The majority of dynamical studies in power systems focus on the high-voltage transmission grids where models consider large generators interacting with crude aggregations of individual small loads. However, new phenomena have been observed indicating that the spatial distribution of collective, nonlinear contribution of these small loads in the low-voltage distribution grid is crucial to the outcome of these dynamical transients. To elucidate the phenomenon, we study the dynamics of voltage and power flows in a spatially extended distribution feeder (circuit) connecting many asynchronous induction motors and discover that this relatively simple 1+1 (space+time) dimensional system exhibits a plethora of nontrivial spatiotemporal effects, some of which may be dangerous for power system stability. Long-range motor-motor interactions mediated by circuit voltage and electrical power flows result in coexistence and segregation of spatially extended phases defined by individual motor states, a “normal” state where the motors’ mechanical (rotation) frequency is slightly smaller than the nominal frequency of the basic ac flows and a “stalled” state where the mechanical frequency is small. Transitions between the two states can be initiated by a perturbation of the voltage or base frequency at the head of the distribution feeder. Such behavior is typical of first-order phase transitions in physics, and this 1+1 dimensional model shows many other properties of a first-order phase transition with the spatial distribution of the motors’ mechanical frequency playing the role of the order parameter. In particular, we observe (a) propagation of the phase-transition front with the constant speed (in very long feeders) and (b) hysteresis in transitions between the normal and stalled (or partially stalled) phases.

To study the influence of dynamic interactions between turbulent vortical structures and polymer stress on turbulent friction drag reduction, a series of simulations of channel flow is performed. We obtain self-consistent evolution of an initial eddy in the presence of polymer stresses by utilizing the finitely extensible nonlinear elastic-Peterlin (FENE-P) model. The initial eddy is extracted by the conditional averages for the second quadrant event from fully turbulent Newtonian flow, and the initial polymer conformation fields are given by the solutions of the FENE-P model equations corresponding to the mean shear flow in the Newtonian case. At a relatively low Weissenberg number We${}_{\tau }$ (=50), defined as the ratio of the polymer relaxation time to the wall time scale, the generation of new vortices is inhibited by polymer-induced countertorques. Thus fewer vortices are generated in the buffer layer. However, the head of the primary hairpin is unaffected by the polymer stress. At larger We${}_{\tau }$ values ($\ge 100$), the hairpin head becomes weaker and vortex autogeneration and Reynolds stress growth are almost entirely suppressed. The temporal evolution of the vortex strength and polymer torque magnitude reveals that polymer extension by the vortical motion results in a polymer torque that increases in magnitude with time until a maximum value is reached over a time scale comparable to the polymer relaxation time. The polymer torque retards the vortical motion and Reynolds stress production, which in turn weakens flow-induced chain extension and torque itself. An analysis of the vortex time scales reveals that with increasing We${}_{\tau }$, vortical motions associated with a broader range of time scales are affected by the polymer stress. This is qualitatively consistent with Lumley's time criterion for the onset of drag reduction.

The propagation of the solitary wave in a dusty plasma bounded in finite geometry has been investigated. By employing the reductive perturbation method, we obtain a quasi Korteweg–de Vries-type equation. It is noted that the larger the value of viscosity coefficient ${\mu }_0$, the stronger the damping of the solitary wave. On the other hand, the larger the value of the radius of bounded geometry $R$, the weaker the damping of the solitary wave. It is also found that the quasisolitary wave exists. However, the solitary wave is a damping one, and it will disappear in the limited case of $R\to 0$ or ${\mu }_0\to +\infty$.

We consider propagating, spatially localized waves in a class of equations that contain variational and nonvariational terms. The dynamics of the waves is analyzed through a collective coordinate approach. Motivated by the variational approximation, we show that there is a natural choice of projection onto collective variables for reducing the governing (nonlinear) partial differential equation (PDE) to coupled ordinary differential equations (ODEs). This projection produces ODEs whose solutions are exactly the stationary states of the effective Lagrangian that would be considered in applying the variational approximation method. We illustrate our approach by applying it to a modified Fisher equation for a traveling front, containing a non-constant-coefficient nonlinear term. We present numerical results that show that our proposed projection captures both the equilibria and the dynamics of the PDE much more closely than previously proposed projections.

