An energy-enstrophy model for the equilibrium statistical mechanics of barotropic flow on a massive nonrotating sphere is introduced and solved exactly for phase transitions to rotating solid-body atmospheres when the kinetic energy level is high. Unlike the Kraichnan theory which is a Gaussian model, we substitute a microcanonical enstrophy constraint for the usual canonical one, a step which is based on sound physical principles. This yields a spherical model with zero total circulation, microcanonical enstrophy constraint, and canonical constraint on energy, leaving angular momentum free as is required for any model whose objective is to predict super-rotation in planetary atmospheres. A closed-form solution of this spherical model, obtained by the Kac-Berlin method of steepest descent, provides critical temperatures and amplitudes of the symmetry-breaking rotating solid-body flows. The critical values depend linearly on the relative enstrophy, with proportionality constant derived from the spectrum of the Laplace-Beltrami operator on the sphere, as expected within an energy-enstrophy theory for macroscopic turbulent flows. This model and its results differ from previous solvable models for related phenomena in the sense that the model is not based on a mean-field assumption.

Air-driven core-annular fluid flows occur in many situations, from lung airways to engineering applications. Here we study, experimentally and theoretically, flows where a viscous liquid film lining the inside of a tube is forced upwards against gravity by turbulent airflow up the center of the tube. We present results on the thickness and mean speed of the film and properties of the interfacial waves that develop from an instability of the air-liquid interface. We derive a long-wave asymptotic model and compare properties of its solutions with those of the experiments. Traveling wave solutions of this long-wave model exhibit evidence of different mass transport regimes: Past a certain threshold, sufficiently large-amplitude waves begin to trap cores of fluid which propagate upward at wave speeds. This theoretical result is then confirmed by a second set of experiments that show evidence of ring waves of annular fluid propagating over the underlying creeping flow. By tuning the parameters of the experiments, the strength of this phenomenon can be adjusted in a way that is predicted qualitatively by the model.

The lateral migration of an elastic capsule under an optical force in a uniform flow was studied to show the separation characteristics according to the elastic properties in the cross-type optical separator. The initially spherical capsule was moved through the fluid flow using a laser beam with a Gaussian distribution focused along the direction normal to the flow device surface. To simulate such a system, a penalty immersed boundary method was adopted to enable fluid-membrane coupling, and a dynamic ray tracing method was applied to the optical force calculation. The effects of the elastic properties of the capsule membrane (the surface Young's modulus and the bending modulus) on the lateral migration were studied. By increasing the surface Young's modulus, the capsule deformed less and the migration distance increased; however, buckling occurred in the capsule with a high surface Young's modulus. Buckling could be suppressed by increasing the bending rigidity. The effects of the flow velocity and the laser beam power were also examined. In the simulation, the $S$ number, i.e., the ratio of the optical force to the viscous force, was adjusted by decreasing the flow velocity or increasing the laser beam power. The migration distance increased as the $S$ number increased, and a constant lateral migration distance was obtained for a rigid particle for a given $S$ number. An elastic capsule under conditions intermediate between a fixed flow velocity and a fixed laser beam power, however, did not yield a constant lateral migration distance due to the extent of the deformation in the different situations. To predict the lateral migration distance of an elastic capsule, a nondimensional parameter, $S_e$, was defined to include the effects of the optical force, the elastic force, and the fluid viscous force. A unified tendency of the lateral migration distance with $S_e$ was obtained for capsules with intermediate elasticity, by varying either the flow velocity or the laser beam power.

A connection between kinetic processes and two-dimensional intermittent plasma turbulence is observed using direct numerical simulations of a hybrid Vlasov-Maxwell model, in which the Vlasov equation is solved for protons, while the electrons are described as a massless fluid. During the development of turbulence, the proton distribution functions depart from the typical configuration of local thermodynamic equilibrium, displaying statistically significant non-Maxwellian features. In particular, temperature anisotropy and distortions are concentrated near coherent structures, generated as the result of the turbulent cascade, such as current sheets, which are nonuniformly distributed in space. Here, the partial variance of increments (PVI) method has been employed to identify high magnetic stress regions within a two-dimensional turbulent pattern. A quantitative association between non-Maxwellian features and coherent structures is established.

The Lande subtraction method has been widely used in Coulomb problems, but the momentum coordinate $p\in (0,\infty )$ is assumed. In past applications, a very large range of $p$ was used for accuracy. We derive the supplementary formulation with $p\in (0,p_{\max })$ at reasonably small $p_{\max }$ for practical calculations. With the recipe, accuracy of the hydrogenic eigenspectrum is dramatically improved compared to the ordinary Lande formula by the same momentum grids. We apply the present formulation to strong-field atomic above-threshold ionization and high-order harmonic generations. We demonstrate that the proposed momentum space method can be another practical theoretical tool for atomic strong-field problems in addition to the existing methods.

