In this paper, we provide a theory for the Wenzel and the Cassie-Baxter states of an electrolyte drop on charged surfaces. An electric double layer (EDL) develops when the electrolyte drop comes in contact with the charged surface. Therefore, the EDL free energy affects these states by triggering a hydrophilicity-inducing tendency. Consequently, an originally hydrophilic condition leads to a superhydrophilic Wenzel state, and an originally hydrophobic condition leads to a less hydrophobic Wenzel state. For the Cassie-Baxter state, this gives rise to the most remarkable situation of a hydrophilic (as compared to the original) Cassie-Baxter state.

We report on homodyne dynamic light scattering measurements of orientational fluctuation modes in both calamitic and bent-core nematic liquid crystals, carried out in the new split-helix resistive magnet at the National High Magnetic Field Laboratory. The relaxation rate and inverse scattered intensity of director fluctuations exhibit a linear dependence on field-squared up to 25 tesla, which is consistent with strictly lowest order coupling of the tensor order parameter Q to field ($Q_{\alpha \beta }$B${}_{\alpha }$B${}_{\beta }$) in the nematic free energy. However, we also observe evidence of field dependence of certain nematic material parameters, an effect which may be expected from the mean field scaling of these quantities with the magnitude of Q and the predicted variation of Q with field.

Recent experiments have shown that defect conformations in spherical nematic liquid crystals can be controlled through variations of temperature, shell thickness, and other environmental parameters. These modifications can be understood as a result of the induced changes in the effective elastic constants of the system. To characterize the relation between defect conformations and elastic anisotropy, we carry out Monte Carlo simulations of a nematic on a spherical surface. As the anisotropy is increased, the defects flow from a tetrahedral arrangement to two coalescing pairs and then to a great circle configuration. We also analyze this flow using a variational method based on harmonic configurations.

We analyze the dynamics of the susceptible-infected-susceptible epidemic model when the transmission rate displays Gaussian white noise fluctuations around its mean value. We obtain analytic expressions for the final size distribution of infectives and the mean infected number of individuals. The model displays a variety of noise-induced transitions as a function of the basic reproductive rate and the noise intensity. We derive a threshold criterion for epidemic invasion in the presence of external noise and determine the mean epidemic duration and the mean epidemic extinction time.

Colonies of flagellated bacteria on agar plates are known to take on diverse morphologies. A diffusion-reaction model is proposed for bacterial-colony pattern formation on a surface due to time scale separation between the slow mass migration of bacteria from the point of inoculation, and the fast, but localized, dynamics of bacterial phenotypic plasticity stimulated by public-goods cooperation and phenotypic switching. By considering two switchable phenotypes in the population, the model generates pattern diversity typifying those reported by experimental studies.

A detailed understanding of the origin of the electrophoretic force on DNA molecules in a solid-state nanopore is important for the development of nanopore-based sequencing technologies. Because of the discrepancies between recent attempts to predict this force and both direct and indirect experimental measurements, this topic has been the focus of much recent discussion. We show that the force is predictable to very good accuracy if all of the experimental conditions are accounted for properly. To resolve this issue, we compare the calculation efficiency and accuracy of numerical solutions of Poisson-Boltzmann and Poisson-Nernst-Planck descriptions of electrolyte behavior in the nanopore in the presence of DNA molecules. Two geometries—axially symmetric and cross-sectional—are compared and shown to be compatible. Numerical solutions are carried out on a sufficiently fine mesh to evaluate the viscous drag force acting on DNA inside a silicon nitride nanopore. By assuming the DNA is immobilized in the axial center of the nanopore, the calculation result of this viscous drag force is found to be rather larger than the experimental result. Because the viscous drag force decreases if DNA is closer to the surface of the nanopore, however, the relevant effective driving force is the average over all possible positions of the DNA in the nanopore. When this positional uncertainty is taken into account, the effective driving force acting on DNA inside the nanopore is found to agree very well with the experimental results.

The problem of graph clustering or community detection has enjoyed a lot of attention in complex networks literature. A quality function, modularity, quantifies the strength of clustering and on maximization yields sensible partitions. However, in most real world networks, there are an exponentially large number of near-optimal partitions with some being very different from each other. Therefore, picking an optimal clustering among the alternatives does not provide complete information about network topology. To tackle this problem, we propose a graph perturbation scheme which can be used to identify an ensemble of near-optimal and diverse clusterings. We establish analytical properties of modularity function under the perturbation which ensures diversity. Our approach is algorithm independent and therefore can leverage any of the existing modularity maximizing algorithms. We numerically show that our methodology can systematically identify very different partitions on several existing data sets. The knowledge of diverse partitions sheds more light into the topological organization and helps gain a more complete understanding of the underlying complex network.

We analyze the behavior of a relativistic particle moving under the influence of a uniform magnetic field and a stationary electrostatic wave. We work with a set of pulsed waves that allows us to obtain an exact map for the system. We also use a method of control for near-integrable Hamiltonians that consists of the addition of a small and simple control term to the system. This control term creates invariant tori in phase space that prevent chaos from spreading to large regions, making the controlled dynamics more regular. We show numerically that the control term just slightly modifies the system but is able to drastically reduce chaos with a low additional cost of energy. Moreover, we discuss how the control of chaos and the consequent recovery of regular trajectories in phase space are useful to improve regular particle acceleration.

