Drops sandwiched between two substrates are often found in lab-on-chip devices based on digital microfluidics. We excite azimuthal oscillations of such drops by periodically modulating the contact line via ac electrowetting. By tuning the frequency of the applied voltage, several shape modes can be selected one by one. The frequency of the oscillations is half the frequency of the contact angle modulation by electrowetting, indicating a parametric excitation. The drop response to sinusoidal driving deviates substantially from sinusoidal behavior in a “stop and go” fashion. Although our simple theoretical model describes the observed behavior qualitatively, the resonances appear at lower frequencies than expected. Moreover, the oscillations produce a nonperiodic fluid transport within the drop with a typical velocity of 1 mm/s. In digital microfluidic devices, where the typical drop size is less than 1 mm, this flow can result in very fast mixing on the spot.

We apply a semiclassical partial-wave-scattering method based on the Wentzel-Kramers-Brillouin approximation to study the transport cross section and the energy loss of neutral or ionized atomic beams in plasmas. This approach reproduces the exact quantum result in a satisfactory manner, even in several extreme conditions of plasma densities and temperatures, and agrees with the results of linear or perturbative calculations for bare ions in the appropriate limits. We pay special attention to low projectile speeds where strong oscillations in the transport cross section and energy loss—as a function of projectile's atomic number—are observed. We study these oscillatory phenomena varying the projectile speed and its ionization degree and the plasma temperature and density. We analyze in physical terms these effects and present a diagram of plasma conditions showing the regions where these oscillations may occur for both neutral and ionized beams.

We present an absolute measurement of the total ion-drag force on one single microparticle at the edge of the dust free region in low pressure complex plasmas: the void. In order to do so, the particle confinement position was monitored as a function of the gas pressure for two particle sizes under normal gravity conditions and under microgravity conditions during parabolic flights. At the border of the void, the ion-drag force on a particle with a radius of 4.90 μm appeared to be $(3.6\pm 0.3)\times {10}^{-12}$ N.

We study the the ground state fidelity and the ground state Loschmidt echo of a three-site interacting XX chain in presence of a staggered field which exhibits special types of quantum phase transitions due to change in the topology of the Fermi surface, apart from quantum phase transitions from gapped to gapless phases. We find that, on one hand, the fidelity is able to detect only the boundaries separating the gapped from the gapless phase; it is completely insensitive to the phase transition from the two Fermi points region to the four Fermi points region lying within this gapless phase. On the other hand, the Loschmidt echo shows a dip only at a special point in the entire phase diagram and hence fails to detect any quantum phase transition associated with the present model. We provide appropriate arguments in support of this anomalous behavior.

In this paper, a control-based approach to replace the conventional method to achieve accurate indentation quantification is proposed for nanomechanical measurement of live cells using atomic force microscope. Accurate indentation quantification is central to probe-based nanomechanical property measurement. The conventional method for in-liquid nanomechanical measurement of live cells, however, fails to accurately quantify the indentation as effects of the relative probe acceleration and the hydrodynamic force are not addressed. As a result, significant errors and uncertainties are induced in the nanomechanical properties measured. In this paper, a control-based approach is proposed to account for these adverse effects by tracking the same excitation force profile on both a live cell and a hard reference sample through the use of an advanced control technique, and by quantifying the indentation from the difference of the cantilever base displacement in these two measurements. The proposed control-based approach not only eliminates the relative probe acceleration effect with no need to calibrate the parameters involved, but it also reduces the hydrodynamic force effect significantly when the force load rate becomes high. We further hypothesize that, by using the proposed control-based approach, the rate-dependent elastic modulus of live human epithelial cells under different stress conditions can be reliably quantified to predict the elasticity evolution of cell membranes, and hence can be used to predict cellular behaviors. By implementing the proposed approach, the elastic modulus of HeLa cells before and after the stress process were quantified as the force load rate was changed over three orders of magnitude from 0.1 to 100 Hz, where the amplitude of the applied force and the indentation were at 0.4–2 nN and 250–450 nm, respectively. The measured elastic modulus of HeLa cells showed a clear power-law dependence on the load rate, both before and after the stress process. Moreover, the elastic modulus of HeLa cells was substantially reduced by two to five times due to the stress process. Thus, our measurements demonstrate that the control-based protocol is effective in quantifying and characterizing the evolution of nanomechanical properties during the stress process of live cells.