Outflow boundary condition (OBC) is a critical issue in computational fluid dynamics. As a type of numerical method for fluid flows, the lattice Boltzmann equation (LBE) method has gained much success in a variety of complex flows, and certain OBCs have been suggested for the LBE in simulating simple single-phase flows. However, very few discussions on the OBCs have been made for the two-phase LBE method. In this work, three types of OBCs that are widely used in the LBE for single-phase flows, i.e., the Neumann boundary condition, the convective boundary condition, and the extrapolation boundary condition, are extended to a two-phase LBE method and their performances are investigated. The comprehensive results of several two-phase flows show that these boundary conditions behave quite differently in the simulations of two-phase flows. Specifically, it is found that the Neumann boundary condition and the extrapolation boundary condition give rather poor predictions, while the type of convective boundary conditions work well, although the choice of the convection velocity has some slight influences on the results. We also apply these OBC schemes to some other two-phase models, and similar observations are found.

It is a well-known fact that the statistical behaviors of level fluctuation and level correlation in the energy-level spectra are the most efficient tool to characterize quantum chaos in nonintegrable quantum systems. The system of interacting trapped bosons is a complex system where the low-lying energy levels are highly influenced by the level repulsion. In this case, interatomic interaction is a dominating fact with strong level correlation between distant levels. Here we numerically calculate the correlation function, number variance, and Dyson-Mehta least-square deviation for the low-lying levels for a few thousand interacting trapped bosons, and our data show good analogy with the Gaussian orthogonal ensemble (GOE) results with a signature of chaos. In the next part of our study, the energy spectrum of these low-lying levels is considered as a discrete signal and the fluctuation of the excitation energy is considered as discrete time series. Then we calculate numerically the height-height correlation function for different order of momentum. In our study logarithmic correlation structure is found instead of multiscaling structure, and we observe that spectral statistics are compatible with those of GOE.

We consider the one-dimensional Glauber dynamics with coupling disorder in terms of bilinear fermion Hamiltonians. Dynamic exponents embodied in the spectrum gap of these latter are evaluated numerically by averaging over both binary and Gaussian disorder realizations. In the first case, these exponents are found to follow the nonuniversal values of those of plain dimerized chains. In the second situation their values are still nonuniversal and subdiffusive below a critical variance above which, however, the relaxation time is suggested to grow as a stretched exponential of the equilibrium correlation length.

Quite recently, we reported a semianalytical equation of state (EOS) for the Ga-Pb alloy [Phys. Rev. B 78, 024205 (2008)], which was based on the first-order perturbation theory of fluid mixtures, within the simplified random phase approximation, in conjunction with the Grosdidier et al. model pair potentials for Ga-Ga and Pb-Pb with a suitable nonadditive pair potential between Ga-Pb unlike pairs. In the present work, we employ the present EOS to calculate the Ga-Pb phase diagram along the immiscibility gap region. The accuracy of the EOS is tested by consulting the empirical binodal curve. A statistical-mechanical-based theory for the surface tension is employed to obtain an analytical expression for the alloy surface tension. We calculated the surface tension along the bimodal curve and at extreme conditions of temperatures and pressures. The surface tension exhibits reasonably well the prewetting transition of Pb atoms at the surface of the Ga-rich liquid alloy and could qualitatively explain the prewetting phenomena occurring in the Ga-rich side of the phase diagram. The predicted prewetting line and wetting temperature qualitatively agree with the empirical measurements.