Using an approach developed earlier for renormalization of the Boltzmann collision integral [Saveliev and Nanbu, Phys. Rev. E 65, 051205 (2002)], we derive an exact divergence form for the fragmentation operator. Then we reduce the fragmentation equation to the continuity equation in size space, with the flux given explicitly. This allows us to obtain self-similar solutions and to find the integral of motion for these solutions (we call it the bare flux). We show how these solutions can be applied as a description of cascade processes in three- and two-dimensional turbulence. We also suggested an empirical cascade model of impact fragmentation of brittle materials.

The H-theorem [$(df/dt)\le 0$] for a free-energy functional, $f=u-\theta s$ (with $u$ and $s$ representing, respectively, the internal energy and a generalized entropy of a given physical system), has been proven previously by making use of a nonlinear Fokker-Planck equation. Herein we focus on a nonlinear Fokker-Planck equation derived by means of a coarse-graining procedure on the equations of motion of a system of interacting vortices, under overdamped motion, in the absence of thermal noise ($T=0$). In this case, we show that the parameter $\theta$ is directly related to the density as well as to the interactions among vortices. Generalized quantities such as entropy, internal energy, free energy, and heat capacity are analyzed for varying $\theta$: important relations and physical behavior analogous to those of standard thermodynamics are found, showing that $\theta$ plays the role of an effective temperature. Estimates of $\theta$ in typical physical situations of different type-II superconductors are presented; in addition to this, possible experimental procedures for varying $\theta$ are proposed.

A system that exhibits nonlinear oscillations in the presence of low friction and weak fluctuations is considered. An expression for the mean density of level crossings whose duration exceeds a certain value is derived under the assumption of the high $Q$ factor of the oscillations.

We consider the localized nonlinear breathing modes that emerge in heterogeneous granular configurations of two materials with a periodicity of three and four beads. We examine as characteristic examples chains with one steel and two aluminum beads, as well as ones with one steel and three aluminum beads, although we briefly touch upon other configurations as well, illustrating their similar characteristics. We analyze the higher order gaps that emerge in such settings and explore the intrinsic localized modes that bifurcate from the edge of the upper bands. A generic surprising feature of such states is that they appear to be more robust than their counterparts bifurcating from the edges of the lower bands. Direct numerical simulations, using driving of the system at suitable frequencies through an actuator or taking advantage of the modulational instabilities of extended band edge states in the system, illustrate the spontaneous formation of localized modes within the corresponding nearest gaps. In these numerical experiments, we also account for the presence of dissipation and analyze its potential role.

Over the past decade, computer simulations have had an increasing role in shedding light on difficult statistical physical phenomena, and in particular on the ubiquitous problem of the glass transition. Here in a wide variety of materials the viscosity of a supercooled liquid increases by many orders of magnitude upon decreasing the temperature over a modest range. A natural concern in these computer simulations is the very small size of the simulated systems compared to experimental ones, raising the issue of how to assess the thermodynamic limit. Here we turn this limitation to our advantage by performing finite size scaling on the system size dependence of the relaxation time for supercooled liquids to emphasize the importance of a growing static length scale in the theory of glass transition. We demonstrate that the static length scale that was discovered by us in Physica A 391, 1001 (2012) fits the bill extremely well, allowing us to provide a finite-size scaling theory for the $\alpha$-relaxation time of the glass transition, including predictions for the thermodynamic limit based on simulations in small systems.

A lattice-gas model describing adsorption on nanoparticles of different sizes and shapes is proposed and the adsorption thermodynamics is studied. The nanoparticle is modeled assuming different geometries, and Monte Carlo simulations are performed in the grand canonical ensemble. Adsorption isotherms, differential heats of adsorption, and other relevant thermodynamic properties are analyzed as a function of nanoparticle sizes. The simulations cover a wide range of interactions, ranging from physical to strong chemical bonds.

The propagation of fronts in the Fisher-Kolmogorov equation with spatially varying diffusion coefficients is studied. Using coordinate changes, WKB approximations, and multiple scales analysis, we provide an analytic framework that describes propagation of the front up to the minimum of the diffusion coefficient. We also present results showing the behavior of the front after it passes the minimum. In each case, we show that standard traveling coordinate frames do not properly describe front propagation. Last, we provide numerical simulations to support our analysis and to show, that around the minimum, the motion of the front is arrested on asymptotically significant time scales.

Dust-acoustic waves are investigated in a three-component plasma consisting of strongly coupled dust particles and Maxwellian electrons and ions. A fluid model approach is used, with the effects of strong coupling being accounted for by an effective electrostatic “pressure” which is a function of the dust number density and the electrostatic potential. Both linear and weakly nonlinear cases are considered by derivation and analysis of the linear dispersion relation and the Korteweg-de Vries equation, respectively. In contrast to previous studies using this model, this paper presents the results arising from an expansion of the dynamical form of the electrostatic pressure, accounting for the variations in its value in the vicinity of the wave.

