Theoretical description and numerical simulation of an evaporating sessile drop are developed. We jointly take into account the hydrodynamics of an evaporating sessile drop, effects of the thermal conduction in the drop, and the diffusion of vapor in air. A shape of the rotationally symmetric drop is determined within the quasistationary approximation. Nonstationary effects in the diffusion of the vapor are also taken into account. Simulation results agree well with the data of evaporation rate measurements for the toluene drop. Marangoni forces associated with the temperature dependence of the surface tension generate fluid convection in the sessile drop. Our results demonstrate several dynamical stages of the convection characterized by different number of vortices in the drop. During the early stage the array of vortices arises near a surface of the drop and induces a nonmonotonic spatial distribution of the temperature over the drop surface. The initial number of near-surface vortices in the drop is controlled by the Marangoni cell size which is similar to that given by Pearson for flat fluid layers. This number quickly decreases with time resulting in three bulk vortices in the intermediate stage. The vortices finally transform into the single convection vortex in the drop existing during about 1/2 of the evaporation time.

A paradigm for Hall discharge modeling is presented whereby only the time scale of the lowest-frequency mode is explicitly resolved. The ability of such a low-frequency model to reproduce with excellent accuracy the breathing mode is demonstrated through comparisons with a fully time-dependent numerical model. Based on this formalism, an approximate linearized model is derived which essentially constitutes a one-dimensional generalization of the classical zero-dimensional predator-prey model. The model highlights the interaction of standing plasma waves with the transport of neutral species, which involves standing and convective waves of similar magnitude. It predicts a frequency which is in close agreement with the frequency of the small perturbation modes observed in simulations. Finally, it is shown that unstable modes are in general strongly nonlinear and characterized by frequencies obeying a scaling law different from that of linear modes.

A recently introduced theory of higher-order lattice Boltzmann models [Chikatamarla and Karlin, Phys. Rev. Lett. 97, 190601 (2006)] is elaborated in detail. A general theory of the construction of lattice Boltzmann models as an approximation to the Boltzmann equation is presented. New lattices are found in all three dimensions and are classified according to their accuracy (degree of approximation of the Boltzmann equation). The numerical stability of these lattices is argued based on the entropy principle. The efficiency and accuracy of many new lattices are demonstrated via simulations in all three dimensions.

We report on numerical simulations of the dynamics of a test particle coupled to competing Boltzmann heat baths of finite size. After discussing some features of the single bath case, we show that the presence of two heat baths further constrains the conditions necessary for the test particle to thermalize with the heat baths. We find that thermalization is a spectral property in which the oscillators of the bath with frequencies in the range of the test particle characteristic frequency determine its degree of thermalization. We also find an unexpected frequency shift of the test particle response with respect to the spectra of the two heat baths. Finally, we discuss implications of our results for the study of high-frequency nanomechanical resonators through cold damping cooling techniques and for engineering reservoirs capable of mitigating the back action on a mechanical system.

In studies of hydrodynamic turbulence and nonequilibrium systems, it has been demonstrated that the observed non-Gaussian probability density functions are often described effectively by a superposition of Gaussian distributions with fluctuating variances. Based on this framework, we propose a general method to characterize intermittent and non-Gaussian time series. In our approach, an observed time series is assumed to be described by the multiplication of Gaussian and amplitude random variables, where the amplitude variable describes the variance fluctuation. It is shown analytically that statistical properties of the log-amplitude fluctuations can be estimated using the logarithmic-absolute moments of the observed time series. This method is applicable to a wide variety of symmetric unimodal distributions with heavy tails in order to quantify the deviation from a Gaussian distribution. By analyzing random cascade-type processes and superstatistical non-Gaussian models with power-law tails, we demonstrate that our method can provide detailed characterization in a wide range of non-Gaussian fluctuations.

