Nonequilibrium dynamics of biomembranes with active multiple-state inclusions is considered. The inclusions represent protein molecules which perform cyclic internal conformational motions driven by the energy brought with adenosine triphosphate (ATP) ligands. As protein conformations cyclically change, this induces hydrodynamical flows and also directly affects the local curvature of a membrane. On the other hand, variations in the local curvature of the membrane modify the transition rates between conformational states in a protein, leading to a feedback in the considered system. Moreover, active inclusions can move diffusively through the membrane so that their surface concentration varies. The kinetic description of this system is constructed and the stability of the uniform stationary state is analytically investigated. We show that, as the rate of supply of chemical energy is increased above a certain threshold, this uniform state becomes unstable and stationary or traveling waves spontaneously develop in the system. Such waves are accompanied by periodic spatial variations of the membrane curvature and the inclusion density. For typical parameter values, their characteristic wavelengths are of the order of hundreds of nanometers. For traveling waves, the characteristic frequency is of the order of a thousand Hz or less. The predicted instabilities are possible only if at least three internal inclusion states are present.

The development of a high-speed microactuator in water is difficult because of electrostatic problems and hydrodynamic resistance. To overcome these problems, we consider using induced-charge electrophoresis (ICEP) to move actuators. We propose rotary microvalves in water using hydrodynamic force due to ICEP and numerically examine the performance of valves. By the multiphysics coupled simulation technique between fluidics and electrostatics based on the boundary element method along with the thin-double-layer approximation, we find rotary valves using ICEP function effectively at high frequency. In the calculations, the electric and flow field problems in a bounded domain are solved, and the proper boundary conditions are discussed. By employing similar actuators using ICEP, we can dramatically improve the performance of promising microfluidic systems such as lab-on-a-chip.

This paper is concerned with liquid films on horizontally vibrating substrates. Using an equation derived by Shklyaev et al. [Phys. Rev. E 79, 051603 (2009)], we show that all periodic and solitary-wave solutions of this equation are unstable regardless of their parameters. Some of the solitary waves, however, are metastable—i.e., still unstable, but with extremely small growth rates—and, thus, can persist without breaking up for a very long time. The crests of these metastable waves are flat and wide, and they all have more or less the same amplitude (determined by the problem’s global parameters). The metastable solitary waves play an important role in the evolution of films for which the state of uniform thickness is unstable. Those were simulated numerically, with two basic scenarios observed depending on the parameter $A=3{\left(\omega /2\nu \right)}^{1/2}{U}_0^2/g$, where $\nu$ is the kinematic viscosity, $g$ is the acceleration due to gravity, and $\omega$ and $U_0$ are the frequency and amplitude (maximum velocity) of the substrate’s vibration. (i) If $A\lesssim 25$, a small number of metastable solitary waves with flat/wide crests emerge from the evolution and exist without coalescing (or even moving) for an extremely long time. (ii) If $A\gtrsim 25$, the solution of the initial-value problem breaks up into a set of noninteracting pulses separated by regions where the film’s thickness rapidly tends to zero.

We use simulations to investigate constitutive relations in dry granular flow. Our system is comprised of polydisperse sets of spherical grains falling down a vertical chute under the influence of gravity. Three phases or states of granular matter are observed: a free-fall dilute granular gas region at the top of the chute, a granular fluid in the middle and then a glassy region at the bottom. We examine a complete closed set of constitutive relations capable of describing the local stresses, heat flow, and dissipation in the different regions. While the pressure can be reasonably described by hard sphere gas models, the transport coefficients cannot. Transport coefficients such as viscosity and heat conductivity increase with decreasing temperature in the fluid and glassy phases. The glass exhibits signs of a finite yield stress and we show that the static sand pile is a limit of our glassy state.

