We analyze two- and three-link planar snakelike locomotion and optimize the motion for efficiency. The locomoting system consists of two or three identical inextensible links connected via hinge joints, and the angles between the links are actuated as prescribed periodic functions of time. An essential feature of snake locomotion is frictional anisotropy: The forward, backward, and transverse coefficients of friction differ. The dynamics are studied analytically and numerically for small and large amplitudes of the internal angles. Efficiency is defined as the ratio between distance traveled and the energy expended within one period, i.e., the inverse of the cost of locomotion. The optimal set of coefficients of friction to maximize efficiency consists of a large backward coefficient of friction and a small transverse coefficient of friction, compared to the forward coefficient of friction. For the two-link case with a symmetrical motion, efficiency is maximized when the internal angle amplitude is approximately $\pi /2$ for a sufficiently large transverse coefficient. For the three-link case, the efficiency-maximizing paths are triangles in the parameter space of internal angles.

Coherent and intense x-ray pulses generated by x-ray free-electron laser (XFEL) sources are paving the way for structural determination of noncrystalline biomolecules. However, due to the small scattering cross section of electrons for x rays, the available incident x-ray intensity of XFEL sources, which is currently in the range of 10${}^{12}$–10${}^{13}$ photons/μm${}^2$/pulse, is lower than that necessary to perform single-molecule diffraction experiments for noncrystalline biomolecules even with the molecular masses of megadalton and submicrometer dimensions. Here, we propose an experimental protocol and analysis method for visualizing the structure of those biomolecules by the combined application of coherent x-ray diffraction imaging and three-dimensional reconstruction methods. To compensate the small scattering cross section of biomolecules, in our protocol, a thin vitreous ice plate containing several hundred biomolecules/μm${}^2$ is used as sample, a setup similar to that utilized by single-molecule cryoelectron microscopy. The scattering cross section of such an ice plate is far larger than that of a single particle. The images of biomolecules contained within irradiated areas are then retrieved from each diffraction pattern, and finally provide the three-dimensional electron density model. A realistic atomic simulation using large-scale computations proposed that the three-dimensional structure determination of the 50S ribosomal subunit embedded in a vitreous ice plate is possible at a resolution of 0.8 nm when an x-ray beam of 10${}^{16}$ photons/500×500 nm${}^2$/pulse is available.

Shape fluctuations of a planar lipid membrane in an ac electric field are investigated using a zero-thickness electromechanical model, which accounts for membrane conductivity and capacitance, and asymmetry in the properties of the fluids separated by the membrane. A linear stability analysis shows that unlike in the case of a dc electric field, a purely capacitive membrane can be destabilized in an ac electric field. The theory highlights that the instability originates from electric pressure exerted on the membrane.

In recent research it was found that the fundamental shear-localizing instability of amorphous solids under external strain, which eventually results in a shear band and failure, consists of a highly correlated array of Eshelby quadrupoles all having the same orientation and some density $\rho$. In this paper we calculate analytically the energy $E(\rho ,\gamma )$ associated with such highly correlated structures as a function of the density $\rho$ and the external strain $\gamma$. We show that for strains smaller than a characteristic strain ${\gamma }_Y$ the total strain energy initially increases as the quadrupole density increases, but that for strains larger than ${\gamma }_Y$ the energy monotonically decreases with quadrupole density. We identify ${\gamma }_Y$ as the yield strain. Its value, derived from values of the qudrupole strength based on the atomistic model, agrees with that from the computed stress-strain curves and broadly with experimental results.

The concept of bounded confidence in social dynamics is introduced into the Kuramoto model. Then a model with projective symmetry is naturally induced by a principal $Z_2$ bundle over a circle. A Möbius strip is constructed as the manifold of interactions such that two “sides” of a local section correspond to antipodal couplings with opposite signs. We show analytically that symmetric polarization of synchronized states (conformist vs contrarian) can emerge from the collective behavior of homogeneously coupled oscillators. In the continuum limit, a generalized asymmetric model reverts to the symmetric case under uniform initial condition, whereas for networks of finite size, it exhibits richer dynamics or the ordinary behavior of the classic model via symmetry breaking, depending on the relevant parameters values. The symmetry and symmetry breaking of the synchronization state are analogous to the concepts of equality and majority of opinions in sociophysical models of opinion formation. The synchronized clusters can be one (consensus), two (polarization), or more (fragmentation), as opinion clusters.

