For a drop on an incline with small tilt angle $\alpha$, when the contact line is a circle of radius $r$, we derive the relation $mgsin\alpha =\gamma r\frac{\pi }{2}(cos{\theta }^{\min }-cos{\theta }^{\max })$ at first order in $\alpha$, where ${\theta }^{\min }$ and ${\theta }^{\max }$ are the contact angles at the back and at the front, $m$ is the mass of the drop and $\gamma$ the surface tension of the liquid. We revisit in this way the Furmidge model for a large range of contact angles. We also derive the same relation at first order in the Bond number $B=\rho g{R}^2/\gamma$, where $R$ is the radius of the spherical cap at zero gravity. The drop profile is computed exactly in the same approximation. Results are compared with surface evolver simulations, showing a surprisingly large range of contact angles for applicability of first-order approximations.

The effects of strongly varying fluid properties, beyond the validity range of the so-called Boussinesq approximation, were experimentally studied in Rayleigh-Bénard (RB) convection. Two experiments were conducted in the same cubical RB convection cell at similar Rayleigh and Prandtl numbers. In one experiment water was used as working fluid and the imposed temperature difference between the top and bottom plates of the cell was such to ensure non-Boussinesq conditions. In the other experiment, taken as a reference for Boussinesq conditions, methanol was used as working fluid, allowing a smaller temperature difference between the plates. In both experiments the instantaneous and time-averaged flow fields were determined experimentally in a vertical cross section of the cell by using particle image velocimetry. Results show a non-Boussinesq effect that manifests itself as an increase of the time-averaged horizontal velocity component close to the bottom wall of the cell and as a global top-bottom asymmetry of the velocity field. This is an experimental study of the whole velocity field of RB convection at non-Boussinesq conditions.

The combined effects of buoyancy-driven Rayleigh-Bénard convection (RC) and surface tension-driven Marangoni convection (MC) are studied in a triple-layer configuration which serves as a simplified model for a liquid metal battery (LMB). The three-layer model consists of a liquid metal alloy cathode, a molten salt separation layer, and a liquid metal anode at the top. Convection is triggered by the temperature gradient between the hot electrolyte and the colder electrodes, which is a consequence of the release of resistive heat during operation. We present a linear stability analysis of the state of pure thermal conduction in combination with three-dimensional direct numerical simulations of the nonlinear turbulent evolution on the basis of a pseudospectral method. Five different modes of convection are identified in the configuration, which are partly coupled to each other: RC in the upper electrode, RC with internal heating in the molten salt layer, and MC at both interfaces between molten salt and electrode as well as anticonvection in the middle layer and lower electrode. The linear stability analysis confirms that the additional Marangoni effect in the present setup increases the growth rates of the linearly unstable modes, i.e., Marangoni and Rayleigh-Bénard instability act together in the molten salt layer. The critical Grashof and Marangoni numbers decrease with increasing middle layer thickness. The calculated thresholds for the onset of convection are found for realistic current densities of laboratory-sized LMBs. The global turbulent heat transfer follows scaling predictions for internally heated RC. The global turbulent momentum transfer is comparable with turbulent convection in the classical Rayleigh-Bénard case. In summary, our studies show that incorporating Marangoni effects generates smaller flow structures, alters the velocity magnitudes, and enhances the turbulent heat transfer across the triple-layer configuration.

The energy of plasma waves can be moved up and down the spectrum using chirped modulations of plasma parameters, which can be driven by external fields. Depending on whether the wave spectrum is discrete (bounded plasma) or continuous (boundless plasma), this phenomenon is called ladder climbing (LC) or autoresonant acceleration of plasmons. It was first proposed by Barth et al. [Phys. Rev. Lett. 115, 075001 (2015)] based on a linear fluid model. In this paper, LC of electron plasma waves is investigated using fully nonlinear Vlasov-Poisson simulations of collisionless bounded plasma. It is shown that, in agreement with the basic theory, plasmons survive substantial transformations of the spectrum and are destroyed only when their wave numbers become large enough to trigger Landau damping. Since nonlinear effects decrease the damping rate, LC is even more efficient when practiced on structures like quasiperiodic Bernstein-Greene-Kruskal (BGK) waves rather than on Langmuir waves per se.

We make use of discrete-element-method numerical simulations of inelastic frictionless cylinders in simple shearing at different length-to-diameter ratios and solid volume fractions to analyze the rate of collisional dissipation of the fluctuation kinetic energy. We show that the nonspherical geometry of the particles is responsible, by inducing rotation, for increasing the dissipation rate of the fluctuation kinetic energy with respect to that for frictionless spheres. We also suggest that the partial alignment of the cylinders induced by shearing concurs with the particle inelasticity in generating correlation in the velocity fluctuations and thus affecting the collisional dissipation rate as the solid volume fraction increases. Finally, we propose simple phenomenological modifications to the expression of the collisional dissipation rate of kinetic theory of granular gases to take into account our findings.