We use a computationally efficient phase-field formulation [B. Echebarria et al., Phys. Rev. E 70, 061604 (2004)] to investigate the origin and dynamics of sidebranching in directional solidification for realistic parameters of a dilute alloy previously studied experimentally [M. Gorgelin and A. Pocheau, Phys. Rev. E 57, 3189 (1998)]. Sidebranching is found to result either from noise amplification or from deterministic oscillations that exist both in two dimensions and in a three-dimensional thin-sample geometry. The oscillatory branch of growth solutions bifurcates subcritically from the main steady-state branch of solutions and exists over a finite range of large array spacings. In contrast, noise-induced sidebranching is associated with a smooth transition where the sidebranching amplitude increases exponentially with spacing up to nonlinear saturation due to the overlap of diffusion fields from neighboring cells, as observed experimentally. In the latter case where sidebranching is noise-induced, we find that increasing the externally imposed thermal gradient reduces the onset velocity and wavelength of sidebranching, as also observed experimentally. We show that this counterintuitive effect is due to tip blunting with increasing thermal gradient that promotes noise amplification in the tip region.

Viscoelastic mechanical properties of biological cells are commonly measured using atomic force microscope (AFM) dynamic indentation with spherical tips. A semiempirical analysis based on numerical simulation is built to determine the cell mechanical properties. It is shown that the existing analysis cannot reflect the accurate values of cell elastic/dynamic modulus due to the effects of substrate, indenter tip size, and cell size. Among these factors, substrate not only increases the true contact radius but also interferes the indentation stress field, which can cause the overestimation of cell moduli. Typically, the substrate effect is much stronger than the other two influences in cell indentation; and, thus, the cell modulii are usually overestimated. It is estimated that the moduli can be overestimated by as high as over 200% using the existing analysis. In order to obtain the accurate properties of cells, correction factors that account for these effects are required in the existing analysis.

We study time-periodic forcing of spatially extended patterns near a Turing-Hopf bifurcation point. A symmetry-based normal form analysis yields several predictions, including that (i) weak forcing near the intrinsic Hopf frequency enhances or suppresses the Turing amplitude by an amount that scales quadratically with the forcing strength, and (ii) the strongest effect is seen for forcing that is detuned from the Hopf frequency. To apply our results to specific models, we perform a perturbation analysis on general two-component reaction-diffusion systems, which reveals whether the forcing suppresses or enhances the spatial pattern. For the suppressing case, our results are consistent with features of previous experiments on the chlorine dioxide-iodine-malonic acid chemical reaction. However, we also find examples of the enhancing case, which has not yet been observed in experiment. Numerical simulations verify the predicted dependence on the forcing parameters.

The kinetic theory is developed for the mass mixing of two incompressible immiscible fluids due to Rayleigh-Taylor instability (as an example for turbulence in variable-density statistically inhomogeneous incompressible fluids). An expression is derived for the fine grain force in terms of the mass-density and velocity fields. This expression enables the conversion of the Navier-Stokes equation into an exact explicit conservation equation in phase space. The equation is a generalization, to the variable-density case, of the Lundgren equation [T. S. Lundgren, Phys. Fluids 10, 969 (1967)]. The conserved quantity is the fine grain density-velocity distribution (FGDVD). The fine grain mass-density and fluid velocity fields are the two lowest moments of the FGDVD. The joint density-velocity probability density function (DVPDF) is the ensemble average of the FGDVD. Using detailed numerical solutions of the Navier-Stokes equation, it is found that the correlation between the acceleration and the FGDVD is weak. This result identifies a small parameter which enables the derivation, by controlled approximations, of closed equations for the DVPDFs. The lowest order yields the mean-field approximation. It is shown by a numerical solution of the closed kinetic equation in the mean-field approximation that it properly describes the time evolution of the system for periods shorter than the relaxation time. Closure schemes beyond the mean field are discussed.