In this paper we apply the general analysis described in our first paper to a binary mixture of cyclohexane and $n$-hexane. We use the square gradient model for the continuous description of a nonequilibrium surface and obtain numerical profiles of various thermodynamic quantities in various stationary state conditions. Details of the numerical procedure are given and discussed. In the second part of this paper we focus on the verification of local equilibrium of the surface as described with excess densities. We give a definition of the temperature and chemical potentials of the surface and verify that these quantities are independent of the choice of the dividing surface. We verify numerically that the surface in a stationary state of the mixture can be described in terms of Gibbs excess densities, which are found to be in good approximation equal to their equilibrium values at the stationary state temperature and chemical potentials of the surface.

While the rotation of smectic layers under an applied field may at first appear to be a relatively simple problem, the dynamic processes involved are rather complex. An applied field produces a torque on the liquid crystal director, but has no direct influence on the smectic layers. If the director is reoriented significantly, however, the layers must also reorient in order to accommodate this (the layered structure is produced by short-range molecular interactions). Indeed, if the liquid crystalline order is not maintained during the realignment then matters become even more complex. In this paper we use time-resolved x-ray scattering to investigate the realignment of smectic-$A$ layers in thin-film devices using a magnetic field. No evidence is found for continuous rotation of the smectic layers under any circumstances in such devices, a result that is not found when using bulk samples. No evidence indicating the formation of the nematic phase is observed during realignment. A molecular-dynamics technique is used to model the system which indicates that the sample becomes significantly disorganized during the realignment process when large angular rotations are induced.

Recent experiments and numerical simulations have shown that the water molecules confined on the surfaces of some substrates, including the surfaces of cellular components in tissues and cells, form icelike ordered structures. If a protein folds in an environment with those icelike ordered water molecules, its behavior may be different from that in bulk water. Here, the effect of this ordered water environment on protein folding is studied by using an off-lattice Gō-like model. It is found that the ordered water environment significantly improves the native state stability and greatly speeds up the folding rate of the proteins.

We develop a thermodynamically consistent phase-field model to simulate the dynamics of multicomponent vesicles. The model accounts for bending stiffness, spontaneous curvature, excess (surface) energy, and a line tension between the coexisting surface phases. Our approach is similar to that recently used by Wang and Du [J. Math. Biol. 56, 347 (2008)] with a key difference. Here, we concentrate on the dynamic evolution and solve the surface mass conservation equation explicitly; this equation was not considered by Wang and Du. The resulting fourth-order strongly coupled system of nonlinear nonlocal equations are solved numerically using an adaptive finite element numerical method. Although the system is valid for three dimensions, we limit our studies here to two dimensions where the vesicle is a curve. Differences between the spontaneous curvatures and the bending rigidities of the surface phases are found numerically to lead to the formation of buds, asymmetric vesicle shapes and vesicle fission even in two dimensions. In addition, simulations of configurations far from equilibrium indicate that phase separation via spinodal decomposition and coarsening not only affect the vesicle shape but also that the vesicle shape affects the phase separation dynamics, especially the coarsening and may lead to lower energy states than might be achieved by evolving initially phase-separated configurations.

Proton translocation coupled to redox chemistry is ubiquitous for membrane enzymes involved in energy generation in cells. In such enzymes, proton transport occurs in special proton conducting channels, which consist of a series of protonatable groups of the protein connected by chains of mobile water molecules. Here we discuss two possible mechanisms of proton transport along such structures: diffusion of a localized charge and delocalized soliton transitions, in which several protons are collectively shifted along a chain of hydrogen bonds.

Using stochastic methods developed for DNA translocation through nanopores, we study the unhooking of a long DNA chain from an isolated stationary micropost. Such methods quickly and efficiently furnish both the full probability distribution of the unhooking time and the ensuing moments for a wide range of chain and field parameters. The results compare favorably to more realistic but computationally intense Brownian dynamics simulations. For typical chain lengths and applied electric fields used in experiments, the unhooking process is effectively deterministic; diffusive fluctuations make a negligible contribution to the first and second moments of the unhooking time. This result lends credence to continuous-time random-walk models of the overall transport process that treat the unhooking as a convective process.