We study a stochastic matrix model to understand the mechanics of risk spreading (or bet hedging) by dispersion. Up to now, this model has been mostly dealt with numerically, except for the well-mixed case. Here, we present an analytical result that shows that optimal dispersion leads to Zipf's law. Moreover, we found that the arithmetic ensemble average of the total growth rate converges to the geometric one, because the sample size is finite.

The edge of chaos is analyzed in a spatially extended system, modeled by the regularized long-wave equation, prior to the transition to permanent spatiotemporal chaos. In the presence of coexisting attractors, a chaotic saddle is born at the basin boundary due to a smooth-fractal metamorphosis. As a control parameter is varied, the chaotic transient evolves to well-developed transient turbulence via a cascade of fractal-fractal metamorphoses. The edge state responsible for the edge of chaos and the genesis of turbulence is an unstable traveling wave in the laboratory frame, corresponding to a saddle point lying at the basin boundary in the Fourier space.

We study deterministic systems, composed of excitable units of FitzHugh–Nagumo type, that are capable of self-generating and self-terminating strong deviations from their regular dynamics without the influence of noise or parameter change. These deviations are rare, short-lasting, and recurrent and can therefore be regarded as extreme events. Employing a range of methods we analyze dynamical properties of the systems, identifying features in the systems’ dynamics that may qualify as precursors to extreme events. We investigate these features and elucidate mechanisms that may be responsible for the generation of the extreme events.

We investigate the origins of $k^{-2}$ spectrum in a decaying Taylor-Green magnetohydrodynamic flow with zero large scale magnetic flux that was reported by Lee et al. [Phys. Rev. E 81, 016318 (2010)]. So far, a possible candidate for this scaling exponent has been the weak turbulence phenomenology. From our numerical simulations, we observe that current sheets in the magnetic Taylor-Green flow are formed in regions of magnetic discontinuities. Based on this observation and by studying the influence of the current sheets on the energy spectrum, using a filtering technique, we argue that the discontinuities are responsible for the $-2$ power law scaling of the energy spectra of this flow.

Modulational instability and breathing motion are studied in the two-dimensional nonlinear Schrödinger (NLS) equation trapped by the one-dimensional harmonic potential. The trapping potential is uniform in the $y$ direction and the wave function is confined in the $x$ direction. A breathing motion appears when the initial condition is close to a stationary solution which is uniform in the $y$ direction. The amplitude of the breathing motion is larger in the two-dimensional system than that in the corresponding one-dimensional system. Coupled equations of the one-dimensional NLS equation and two variational parameters are derived by the variational approximation to understand the amplification of the breathing motion qualitatively. On the other hand, there is a breathing solution in the $x$ direction which is uniform in the $y$ direction to the two-dimensional NLS equation. It is shown that the modulational instability along the $y$ direction is suppressed when the breathing motion is sufficiently strong, even if the norm is above the critical value of the collapse.

We report an exact transparent boundary condition (TBC) on the surface of a rectangular cuboid for the three-dimensional (3D) time-dependent Schrödinger equation. It is obtained as a generalization of the well-known TBC for the 1D Schrödinger equation and of the exact TBC in the rectangular domain for the 3D parabolic wave equation, which we reported earlier. Like all other TBCs, it is nonlocal in time domain and relates the boundary transverse derivative of the wave function at any given time to the boundary values of the same wave function at all preceding times. We develop a discretization of this boundary condition for the implicit Crank-Nicolson finite difference scheme. Several numerical experiments demonstrate evolution of the wave function in free space as well as propagation through a number of 3D spherically symmetrical and asymmetrical barriers, and, finally, scattering off an asymmetrical 3D potential. The proposed boundary condition is simple and robust, and can be useful in computational quantum mechanics when an accurate numerical solution of the 3D Schrödinger equation is required.

This article introduces a highly parallel algorithm for molecular dynamics simulations with short-range forces on single node multi- and many-core systems. The algorithm is designed to achieve high parallel speedups for strongly inhomogeneous systems like nanodevices or nanostructured materials. In the proposed scheme the calculation of the forces and the generation of neighbor lists are divided into small tasks. The tasks are then executed by a thread pool according to a dependent task schedule. This schedule is constructed in such a way that a particle is never accessed by two threads at the same time. Benchmark simulations on a typical 12-core machine show that the described algorithm achieves excellent parallel efficiencies above 80% for different kinds of systems and all numbers of cores. For inhomogeneous systems the speedups are strongly superior to those obtained with spatial decomposition. Further benchmarks were performed on an Intel Xeon Phi coprocessor. These simulations demonstrate that the algorithm scales well to large numbers of cores.