We show that in a finite one-dimensional (1D) system with diffusive thermal transport described by the Fourier's law, negative differential thermal conductance (NDTC) cannot occur when the temperature at one end is fixed and there are no abrupt junctions. We demonstrate that NDTC in this case requires the presence of junction(s) with temperature-dependent thermal contact resistance (TCR). We derive a necessary and sufficient condition for the existence of NDTC in terms of the properties of the TCR for systems with a single junction. We show that under certain circumstances we even could have infinite (negative or positive) differential thermal conductance in the presence of the TCR. Our predictions provide theoretical basis for constructing NDTC-based devices, such as thermal amplifiers, oscillators, and logic devices.

Dynamic hysteresis phenomena are widespread in physical sciences and describe the complex behavior of systems driven out of equilibrium by a periodic forcing. We use here paramagnetic colloids above a stripe-patterned garnet film as the model system to study dynamic hysteresis, the latter induced when the particles are periodically translated by an oscillating magnetic field. In contrast to the expected behavior for a bistable system, we observe that the area of the hysteresis loop decreases by increasing the driving frequency and reduces to zero for frequencies higher than $5–7{\text{s}}^{-1}$. To explain the experimental results, we develop a simple model based on an overdamped Brownian particle driven by a periodic potential with an oscillating amplitude.

Transient polyelectrolyte hydrogels were formed by self-assembly of triblock copolyelectrolytes with a central hydrophilic block, poly(acrylic acid) (PAA), and two hydrophobic end blocks, poly($n$-butyl acrylate${}_{50\%}$-stat-acrylic acid${}_{50\%}$) [P($n$BA${}_{50\%}$-stat-AA${}_{50\%}$)]. The relaxation of the concentration fluctuations was investigated by dynamic light scattering as a function of the concentration, the pH, the temperature, and the ionic strength. A relatively fast mode was observed at all polymer concentrations caused by cooperative diffusion of the polymers. Above the critical percolation concentration a second slow relaxation mode was observed caused by a linear displacement of small heterogeneities in the network with constant velocity. The relative amplitude of the slow mode was determined by the strength of the electrostatic repulsion. The velocity of the displacement in the transient network is shown to be directly correlated to the terminal relaxation time of the shear modulus and has the same Arrhenius temperature dependence. Both the velocity of the displacement and the mechanical relaxation strongly slow down with decreasing degree of ionization below 0.7 and increasing ionic strength above 0.5 M. A ballistic relaxation process has been reported earlier for colloidal gels, and the present study shows that it can also occur in polymeric networks.

A liquid drop trapped in a microchannel, in which both contact angle (wettability) and opening angle (geometry) can vary with position, is investigated based on the minimization of free energy. The calculus of variation yields the Young-Laplace equation and its further integration leads to the general force balance. The equilibrium position of the trapped drop is determined by the balance between the area-mean capillary force and the area-mean hydrostatic pressure difference. Trapped liquid drops in truncated cones and hyperboloids are studied to elucidate our theory. As the volume of the drop trapped in the hydrophilic cones is increased, four regimes separated by three critical volumes are identified. The drop is either trapped at the narrow end or away from the cone top. The solution at the cone top satisfies the force balance by adjusting the upper contact angle, which is experimentally observed and verified by Surface Evolver (SE) simulations. Multiple stable states can exist in a particular regime. The hyperboloid tube in which the opening angle varies with position is also considered. As the gravitational strength is increased in hydrophilic hyperboloid, four regimes separated by three critical gravitational strengths are identified. The drop is either trapped near the neck or below the neck. Unlike hydrophilic cones, the drop stays near the neck of the hyperboloid due to varying opening angles. Multiple stable states are also observed. For both cone and hyperboloid, hydrophobic cases are studied as well and all theoretical solutions of the force balance agree well with SE simulation outcomes.