This paper concerns plasmas in which the electrons and ions may have different temperatures. This is a case that must be examined because nuclear fusion processes, such as those that appear in ICF capsules, have ions whose temperature runs away from the electron temperature. A fast charged particle traversing a plasma—such as the $\alpha$ particle created in deuterium-tritium fusion—loses its energy to both the electrons and the ions in the plasma. In this paper, we present and discuss the results for the energy partition, the fractions $E_e/E_0$ and $E_{\mathrm{I}}/E_0$ of the initial energy $E_0$ of this projectile particle that are deposited into the electrons and ions when it has slowed to its minimum energy distribution. The calculations, performed in the following paper [Brown, Preston, and Singleton Jr., Phys. Rev. E 86, 016407 (2012)], use a well-defined Fokker-Planck equation for the phase-space distribution of the charged projectiles in a weakly to moderately coupled plasma. The Fokker-Planck equation holds to first subleading order in the dimensionless plasma coupling constant, which translates to computing to order $n\ln n$ (leading) and $n$ (subleading) in the plasma density $n$. We present an examination of the energy partition for the general case, in which the temperatures of the ions and electrons in the background plasma are not equal. The energy partitions for a background plasma in thermal equilibrium have been previously computed, but the order $n$ terms have not been calculated, only estimated. Our Fokker-Planck formulation provides an unambiguous, precise definition of the energy fractions.

The preceding paper [Brown, Preston, and Singleton Jr., Phys. Rev. E 86, 016406 (2012)] presented precise results for the partition of the initial energy $E_0$ of a fast particle into the ions and electrons—$E_{\mathrm{I}}/E_0$ and $E_e/E_0$—when the fast particle slows in a plasma whose ion and electron temperatures may differ. As emphasized in that paper, this is an important problem because nuclear fusion reactions, such as those that occur in an inertial confinement fusion capsule, involve ion temperatures that run away from the electron temperatures. As also noted in the preceding paper, a precise evaluation entails the use of a well-defined Fokker-Planck equation for the phase-space evolution of initially fast projectile particles. When the plasma has differing ion and electron temperatures, the projectiles must slow into a “schizophrenic” final ensemble of particles that has neither the electron nor the ion temperature. This is not a simple Maxwell-Boltzmann distribution since the electrons are not in thermal equilibrium with the ions. Thus, detailed calculations are required for the solution of the problem. These we provide here for a weakly to moderately coupled plasma. The Fokker-Planck equation holds to first subleading order in the dimensionless plasma coupling constant, which translates to computing to order $n\ln n$ (leading) and $n$ (subleading) in the plasma density $n$. The energy partitions for a background plasma in thermal equilibrium have been previously computed, but the order $n$ terms have not been calculated, only estimated. The “schizophrenic” final ensemble of slowed particles gives a new mechanism to bring the electron and ion temperatures together. The rate at which this new mechanism brings the electrons and ions in the plasma into thermal equilibrium will be computed.

We present space-time evolution of large-amplitude upper hybrid modes in a cold homogeneous plasma in the presence of an inhomogeneous magnetic field. Using the method of Lagrange variables, an exact space-time-dependent solution is obtained in parametric form. It is found that the magnetic field inhomogeneity causes various nonlinearly excited modes to couple, resulting in phase mixing and eventual breaking of the initially excited mode. The occurrence of wave breaking is seen by the appearance of spikes in the density profile. These results will be of relevance to laboratory and space plasma situations in which the external magnetic field is inhomogeneous.

The photoacoustic effect for a one-dimensional structure, the sound speed of which varies sinusoidally in space, is shown to be governed by an inhomogeneous Mathieu equation with the forcing term dependent on the spatial and temporal properties of the exciting optical radiation. New orthogonality relations, traveling wave Mathieu functions, and solutions to the inhomogeneous Mathieu equation are found, which are used to determine the character of photoacoustic waves in infinite and finite length phononic structures. Floquet solutions to the Mathieu equation give the positions of the band gaps, the damping of the acoustic waves within the band gaps, and the dispersion relation for photoacoustic waves. The solutions to the Mathieu equation give the photoacoustic response of the structure, show the space equivalent of subharmonic generation and acoustic confinement when waves are excited within band gaps.

The pseudopotential lattice Boltzmann (LB) model is a widely used multiphase model in the LB community. In this model, an interaction force, which is usually implemented via a forcing scheme, is employed to mimic the molecular interactions that cause phase segregation. The forcing scheme is therefore expected to play an important role in the pseudoepotential LB model. In this paper, we aim to address some key issues about forcing schemes in the pseudopotential LB model. First, theoretical and numerical analyses will be made for Shan-Chen's forcing scheme [Shan and Chen, Phys. Rev. E 47, 1815 (1993)] and the exact-difference-method forcing scheme [Kupershtokh et al., Comput. Math. Appl. 58, 965 (2009)]. The nature of these two schemes and their recovered macroscopic equations will be shown. Second, through a theoretical analysis, we will reveal the physics behind the phenomenon that different forcing schemes exhibit different performances in the pseudopotential LB model. Moreover, based on the analysis, we will present an improved forcing scheme and numerically demonstrate that the improved scheme can be treated as an alternative approach to achieving thermodynamic consistency in the pseudopotential LB model.