Motor proteins are biological enzymes that convert chemical energy to mechanical work in cells. Kinesin-1 is a motor protein that transports vesicles along microtubules and is widely believed to be responsible for anterograde transport of synaptic vesicles in neurons. Advances in single-molecule techniques have shown that single kinesin motors are capable of processive movement along the microtubule at a maximum velocity of approximately $1\mu \text{m}/\text{s}$. The velocity decreases roughly linearly in response to load until reaching stall at a load of approximately 6 pN. Several theoretical models have been proposed that describe the steady-state motion of single kinesin motors. Growing evidence suggests that kinesin functions collectively in cells, whereby several motors work in a coordinated manner to transport a vesicle. A transient description is required to describe collective dynamics, as the interactions among coupled motors induce time-varying forces on each motor. Herein a mechanistic model of kinesin is proposed that is capable of accurately describing transient and steady-state dynamics. Each domain of the protein is modeled via a mechanical potential. The mechanical potentials are related explicitly to the chemical kinetics of each motor domain. The mechanistic model was used to simulate the collective behavior of coupled kinesin motors under varying loads, cargo linker stiffnesses, and numbers of motors. To analyze the simulations of coordinated transport, several metrics were developed that are specifically tailored to characterizing the synchronization of nonlinear nonsmooth oscillators such as kinesin. The model results suggest that, in the cell, the dynamics of coupled motors under low loads are loosely correlated. When the load is increased, such as when the cargo encounters an obstacle such as another vesicle or the cytoskeleton, motors become more correlated in response to increased loads, allowing them to produce greater forces. Increasing the number of motors involved in the transport does not appreciably increase the dimension of the trajectory, implying large numbers of motors are able to function in a highly correlated manner without becoming fully synchronized.

Recent experiments have shown that the force-extension (F-x) curve for single-stranded DNA (ssDNA) consisting only of adenine [poly(dA)] is significantly different from thymine [poly(dT)]. Here, we show that the base stacking interaction is not sufficient to describe the F-x curves as seen in the experiments. A reduction in the reaction coordinate arising from the formation of helix at low forces and an increase in the distance between consecutive phosphates of unstacked bases in the stretched state at high force in the proposed model qualitatively reproduce the experimentally observed features. The multistep plateau in the F-x curve is a signature of structural change in ssDNA.

Spiral wave is shown to drift in heterogeneous excitable media, yet the dynamics remains incompletely understood. In this study, we investigated the effects of heterogeneities in excitable media on the drifting behaviors of dense and sparse spiral waves. Dense spiral waves occur in media of normal excitability and sparse spiral waves in media of low excitability. We numerically simulated the spiral wave drifting in a reaction-diffusion system with the Barkley kinetics and showed that dense and sparse spiral waves drifted differently under the same heterogeneous medium. To understand the drifting behaviors, we developed a kinematic model to describe the tip properties of the spiral waves under different conditions and showed that the kinematic model could well recapitulate the results observed in the reaction-diffusion system.

An infinite square well with a rectangular step is one of the simplest systems to exhibit non-Newtonian ray-splitting periodic orbits in the classical limit. We examine eigenvalue spacings in the quantum version of this system. The sequence of spacings shows deviations from uniformity at energies just above the step height and distinct resonance features are visible at certain energies. Semiclassical analysis shows that these features are directly related to the presence of non-Newtonian orbits in the classical system. In addition, the resonance features are shown to produce revivals in suitably constructed wave packets peaked at the resonance energy.

We demonstrate that diffusively coupled limit-cycle oscillators on random networks can exhibit various complex dynamical patterns. Reducing the system to a network analog of the complex Ginzburg-Landau equation, we argue that uniform oscillations can be linearly unstable with respect to spontaneous phase modulations due to diffusional coupling—the effect corresponding to the Benjamin-Feir instability in continuous media. Numerical investigations under this instability in random scale-free networks reveal a wealth of complex dynamical regimes, including partial amplitude death, clustering, and chaos. A dynamic mean-field theory explaining different kinds of nonlinear dynamics is constructed.