We demonstrate manipulation and transport of microparticles and even fluorescent molecules by the thermally induced gradient of the order parameter in the nematic liquid crystal. We use IR light absorption of the tightly focused beam of laser tweezers to heat locally a thin layer of the nematic liquid crystal by several degrees. This creates a spatial gradient of temperature of the nematic liquid crystal over separations of several tens of micrometers. We show that a dipolar colloidal particle is attracted into the hot spot of the laser tweezers. The depth of the trapping potential scales linearly with particle radius, indicating that the trapping mechanism is due to elastic self-energy of the distorted nematic liquid crystal around the particle and softening of the elasticity with increased temperature of the liquid crystal. We also demonstrate that this thermal trapping mechanism is efficient down to the nanoscale, as fluorescent molecules are also transported into hotter regions of the liquid crystal. This effect is absent in the isotropic phase, which calls into question particle transport due to the Soret effect.

We present an analytical approach to determining the expected cascade size in a broad range of dynamical models on the class of highly clustered random graphs introduced by Gleeson [J. P. Gleeson, Phys. Rev. E 80, 036107 (2009)]. A condition for the existence of global cascades is also derived. Applications of this approach include analyses of percolation, and Watts's model. We show how our techniques can be used to study the effects of in-group bias in cascades on social networks.

The distribution of zeros of the Husimi function has proven a useful tool in the characterization of regular and chaotic quantum states of dynamical systems. In a previous paper [Phys. Rev. E 82, 026201 (2010)], we showed how the quantum transition from order to chaos in three different molecular systems (LiCN, HCN, and HO${}_2$) can be understood by means of the correlation diagram of eigenenergies versus the Planck's constant. An order-chaos frontier of scars (eigenstates localized over unstable and stable complementary, in the sense of the Poincaré-Birkhoff theorem, periodic orbits) was observed. In this paper, we show how the distribution of zeros of the Husimi function can be related to the onset of chaos in these molecular systems, showing a very interesting feature at the frontier of scars; namely, some zeros of the Husimi function localize over the stable and unstable fixed points corresponding to the two complementary periodic orbits, this representing the quantum equivalent to the Poincaré-Birkhoff theorem.

Extreme surface waves in a deep-water long-crested sea are often interpreted as a manifestation in the real world of the so-called breathing solitons of the focusing nonlinear Schrödinger equation. While the spontaneous emergence of such coherent structures from nonlinear wave dynamics was demonstrated to take place in fiber-optics systems, the same point remains far more controversial in the hydrodynamic case. With the aim to shed further light on this matter, the emergence of breatherlike coherent wave groups in a long-crested random sea is investigated here by means of high-resolution spectral simulations of the fully nonlinear two-dimensional Euler equations. The primary focus of our study is to parametrize the structure of random wave fields with respect to the Benjamin-Feir index, which is a nondimensional measure of the energy localization in Fourier space. This choice is motivated by previous results, showing that extreme-wave activity in a long-crested sea is highly sensitive to such a parameter, which is varied here by changing both the characteristic spectral bandwidth and the average wave steepness. It is found that coherent wave groups, closely matching realizations of Kuznetsov-Ma breathers in Euler dynamics, develop within wave fields characterized by sufficiently narrow-banded spectra. The characteristic spatial and temporal scales of wave group dynamics, and the corresponding occurrence of extreme events, are quantified and discussed by means of space-time autocorrelations of the surface elevation envelope and extreme-event statistics.

Nonlocal electrostatic interactions associated with finite solvent size and ion polarizability are investigated within the mean-field linear response theory. To this end, we introduce a field-theoretic model of a polar liquid composed of linear multipole solvent molecules and embedding polarizable ions modeled as Drude oscillators. Unlike previous dipolar Poisson-Boltzmann formulations treating the solvent molecules as point dipoles, our model is able to qualitatively reproduce the non-local dielectric response behavior of polar liquids observed in molecular dynamics simulations and atomic force microscope experiments for water solvent at charged interfaces. The present theory explains the formation of the associated interfacial hydration layers in terms of a cooperative dipolar response mechanism driven by the reaction of the solvent molecules to their own polarization field. We also incorporate into the theory the relative multipole moments of water molecules obtained from quantum mechanical calculations and show that the multipolar contributions to the dielectric permittivity are largely dominated by the dipolar one. We find that this stems from the mutual cancellation of the first two interfacial hydration layers of opposite net charge for multipolar liquids. Within the same nonlocal dielectric response theory, we show that the induced ion polarizability reverses the interfacial ion density trends predicted by the Poisson-Boltzmann theory, resulting in a surface affinity of coions and exclusion of counterions. The results indicate that the consideration of the discrete charge composition of solvent molecules and ions is the key step towards a microscopic understanding of nonlocal electrostatic effects in polar solvents.