We study the effect of a weak random additive noise in a linear chain of $N$ locally coupled logistic maps at the edge of chaos. Maps tend to synchronize for a strong enough coupling, but if a weak noise is added, very intermittent fluctuations in the returns time series are observed. This intermittency tends to disappear when noise is increased. Considering the probability distribution functions (pdfs) of the returns, we observe the emergence of fat tails which can be satisfactorily reproduced by $q$-Gaussians’ curves typical of nonextensive statistical mechanics. The interoccurrence times of these extreme events are also studied in detail. Similarities with the recent analysis of financial data are also discussed.

Synthetic models of Eulerian turbulence like so-called kinematic simulations (KS) are often used as computational shortcuts for studying Lagrangian properties of turbulence. These models have been criticized by Thomson and Devenish (2005), who argued on physical grounds that sweeping decorrelation effects suppress pair dispersion in such models. We derive analytical results for Eulerian turbulence modeled by Gaussian random fields, in particular for the case with zero mean velocity. Our starting point is an exact integrodifferential equation for the particle pair separation distribution obtained from the Gaussian integration-by-parts identity. When memory times of particle locations are short, a Markovian approximation leads to a Richardson-type diffusion model. We obtain a time-dependent pair diffusivity tensor of the form $K_{ij}(\mathbf{r},t)=S_{ij}\left(\mathbf{r}\right)\tau (r,t)$, where $S_{ij}\left(\mathbf{r}\right)$ is the structure-function tensor and $\tau (r,t)$ is an effective correlation time of velocity increments. Crucially, this is found to be the minimum value of three times: the intrinsic turnover time ${\tau }_{\mathrm{eddy}}\left(r\right)$ at separation $r$, the overall evolution time $t,$ and the sweeping time $r/v_0$ with $v_0$ the rms velocity. We study the diffusion model numerically by a Monte Carlo method. With inertial ranges like the largest achieved in most current KS (about 6 decades long), our model is found to reproduce the $t^{9/2}$ power law for pair dispersion predicted by Thomson and Devenish and observed in the KS. However, for much longer ranges, our model exhibits three distinct pair-dispersion laws in the inertial range: a Batchelor $t^2$ regime, followed by a Kraichnan-model-like $t^1$ diffusive regime, and then a $t^6$ regime. Finally, outside the inertial range, there is another $t^1$ regime with particles undergoing independent Taylor diffusion. These scalings are exactly the same as those predicted by Thomson and Devenish for KS with large mean velocities, which we argue hold also for KS with zero mean velocity. Our results support the basic conclusion of Thomson and Devenish (2005) that sweeping effects make Lagrangian properties of KS fundamentally differ from those of hydrodynamic turbulence for very extended inertial ranges.

A one-dimensional model of inertial pumping is introduced and solved. The pump is driven by a high-pressure vapor bubble generated by a microheater positioned asymmetrically in a microchannel. The bubble is approximated as a short-term impulse delivered to the two fluidic columns inside the channel. Fluid dynamics is described by a Newton-like equation with a variable mass, but without the mass derivative term. Because of smaller inertia, the short column refills the channel faster and accumulates a larger mechanical momentum. After bubble collapse the total fluid momentum is nonzero, resulting in a net flow. Two different versions of the model are analyzed in detail, analytically and numerically. In the symmetrical model, the pressure at the channel-reservoir connection plane is assumed constant, whereas in the asymmetrical model it is reduced by a Bernoulli term. For low and intermediate vapor bubble pressures, both models predict the existence of an optimal microheater location. The predicted net flow in the asymmetrical model is smaller by a factor of about 2. For unphysically large vapor pressures, the asymmetrical model predicts saturation of the effect, while in the symmetrical model net flow increases indefinitely. Pumping is reduced by nonzero viscosity, but to a different degree depending on the microheater location.

This paper proposes a control strategy in which immersed bodies are driven to rotate not by external forces but by the flow itself. Due to the asymmetric distribution of the shear stress exerted on the surfaces, two side-by-side arranged cylinders rotate about their axes to produce moving fluid-solid boundaries. It is shown that the drag and the lift coefficients are significantly reduced in comparison with the stationary cylinder system. Different from the slip-boundary technique, the drag-reduction mechanism is explained in terms of a pressure-recovery effect introduced by the rotating surfaces.

