An electrical method is used to study the early stages of coalescence of two low-viscosity drops. A drop of aqueous NaCl solution is suspended in air above a second drop of the same solution, which is grown until the drops touch. At that point a rapidly widening bridge forms between them. By measuring the resistance and capacitance of the system during this coalescence event, one can obtain information about the time dependence of the characteristic bridge radius and its characteristic height. At early times, a new asymptotic regime is observed that is inconsistent with previous theoretical predictions. The measurements at several drop radii and approach velocities are consistent with a model in which the two liquids coalesce with a slightly deformed interface.

A set of boundary conditions requiring vanishing of the normal components of the $\mathbf{D}$ and $\mathbf{B}$ vectors at the boundary surface is introduced and labeled as that of DB boundary. Basic properties of the DB boundary are studied in this paper. Reflection of an arbitrary plane wave, incident with a complex propagation vector, is analyzed for the planar DB boundary. It is shown that waves polarized transverse electric (TE) and transverse magnetic (TM) with respect to the normal of the boundary are reflected as from respective perfect electric conductor and perfect magnetic conductor planes. The basic problem of current source above the planar DB boundary is solved by applying TE and TM decomposition for the source. Realization of the DB boundary in terms of an interface of uniaxially anisotropic metamaterial half-space with zero axial medium parameters is considered. It is also shown that such a medium with small axial parameters acts as a spatial filter for waves incident at the interface which could be used for narrowing the beam of a directive antenna. Application of DB boundary as an isotropic soft surface with low interaction between antenna apertures also appears possible.

It is shown that cascade quasisynchronous frequency conversion due to quadratic nonlinearity can be described in terms of an effective cubic nonlinearity. This enables one to reduce a four-mode interaction problem to solving a system of two coupled nonlinear Schrödinger equations for the amplitudes of the waves participating in both nonlinear processes. Exact analytic solutions of the corresponding system are found in the form of multicomponent cnoidal waves with components expressed through a sum and a difference of two similar fundamental solutions of the Lamé equation with shifted arguments. It is shown that solutions obtained in such a way enable one to optimize the conversion efficiency because of full coverage of the range of possible boundary conditions.

Modeling and simulating gas flows in and around microdevices are a challenging task in both science and engineering. In practical applications, a gas is usually a mixture made of different components. In this paper we propose a lattice Boltzmann equation (LBE) model for microscale flows of a binary mixture based on a recently developed LBE model for continuum mixtures [P. Asinari and L.-S. Luo, J. Comput. Phys. 227, 3878 (2008)]. A consistent boundary condition for gas-solid interactions is proposed and analyzed. The LBE is validated and compared with theoretical results or other reported data. The results show that the model can serve as a potential method for flows of binary mixture in the microscale.

Systems of platelet-shaped nanostacks of the synthetic clay Na-fluorohectorite, suspended in saline solutions of various salt concentrations, exhibit a rich phase behavior with up to four phases coexisting in a single sample tube. They are studied here using small-angle x-ray scattering: the anisotropy of the obtained images is quantified, and, together with x-ray absorption measurements, this provides a precise determination of the phase boundaries, as well as a measure of the orientational ordering of the clay colloids in the various gel phases. The coexistence of different phases results from a sedimentation-induced vertical gradient in particle fraction. Quantitative relation of the vertical coordinate to the clay particle fraction in these samples allows determination of a phase diagram for these Na-fluorohectorite systems, as a function of the particle fraction and salt concentration.

The activity of spiking neurons is frequently described by renewal point process models that assume the statistical independence and identical distribution of the intervals between action potentials. However, the assumption of independent intervals must be questioned for many different types of neurons. We review experimental studies that reported the feature of a negative serial correlation of neighboring intervals, commonly observed in neurons in the sensory periphery as well as in central neurons, notably in the mammalian cortex. In our experiments we observed the same short-lived negative serial dependence of intervals in the spontaneous activity of mushroom body extrinsic neurons in the honeybee. To model serial interval correlations of arbitrary lags, we suggest a family of autoregressive point processes. Its marginal interval distribution is described by the generalized gamma model, which includes as special cases the log-normal and gamma distributions, which have been widely used to characterize regular spiking neurons. In numeric simulations we investigated how serial correlation affects the variance of the neural spike count. We show that the experimentally confirmed negative correlation reduces single-neuron variability, as quantified by the Fano factor, by up to 50%, which favors the transmission of a rate code. We argue that the feature of a negative serial correlation is likely to be common to the class of spike-frequency-adapting neurons and that it might have been largely overlooked in extracellular single-unit recordings due to spike sorting errors.

