The primitive model of ionic systems is investigated within a field-theoretic description for the whole range of diameter-, $\lambda$, and charge, $Z$ ratios of the two ionic species. Two order parameters (OP) are identified. The relation of the OP’s to physically relevant quantities is nontrivial. Each OP is a linear combination of the charge density and the number-density waves. Instabilities of the disordered phase associated with the two OP’s are determined in the mean-field approximation (MF). In MF a gas-liquid separation occurs for any $Z$ and $\lambda \ne 1$. In addition, an instability with respect to various types of periodic ordering of the two kinds of ions is found. Depending on $\lambda$ and $Z$, one or the other transition is metastable in different thermodynamic states. For sufficiently large size disparity we find a sequence of fluid-crystal-fluid transitions for the increasing volume fraction of ions, in agreement with experimental observations. The instabilities found in MF represent weak ordering of the most probable instantaneous states, and are identified with structural loci associated with pretransitional effects.

In this paper, we report the long-range ordering effect observed in the electro-crystallization of Zn and ZnO from an ultrathin aqueous electrolyte layer of $\mathrm{Zn}\mathrm{S}{\mathrm{O}}_4$. The deposition branches are regularly angled, covered with random-looking, scalelike crystalline platelets of ZnO. Although the orientation of each crystalline platelet of ZnO appears random, transmission electron microscopy shows that they essentially possess the same crystallographic orientation as the single-crystalline zinc electrodeposit underneath. Based on the experimental observations, we suggest that this unique long-range ordering effect results from an epitaxial nucleation effect in electrocrystallization.

We calculate the surface phase diagram of a two-dimensional hard-rod fluid confined between two hard lines. In the first stage we study a semi-infinite system consisting of an isotropic fluid in contact with a single hard line. We have found complete wetting by the columnar phase at the wall-isotropic fluid interface. When the fluid is confined between two hard walls, capillary columnar ordering occurs via a first-order phase transition. For higher chemical potentials the system exhibits layering transitions even for very narrow slits (near the one-dimensional limit). The theoretical model used was a density-functional theory based on the fundamental-measure functional applied to a fluid of hard rectangles in the restricted-orientation approximation (Zwanzig model). The results presented here can be checked experimentally in two-dimensional granular media made of rods, where vertical motions induced by an external source and excluded volume interactions between the grains allow the system to explore those stationary states which entropically maximize packing configurations. We claim that some of the surface phenomena found here can be present in two-dimensional granular-media fluids.

The numerical study of the system of hydrodynamic equations that include both director motion and fluid flow, for a number of dynamic regimes in the $4\text{−}n$-pentyl-$4^{\prime }$-cyanobiphenyl multilayer film on the water surface has been carried out. Calculations show that the relaxation time over which the torques exerted per unit of liquid crystals volume puts the director $\widehat{\mathbf{n}}$ to be normal to the air-water interface, is one order of magnitude less in the case of accounting for the backflow effect than without accounting for that effect. The role of the charged water surface potential on the orientational relaxation process in the 5CB multilayer film on the water surface also has been investigated.

We studied the microscopic polymer conformations in the droplet detachment process of an elastic semidilute polyelectrolytic xanthan solution by measuring the instantaneous birefringence. As in earlier studies, we observe the suppression of the finite time singularity of the pinch-off process and the occurrence of an elastic filament. Our microscopic measurements reveal that the relatively stiff xanthan molecules are already significantly prestretched to about 90% of their final extension at the moment the filament appears. At later stages of the detachment process, we find evidence of a concentration enhancement due to the elongational flow.

Epileptic seizures are generally considered to result from excess and synchronized neural activity. Additionally, changes in amplitude and frequency are often seen in local field potential or electroencephalogram recordings during a seizure event. To investigate how seizures initiate, and how dynamical changes occur during seizure progression, we develop a neocortical network model based on a model suggested by Wilson [J. Theor. Biol. 200, 375 (1999)]. We propose a possible mechanism for seizure initiation as a bifurcation, and suggest that experimentally observed changes in field potential amplitude and frequency during the course of a seizure may be explained by noise-induced transitions among multistable states.

Using molecular dynamics we study heat conduction and diffusion of hard disks in one-dimensional narrow channels. When collisions preserve momentum the heat conduction $\kappa$ diverges with the number of disks $N$ as $\kappa \sim N^{\alpha }$ $(\alpha \approx 1∕3)$. Such a behavior is seen both when the ordering of disks is fixed (“pen-case” model), and when they can exchange their positions. Momentum conservation results also in sound-wave effects that enhance diffusive behavior and on an intermediate time scale (that diverges in the thermodynamic limit) normal diffusion takes place even in the “pen-case” model. When collisions do not preserve momentum, $\kappa$ remains finite and sound-wave effects are absent.