We investigate experimentally and numerically turbulent Taylor-Couette flow with independently rotating cylinders and radius ratio $\eta =0.5$. The torque acting on the inner wall is measured to analyze the transverse current of azimuthal motion $J_{\omega }$. The scaling of the torque with shear Reynolds number is determined for the outer cylinder at rest. For constant shear Reynolds number we investigate various ratios of angular velocities and find a torque maximum for counter-rotating cylinders that deviates from the prediction suggested by van Gils et al. [J. Fluid Mech. 706, 118 (2012)]. The direct comparison between the experiment and the numerical simulation shows a good agreement in the torques.

We study the gravity-exchange flow of two immiscible fluids in a porous medium and show that, in contrast with the miscible case, a portion of the initial interface remains pinned at all times. We elucidate, by means of micromodel experiments, the pore-level mechanism responsible for capillary pinning at the macroscale. We propose a sharp-interface gravity-current model that incorporates capillarity and quantitatively explains the experimental observations, including the $x\sim t^{1/2}$ spreading behavior at intermediate times and the fact that capillarity stops a finite-release current. Our theory and experiments suggest that capillary pinning is potentially an important, yet unexplored, trapping mechanism during CO${}_2$ sequestration in deep saline aquifers.

The Brownian motion of a microscopic particle in a fluid is one of the cornerstones of statistical physics and the paradigm of a random process. One of the most powerful tools to quantify it was provided by Langevin, who explicitly accounted for a short-time correlated “thermal” force. The Langevin picture predicts ballistic motion, $\langle x^2\rangle \sim t^2$ at short-time scales, and diffusive motion $\langle x^2\rangle \sim t$ at long-time scales, where $x$ is the displacement of the particle during time $t$, and the average is taken over the thermal distribution of initial conditions. The Langevin equation also predicts a superdiffusive regime, where $\langle x^2\rangle \sim t^3$, under the condition that the initial velocity is fixed rather than distributed thermally. We analyze the motion of an optically trapped particle in air and indeed find $t^3$ dispersion. This observation is a direct proof of the existence of the random, rapidly varying force imagined by Langevin.

We study the long-time behavior of the scaled walker (particle) position associated with decoupled continuous-time random walks which is characterized by superheavy-tailed distribution of waiting times and asymmetric heavy-tailed distribution of jump lengths. Both the scaling function and the corresponding limiting probability density are determined for all admissible values of tail indexes describing the jump distribution. To analytically investigate the limiting density function, we derive a number of different representations of this function and, in this way, establish its main properties. We also develop an efficient numerical method for computing the limiting probability density and compare our analytical and numerical results.

The effect of partial absorption on a diffusive particle which stochastically resets its position with a finite rate $r$ is considered. The particle is absorbed by a target at the origin with absorption “velocity” $a$; as the velocity $a$ approaches $\infty$ the absorption property of the target approaches that of a perfectly absorbing target. The effect of partial absorption on first-passage time problems is studied, in particular, it is shown that the mean time to absorption (MTA) is increased by an additive term proportional to $1/a$. The results are extended to multiparticle systems where independent searchers, initially uniformly distributed with a given density, look for a single immobile target. It is found that the average survival probability $P^{av}$ is modified by a multiplicative factor which is a function of $1/a$, whereas the decay rate of the typical survival probability $P^{typ}$ is decreased by an additive term proportional to $1/a$.

The thermal conductance at solid-gas interfaces with different interfacial bonding strengths is calculated through Green-Kubo equilibrium molecular dynamics (EMD) simulations. Due to the finite size of the simulation system, the long-time integral of the time correlation function of heat power across the solid-gas interface exhibits an exponential decay, which contains the information on interfacial thermal conductance. If an adsorbed gas layer is formed on the solid surface, it is found that the solid-gas interface needs to be defined at a plane outside the adsorbed layer so as to obtain the correct result from the Green-Kubo formula. The EMD simulation result agrees very well with that obtained from nonequilibrium molecular dynamics simulations. By calculating the average solid-gas interaction time as a function of solid-gas interaction strength, we find the incident gas atoms thermalize with the metal surface much more rapidly when the surface is covered by adsorbed gas molecules.

