In this paper, we study the sedimentation of droplet onto horizontal surfaces using a Shan and Chen multicomponent lattice Boltzmann model [Shan and Chen, Phys. Rev. E 47, 1815 (1993)]. Numerical simulations are performed for static nonwetting droplets and are compared with a theoretical model. Further simulations are performed using wetting droplets and changing the wetting characteristics of the surface. Novel study of droplet sedimentation with different wetting characteristics of wall surface shows three different regimes of droplet shapes. The process of different regimes can be controlled by changing the wetting characteristics of surface. It is observed that the droplet attains nonequilibrium region as the attraction force of surrounding droplet with the wall increases. This can lead to eventual breakup of the droplet.

It is shown that delocalized vortex solitons in relativistic pair plasmas with small temperature asymmetries can be unstable for intermediate intensities of the background electromagnetic field. Instability leads to the generation of ever-expanding cavitating bubbles in which the electromagnetic fields are zero. The existence of such electromagnetic bubbles is demonstrated by qualitative arguments based on a hydrodynamic analogy, and by numerical solutions of the appropriate nonlinear Schrödinger equation with a saturating nonlinearity.

We introduce and discuss the one-dimensional Lévy crystal as a probable candidate for an experimentally accessible realization of space-fractional quantum mechanics (SFQM) in a condensed-matter environment. The discretization of the space-fractional Schrödinger equation with the help of shifted Grünwald-Letnikov derivatives delivers a straightforward route to define the Lévy crystal of order $\alpha \in (1,2]$. As key ingredients for its experimental identification we study the dispersion relation as well as the density of states for arbitrary $\alpha \in (1,2]$. It is demonstrated that in the limit of small wave numbers all interesting properties of continuous-space SFQM are recovered, while for $\alpha \to 2$ the well-established nearest-neighbor one-dimensional tight-binding chain arises.

We obtain compact, exact, analytical expressions for the first-passage-time distribution for a particle undergoing biased diffusion in a planar wedge for wedge angles $\pi /p$, where $p$ is a positive integer. We then provide the long-time limit of the first-passage time and found it to be dependent on the drift direction and wedge angle. We finally provide exact expressions for the mean first-passage time for specific cases.

Numerical simulations by Tanaka and co-workers indicate that glass-forming systems of moderately polydisperse hard-core particles, in both two and three dimensions, exhibit diverging correlation lengths. These correlations are described by Ising-like critical exponents, and are associated with diverging, Vogel-Fulcher-Tamann, structural relaxation times. Related simulations of thermalized hard disks indicate that the curves of pressure versus packing fraction for different polydispersities exhibit a sequence of transition points, starting with a liquid-hexatic transition for the monodisperse case, and crossing over with increasing polydispersity to glassy, Ising-like critical points. I propose to explain these observations by assuming that glass-forming fluids contain twofold degenerate, locally ordered clusters of particles, similar to the two-state systems that have been invoked to explain other glassy phenomena. This paper starts with a brief statistical derivation of the thermodynamics of thermalized, hard-core particles. It then discusses how a two-state, Ising-like model can be described within that framework in terms of a small number of statistically relevant, internal state variables. The resulting theory agrees accurately with the simulation data. I also propose a rationale for the observed relation between the Ising-like correlation lengths and the Vogel-Fulcher-Tamann formula.

The contribution of flexoelectric polarization to the dielectric susceptibility in helicoidal liquid crystals is formulated for the static equilibrium case, and further in the case of a time-varying field. A dispersion of the dielectric permittivity due to the frequency response of flexoelectric switching is described. The special case of a negative dielectric-anisotropy nematic material is considered and experimentally shown to agree with the analytical theory. It is further demonstrated how relaxation of the flexoelectric contribution to the dielectric tensor in this special case can be exploited to switch between states in cholesteric liquid crystal structures by altering the applied time-dependent field amplitude, if $\Delta \varepsilon <0$ and ${(e_1-e_3)}^2/(K_1+K_3)>-\Delta \varepsilon {\varepsilon }_0$. Consequentially, a versatile mechanism for driving between states in liquid crystal systems has been demonstrated and its implications for technology are suggested, and include dual-mode, bistable, and transflective displays.

The elastic properties of a self-assembled bilayer membrane are studied using the self-consistent field theory, applied to a model system composed of flexible amphiphilic chains dissolved in hydrophilic polymeric solvents. Examining the free energy of bilayer membranes with different geometries allows us to calculate their bending modulus, Gaussian modulus, two fourth-order membrane moduli, and the line tension. The dependence of these parameters on the microscopic characteristics of the amphiphilic chain, characterized by the volume fraction of the hydrophilic component, is systematically studied. The theoretical predictions are compared with the results from a simple monolayer model, which approximates a bilayer membrane by two monolayers. The region of validity of the linear elasticity theory is analyzed by examining the higher-order contributions.