We analyze the generation of terahertz radiation when an intense, short laser pulse is mixed with its frequency-doubled counterpart in plasma. The nonlinear coupling of the fundamental and the frequency-doubled laser pulses in plasma is shown to be characterized by a third order susceptibility which has a time dependence characteristic of the laser pulse durations. The terahertz generation process depends on the relative polarizations of the lasers and the terahertz frequency is $\omega \sim 1/{\tau }_L$, where ${\tau }_L$ is the laser pulse duration. Since the laser pulse duration is typically in the picosecond or subpicosecond regime the resulting radiation is in the terahertz or multiterahertz regime. To obtain the third order susceptibility we solve the plasma fluid equations correct to third order in the laser fields, including both the relativistic and ponderomotive force terms. The relativistic and ponderomotive contributions to the susceptibility nearly cancel in the absence of electron collisions. Therefore, in this terahertz generation mechanism collisional effects play a critical role. Consistent with recent experimental observations, our model shows that (1) the terahertz field amplitude is proportional to $I_1\sqrt{I_2}$, where $I_1$ and $I_2$ are the intensities of the fundamental and second harmonic laser pulses, respectively, (2) the terahertz emission is maximized when the polarization of the laser beams and the terahertz are aligned, (3) for typical experimental parameters, the emitted terahertz field amplitude is on the order of tens of kilovolts/cm with duration comparable to that of the drive laser pulses, and (4) the direction of terahertz emission depends sensitively on experimental parameters.

Metastable escape is ubiquitous in many physical systems and is becoming a concern in engineering design as these designs (e.g., swarms of vehicles, coupled building energetics, nanoengineering, etc.) become more inspired by dynamics of biological, molecular and other natural systems. In light of this, we study a chain of coupled bistable oscillators which has two global conformations and we investigate how specialized or targeted disturbance is funneled in an inverse energy cascade and ultimately influences the transition process between the conformations. We derive a multiphase averaged approximation to these dynamics which illustrates the influence of actions in modal coordinates on the coarse behavior of this process. An activation condition that predicts how the disturbance influences the rate of transition is then derived. The prediction tools are derived for deterministic dynamics and we also present analogous behavior in the stochastic setting and show a divergence from Kramers activation behavior under targeted activation conditions.

Two electroconvection (EC) pattern morphologies—a cellular and a subsequent roll pattern—have been detected in the same frequency range in a nematic with positive permittivity and conductivity anisotropies. The frequency dependences of the onset voltages and critical wave numbers have been determined both for homeotropic and planar alignments. It has been proven that both pattern morphologies have a dielectric time symmetry. We also discuss possible sources for the pattern formation in the frame of both the isotropic (Felici-Benard) mechanism, as well as the standard model of EC.

The minimum spanning tree (MST) is a combinatorial optimization problem: given a connected graph with a real weight (“cost”) on each edge, find the spanning tree that minimizes the sum of the total cost of the occupied edges. We consider the random MST, in which the edge costs are (quenched) independent random variables. There is a strongly disordered spin-glass model due to Newman and Stein [Phys. Rev. Lett. 72, 2286 (1994)], which maps precisely onto the random MST. We study scaling properties of random MSTs using a relation between Kruskal’s greedy algorithm for finding the MST, and bond percolation. We solve the random MST problem on the Bethe lattice (BL) with appropriate wired boundary conditions and calculate the fractal dimension $D=6$ of the connected components. Viewed as a mean-field theory, the result implies that on a lattice in Euclidean space of dimension $d$, there are of order $W^{d-D}$ large connected components of the random MST inside a window of size $W$, and that $d=d_c=D=6$ is a critical dimension. This differs from the value 8 suggested by Newman and Stein. We also critique the original argument for 8, and provide an improved scaling argument that again yields $d_c=6$. The result implies that the strongly disordered spin-glass model has many ground states for $d>6$, and only of order one below six. The results for MSTs also apply on the Poisson-weighted infinite tree, which is a mean-field approach to the continuum model of MSTs in Euclidean space, and is a limit of the BL. In a companion paper we develop an $\epsilon =6-d$ expansion for the random MST on critical percolation clusters.

Continuing the program begun by the authors in a previous paper, we develop an exact low-density expansion for the random minimum spanning tree (MST) on a finite graph and use it to develop a continuum perturbation expansion for the MST on critical percolation clusters in space dimension $d$. The perturbation expansion is proved to be renormalizable in $d=6$ dimensions. We consider the fractal dimension $D_{\mathrm{p}}$ of paths on the latter MST; our previous results lead us to predict that $D_{\mathrm{p}}=2$ for $d>d_c=6$. Using a renormalization-group approach, we confirm the result for $d>6$ and calculate $D_{\mathrm{p}}$ to first order in $\epsilon =6-d$ for $d<6$ using the connection with critical percolation, with the result $D_{\mathrm{p}}=2-\epsilon ∕7+O\left({\epsilon }^2\right)$.