Many real-world networks depend on other networks, often in nontrivial ways, to maintain their functionality. These interdependent “networks of networks” are often extremely fragile. When a fraction $1-p$ of nodes in one network randomly fails, the damage propagates to nodes in networks that are interdependent and a dynamic failure cascade occurs that affects the entire system. We present dynamic equations for two interdependent networks that allow us to reproduce the failure cascade for an arbitrary pattern of interdependency. We study the “rich club” effect found in many real interdependent network systems in which the high-degree nodes are extremely interdependent, correlating a fraction $\alpha$ of the higher-degree nodes on each network. We find a rich phase diagram in the plane $p-\alpha$, with a triple point reminiscent of the triple point of liquids that separates a nonfunctional phase from two functional phases.

Directed-ratchet transport (DRT) in a one-dimensional lattice of spherical beads, which serves as a prototype for granular chains, is investigated. We consider a system where the trajectory of the central bead is prescribed by a biharmonic forcing function with broken time-reversal symmetry. By comparing the mean integrated force of beads equidistant from the forcing bead, two distinct types of directed transport can be observed—spatial and temporal DRT. Based on the value of the frequency of the forcing function relative to the cutoff frequency, the system can be categorized by the presence and magnitude of each type of DRT. Furthermore, we investigate and quantify how varying additional parameters such as the biharmonic weight affects DRT velocity and magnitude. Finally, friction is introduced into the system and is found to significantly inhibit spatial DRT. In fact, for sufficiently low forcing frequencies, the friction may even induce a switching of the DRT direction.

Wetting transitions are studied in the two-dimensional Ising ferromagnet confined between walls where competitive surface fields act. In our finite samples of size $L\times M$, the walls are separated by a distance $L$, $M$ being the length of the sample. The surface fields are taken to be short-range and nonuniform, i.e., of the form $H_1,\delta H_1,H_1,\delta H_1,...$, where the parameter $-1\le \delta \le 1$ allows us to control the nonuniformity of the fields. By performing Monte Carlo simulations we found that those competitive surface fields lead to the occurrence of an interface between magnetic domains of different orientation that runs parallel to the walls. In finite samples, such an interface undergoes a localization-delocalization transition, which is the precursor of a true wetting transition that takes place in the thermodynamic limit. By exactly working out the ground state ($T=0$), we found that besides the standard nonwet and wet phases, a surface antiferromagnetic-like state emerges for $\delta <-1/3$ and large fields ($H_1>3)$, $H_1^{\mathrm{tr}}/J=3$, ${\delta }^{\mathrm{tr}}=-1/3,T=0,$ being a triple point where three phases coexist. By means of Monte Carlo simulations it is shown that these features of the phase diagram remain at higher temperatures; e.g., we examined in detail the case $T=0.7\times T_{cb}$. Furthermore, we also recorded phase diagrams for fixed values of $\delta$, i.e., plots of the critical field at the wetting transition ($H_{1w}$) versus $T$ showing, on the one hand, that the exact results of Abraham [Abraham, Phys. Rev. Lett. 44, 1165 (1980)] for $\delta =1$ are recovered, and on the other hand, that extrapolations to $T\to 0$ are consistent with our exact results. Based on our numerical results we conjectured that the exact result for the phase diagram worked out by Abraham can be extended for the case of nonuniform fields. In fact, by considering a nonuniform surface field of some period $\lambda$, with $\lambda \ll M$, e.g., $[H_1(x,\lambda )>0]$, one can obtain the effective field $H^{\text{eff}}$ at a $\lambda$ coarse-grained level given by $H^{\text{eff}}=\frac{1}{\lambda }{\sum }_{x=1}^{\lambda }{H}_1(x,\lambda )$. Then we conjectured that the exact solution for the phase diagram is now given by $H^{\text{eff}}/J=F\left(T\right)$, where $F\left(T\right)$ is a function of the temperature $T$ that straightforwardly follows from Abraham's solution. The conjecture was exhaustively tested by means of computer simulations. Furthermore, it is found that for $\delta \ne 1$ the nonwet phase becomes enlarged, at the expense of the wet one, i.e., a phenomenon that we call “surface nonuniformity-induced nonwetting,” similar to the already known case of “roughness-induced nonwetting.”

