Low-pressure pulsed plasmas are widely used in various technological applications. Understanding of the phenomena taking place in afterglow phase of the discharge makes possible the optimization of the operation conditions and improvement of the technical parameters. At low pressure the electron component of the plasma determines the main features of the discharge since its behavior dominates all other plasma properties. We study the electron kinetics in a low-pressure afterglow plasma of an inductively coupled discharge by means of a self-consistent model which uses the nonlocal kinetic approach. The main features of the model are given. Special attention is paid to determination of the steady state of the discharge from which the decay of the plasma begins. Emphasis is also put on the description of the collisional interaction between the electrons and gas. Results of theoretical investigations for argon at a pressure of $2–4\mathrm{Pa}$ are presented. Calculated temporal evolutions of the isotropic part of the electron velocity distribution function, electron density, mean electron energy, and wall potential are discussed in comparison with experimental data.

We report on the early time ordering in a nematic liquid crystal subjected to a sudden change in an external ac electric field. We compare time evolution for two different initial states of electroconvection. Electroconvection is a highly driven state of a nematic liquid crystal involving convective motion of the fluid and periodic variations of the molecular alignment. By suddenly changing either the voltage or the frequency of the applied ac field, the system is brought to the same thermodynamic conditions. The time ordering of the system is characterized by the evolution of features of the power spectrum, including the average wave number, total power, and shape of the power spectrum. We observe that ordering of the system occurs faster after a sudden change in frequency than it does after a sudden change in voltage.

We investigate shear strength properties of wet granular materials in the pendular state (i.e., the state where the liquid phase is discontinuous) as a function of water content. Sand and glass beads were wetted and tested in a direct shear cell and under various confining pressures. In parallel, we carried out three-dimensional molecular dynamics simulations by using an explicit equation expressing capillary force as a function of interparticle distance, water bridge volume, and surface tension. We show that, due to the peculiar features of capillary interactions, the major influence of water content over the shear strength stems from the distribution of liquid bonds. This property results in shear strength saturation as a function of water content. We arrive at the same conclusion by a microscopic analysis of the shear strength. We propose a model that accounts for the capillary force, the granular texture, and particle size polydispersity. We find fairly good agreement of the theoretical estimate of the shear strength with both experimental data and simulations. From numerical data, we analyze the connectivity and anisotropy of different classes of liquid bonds according to the sign and level of the normal force as well as the bond direction. We find that weak compressive bonds are almost isotropically distributed whereas strong compressive and tensile bonds have a pronounced anisotropy. The probability distribution function of normal forces is exponentially decreasing for strong compressive bonds, a decreasing power-law function over nearly one decade for weak compressive bonds, and an increasing linear function in the range of tensile bonds. These features suggest that different bond classes do not play the same role with respect to the shear strength.

We studied molecular organization in cylindrical nanocavities using liquid crystals. NMR analysis shows high surface-induced ordering way above the bulk critical temperature. The surface-order evolution reveals replacement of the isotropic phase by a paranematic phase and surface-induced disordering in the nematic phase. Due to strong surface potential and nanoconfinement, complete wetting and continuous evolution of the surface-order parameter are observed through the nematic-paranematic transition. As we show, the counter-intuitive absence of complete phase transition at the interface while an abrupt phase transition was measured in the averaged order parameter is in good agreement with established theories.

We present particle-based simulations and a continuum theory for steady rotating flocks formed by self-propelling particles (SPPs) in two-dimensional space. Our models include realistic but simple rules for the self-propelling, drag, and interparticle interactions. Among other coherent structures, in particle-based simulations we find steady rotating flocks when the velocity of the particles lacks long-range alignment. Physical characteristics of the rotating flock are measured and discussed. We construct a phenomenological continuum model and seek steady-state solutions for a rotating flock. We show that the velocity and density profiles become simple in two limits. In the limit of weak alignment, we find that all particles move with the same speed and the density of particles vanishes near the center of the flock due to the divergence of centripetal force. In the limit of strong body force, the density of particles within the flock is uniform and the velocity of the particles close to the center of the flock becomes small.