Complex networks have acquired a great popularity in recent years, since the graph representation of many natural, social, and technological systems is often very helpful to characterize and model their phenomenology. Additionally, the mathematical tools of statistical physics have proven to be particularly suitable for studying and understanding complex networks. Nevertheless, an important obstacle to this theoretical approach is still represented by the difficulties to draw parallelisms between network science and more traditional aspects of statistical physics. In this paper, we explore the relation between complex networks and a well known topic of statistical physics: renormalization. A general method to analyze renormalization flows of complex networks is introduced. The method can be applied to study any suitable renormalization transformation. Finite-size scaling can be performed on computer-generated networks in order to classify them in universality classes. We also present applications of the method on real networks.

A construct of anisotropy in bistable media is adopted to characterize the effects of anisotropy on pattern formation by means of anisotropic line tension. A velocity curvature relation is further derived to account for the anisotropic wave propagations. Stability analysis of transverse perturbations indicates that a sufficiently strong complex anisotropy can induce dynamical instabilities and even lead to a breakup of the wave patterns. Numerical simulations show that complex anisotropy can induce rich spatiotemporal behaviors in bistable media. The results of analysis and simulations demonstrate that this method successfully incorporates complex anisotropy into the reaction diffusion model and has general significance.

We analyze a large system of globally coupled phase oscillators whose natural frequencies are bimodally distributed. The dynamics of this system has been the subject of long-standing interest. In 1984 Kuramoto proposed several conjectures about its behavior; ten years later, Crawford obtained the first analytical results by means of a local center manifold calculation. Nevertheless, many questions have remained open, especially about the possibility of global bifurcations. Here we derive the system’s stability diagram for the special case where the bimodal distribution consists of two equally weighted Lorentzians. Using an ansatz recently discovered by Ott and Antonsen, we show that in this case the infinite-dimensional problem reduces exactly to a flow in four dimensions. Depending on the parameters and initial conditions, the long-term dynamics evolves to one of three states: incoherence, where all the oscillators are desynchronized; partial synchrony, where a macroscopic group of phase-locked oscillators coexists with a sea of desynchronized ones; and a standing wave state, where two counter-rotating groups of phase-locked oscillators emerge. Analytical results are presented for the bifurcation boundaries between these states. Similar results are also obtained for the case in which the bimodal distribution is given by the sum of two Gaussians.

We study numerically the effects of nonlinearity on the Anderson localization in lattices with disorder in one and two dimensions. The obtained results show that at moderate strength of nonlinearity a spreading over the lattice in time takes place with an algebraic growth of number of populated sites $\Delta n\propto t^{\nu }$. This spreading continues up to a maximal dimensionless time scale $t={10}^9$ reached in the numerical simulations. The numerical values of $\nu$ are found to be approximately 0.15–0.2 and 0.25 for the dimension $d=1$ and 2, respectively, being in a satisfactory agreement with the theoretical value $d∕(3d+2)$. During the computational times $t⩽{10}^9$ the localization is preserved below a certain critical value of nonlinearity. We also discuss the properties of the fidelity decay induced by a perturbation of nonlinear field.

Exploring all its ramifications, we give an overview of the simple yet fundamental bouncing ball problem, which consists of a ball bouncing vertically on a sinusoidally vibrating table under the action of gravity. The dynamics is modeled on the basis of a discrete map of difference equations, which numerically solved fully reveals a rich variety of nonlinear behaviors, encompassing irregular nonperiodic orbits, subharmonic and chaotic motions, chattering mechanisms, and also unbounded nonperiodic orbits. For periodic motions, the corresponding conditions for stability and bifurcation are determined from analytical considerations of a reduced map. Through numerical examples, it is shown that a slight change in the initial conditions makes the ball motion switch from periodic to chaotic orbits bounded by a velocity strip $v=\pm \Gamma ∕(1-\epsilon )$, where $\Gamma$ is the nondimensionalized shaking acceleration and $\epsilon$ the coefficient of restitution which quantifies the amount of energy lost in the ball-table collision.

A systematic study of the thermal dissipation field and its statistical properties is carried out in turbulent Rayleigh-Bénard convection. A local temperature gradient probe consisting of four identical thermistors is made to measure the normalized thermal dissipation rate ${ϵ}_N\left(\mathbf{r}\right)$ in two convection cells filled with water. The measurements are conducted over varying Rayleigh numbers Ra $(8.9\times {10}^8\lesssim \mathrm{Ra}\lesssim 9.3\times {10}^9)$ and spatial positions $\mathbf{r}$ across the entire cell. It is found that ${ϵ}_N\left(\mathbf{r}\right)$ contains two contributions; one is generated by thermal plumes, present mainly in the plume-dominated bulk region, and decreases with increasing Ra. The other contribution comes from the mean temperature gradient, being concentrated in the thermal boundary layers, and increases with Ra. The experiment provides a complete physical picture about the thermal dissipation field and its statistical properties in turbulent convection.