We present a probabilistic theory of random walks in turbid media with nonscattering regions. It is shown that important characteristics such as diffusion constants, average step lengths, crossing statistics, and void spacings can be analytically predicted. The theory is validated using Monte Carlo simulations of light transport in heterogeneous systems in the form of random sphere packings and good agreement is found. The role of step correlations is discussed and differences between unbounded and bounded systems are investigated. Our results are relevant to the optics of heterogeneous systems in general and represent an important step forward in the understanding of media with strong (fractal) heterogeneity in particular.

In this study we have incorporated two time scales into the phase-field-crystal model of a binary alloy to explore different solute trapping properties as a function of crystal-melt interface velocity. With only diffusive dynamics, we demonstrate that the segregation coefficient, $K$ as a function of velocity for a binary alloy is consistent with the model of Kaplan and Aziz where $K$ approaches unity in the limit of infinite velocity. However, with the introduction of wavelike dynamics in both the density and concentration fields, the trapping follows the kinetics proposed by Sobolev [Phys. Lett. A 199, 383 (1995)], where complete trapping occurs at a finite velocity.

Self-organized interfacial instabilities of an ultrathin bilayer confined between a pair of rigid surfaces is explored. The bilayers are classified based on the macroscopic dewetting behaviors of the liquid films sandwiched between a pair of confining surfaces having surface energy higher or lower than the liquid films. Linear and nonlinear analyses employing the governing equations originating from the continuum description together with molecular dynamics (MD) simulations unveil the salient spatiotemporal features of the dewetting process. The study uncovers that, under the destabilizing influence of the intermolecular interactions, the interface of a confined bilayer can deform into interesting embedded and encapsulated patterns with nanoscale periodicity. The continuum and MD simulations collectively show the detailed route to dewetting starting from the formation of holes in the early stage, their growth to achieve equilibrium contact angle at the intermediate phase, and then to evolve into the equilibrium morphologies at the later stage. Examples are shown where the length and the time scales of the simulated nanostructures from both the continuum and MD approaches are found to agree with the same obtained from the linear stability analysis. We also highlight the deviations that are observed in the continuum and MD approaches. The study confirms that the reduced stabilizing interfacial tension at the liquid-liquid interface together with enhanced intermolecular interaction because of the thinness of the layers can be an alternative strategy for pattern miniaturization exploiting the instabilities of a thin confined bilayer. Further, the study shows that use of topographical patterns on the bounding surfaces can impose periodic order to the holes, droplets, columns, and channels, which can find important applications in the diverse areas of nanotechnology.

We report, for a rodlike nematic liquid crystal with small positive dielectric and conductivity anisotropies, and in the 90°-twisted configuration, low frequency (<2 Hz) square wave electric field generated Carr-Helfrich director modulation appearing transiently over a few seconds at each polarity reversal and vanishing almost completely under steady field conditions. Significantly, the instability is polarity sensitive, with the maximum distortion localized in the vicinity of the negative electrode, rather than in the midplane of the layer. This is revealed by the wave vector alternating in the two halves of the driving cycle between the alignment directions at the two substrates. Besides the Carr-Helfrich mechanism, quadrupolar flexoelectric polarization arising under electric field gradient is strongly indicated as being involved in the development of the transient periodic order. Similar transient instability is also observed in other nematic compounds with varying combinations of dielectric and conductivity anisotropies, showing its general nature. The study also deals with various characteristics of the electro-optic effect that emerge from the temporal variation of optical response for different driving voltages, frequencies, and temperatures.

A 10-nm-long DNA molecule can bend through large angles reversibly. Past the linear regime, its equilibrium nonlinear bending elasticity is governed by a critical bending torque ${\tau }_c\approx 30\mathrm{pN}\times \mathrm{nm}$ at which the molecule develops a kink. This nonlinearity has long been attributed to the nucleation of a bubble or melted region in the molecule. Here we measure the temperature dependence of the critical bending torque for nicked DNA, and determine that the entropy associated with the kink in the nonlinear regime is negligible. Thus in the case of nicked DNA the kink is not a bubble, but a compact region deformed beyond a yield strain. We further argue that, with our boundary conditions, the same is likely true for intact DNA. The present measurements confirm that the critical bending torque ${\tau }_c$ is a materials parameter of DNA mechanics analogous to the bending modulus $B\approx 200\mathrm{pN}\times \mathrm{nm}$.