A continuous time random walk (CTRW) model with waiting times following the Lévy-stable distribution with exponential cutoff in equilibrium is a simple theoretical model giving rise to normal, yet non-Gaussian, diffusion. The distribution of the particles' displacements is explicitly time dependent and does not scale. Since fluorescent correlation spectroscopy (FCS) is often used to investigate diffusion processes, we discuss the influence of this lack of scaling on the possible outcome of the FCS measurements and calculate the FCS autocorrelation curves for such equilibrated CTRWs. The results show that although the deviations from Gaussian behavior may be detected when analyzing the short- and long-time asymptotic behavior of the corresponding curves, their bodies are still perfectly fitted by the fit forms used for normal diffusion. The diffusion coefficients obtained from the fits may however differ considerably from the true tracer diffusion coefficients as describing the time dependence of the mean squared displacement.

Recent studies have demonstrated that defocusing cubic nonlinearity with local strength growing from the center to the periphery faster than $r^D$, in space of dimension $D$ with radial coordinate $r$, supports a vast variety of robust bright solitons. In the framework of the same model, but with a weaker spatial-growth rate $\sim r^{\alpha }$ with $\alpha \le D$, we test here the possibility to create stable localized continuous waves (LCWs) in one-dimensional (1D) and 2D geometries, localized dark solitons (LDSs) in one dimension, and localized dark vortices (LDVs) in two dimensions, which are all realized as loosely confined states with a divergent norm. Asymptotic tails of the solutions, which determine the divergence of the norm, are constructed in a universal analytical form by means of the Thomas-Fermi approximation (TFA). Global approximations for the LCWs, LDSs, and LDVs are constructed on the basis of interpolations between analytical approximations available far from (TFA) and close to the center. In particular, the interpolations for the 1D LDS, as well as for the 2D LDVs, are based on a deformed-tanh expression, which is suggested by the usual 1D dark-soliton solution. The analytical interpolations produce very accurate results, in comparison with numerical findings, for the 1D and 2D LCWs, 1D LDSs, and 2D LDVs with vorticity $S=1$. In addition to the 1D fundamental LDSs with the single notch and 2D vortices with $S=1$, higher-order LDSs with multiple notches are found too, as well as double LDVs, with $S=2$. Stability regions for the modes under consideration are identified by means of systematic simulations, the LCWs being completely stable in one and two dimensions, as they are ground states in the corresponding settings. Basic evolution scenarios are identified for those vortices that are unstable. The settings considered in this work may be implemented in nonlinear optics and in Bose-Einstein condensates.

The active interaction between the bacteria and fluid generates turbulent structures even at zero Reynolds number. The velocity of such a flow obtained experimentally has been quantitatively investigated based on streamline segment analysis. There is a clear transition at about 16 times the organism body length separating two different scale regimes, which may be attributed to the different influence of the viscous effect. Surprisingly the scaling extracted from the streamline segment indicates the existence of scale similarity even at the zero Reynolds number limit. Moreover, the multifractal feature can be quantitatively described via a lognormal formula with the Hurst number $H=0.76$ and the intermittency parameter $\mu =0.20$, which is coincidentally in agreement with the three-dimensional hydrodynamic turbulence result. The direction of cascade is measured via the filter-space technique. An inverse energy cascade is confirmed. For the enstrophy, a forward cascade is observed when $r/R\le 3$, and an inverse one is observed when $r/R>3$, where $r$ and $R$ are the separation distance and the bacteria body size, respectively. Additionally, the lognormal statistics is verified for the coarse-grained energy dissipation and enstrophy, which supports the lognormal formula to fit the measured scaling exponent.

Configurations of a single semiflexible polymer is studied when it is pushed into a nanochannel in the case where the polymer persistence length $l_p$ is much longer than the channel diameter $D:l_p/D\gg 1$. Using numerical simulations, we show that the polymer undergoes a sequence of recurring structural transitions upon longitudinal compression: random deflection along the channel, a helix going around the channel wall, double-fold random deflection, double-fold helix, etc. We find that the helix transition can be understood as buckling of deflection segments, and the initial helix formation takes place at very small compression with no appreciable weak compression regime of the random deflection polymer.