In this paper we formalize the small-world effect which describes the surprising fact that a hybrid graph composed of a local graph component and a very sparse random graph has a diameter of $O\left(\ln n\right)$ whereby the diameter of both components alone is much higher. We show that a large family of these hybrid graphs shows this effect and that this generalized family also includes classic small-world models proposed by various authors although not all of them are captured by the small-world definition given by Watts and Strogatz. Furthermore, we give a detailed upper bound of the hybrid’s graph diameter for different choices of the expected number of random edges by applying a new kind of proof pattern that is applicable to a large number of hybrid graphs. The focus in this paper is on presenting a flexible family of hybrid graphs showing the small-world effect that can be tuned closely to real-world systems.

Based on the weighted scale-free network model proposed by Barrat, Barthélemy, and Vespignani [Phys. Rev. Lett. 92, 228701 (2004)] and enlightened by our local-world concept [Li and Chen, Physica A 328, 274 (2003)], we propose two generalized local-world (GLW) models for weighted complex networks. Theoretical analysis and numerical simulations show that the GLW models generate weighted networks as a crossover between exponential and scale-free weighted networks, and exhibit an alteration from assortative networks to disassortative networks.

We report on the dynamics and structure of the turbulent velocity field in a high-Rayleigh-number $(\mathrm{Ra}=5.9\times {10}^8)$ thermal convection cell with an aspect ratio of 4. Spectral density functions (measured with laser Doppler velocimetry) indicated the existence of a large-scale periodic component. The long-time mean flow field (measured with particle image velocimetry) revealed that the large-scale circulation in the aspect-ratio-4 cell consists of two corotating rolls. The periodicity in the flow could be traced back to the alternating growth and decay of these rolls.

This Comment corrects the error which appeared in the calculation of the degree distribution of random Apollonian networks [T. Zhou, G. Yan, and B. H. Wang, Phys. Rev. E. 71, 046141 (2005)]. As a result, the expression of $P\left(k\right)$, which gives the probability that a randomly selected node has exactly $k$ edges, has the form $P\left(k\right)\propto 1∕\left[k(k+1)(k+2)\right]$.

We give a brief review on the analytic approaches for finding the degree distribution. The method used in the comment (master-equation) and the one in the original paper (rate-equation) [T. Zhou, G. Yan, and B. H. Wang, Phys. Rev. E 71, 046141 (2005)] are two mainstream methods. The former is more accurate, and the latter is more widely used since it can solve some complicated problems that cannot be easily solved by the former approach. The analytic forms of finding the degree distribution obtained by the above two methods have the same asymptotic behaviors.

We investigate the asymptotic time behavior of the solutions of a large class of linear differential equations that generalize the free-particle Schrödinger and diffusion equations, containing the standard ones as particular cases. We find general scalings that depend only on characteristic features of both the arbitrary initial condition and the Green function associated with the evolution equation. Basically, the amplitude of a long-time solution can be expressed in terms of low order moments of the initial condition (if finite) and low order spatial derivatives of the Green function. These derivatives can also be of the fractional type, which naturally arise when moments are divergent. We apply our results to a large class of differential equations that includes the fractional Schrödinger and Lévy diffusion equations. In particular, we show that, except for threshold cases, the amplitude of a packet may follow the asymptotic law $t^{-\alpha }$, with arbitrary positive $\alpha$.