In spite of numerous papers dedicated to the subject, the behavior of the helical pitch in the smectic $C^{\ast }$ phase near the smectic A phase is still controversial. In particular, it is not clear to what extent the measured pitch values are influenced by surface effects. In order to shed light on this problem, careful pitch measurements have been performed using different methods and sample preparations. We have found that the diffraction of light on planar-oriented samples may give incorrect pitch results because of strong influence of the surfaces and possibly of the sample texture on the helical structure. We have demonstrated that using appropriate preparation of samples the bulk properties of the helix can be determined. It has been found that a maximum of pitch can indeed occur but then only when very close to the transition point smectic $C^{\ast }\to \text{smectic}$ A (about 0.1 K). The results of helical pitch measurements have been compared with predictions of theories.

We study synchronization in delay-coupled oscillator networks using a master stability function approach. Within a generic model of Stuart-Landau oscillators (normal form of supercritical or subcritical Hopf bifurcation), we derive analytical stability conditions and demonstrate that by tuning the coupling phase one can easily control the stability of synchronous periodic states. We propose the coupling phase as a crucial control parameter to switch between in-phase synchronization or desynchronization for general network topologies or between in-phase, cluster, or splay states in unidirectional rings. Our results are robust even for slightly nonidentical elements of the network.

Two edge-emitting lasers mutually coupled through orthogonal optical injection exhibit square-wave oscillations in their polarization modes. The TE and TM modes within each individual laser are always in antiphase, but the TE mode of one laser leads the TM of the other by the one-way time of flight between lasers. The duty cycle of the square waves is tunable with pump current and coupling strength, while the total period remains close to the roundtrip time. Numerical simulations give similar results and reveal the role of noise in stabilizing the oscillations.

We present a dynamic model to study ordering of particles on arbitrary curved surfaces. Thereby the particles are represented as maxima in a density field and a surface partial differential equation for the density field is solved to the minimal energy configuration. We study annihilation of dislocations within the ordered system and premelting along grain-boundary scars. The obtained minimal energy configurations on a sphere are compared with existing results and scaling laws are computed for the number of excess dislocations as a function of system size.

We study warm dense matter formed by subpicosecond laser irradiation at several ${10}^{19}\text{W}/{\text{cm}}^2$ of thin Ti foils using x-ray spectroscopy with high spectral $\left(E/\Delta E\sim 15,000\right)$ and one-dimensional spatial $\left(\Delta x=13.5\mu \text{m}\right)$ resolutions. $\text{Ti}K\alpha$ doublets modeled by line-shape calculations are compared with Abel-inverted single-pulse experimental spectra and provide radial distributions of the bulk-electron temperature and the absolute-photon number $K\alpha$ yield in the target interiors. A core with $\sim 40\text{eV}$ extends homogeneously up to ten times the laser-focus size. The spatial distributions of the bulk-electron temperature and $K\alpha$ yield are strongly correlated.

Technological applications of discotic nematogens are limited by the robustness of the columnar phases. This investigation employs Monte Carlo simulations to explore the potentiality of tailoring specific interactions of either stacking or peripheral type in order to enhance nematic stability. It is concluded that the nematic phase is favored for discotic particles systems with homogeneous or weakly directional interactions. However, a substantial increase in the directionality of the interaction (stacking or edge-to-edge) leads systematically to a suppression of the nematic domains in favor of the columnar phases.

The exit time of a subdiffusive process from a bounded domain with a partially absorbing/reflecting boundary is considered. The short-time and long-time behaviors of the exit time probability density are investigated by using a spectral decomposition on the basis of the Laplace operator eigenfunctions. Rotation-invariant domains are analyzed in depth in order to illustrate the use of theoretical formulas and to compare them to numerical simulations. The asymptotic results obtained are relevant for describing subdiffusion inside a living cell with a semipermeable membrane, in a chemical reactor filled with catalytic grains of finite reactivity, or in mineral or biological samples which are probed by nuclear magnetic resonance measurements subject to surface relaxation.