ASAT) exhibit a sampling bias, as does “Metropolis-coupled Markov chain Monte Carlo” (MCMCMC) (also known as “parallel tempering”) when run for feasible times. Nevertheless, unbiased samples of solutions can be obtained using the “ballistic-networking approach,” which is introduced here. It is a generalization of “ballistic search” methods and yields also a cluster structure of the solution space. As application, solutions of 3-SAT instances are generated using ASAT plus ballistic networking. The numerical results are compatible with a previous analytical prediction of a simple solution-space structure for small values of $\alpha$ and a transition to a clustered phase at ${\alpha }_c\approx 3.86$, where the solution space breaks up into several non-negligible clusters. Furthermore, in the thermodynamic limit there are, even for $\alpha =4.25$ close to the SAT-UNSAT transition ${\alpha }_s\approx 4.267$, always clusters without any frozen variables. This may explain why some SLS algorithms are able to solve very large 3-SAT instances close to the SAT-UNSAT transition.

Since the Kramers problem cannot be, in general, solved in terms of elementary functions, various numerical techniques or approximate methods must be employed. We present a study of characteristics for a particle in a damped well, which can be considered as a discretized version of the Melnikov [Phys. Rev. E 48, 3271 (1993)] turnover theory. The main goal is to justify the direct computational scheme to the basic Wiener-Hopf model. In contrast to the Melnikov approach, which implements factorization through a Cauchy-theorem-based formulation, we employ the Wiener-Levy theorem to reduce the Kramers problem to a Wiener-Hopf sum equation written in terms of Toeplitz matrices. This latter can provide a stringent test for the reliability of analytic approximations for energy distribution functions occurring in the Kramers problems at arbitrary damping. For certain conditions, the simulated characteristics are compared well with those determined using the conventional Fourier-integral formulas, but sometimes may differ slightly depending on the value of a dissipation parameter. Another important feature is that, with our method, we can avoid some complications inherent to the Melnikov method. The calculational technique reported in the present paper may gain particular importance in situations where the energy losses of the particle to the bath are a complex-shaped function of the particle energy and analytic solutions of desired accuracy are not at hand. In order to appreciate more readily the significance and scope of the present numerical approach, we also discuss concrete aspects relating to the field of superionic conductors.

Single-file diffusion (SFD) of an infinite one-dimensional chain of interacting particles has a long-time mean-square displacement $\propto t^{1/2}$, independent of the type of interparticle repulsive interaction. This behavior is also observed in finite-size chains, although only for certain intervals of time $t$ depending on the chain length $L$, followed by the $\propto t$ for $t\to \infty$, as we demonstrate for a closed circular chain of diffusing interacting particles. Here, we show that spatial correlation of noise slows down SFD and can result, depending on the amount of correlated noise, in either subdiffusive behavior $\propto t^{\alpha }$, where $0<\alpha <1/2$, or even in a total suppression of diffusion (in the limit $N\to \infty$). Spatial correlation can explain the subdiffusive behavior in recent SFD experiments in circular channels.

Chemotactic cell migration is a fundamental phenomenon in complex biological processes. A rigorous understanding of the chemotactic mechanism of crawling cells has important implications for various medical and biological applications. In this paper, we propose a three-dimensional model of a single crawling cell to study its chemotaxis. A single-cell study of chemotaxis has an advantage over studies of a population of cells in that it provides a clearer observation of cell migration, which leads to more accurate assessments of chemotaxis. The model incorporates the surface energy of the cell and the interfacial interaction between the cell and substrate. The semi-implicit Fourier spectral method is applied to achieve high efficiency and numerical stability. The simulation results provide the kinetic and morphological traits of a crawling cell during chemotaxis.

The air transportation network, a fundamental component of critical infrastructure, is formed from a collection of individual air carriers, each one with a methodically designed and engineered network structure. We analyze the individual structures of the seven largest passenger carriers in the USA and find that networks with dense interconnectivity, as quantified by large $k$ cores for high values of $k$, are extremely resilient to both targeted removal of airports (nodes) and random removal of flight paths (edges). Such networks stay connected and incur minimal increase in an heuristic travel time despite removal of a majority of nodes or edges. Similar results are obtained for targeted removal based on either node degree or centrality. We introduce network rewiring schemes that boost resilience to different levels of perturbation while preserving total number of flight and gate requirements. Recent studies have focused on the asymptotic optimality of hub-and-spoke spatial networks under normal operating conditions, yet our results indicate that point-to-point architectures can be much more resilient to perturbations.