We performed equilibrium and nonequilibrium molecular dynamics simulation to study electro-osmotic flows inside charged nanochannels with different types of surface roughness. We modeled surface roughness as a sequence of two-dimensional subnanoscale grooves and ridges (step function-type roughness) along the flow direction. The amplitude, spatial period, and symmetry of surface roughness were varied. The amplitude of surface roughness was on the order of the Debye length. The walls have uniform negative charges at the interface with fluids. We included only positive ions (counterions) for simplicity of computation. For the smooth wall, we compared our molecular dynamics simulation results to the well-known Poisson-Boltzmann theory. The density profiles of water molecules showed “layering” near the wall. For the rough walls, the density profiles measured from the wall are similar to those for the smooth wall except near where the steps are located. Because of the layering of water molecules and the finite size effect of ions and the walls, the ionic distribution departs from the Boltzmann distribution. To further understand the structure of water molecules and ions, we computed the polarization density. Near the wall, its z component dominates the other components, indicating the preferred orientation (“ordering”) of water molecules. Especially, inside the groove for the rough walls, its maximum is 10% higher (stronger ordering) than for the smooth wall. The dielectric constant, computed with a Clausius-Mosotti-type equation, confirmed the ordering near the wall and the enhanced ordering inside the groove. The residence time and the diffusion coefficient, computed using the velocity autocorrelation function, showed that the diffusion of water and ions along the direction normal to the wall is significantly reduced near the wall and further decreases inside the groove. Along the flow direction, the diffusion of water and ions inside the groove is significantly lowered while it is similar to the bulk value elsewhere. We performed nonequilibrium molecular dynamics simulation to compute electro-osmotic velocities and flow rates. The velocity profiles correspond to those for overlapped electric double layers. For the rough walls, velocity inside the groove is close to zero, meaning that the channel height is effectively reduced. The flow rate was found to decrease as the period of surface roughness decreases or the amplitude of surface roughness increases. We defined the ζ potential as the electrostatic potential at the location of a slip plane. We computed the electrostatic potential with the ionic distribution and the dielectric constant both from our molecular dynamics simulation. We estimated the slip plane from the velocity profile. The ζ potential showed the same trend as the flow rate: it decreases with an increasing amplitude and a decreasing period of surface roughness.

We report measurements of the static shear modulus of electrorheological (ER) fluids consisting of water-wetted silica microspheres in silicone oil. A shear-annealing method, using creep-recovery (CR) cycles under an external electric field, is used to enhance ER properties of the fluid. The shear-annealing method enables the silica spheres in the ER fluid to form better aligned and denser column microstructures. A stable state with elastic shear deformation is obtained after a sufficient number of CR cycles, with an optimal combination of stress duration and shear strength. Static shear modulus is obtained by measuring the elastic deformations at different shear stresses for an electric field frequency from $10\text{to}1000\mathrm{Hz}$. A water-bridge model is proposed to explain the enhanced shear modulus.

The velocity discretization is a critical step in deriving the lattice Boltzmann (LBE) from the continuous Boltzmann equation. This problem is considered in the present paper, following an alternative approach and giving the minimal discrete velocity sets in accordance with the order of approximation that is required for the LBE with respect to the continuous Boltzmann equation and with the lattice structure. Considering $N$ to be the order of the polynomial approximation to the Maxwell-Boltzmann equilibrium distribution, it is shown that solving the discretization problem is equivalent to finding the inner product in the discrete space induced by the inner product in the continuous space that preserves the norm and the orthogonality of the Hermite polynomial tensors in the Hilbert space generated by the functions that map the velocity space onto the real numbers space. As a consequence, it is shown that, for each order $N$ of approximation, the even-parity velocity tensors are isotropic up to rank $2N$ in the discrete space. The norm and the orthogonality restrictions lead to space-filling lattices with increased dimensionality when compared with presently known lattices. This problem is discussed in relation with a discretization approach based on a finite set of orthogonal functions in the discrete space. Two-dimensional square lattices intended to be used in thermal problems and their respective equilibrium distributions are presented and discussed.

We analyze in which experimental conditions the concept of electrical impedance is useful for an electrolytic cell. The analysis is performed by solving numerically the differential equations governing the phenomenon of the redistribution of the ions in the presence of an external electric field and comparing the results with the ones obtained by solving the linear approximation of these equations. The control parameter in our study is the amplitude of the applied voltage, assumed a simple harmonic function of the time. We show that the bulk distribution of ions close to the electrodes differs from the one obtained by means of the linear analysis already for small amplitudes of the applied voltage. Nevertheless, the concept of electrical impedance remains valid. For larger amplitudes, the current in the circuit is no longer harmonic at the same frequency of the applied voltage. Therefore the concept of electrical impedance is no longer meaningful.

We study the equilibrium behavior of one-dimensional granular clusters and one-particle granular gases for a variety of velocity-dependent coefficients of restitution $r$. We obtain equations describing the long-time behavior for the cluster’s pressure, rms velocity, and granular interspacing. We show that for extremely long times, clusters with velocity-dependent coefficients of restitution are unstable and dissolve into homogeneous, quasielastic gases, but clusters with velocity-independent $r$ are permanent. This is in accordance with hydrodynamic studies pointing to the transient nature of density instabilities for granular gases with velocity-dependent $r$.