We study the betweenness centrality of fractal and nonfractal scale-free network models as well as real networks. We show that the correlation between degree and betweenness centrality $C$ of nodes is much weaker in fractal network models compared to nonfractal models. We also show that nodes of both fractal and nonfractal scale-free networks have power-law betweenness centrality distribution $P\left(C\right)\sim C^{-\delta }$. We find that for nonfractal scale-free networks $\delta =2$, and for fractal scale-free networks $\delta =2-1∕d_B$, where $d_B$ is the dimension of the fractal network. We support these results by explicit calculations on four real networks: pharmaceutical firms $(N=6776)$, yeast $(N=1458)$, WWW $(N=2526)$, and a sample of Internet network at the autonomous system level $(N=20566)$, where $N$ is the number of nodes in the largest connected component of a network. We also study the crossover phenomenon from fractal to nonfractal networks upon adding random edges to a fractal network. We show that the crossover length ${\ell }^{*}$, separating fractal and nonfractal regimes, scales with dimension $d_B$ of the network as $p^{-1∕d_B}$, where $p$ is the density of random edges added to the network. We find that the correlation between degree and betweenness centrality increases with $p$.

We present experimental results for two different sinusoidal functions competing to phase synchronize a Chua oscillator. Our approach involves real-time observation of the synchronization process. It shows that depending on the amplitude and frequency values of the two sinusoidal functions, the Chua oscillator can stay phase synchronized to one or the other of the inputs all the time or can alternate synchronous states between them. Numerical simulations show good agreement with the experimental observations.

The coalescence of a pair of droplets on a surface is investigated experimentally with images from detailed flow visualisations revealing the morphology of the process. It is found that they merge and evolve to a final state with a footprint that is peanut like in shape, with bulges along the longer sides resulting from the effects of inertia during spreading. The associated dynamics involve a subtle interplay between (i) the motion of the wetting process due to relaxation of the contact angle and (ii) a rapid rise in free-surface height above the point where coalescence began due to negative pressure generated by curvature. During the early stages of the motion, a traveling wave propagates from the point of initial contact up the side of each droplet as liquid is drawn into the neck region, and only when it reaches the apex of each do their heights start to decrease. A further feature of the rapid rise in height of the neck region is that the free surface there overshoots significantly its final equilibrium position; it reaches a height greater than that of the starting droplets, producing a self-excited oscillation that persists long after the system reaches its final morphological state in relation to its footprint.

Splashing occurs when a liquid drop hits a dry solid surface at high velocity. We report experimental studies of how the splash depends on the roughness and the texture of the surfaces as well as the viscosity of the liquid. For smooth surfaces, there is a “corona” splash caused by the presence of air surrounding the drop. There are several regimes that occur as the velocity and liquid viscosity are varied. There is also a “prompt” splash that depends on the roughness and texture of the surfaces. A measurement of the size distribution of the ejected droplets is sensitive to the surface roughness. For a textured surface in which pillars are arranged in a square lattice, experiment shows that the splashing has a fourfold symmetry. The splash occurs predominantly along the diagonal directions. In this geometry, two factors affect splashing the most: the pillar height and spacing between pillars.

The effect of a linear harmonic vibration on heat propagation is investigated in near-critical $\mathrm{S}{\mathrm{F}}_6$ under weightlessness conditions in space. Heat was issued from a pointlike source (thermistor), a situation representative of an industrial use of pressurized supercritical fluid storage. Two kinds of vibrations were used, large amplitude $\left(64\mathrm{mm}\right)$ at $0.2\mathrm{Hz}$ and low amplitude $\left(0.8\mathrm{mm}\right)$ at $1.6\mathrm{Hz}$, with temperatures from $5\mathrm{K}\text{to}20\mathrm{mK}$ from the critical temperature. The vibrations are seen to strongly affect the evolution and shape of the hot boundary layer (HBL), the heat exchange between the heat source and the fluid, and the bulk thermalization process by the adiabatic piston-effect process. The HBL is initially convected as symmetrical plumes over a distance that only depends on the vibration velocity and which corresponds to a Rayleigh-Bénard-like instability where the vibration acceleration acts as the earth gravity. Then the extremities of the plumes are convected perpendicularly to the direction of oscillation as two “pancakes,” a process encountered in the vibrational Rayleigh-Bénard instability. When the vibration velocity is small, only one pancake centered at the hot source is observed. Temperature evolutions of the hot source and the fluid are studied in different locations. Convection flows and adiabatic piston effect compete to determine the thermal dynamics, with the latter being the most efficient near the critical point. The experimental results are compared with a two-dimensional numerical simulation that highlights the similarities and differences between the very compressible van der Waals gas and an ideal gas.