We present a family of discrete breathers, which exists in a nonlinear polarizability model of ferroelectric materials. The core-shell model is set up in its nondimensionalized Hamiltonian form and its linear spectrum is examined in a range of temperatures. Subsequently, seeking localized solutions in the gap of the linear spectrum, we establish that numerically exact and potentially stable discrete breathers exist for a wide range of frequencies therein. In addition, we present nonlinear normal mode, extended spatial profile solutions from which the breathers bifurcate, as well as other associated phenomena such as the formation of phantom breathers within the model. The full bifurcation picture of the emergence and disappearance of the breathers is complemented by direct numerical simulations of their dynamical instability, when the latter arises. The effect of breathers on properties such as nonlinear dielectric response is discussed.

A wide variety of methods have been used to compute percolation thresholds. In lattice percolation, the most powerful of these methods consists of microcanonical simulations using the union-find algorithm to efficiently determine the connected clusters, and (in two dimensions) using exact values from conformal field theory for the probability, at the phase transition, that various kinds of wrapping clusters exist on the torus. We apply this approach to percolation in continuum models, finding overlaps between objects with real-valued positions and orientations. In particular, we find precise values of the percolation transition for disks, squares, rotated squares, and rotated sticks in two dimensions and confirm that these transitions behave as conformal field theory predicts. The running time and memory use of our algorithm are essentially linear as a function of the number of objects at criticality.

The distribution of the performed work for spin glasses with gauge symmetry is considered. With the aid of gauge symmetry, which leads to exact (rigorous) results in spin glasses, we find a fascinating relation of the performed work to the fluctuation theorem. The integral form of the resultant relation reproduces the Jarzynski-type equation for spin glasses that we have obtained. We show that similar relations can be established not only for the distribution of the performed work but also for that of the free energy of spin glasses with gauge symmetry, which provides another interpretation of the phase transition in spin glasses.

We have performed first-principles molecular-dynamics simulations based on density-functional theory to study the thermophysical properties of ethane under extreme conditions. We present results for the equation of state of fluid ethane in the warm dense region. The optical conductivity is calculated via the Kubo-Greenwood formula from which the dc conductivity and optical reflectivity are derived. The close correlation between the nonmetal-metal transition of ethane and its decomposition, that ethane dissociates significantly into molecular and/or atomic hydrogen and some long alkane chains, has been systematically studied by analyzing the optical conductivity spectra, pair correlation functions, electronic density of states, and charge density distribution of fluid ethane.

The main mechanism of the cellular pattern which forms at the surface of a thin layer of a cohesive granular material submitted to in-plane stretching has been identified as the “strain softening” arising from the features of grain-grain interactions. We perform measurements of the strain field associated with such structures by using a correlation image technique and additionally characterize the cohesion and shear modulus of the samples. We show that for high cohesion, the layer is fragile and the surface deformation is highly nonlinear, whereas at low cohesion, a smooth and linearly growing structure is observed as a function of external stretching. Analysis of the wavelength as a function of cohesion along with independent measurement of the shear modulus indicate that a simple model of strain softening is acceptable if a mechanism of cluster formation due to cohesion is taking place.

The rotation of a particle has significant influence on the dynamic response of a granular bed subjected to the oblique impact of a spherical projectile. Based on the discrete element method, the dynamical behavior of two-dimensional granular media impacted obliquely by rotating particles has been examined in this work, especially for the influence of rotational angular velocity on its penetration depth. The simulations show that the incident rotational velocity will not only act on the characteristics of velocity distribution of the bed after impacting, but also influence the trajectory of the projectile qualitatively. For low angular velocities, particle rotations will significantly increase the vertical penetration depths, while the different directions of rotation will exert opposite effects on the horizontal penetration depths. In addition, the influence of particle rotation on its penetration depth will be enhanced with increasing angular velocity, but such effect will reach an asymptotic plateau for sufficiently large angular velocities. This indicates that the angular velocity has an obvious criticality. Furthermore, the variation of critical angular velocity may be linear with the impact velocity and square with the impacting angle, approximately. Finally, the influence of the initial particle rotation on the scaling law of penetration depth is also considered, and we find that the linear scaling with impact velocity is still applicable for most impact conditions.

A study of the complex drying dynamics of polymeric mixtures with optical microscopy and gravimetric measurement is presented. Droplet formation is observed, followed by a collapse that leads to the residual craters in the dried film. The process is followed in situ under well-defined temperature and hygrometric conditions to determine the origin and nature of these droplets and craters. The drying process is usually completed within 1 h. The observations are explained using a simple diffusion model based on experimental results collected from mass and optical measurements as well as Raman confocal microspectrometry. Although the specific polymeric mixtures used here are of interest to the cosmetic industry, the general conclusions reached can apply to other polymeric aqueous solutions with applications to commercial and artistic painting.