We have studied spatial and temporal dynamic heterogeneity (DH) in a system of hard-sphere particles, subjected to active forces with constant amplitude and random direction determined by rotational diffusion with correlation time $\tau$. We have used a variety of observables to characterize the DH behavior, including the deviation from standard Stokes-Einstein (SE) relation, a non-Gaussian parameter ${\alpha }_2\left(\mathrm{\Delta }t\right)$ for the distribution of particle displacement within a certain time interval $\mathrm{\Delta }t$, a four-point susceptibility ${\chi }_4\left(\mathrm{\Delta }t,\mathrm{\Delta }L\right)$ for the correlation in dynamics between any two points in space separated by distance $\mathrm{\Delta }L$ within some time window $\mathrm{\Delta }t$, and a vector spatial-temporal correlation function $S_{\mathrm{vec}}\left(R,\mathrm{\Delta }t\right)$ for vector displacements within time interval $\mathrm{\Delta }t$ of particle pairs originally separated by $R$. By mapping the particle motion into a continuous-time random walk with constant jump length, we can obtain the average waiting time $〈t_x〉\propto D_s^{-1}$ and persistence time $〈t_p〉\propto \eta$, with $D_s$ the self-diffusion coefficient and $\eta$ the shear viscosity, such that the observable $\lambda =〈t_p〉/〈t_x〉\propto D_s\eta$ can be calculated as a function of the control parameter $\tau$ to show how it deviates from its SE value ${\lambda }_0$. Interestingly, we find $\lambda /{\lambda }_0$ shows a nonmonotonic behavior for large volume fraction ${\phi }_a$, wherein $\lambda /{\lambda }_0$ undergoes a minimum at a certain intermediate value of $\tau$, indicating that both small and large particle activity may lead to strong DH. Such a reentrance phenomenon is further demonstrated in terms of the non-Gaussian parameters ${\alpha }_2$, four-point susceptibility ${\chi }_4$, and vector spatiotemporal correlation functions $S_{\mathrm{vec}}$, respectively. Detail analysis shows that it is the competition between the dual roles of particle activity, namely, activity-induced higher effective temperature and activity-induced clustering, that leads to such nontrivial nonmonotonic behaviors. In addition, we find that DH may also show a maximum level at an intermediate value of ${\phi }_a$ if $\tau$ is large enough, implying that a more crowded system may be less heterogeneous than a less crowded one for a system with high particle activity.

We study the hydrodynamic mechanisms involved in the motion of the contact line formed at the end region of a liquid filament laying on a planar and horizontal substrate. Since the flow develops under partially wetting conditions, the tip of the filament recedes and forms a bulged region (head) that subsequently develops a neck region behind it. Later the neck breaks up leading to a separated drop, while the rest of the filament restarts the sequence. One main feature of this flow is that the whole dynamics and final drop shapes are strongly influenced by the hysteresis of the contact angle typical in most of the liquid-substrate systems. The time evolution till breakup is studied experimentally and pictured in terms of a hybrid wettability theory which involves the Cox-Voinov hydrodynamic approach combined with the molecular kinetic theory developed by Blake. The parameters of this theory are determined for our liquid-substrate system (silicone oil–coated glass). The experimental results of the retracting filament are described in terms of a simple heuristic model and compared with numerical simulations of the full Navier-Stokes equations. This study is of special interest in the context of pulsed laser-induced dewetting.

The influence of the uniaxial small-scale anisotropy on the kinematic magnetohydrodynamic turbulence is investigated by using the field theoretic renormalization group technique in the one-loop approximation of a perturbation theory. The infrared stable fixed point of the renormalization group equations, which drives the scaling properties of the model in the inertial range, is investigated as the function of the anisotropy parameters and it is shown that, at least at the one-loop level of approximation, the diffusion processes of the weak passive magnetic field in the anisotropically driven kinematic magnetohydrodynamic turbulence are completely equivalent to the corresponding diffusion processes of passively advected scalar fields in the anisotropic Navier-Stokes turbulent environments.

Plasma amplifiers offer a route to side-step limitations on chirped pulse amplification and generate laser pulses at the power frontier. They compress long pulses by transferring energy to a shorter pulse via the Raman or Brillouin instabilities. We present an extensive kinetic numerical study of the three-dimensional parameter space for the Raman case. Further particle-in-cell simulations find the optimal seed pulse parameters for experimentally relevant constraints. The high-efficiency self-similar behavior is observed only for seeds shorter than the linear Raman growth time. A test case similar to an upcoming experiment at the Laboratory for Laser Energetics is found to maintain good transverse coherence and high-energy efficiency. Effective compression of a $10\mathrm{kJ}$, nanosecond-long driver pulse is also demonstrated in a 15-cm-long amplifier.

The statistics of work performed on a system by a sudden random quench is investigated. Considering systems with finite dimensional Hilbert spaces we model a sudden random quench by randomly choosing elements from a Gaussian unitary ensemble (GUE) consisting of Hermitian matrices with identically, Gaussian distributed matrix elements. A probability density function (pdf) of work in terms of initial and final energy distributions is derived and evaluated for a two-level system. Explicit results are obtained for quenches with a sharply given initial Hamiltonian, while the work pdfs for quenches between Hamiltonians from two independent GUEs can only be determined in explicit form in the limits of zero and infinite temperature. The same work distribution as for a sudden random quench is obtained for an adiabatic, i.e., infinitely slow, protocol connecting the same initial and final Hamiltonians.