We use Monte Carlo simulations to examine the simplest model of a room-temperature ionic liquid (RTIL), called the “restricted primitive model,” at a metal surface. We find that at moderately low temperatures the capacitance of the metal-RTIL interface is so large that the effective thickness of the electrostatic double layer is up to three times smaller than the ion radius. To interpret these results we suggest an approach which is based on the interaction between discrete ions and their image charges in the metal surface and which therefore goes beyond the mean-field approximation. When a voltage is applied across the interface, the strong image attraction causes counterions to condense onto the metal surface to form compact ion-image dipoles. These dipoles repel each other to form a correlated liquid. When the surface density of these dipoles is low, the insertion of an additional dipole does not require much energy. This leads to a large capacitance $C$ that decreases monotonically with voltage $V$, producing a “bell-shaped” curve $C\left(V\right)$. We also consider what happens when the electrode is made from a semimetal rather than a perfect metal. In this case, the finite screening radius of the electrode shifts the reflection plane for image charges to the interior of the electrode, and we arrive at a “camel-shaped” $C\left(V\right)$. These predictions seem to be in qualitative agreement with experiment.

We compute Lyapunov vectors (LVs) corresponding to the largest Lyapunov exponents in delay-differential equations with large time delay. We find that characteristic LVs, and backward (Gram-Schmidt) LVs, exhibit long-range correlations, identical to those already observed in dissipative extended systems. In addition we give numerical and theoretical support to the hypothesis that the main LV belongs, under a suitable transformation, to the universality class of the Kardar-Parisi-Zhang equation. These facts indicate that in the large delay limit (an important class of) delayed equations behave exactly as dissipative systems with spatiotemporal chaos.

The longitudinal response function for a thermal electron gas is calculated including two quantum effects exactly, degeneracy, and the quantum recoil. The Fermi-Dirac distribution is expanded in powers of a parameter that is small in the nondegenerate limit and the response function is evaluated in terms of the conventional plasma dispersion function to arbitrary order in this parameter. The infinite sum is performed in terms of polylogarithms in the long-wavelength and quasistatic limits, giving results that apply for arbitrary degeneracy. The results are applied to the dispersion relations for Langmuir waves and to screening, reproducing known results in the nondegenerate and completely degenerate limits, and generalizing them to arbitrary degeneracy.

Differential growth processes play a prominent role in shaping leaves and biological tissues. Using both analytical and numerical calculations, we consider the shapes of closed, elastic strips which have been subjected to an inhomogeneous pattern of swelling. The stretching and bending energies of a closed strip are frustrated by compatibility constraints between the curvatures and metric of the strip. To analyze this frustration, we study the class of “conical” closed strips with a prescribed metric tensor on their center line. The resulting strip shapes can be classified according to their number of wrinkles and the prescribed pattern of swelling. We use this class of strips as a variational ansatz to obtain the minimal energy shapes of closed strips and find excellent agreement with the results of a numerical bead-spring model. We derive and test a surprising resonance condition for strips with minimal bending energy along the strip center line to exist.

Employing Molecular Dynamics simulations of a chemically realistic model of 1,4-polybutadiene between graphite walls we show that the mass exchange between layers close to the walls is a slow process already in the melt state. For the glass transition of confined polymers this process competes with the slowing down due to packing effects and intramolecular rotation barriers.

The efficiency of four different and representative models of heat engines under maximum conditions for a figure of merit representing a compromise between useful energy and lost energy (the $\Omega$ criterion) is investigated and compared with previous results for the same models where the efficiency is considered at maximum power conditions. It is shown that the maximum $\Omega$ regime is more efficient and, additionally, that the resulting efficiencies present a similar behavior. For each performance regime we obtain explicit equations accounting for lower and upper bounds. The optimization of refrigeration devices is far from being as clear as heat engines, and some remarks on it are finally considered.

Liquid crystal elastomers are cross-linked polymer networks covalently bonded with liquid crystal mesogens. In the nematic phase, due to strong coupling between mechanical strain and orientational order, these materials display strain-induced instabilities associated with formation and evolution of orientational domains. Using a three-dimensional finite element elastodynamics simulation, we investigate one such instability, the onset of stripe formation in a monodomain film stretched along an axis perpendicular to the nematic director. In our simulation, we observe the formation of striped domains with alternating director rotation. This model allows us to explore the fundamental physics governing dynamic mechanical response of nematic elastomers and also provides a potentially useful computational tool for engineering device applications.

In this work we derive analytically various thermodynamic properties of bolalipid membranes using microscopic model (elastic strings) and path-integral technique. Among calculated characteristics are lateral pressure profile (with and without hairpin bolalipids), chain orientational order parameter, pressure-area isotherms, coefficient of thermal area expansion, compressibility modulus, and area per bolalipid chain as a function of temperature. Results are compared with our previous ones for a monopolar lipid bilayer and with results of other relevant studies. The limiting case of absolutely rigid strings is also considered. Evaluation of quantum effects is made and found to be negligible.