We consider the translocation of a neutral (uncharged) nanoparticle through a pore in a thin membrane with constant surface charge density. If the concomitant Debye screening layer is sufficiently thin, the resulting forces experienced by the particle on its way through the pore are negligible. But when the Debye length becomes comparable to the pore diameter, the particle encounters a quite significant potential barrier while approaching and entering the pore, and symmetrically upon exiting the pore. The main reason is an increasing pressure, which acts on the particle when it intrudes into the counter ion cloud of the Debye screening layer. In case the polarizability of the particle is different (usually smaller) than that of the ambient fluid, a second, much smaller contribution to the potential barrier is due to self-energy effects. Our numerical treatment of the problem is complemented by analytical approximations for sufficiently long cylindrical particles and pores, which agree very well with the numerics.

We present an analysis of the effect of the temperature on the flow of multiphase systems made of multiple miscible components in uniform cylindrical capillaries in adiabatic conditions. The temperature was explicitly included in the dynamic contact angle, tension at the three-phase contact line, and densities and viscosities of the fluids. The mathematical framework accounted for conservative forces (gravity, inertial, and interfacial tensions), nonconservative forces (viscous dissipation), and fluid retardation effects in the reservoirs at the two capillary ends. Temperature-dependent flow regimes ranged from nonoscillatory to oscillatory in a two-phase binary liquid (water-ethanol) system and in a two-phase pure liquid (ether) system. The Ca-Bo orbits highlighted dynamic attractors that depended on specific system characteristics as well as temperature. We conclude that temperature alone expresses and important role in the dynamical characteristics of capillary rise flow around its equilibrium.

In this paper, we aim to address an important issue about the pseudopotential lattice Boltzmann (LB) model, which has attracted much attention as a mesoscopic model for simulating interfacial dynamics of complex fluids, but suffers from the problem that the surface tension cannot be tuned independently of the density ratio. In the literature, a multirange potential was devised to adjust the surface tension [Sbragaglia et al., Phys. Rev. E 75, 026702 (2007)]. However, it was recently found that the density ratio of the system will be changed when the multirange potential is employed to adjust the surface tension. An alternative approach is therefore proposed in the present work. The basic strategy is to add a source term to the LB equation so as to tune the surface tension of the pseudopotential LB model. The proposed approach can guarantee that the adjustment of the surface tension does not affect the mechanical stability condition of the pseudopotential LB model, and thus provides a separate control of the surface tension and the density ratio. Meanwhile, it still retains the mesoscopic feature and the computational simplicity of the pseudopotential LB model. Numerical simulations are carried out for stationary droplets, capillary waves, and droplet splashing on a thin liquid film. The numerical results demonstrate that the proposed approach is capable of achieving a tunable surface tension over a very wide range and can keep the density ratio unchanged when adjusting the surface tension.

The mean action time is the mean of a probability density function that can be interpreted as a critical time, which is a finite estimate of the time taken for the transient solution of a reaction-diffusion equation to effectively reach steady state. For high-variance distributions, the mean action time underapproximates the critical time since it neglects to account for the spread about the mean. We can improve our estimate of the critical time by calculating the higher moments of the probability density function, called the moments of action, which provide additional information regarding the spread about the mean. Existing methods for calculating the $n\text{th}$ moment of action require the solution of $n$ nonhomogeneous boundary value problems which can be difficult and tedious to solve exactly. Here we present a simplified approach using Laplace transforms which allows us to calculate the $n\text{th}$ moment of action without solving this family of boundary value problems and also without solving for the transient solution of the underlying reaction-diffusion problem. We demonstrate the generality of our method by calculating exact expressions for the moments of action for three problems from the biophysics literature. While the first problem we consider can be solved using existing methods, the second problem, which is readily solved using our approach, is intractable using previous techniques. The third problem illustrates how the Laplace transform approach can be used to study coupled linear reaction-diffusion equations.

We consider the shear rheology of concentrated suspensions of non-Brownian frictional particles. The key result of our study is the emergence of a pronounced shear-thickening regime, where frictionless particles would normally undergo shear thinning. We can clarify that shear thickening in our simulations is due to enhanced energy dissipation via frictional interparticle forces. Moreover, we evidence the formation of dynamically correlated particle clusters of size $\xi$, which contribute to shear thickening via an increase in viscous dissipation. A scaling argument gives for the associated viscosity ${\eta }_v\sim {\xi }^2$, which is in very good agreement with the data.