The Euler equation (EE) is one of the basic equations in many physical fields such as fluids, plasmas, condensed matter, astrophysics, and oceanic and atmospheric dynamics. A symmetry group theorem of the $(2+1)$-dimensional EE is obtained via a simple direct method which is thus utilized to find exact analytical vortex and circumfluence solutions. A weak Darboux transformation theorem of the $(2+1)$-dimensional EE can be obtained for an arbitrary spectral parameter from the general symmetry group theorem. Possible applications of the vortex and circumfluence solutions to tropical cyclones, especially Hurricane Katrina 2005, are demonstrated.

We build an “all-electron” norm-conserving pseudopotential for boron which extends the use of ab initio molecular dynamics simulations up to 50 times the normal density ${\rho }_0$. This allows us to perform ab initio simulations of dense plasmas from the regime where quantum mechanical effects are important to the regime where semiclassical simulations based on the Thomas-Fermi approach are, by default, the only simulation method currently available. This study first allows one to establish, for the case of boron, the density regime from which the semiclassical Thomas-Fermi approach is legitimate and sufficient. It further brings forward various issues pertaining to the construction of pseudopotentials aimed at high-pressure studies.

The statistical mechanics of simple glass forming systems in two dimensions is worked out. The glass disorder is encoded via a Voronoi tesselation, and the statistical mechanics is performed directly in this encoding. The theory provides, without free parameters, an explanation of the glass transition phenomenology, including the identification of two different temperatures, $T_g$ and $T_c$, the first associated with jamming and the second associated with crystallization at very low temperatures.

We consider the model of the directed polymer in a random medium of dimension $1+3$, and investigate its multifractal properties at the localization-delocalization transition. In close analogy with models of the quantum Anderson localization transition, where the multifractality of critical wavefunctions is well established, we analyze the statistics of the position weights $w_L\left(\vec{r}\right)$ of the endpoint of the polymer of length $L$ via the moments $Y_q\left(L\right)={\sum }_{\vec{r}}{\left[w_L\left(\vec{r}\right)\right]}^q$. We measure the generalized exponents $\tau \left(q\right)$ and $\tilde{\tau }\left(q\right)$ governing the decay of the typical values $Y_q^{\mathrm{typ}}\left(L\right)=e^{\overline{\ln Y_q\left(L\right)}}\sim L^{-\tau \left(q\right)}$ and disorder-averaged values $\overline{Y_q\left(L\right)}\sim L^{-\tilde{\tau }\left(q\right)}$, respectively. To understand the difference between these exponents, $\tau \left(q\right)\ne \tilde{\tau }\left(q\right)$ above some threshold $q>q_c\sim 2$, we compute the probability distributions of $y=Y_q\left(L\right)∕Y_q^{\mathrm{typ}}\left(L\right)$ over the samples: We find that these distributions becomes scale invariant with a power-law tail $1∕y^{1+x_q}$. These results thus correspond to the Evers-Mirlin scenario [Phys. Rev. Lett. 84, 3690 (2000)] for the statistics of inverse participation ratios at the Anderson localization transitions. Finally, the finite-size scaling analysis in the critical region yields the correlation length exponent $\nu \sim 2$.

By using the asymptotic theory of Pemantle and Wilson [R. Pemantle and M. C. Wilson, J. Comb. Theory, Ser. A 97, 129 (2002)], asymptotic expansions of the free energy of the monomer-dimer model on two-dimensional semi-infinite $\infty \times n$ lattices in terms of dimer density are obtained for small values of $n$, at both high- and low-dimer-density limits. In the high-dimer-density limit, the theoretical results confirm the dependence of the free energy on the parity of $n$, a result obtained previously by computational methods by Y. Kong [Y. Kong, Phys. Rev. E 74, 061102 (2006); Phys. Rev. E 73, 016106 (2006);Phys. Rev. E 74, 011102 (2006)]. In the low-dimer-density limit, the free energy on a cylinder $\infty \times n$ lattice strip has exactly the same first $n$ terms in the series expansion as that of an infinite $\infty \times \infty$ lattice.

The minimal-work principle asserts that work done on a thermally isolated equilibrium system is minimal for the slowest (adiabatic) realization of a given process. This principle, one of the formulations of the second law, is operationally well defined for any finite (few particle) Hamiltonian system. Within classical Hamiltonian mechanics, we show that the principle is valid for a system of which the observable of work is an ergodic function. For nonergodic systems the principle may or may not hold, depending on additional conditions. Examples displaying the limits of the principle are presented and their direct experimental realizations are discussed.