Linear fluid equations for relativistic and collisionless plasmas are derived. Closure relations for the fluid equations are analytically computed from the relativistic Vlasov equation in the Fourier space $\left(\omega ,k\right)$, where $\omega$ and $k$ are the conjugate variables of time $t$ and space $x$ variables, respectively. The mathematical method used is based on the projection operator techniques and the continued fraction mathematical tools. The generalized heat flux and stress tensor are calculated for arbitrary parameter $\omega /kc$ where $c$ is the speed of light, and for arbitrary relativistic parameter $z=m{c}^2/T$, where $m$ is the particle rest mass and $T$, the plasma temperature in energy units.

The Lagrange-mesh method is an approximate variational calculation which has the simplicity of a mesh calculation. Combined with the imaginary-time method, it is applied to the iterative resolution of the Gross-Pitaevskii equation. Two variants of a fourth-order factorization of the exponential of the Hamiltonian and two types of mesh (Lagrange-Hermite and Lagrange-sinc) are employed and compared. The accuracy is checked with the help of these comparisons and of the virial theorem. The Lagrange-Hermite mesh provides very accurate results with short computing times for values of the dimensionless parameter of the nonlinear term up to ${10}^4$. For higher values up to ${10}^7$, the Lagrange-sinc mesh is more efficient. Examples are given for anisotropic and nonseparable trapping potentials.

We present an approach to mapping between random walks and vibrational dynamics on general networks. Random walk occupation probabilities, first passage time distributions and passage probabilities between nodes are expressed in terms of thermal vibrational correlation functions. Recurrence is demonstrated equivalent to the Landau-Peierls instability. Fractal networks are analyzed as a case study. In particular, we show that the spectral dimension governs whether or not the first passage time distribution is well represented by its mean. We discuss relevance to universal features arising in protein vibrational dynamics.

We consider the partially asymmetric simple exclusion process (PASEP) when its steady-state probability distribution function can be written in terms of a linear superposition of product measures with a finite number of shocks. In this case the PASEP can be mapped into an equilibrium walk model, defined on a diagonally rotated square lattice, in which each path of the walk model has several transits with the horizontal axis. We show that the multiple-point density correlation function in the PASEP is related to the probability that a path has multiple contacts with the horizontal axis from the above or below.

We study the adhesion of liquid droplets to rough surfaces, focusing on how adhesion changes with surface chemistry and roughness. For hydrophobic surfaces (equilibrium contact angle ${\theta }_{\text{e}}>90°$), although increasing surface roughness augments apparent contact angle, it does not necessarily always reduce adhesion. In a domain defined by roughness and equilibrium contact angle, this study identifies regions where adhesion increases or decreases with increasing roughness. The two regions do not border at ${\theta }_{\text{e}}=90°$. It is found that making surfaces with low roughness ratio (close to 1) does not reduce adhesion unless the surface material is highly hydrophobic $\left({\theta }_{\text{e}}>120°\right)$. In other words, to reduce adhesion for existing hydrophobic materials $\left(90°<{\theta }_{\text{e}}<120°\right)$, high roughness ratios are needed. Additionally, to reduce adhesion, the geometry of microstructures should be designed such that wetted fraction decreases with increasing roughness ratio. This study is of particular importance for the design of textured superhydrophobic surfaces.

Deuterium NMR spectroscopy has been used to study the director dynamics of the nematic liquid-crystal system cetyl trimethylammonium bromide/${\text{D}}_2\text{O}$ under the action of applied viscous torques. Shear forces were applied using a custom-built Couette cell that was introduced into an NMR superconducting magnet, so that its rotational axis was parallel to the magnetic field direction, along which the liquid-crystal director originally aligned. Subsequently, the inner cylinder of the cell was rotated continuously at different rates using a stepper motor. The resulting time evolution and ultimate steady-state orientation of the director, governed by the competition between the applied viscous torque with elastic and magnetic terms, was measured via observed changes in the deuterium spectrum. Using a simple gearbox allowed unprecedented access to a low-shear-rate regime in which, above a threshold shear rate, the director of part of the sample was observed to reorient, while the remaining part still aligned with the magnetic field. Subsequent increases in the applied rotational rate were found to increase the relative proportion of the orienting fraction. Spatially resolved NMR spectra showed that the orienting and field-aligned fractions formed separated bands across the gap of the Couette cell, with director reorientation being initiated at the moving inner wall. The behavior was found to be consistent with the often ignored variation in velocity gradient manifest across the gap of a cylindrical cell, so that as the angular frequency of the inner cylinder was increased the radial location of the critical shear rate required for reorientation traversed the gap. Once the applied rotational rate was sufficient to reorient the director of the entire sample, the dependence of the exhibited steady-state orientation on the average applied shear rate was measured. These results could be fitted to an analytical solution of the force-balance equation, made tractable by the assumption that the elasticity term was of minor significance and could be ignored. Additionally, the use of a numerical solution of the full force-balance equation, which explicitly includes elasticity and secondary flow and additionally allows the time evolution of the director orientation to be calculated, was investigated.