We study analytically the probability distribution of the heat released by an ensemble of harmonic oscillators to the thermal bath, in the nonequilibrium relaxation process following a temperature quench. We focus on the asymmetry properties of the heat distribution in the nonstationary dynamics, in order to study the forms taken by the fluctuation theorem as the number of degrees of freedom is varied. After analyzing in great detail the cases of one and two oscillators, we consider the limit of a large number of oscillators, where the behavior of fluctuations is enriched by a condensation transition with a nontrivial phase diagram, characterized by reentrant behavior. Numerical simulations confirm our analytical findings. We also discuss and highlight how concepts borrowed from the study of fluctuations in equilibrium under symmetry-breaking conditions [Gaspard, J. Stat. Mech. (2012) P08021] turn out to be quite useful in understanding the deviations from the standard fluctuation theorem.

$F_o{F}_1$-ATPase is a motor protein complex that utilizes transmembrane ion flow to drive the synthesis of adenosine triphosphate (ATP) from adenosine diphosphate (ADP) and phosphate (Pi). While many theoretical models have been proposed to account for its rotary activity, most of them focus on the $F_o$ or $F_1$ portions separately rather than the complex as a whole. Here, we propose a simple but new torque-coupled thermodynamic model of $F_o{F}_1$-ATPase. Solving this model at steady state, we find that the monotonic variation of each portion's efficiency becomes much more robust over a wide range of parameters when the $F_o$ and $F_1$ portions are coupled together, as compared to cases when they are considered separately. Furthermore, the coupled model predicts the dependence of each portion's kinetic behavior on the parameters of the other. Specifically, the power and efficiency of the $F_1$ portion are quite sensitive to the proton gradient across the membrane, while those of the $F_o$ portion as well as the related Michaelis constants for proton concentrations respond insensitively to concentration changes in the reactants of ATP synthesis. The physiological proton gradient across the membrane in the $F_o$ portion is also shown to be optimal for the Michaelis constants of ADP and phosphate in the $F_1$ portion during ATP synthesis. Together, our coupled model is able to predict key dynamic and thermodynamic features of the $F_o{F}_1$-ATPase in vivo semiquantitatively, and suggests that such coupling approach could be further applied to other biophysical systems.

Clathrin-mediated endocytosis in yeast is driven by a protein patch containing close to 100 different types of proteins. Among the proteins are $5000–10000$ copies of polymerized actin, and successful endocytosis requires growth of the actin network. Since it is not known exactly how actin network growth drives endocytosis, we calculate the spatial distribution of actin growth required to generate the force that drives the process. First, we establish the force distribution that must be supplied by actin growth, by combining membrane-bending profiles obtained via electron microscopy with established theories of membrane mechanics. Next, we determine the profile of actin growth, using a continuum mechanics approach and an iterative procedure starting with an actin growth profile obtained from a linear analysis. The profile has fairly constant growth outside a central hole of radius 45–50 nm, but very little growth in this hole. This growth profile can reproduce the required forces if the actin shear modulus exceeds 80 kPa, and the growing filaments can exert very large polymerization forces. The growth profile prediction could be tested via electron-microscopy or super-resolution experiments in which the turgor pressure is suddenly turned off.

We apply the concept of a frequency-dependent effective temperature based on the fluctuation-dissipation ratio to a driven Brownian particle in a nonequilibrium steady state. Using this system as a thermostat for a weakly coupled harmonic oscillator, the oscillator thermalizes according to a canonical distribution at the respective effective temperature across the entire frequency spectrum. By turning the oscillator from a passive thermometer into a heat engine, we realize the cyclic extraction of work from a single thermal reservoir, which is feasible only due to its nonequilibrium nature.

We use a Monte Carlo simulation to study the diluted antiferromagnetic Ising model on frustrated lattices including the pyrochlore lattice to show the dilution effects. Using the Wang-Landau algorithm, which directly calculates the energy density of states, we accurately calculate the entropy of the system. We discuss the nonmonotonic dilution concentration dependence of residual entropy for the antiferromagnetic Ising model on the pyrochlore lattice, and compare it to the generalized Pauling approximation proposed by Ke et al. [Phys. Rev. Lett. 99, 137203 (2007)]. We also investigate other frustrated systems, the antiferromagnetic Ising model on the triangular lattice and the kagome lattice, demonstrating the difference in the dilution effects between the system on the pyrochlore lattice and that on other frustrated lattices.