The transition between two basic structures, a disk and an enclosed vesicle, of a finite membrane is studied by examining the minimum energy path (MEP) connecting these two states. The MEP is constructed using the string method applied to continuum elastic membrane models. The results reveal that, besides the commonly observed disk and vesicle, open vesicles (bowl-shaped vesicles or vesicles with a pore) can become stable or metastable shapes. The emergence, stability, and probability distribution of these open vesicles are analyzed. It is demonstrated that open vesicles can be stabilized by higher-order elastic energies. The estimated probability distribution of the different structures is in good agreement with available experiments.

Ion channel gating kinetics can be described using Kramers' diffusion theory of reaction rates between several closed and open states, where transition rates between states depend exponentially on the membrane potential $V$. It has been suggested that transition rates have a more complex dependence on $V$ at voltage extremes, but this has never been quantified. We measured the rate constant of the last closed to open transition in a voltage-gated ion channel and show that it does not depend exponentially on membrane potential at values of $V$ greater than $\approx$150 mV. To explain this behavior, we estimate the effects of electrical polarization of the water contained in crevices within the channel protein, using an electrostatic model of the approximate three-dimensional geometry and the nonlinear effects of charges on the polarization of water.

In this study, we characterize the oscillating pulse edges developed in a traveling-wave field-effect transistor (TWFET). Recently, it has been found that a stable shock front can develop on a TWFET, which can travel in one direction only. Once the reflected pulse edge at the far end is transmitted to the input, the shock front develops and begins to travel on the device again. This process establishes a permanent edge oscillation. This paper discusses the device setup necessary to excite such oscillations and how pulse edges oscillate on a TWFET. By applying the phase reduction scheme to the transmission equations of a TWFET, we obtain phase sensitivity, which appropriately explains the measured spatial dependence of the locking range in frequency. Moreover, multiple oscillating edges can develop simultaneously, which are mutually synchronized. The dynamics of these multiple edges are also described.

We investigate the evolution of magnetohydrodynamic (or hydromagnetic as coined by Chandrasekhar) perturbations in the presence of stochastic noise in rotating shear flows. The particular emphasis is the flows whose angular velocity decreases but specific angular momentum increases with increasing radial coordinate. Such flows, however, are Rayleigh stable but must be turbulent in order to explain astrophysical observed data and, hence, reveal a mismatch between the linear theory and observations and experiments. The mismatch seems to have been resolved, at least in certain regimes, in the presence of a weak magnetic field, revealing magnetorotational instability. The present work explores the effects of stochastic noise on such magnetohydrodynamic flows, in order to resolve the above mismatch generically for the hot flows. We essentially concentrate on a small section of such a flow which is nothing but a plane shear flow supplemented by the Coriolis effect, mimicking a small section of an astrophysical accretion disk around a compact object. It is found that such stochastically driven flows exhibit large temporal and spatial autocorrelations and cross-correlations of perturbation and, hence, large energy dissipations of perturbation, which generate instability. Interestingly, autocorrelations and cross-correlations appear independent of background angular velocity profiles, which are Rayleigh stable, indicating their universality. This work initiates our attempt to understand the evolution of three-dimensional hydromagnetic perturbations in rotating shear flows in the presence of stochastic noise.

The nonlinear interaction of intense femtosecond laser pulses with a self-induced plasma channel in air and the energy transfer between two intersecting laser pulses were simulated using the finite-difference time-domain particle-in-cell method. Implementation of a simple numerical code enabled modeling of various phenomena, including pulse self-modulation in the spatiotemporal and spectral domains, conical emission, and energy transfer between two intersecting laser beams. The mechanism for energy transfer was found to be related to a plasma waveguide array induced by Moiré patterns of the interfering electric fields. The simulation results provide a persuasive replication and explanation of previous experimental results, when carried out under comparable physical conditions, and lead to prediction of others. This approach allows us to further examine the effect of the laser and plasma parameters on the simulation results and to investigate the underlying physics.

We investigate translocation mechanisms in smectic A liquid crystals (LCs) by a realistic, coarse-grained model of a LC compound comprising a stiff azobenzene core with flexible tails. We observe that the molecules can permeate from one smectic layer to the next via two different mechanisms, with and without significant reorientation, the former being facilitated through transverse interlayer intermediates. This is possible due to the intrinsic flexibility of the molecules. The two processes lead to characteristic signatures in the Van Hove self-correlation function, which can also be observed experimentally.

We consider a chain of one-dimensional dipole moments connected to two thermal baths with different temperatures. The system is in nonequilibrium steady state and heat flows through it. Assuming that fluctuation of the dipole moment is a small parameter, we develop an analytically solvable model for the problem. The effect of disorder is introduced by randomizing the positions of the dipole moments. We show that the disorder leads to Anderson-like transition from conducting to a thermal insulating state of the chain. It is shown that considered chain supports both ballistic and diffusive heat transports depending on the strength of the disorder. We demonstrate that nonequilibrium leads to the emergence of the long-range order between dipoles along the chain and make the conjecture that the interplay between nonequilibrium and next-to-nearest-neighbor interactions results in the emergence of long-range correlations in low-dimensional classical systems.