Fluctuations in fluid velocity and fluctuations in electric fields may both give rise to forces acting on small particles in colloidal suspensions. Such forces in part determine the thermodynamic stability of the colloid. At the classical statistical thermodynamic level, the fluid velocity and electric field contributions to the forces are comparable in magnitude. When quantum fluctuation effects are taken into account, the electric-fluctuation-induced van der Waals forces dominate those induced by purely fluid-mechanical motions. The physical principles are applied in detail for the case of colloidal particle attraction to the walls of the suspension container and more briefly for the case of forces between colloidal particles.

Structure and conformation of spontaneous self-assembled calix[8]arenes derivatives are studied by means of static and dynamic light scattering and electrophoretic mobility. These amphiphilic molecules are in the aggregated form in aqueous solution, in a wide range of $p\mathrm{H}$; they take a vesicle structure in neutral and basic $p\mathrm{H}$ environment, but, in relatively strong acidic conditions (below $p\mathrm{H}=4.5$), a transition from vesicle to micelle occurs. The structural change is driven by the surface charge density. At neutral $p\mathrm{H}$ calix[8]arenes take a negative surface charge, which prevents coagulation and ensures stability; at acidic $p\mathrm{H}$ the surface charge tend to become positive because of the protonation of the hydrophilic head. These $p\mathrm{H}$-responsive aggregates, able to release an encapsulated hydrophilic guest, are promising systems for application as nanocarriers.

Vibrational dynamics of proteins and energy flow depend on protein geometry as well as interactions of a protein molecule with the surrounding solvent. We compute the mass fractal dimension $D$ of proteins ranging from 100 to over 10 000 amino acids comparing values for the bare protein with those computed when buried and hydration waters are included in the calculation. Including water in the calculation increases $D$ by about 0.3 to 2.87 on average above $D$ computed for the dehydrated protein. The mass fractal dimension of proteins that are partially unfolded by molecular dynamics (MD) simulation is also computed and found to vary little when the radius of gyration changes within about 10% of that for the Protein Data Bank structure. MD simulations of vibrational energy diffusion in proteins reveal that the exponent characterizing anomalous diffusion of vibrational energy does not change much with hydration, which is seen to be due to an increase in the spectral dimension with hydration by a factor similar to the increase in $D$.

Counterions at charged rodlike polymers exhibit a condensation transition at a critical temperature (or, equivalently, at a critical linear charge density for polymers), which dramatically influences various static and dynamic properties of charged polymer solutions. We address the critical and universal aspects of this transition for counterions at a single charged cylinder in two and three spatial dimensions using numerical and analytical methods. By introducing a Monte Carlo sampling method in logarithmic radial scale, we are able to numerically simulate the critical limit of infinite system size (corresponding to the infinite-dilution limit) within tractable equilibration times. The critical exponents are determined for the inverse moments of the counterionic density profile (which play the role of the order parameters and represent the mean inverse localization length of counterions) both within mean-field theory and within Monte Carlo simulations. In three dimensions (3D), we demonstrate that correlation effects (neglected within mean-field theory) lead to an excessive accumulation of counterions near the charged cylinder below the critical temperature (i.e., in the condensation phase), while surprisingly, the critical region exhibits universal critical exponents in accordance with mean-field theory. Also in contrast with the typical trend in bulk critical phenomena, where fluctuations become more enhanced in lower dimensions, we demonstrate, using both numerical and analytical approaches, that mean-field theory becomes exact for the two-dimensional (2D) counterion-cylinder system at all temperatures (Manning parameters), when the number of counterions tends to infinity. For a finite number of particles, however, the 2D problem displays a series of peculiar singular points (with diverging heat capacity), which reflect successive delocalization events of individual counterions from the central cylinder. In both 2D and 3D, the heat capacity shows a universal jump at the critical point and the internal energy develops a pronounced peak. The asymptotic behavior of the energy peak location is used to determine the critical temperature, which is also found to be in agreement with the mean-field prediction.