A wide range of glassy and disordered materials exhibit complex, nonexponential, structural relaxation (aging). We propose a simple nonlinear rate equation $\dot{\delta }=a[1-\exp \left(b\delta \right)]$, where $\delta$ is the normalized deviation of a macroscopic variable from its equilibrium value, to describe glassy relaxation. Analysis of extensive experimental data shows that this equation quantitatively captures structural relaxation, where $a$ and $b$ are both temperature- and, more importantly, history-dependent parameters. This analysis explicitly demonstrates that structural relaxation cannot be accurately described by a single nonequilibrium variable. Relaxation rates extracted from the data imply the existence of cooperative rearrangements on a supermolecular scale.

Trails (bond-avoiding walks) provide an alternative lattice model of polymers to self-avoiding walks, and adding self-interaction at multiply visited sites gives a model of polymer collapse. Recently a two-dimensional model (triangular lattice) where doubly and triply visited sites are given different weights was shown to display a rich phase diagram with first- and second-order collapse separated by a multicritical point. A kinetic growth process of trails (KGTs) was conjectured to map precisely to this multicritical point. Two types of low-temperature phases, a globule phase and a maximally dense phase, were encountered. Here we investigate the collapse properties of a similar extended model of interacting lattice trails on the simple cubic lattice with separate weights for doubly and triply visited sites. Again we find first- and second-order collapse transitions dependent on the relative sizes of the doubly and triply visited energies. However, we find no evidence of a low-temperature maximally dense phase with only the globular phase in existence. Intriguingly, when the ratio of the energies is precisely that which separates the first-order from the second-order regions anomalous finite-size scaling appears. At the finite-size location of the rounded transition clear evidence exists for a first-order transition that persists in the thermodynamic limit. This location moves as the length increases, with its limit apparently at the point that maps to a KGT. However, if one fixes the temperature to sit at exactly this KGT point, then only a critical point can be deduced from the data. The resolution of this apparent contradiction lies in the breaking of crossover scaling and the difference in the shift and transition width (crossover) exponents.

Spatial pattern formation in fluctuating media is researched analytically from the point of view of the order parameters concept. A reaction-diffusion system with external noise is considered as a model of such media. Stochastic equations for unstable mode amplitudes (order parameters), the dispersion equation for averaged amplitudes of unstable modes, and the Fokker-Planck equation for the order parameters are obtained. The theory developed makes it possible to analyze different noise-induced effects including the variation of boundaries of ordering and disordering phase transitions depending on the parameters of external noise

Negative thermophoresis is a phenomenon of particle transport induced by a temperature gradient, by which small particles migrate from low to high temperatures. In gas media, it depends strongly on the gas-particle interaction and temperature. In this paper, we show that negative thermophoresis is possible in the free molecular regime and a theoretical criterion is derived. On the basis of a general gas-particle interaction potential, an empirical necessary condition for negative thermophoresis that the potential parameters should satisfy is also obtained. Finally, the temperature ranges for the occurrence of negative thermophoresis are determined for a series of gas-particle interaction parameters.

The Potts model is a powerful tool to uncover community structure in complex networks. Here, we propose a framework to reveal the optimal number of communities and stability of network structure by quantitatively analyzing the dynamics of the Potts model. Specifically we model the community structure detection Potts procedure by a Markov process, which has a clear mathematical explanation. Then we show that the local uniform behavior of spin values across multiple timescales in the representation of the Markov variables could naturally reveal the network's hierarchical community structure. In addition, critical topological information regarding multivariate spin configuration could also be inferred from the spectral signatures of the Markov process. Finally an algorithm is developed to determine fuzzy communities based on the optimal number of communities and the stability across multiple timescales. The effectiveness and efficiency of our algorithm are theoretically analyzed as well as experimentally validated.

The suppression of friction between sliding objects, modulated or enhanced by mechanical vibrations, is well established. However, the precise conditions of occurrence of these phenomena are not well understood. Here we address these questions focusing on a simple spring-block model, which is relevant to investigate friction both at the atomistic as well as the macroscopic scale. This allows us to investigate the influence on friction of the properties of the external drive, of the geometry of the surfaces over which the block moves, and of the confining force. Via numerical simulations and a theoretical study of the equations of motion, we identify the conditions under which friction is suppressed and/or recovered, and we evidence the critical role played by surface modulations and by the properties of the confining force.

In this paper we study how deterministic features presented by a system can be used to perform direct transport in a quasisymmetric potential and weak dissipative system. We show that the presence of nonhyperbolic regions around acceleration areas of the phase space plays an important role in the acceleration of particles giving rise to direct transport in the system. Such an effect can be observed for a large interval of the weak asymmetric potential parameter allowing the possibility to obtain useful work from unbiased nonequilibrium fluctuation in real systems even in a presence of a quasisymmetric potential.