We examine the generating function of the time-integrated energy for the one-dimensional Glauber-Ising model. At long times, the generating function takes on a large-deviation form and the associated cumulant generating function has singularities corresponding to continuous trajectory (or “space-time”) phase transitions between paramagnetic trajectories and ferromagnetically or antiferromagnetically ordered trajectories. In the thermodynamic limit, the singularities make up a whole curve of critical points in the complex plane of the counting field. We evaluate analytically the generating function by mapping the generator of the biased dynamics to a non-Hermitian Hamiltonian of an associated quantum spin chain. We relate the trajectory phase transitions to the high-order cumulants of the time-integrated energy which we use to extract the dynamical Lee-Yang zeros of the generating function. This approach offers the possibility to detect continuous trajectory phase transitions from the finite-time behavior of measurable quantities.

A systematic study on the performance of two empirical gas-wall interaction models, the Maxwell model and the Cercignani-Lampis (CL) model, in the entire Knudsen range is conducted. The models are evaluated by examining the accuracy of key macroscopic quantities such as temperature, density, and pressure, in three benchmark thermal problems, namely the Fourier thermal problem, the Knudsen force problem, and the thermal transpiration problem. The reference solutions are obtained from a validated hybrid DSMC-MD algorithm developed in-house. It has been found that while both models predict temperature and density reasonably well in the Fourier thermal problem, the pressure profile obtained from Maxwell model exhibits a trend that opposes that from the reference solution. As a consequence, the Maxwell model is unable to predict the orientation change of the Knudsen force acting on a cold cylinder embedded in a hot cylindrical enclosure at a certain Knudsen number. In the simulation of the thermal transpiration coefficient, although all three models overestimate the coefficient, the coefficient obtained from CL model is the closest to the reference solution. The Maxwell model performs the worst. The cause of the overestimated coefficient is investigated and its link to the overly constrained correlation between the tangential momentum accommodation coefficient and the tangential energy accommodation coefficient inherent in the models is pointed out. Directions for further improvement of models are suggested.

We present a theory to obtain the pressure tensor for a class of nonideal multicomponent lattice Boltzmann models, thus extending the theory presented by X. Shan [Phys. Rev. E 77, 066702 (2008)] for single-component fluids. We obtain the correct form of the pressure tensor directly on the lattice and the resulting equilibrium properties are shown to agree very well with those measured from numerical simulations. Results are compared with those of alternative theories.

We investigate the spreading and splashing of granular drops during impact with a solid target. The granular drops are formed from roughly spherical balls of sand mixed with water, which is used as a binder to hold the ball together during free-fall. We measure the instantaneous spread diameter for different impact speeds and find that the normalized spread diameter $d/D$ grows as ${(tV/D)}^{1/2}$. The speeds of the grains ejected during the “splash” are measured and they rarely exceed twice that of the impact speed.

Explosive synchronization (ES) has recently attracted much attention, where its two necessary conditions are found to be a scale-free network topology and a positive correlation between the natural frequencies of the oscillators and their degrees. Here we present a framework for ES to be observed in a general complex network, where a positive correlation between coupling strengths of the oscillators and the absolute of their natural frequencies is assumed and the previous studies are included as specific cases. In the framework, the previous two necessary conditions are replaced by another one, thus fundamentally deepening the understanding of the microscopic mechanism toward synchronization. A rigorous analytical treatment by a mean field is provided to explain the mechanism of ES in this alternate framework.

We study the thermodynamics of the relativistic quantum O$\left(N\right)$ model in two space dimensions. In the vicinity of the zero-temperature quantum critical point (QCP), the pressure can be written in the scaling form $P\left(T\right)=P\left(0\right)+N(T^3/c^2){\mathcal{F}}_N(\Delta /T)$, where $c$ is the velocity of the excitations at the QCP and $\left|\Delta \right|$ a characteristic zero-temperature energy scale. Using both a large-$N$ approach to leading order and the nonperturbative renormalization group, we compute the universal scaling function ${\mathcal{F}}_N$. For small values of $N$ ($N\lesssim 10$) we find that ${\mathcal{F}}_N\left(x\right)$ is nonmonotonic in the quantum critical regime ($\left|x\right|\lesssim 1$) with a maximum near $x=0$. The large-$N$ approach—if properly interpreted—is a good approximation both in the renormalized classical ($x\lesssim -1$) and quantum disordered ($x\gtrsim 1$) regimes, but fails to describe the nonmonotonic behavior of ${\mathcal{F}}_N$ in the quantum critical regime. We discuss the renormalization-group flows in the various regimes near the QCP and make the connection with the quantum nonlinear sigma model in the renormalized classical regime. We compute the Berezinskii-Kosterlitz-Thouless transition temperature in the quantum O(2) model and find that in the vicinity of the QCP the universal ratio $T_{\mathrm{BKT}}/{\rho }_s\left(0\right)$ is very close to $\pi /2$, implying that the stiffness ${\rho }_s\left(T_{\mathrm{BKT}}^{-}\right)$ at the transition is only slightly reduced with respect to the zero-temperature stiffness ${\rho }_s\left(0\right)$. Finally, we briefly discuss the experimental determination of the universal function ${\mathcal{F}}_2$ from the pressure of a Bose gas in an optical lattice near the superfluid–Mott-insulator transition.