In this paper, the onset of motion of an isolated cylinder partially exposed to a shear flow is experimentally investigated. The experiments are performed in a small narrow channel which provides a vertical shear layer flow whose sizes correspond with the channel width. The bottom of the channel is smooth except in the test zone, at long distance from the inlet, where the cylinder is placed with its principal axis perpendicularly directed to the main flow. The geometry of the channel bottom at the test zone is such that the cylinder is partially buried and presents different expositions to the incident flow. In this way, the geometrical constraints imposed by the sediment bed on a single particle in a natural sediment transport situation are reproduced in an idealized context. The results are interpreted in terms of the relation between the particle mobility parameter at the critical condition and the here defined particle burial degree with respect to the bed geometrical constraints $\beta$. We emphasize the role played by this burial degree that is dependent on the particle exposure to the incident flow $E$ and the resistance to the motion by mechanical contacts with its surroundings given by the so-called static pivot angle $\varphi$.

We report experiments demonstrating enhanced coupling efficiencies of high-contrast laser irradiation to nanofabricated conical targets. Peak temperatures near 200 eV are observed with modest laser energy (10 J), revealing similar hot-electron localization and material heating to reduced mass targets (RMTs), despite having a significantly larger mass. Collisional particle-in-cell simulations attribute the enhancement to self-generated resistive $\left(\sim 10\text{MG}\right)$ magnetic fields forming within the curvature of the cone wall, which confine energetic electrons to heat a reduced volume at the tip. This represents a different electron confinement mechanism (magnetic, as opposed to electrostatic sheath confinement in RMTs) controllable by target shape.

A solution method of the Holstein-Biberman equation in the case of two-dimensional finite-size geometry by means of transformation of the integral operator to a four-dimensional matrix is presented. Using this matrix the array of two-dimensional eigenvalues and eigenfunctions of the radiation transport operator in the case of finite cylinder is determined. The exact two-dimensional characteristics have been compared with approximate functions determined as a combination of corresponding eigenvalues and eigenfunctions for the one-dimensional problems (cylinder of infinite length and slab). The spatiotemporal evolution of excited atom densities for two typical forms of the excitation source in a nonequilibrium plasma has been analyzed. The reasons for the distinct difference in the formation of spatiotemporal distributions of resonance and metastable atoms in the case when the spatial distribution of the excitation source does not coincide with the fundamental mode are discussed. Resonance atoms follow the excitation source while the diffusion effectively takes metastable atoms out from the excitation source. Rearrangement of metastable atoms to the fundamental mode during their decay lasts about one effective diffusion lifetime while the corresponding process for the resonance atoms takes much longer (several effective lifetimes). The differences are caused by the effective suppression of higher diffusion modes compared with radiation modes. The developed solution method treats the radiation transport processes at the same accuracy level as diffusion transport of other plasma components and it is suitable for a self-consistent modeling of nonequilibrium plasmas.

We demonstrate that the band structure of a photonic crystal consisting of alternating layers of right-handed material (RHM) and left-handed material (LHM) can exhibit two types of zero-$\overline{n}$ gaps of zero width. It is shown that each type has an associated null-gap condition which determines the scaling properties of the frequency ${\nu }_0$ at which the corresponding null gap occurs. Specifically, while scaling in the layer thicknesses does not modify the value of the frequency ${\nu }_0$ determined by one of these conditions, the frequency ${\nu }_0$ associated with the other one does not exhibit such a scaling behavior. We have also shown that near the touching point ${\nu }_0$ (for both types of null gaps) and around the center of the Brillouin zone, the dispersion curves exhibit a linear dependence on the Bloch wave vector $k$. As a consequence, the corresponding density of states and group velocity are practically flat as functions of $k$ in the neighborhood of $k=0$. Another interesting property of the considered structure is that an electromagnetic wave with frequency ${\nu }_0$ can be transmitted through a finite RHM-LHM photonic crystal without any change in amplitude and phase.