In this work, the adsorption-desorption kinetic in the framework of the lattice gas model is analyzed. The transition probabilities are written as an expansion of the occupation configurations. Due to that, the detail balance principle determine half of the adsorption $A_i$ and desorption $D_i$ coefficients, consequently, different functional relations between them are proposed. Introducing additional constrains, it is demonstrated that when those coefficients are linearly related through a parameter $\gamma$, there are values of lateral interaction $V$, that lead to anomalous behavior in the adsorption isotherms, the sticking coefficient and the thermal programmed desorption spectra. Diagrams for the allowed values of $V$ and $\gamma$ are also shown. Alternatively, a more reliable formulation for the adsorption desorption kinetic based on the transition state theory is introduced. In such way the equilibrium and non equilibrium observables do not present anomalous or inconsistent behavior.

We study the Bose-Hubbard model with an external harmonic field, which is effective for modeling a cold atomic Bose gas trapped in an optical lattice. We modify the directed-loop algorithm to simulate large systems efficiently. As a demonstration we carry out the simulation of a system consisting of $1.8\times {10}^5$ particles on a ${64}^3$ lattice. These numbers are comparable to those in the pioneering experimental work by Greiner et al. [Nature (London) 415, 39 (2002)]. Furthermore, we observe coherence between two superfluid spheres separated by a Mott insulator region in a “wedding-cake” structure.

We propose a theoretical description of a possible orientational glass transition in solid molecular para-hydrogen and ortho-deuterium under pressure supposing that they are mixtures of $J=0$ and $J=2$ states of molecules. The theory uses the basic concepts and methods of standard spin-glass theory. We expect our orientational glass to correspond to the ${\mathrm{II}}^{\prime }$ phase of the high-pressure hydrogen phase diagram.

Kawai, Parrondo, and Van den Broeck [Phys. Rev. Lett. 98, 080602 (2007)] have recently established a quantitative relationship between dissipated work and a microscopic, information-theoretic measure of irreversibility. We illustrate this result using the exactly solvable system of a Brownian particle in a dragged harmonic trap.

With Monte Carlo simulations, we investigate the relaxation dynamics of domain walls at the Kosterlitz-Thouless phase transition, taking the two-dimensional $XY$ model as an example. The dynamic scaling behavior is carefully analyzed, and a domain-wall roughening process is observed. Two-time correlation functions are calculated and aging phenomena are investigated. Inside the domain interface, a strong logarithmic correction to scaling is detected.

We report on the dynamical behavior of paramagnetic ellipsoidal particles dispersed in water and floating above a flat plane when subjected to an external precessing magnetic field. When the magnetic field and the long axis of the particles are on the same plane, two clear regimes are distinguished in which the particles follow the magnetic modulation synchronously or asynchronously. Both regimes are also observed when the field precesses at an angle $\vartheta <90°$ with respect to the normal to the confining plane, while the transition frequency increases with decreasing precession angle. We combine experimental observations with a theoretical model to characterize the particle dynamics. The possibility to control and/or reorient microscopic elongated particles by changing the frequency or strength of the applied field makes them suitable in microfluidic devices such as microgates for microchannels or active fluid mixers when placed close to channel junctions.

We formulate a phase-field description of step dynamics on vicinal surfaces that makes use of a single dynamical field, at variance with previous analogous works in which two coupled fields are employed, namely, a phase-field proper plus the physical adatom concentration. Within an asymptotic sharp interface limit, our formulation is shown to retrieve the standard Burton-Cabrera-Frank model in the general case of asymmetric attachment coefficients (Ehrlich-Schwoebel effect). We confirm our analytical results by means of numerical simulations of our phase-field model. Our present formulation seems particularly well adapted to generalization when additional physical fields are required.

Transitions between dynamical states in integrate-and-fire neuron models with periodic stimuli result from tangent or discontinuous bifurcations of a return map. We study their characteristic scaling laws and show that discontinuous bifurcations exhibit a kind of phase transition intermediate between continuous and first order. In the model-independent spirit of our analysis we show that a six-dimensional (6D) gating variable model with an attracting limit cycle has similar phase transitions, governed by a 1D return map. This reduction to 1D map dynamics should extend to real neurons in a periodic current clamp setting.