Experiments and simulations of the compaction force in a confined binary granular mixture column were conducted. We measured the resistance force encountered by a piston pushing a vertical granular mixture in this confined arrangement. Granular mixtures with two different particle sizes were considered; the size ratio and the size fraction were both varied. An important decrease of the compaction force was found for volumetric fractions between 15$\%$ and 40$\%$ and size ratios larger than 3. By conducting some supplementary discrete element simulations, we found that the force chain network is fractured and redistributed when small particles are present. Hence we argue that the reduction of compaction force results from the redistribution of force within the granular column.

We derive, from the dimensional-crossover criterion, a fundamental-measure density functional for parallel hard curved rectangles moving on a cylindrical surface. We derive it from the density functional of circular arcs of length $\sigma$ with centers of mass located on an external circumference of radius $R_0$. The latter functional in turn is obtained from the corresponding two-dimensional functional for a fluid of hard disks of radius $R$ on a flat surface with centers of mass confined onto a circumference of radius $R_0$. Thus the curved length of closest approach between the two centers of mass of hard disks on this circumference is $\sigma =2R_0{\sin }^{-1}(R/R_0)$, the length of the circular arcs. From the density functional of circular arcs, and by applying a dimensional expansion procedure to the spatial dimension orthogonal to the plane of the circumference, we finally obtain the density functional of curved rectangles of edge lengths $\sigma$ and $L$. Along with the derivation, we show that, when the centers of mass of the disks are confined to the exterior circumference of a circle of radius $R_0$, (i) for $R_0>R$, the exact Percus one-dimensional (1D) density functional of circular arcs of length $2R_0{\sin }^{-1}(R/R_0)$ is obtained, and (ii) for $R_0<R$, the zero-dimensional limit (a cavity that can hold one particle at most) is recovered. We also show that, for $R_0>R$, the obtained functional is equivalent to that of parallel hard rectangles on a flat surface of the same lengths, except that now the density profile of curved rectangles is a periodic function of the azimuthal angle, $\rho (\varphi ,z)=\rho (\varphi +2\pi ,z)$. The phase behavior of a fluid of aligned curved rectangles is obtained by calculating the free-energy branches of smectic, columnar, and crystalline phases for different values of the ratio $R_0/R$ in the range $1<R_0/R⩽4$; the smectic phase turns out to be the most stable except for $R_0/R=4$, where the crystalline phase becomes reentrant in a small range of packing fractions. When $R_0/R<1$ the transition is absent, since the density functional of curved rectangles reduces to the 1D Percus functional.

A measure is derived to quantify directed information transfer between pairs of vertices in a weighted network, over paths of a specified maximal length. Our approach employs a general, probabilistic model of network traffic, from which the informational distance between dynamics on two weighted networks can be naturally expressed as a Jensen Shannon divergence. Our network transfer entropy measure is shown to be able to distinguish and quantify causal relationships between network elements, in applications to simple synthetic networks and a biological signaling network. We conclude with a theoretical extension of our framework, in which the square root of the Jensen Shannon Divergence induces a metric on the space of dynamics on weighted networks. We prove a convergence criterion, demonstrating that a form of convergence in the structure of weighted networks in a family of matrix metric spaces implies convergence of their dynamics with respect to the square root Jensen Shannon divergence metric.