We observe unsteady flow behavior of liquid metal during a pressure-driven injection process into a closed-ended polydimethylsiloxane microchannel. Constant pressure is applied at the inlet to allow eutectic gallium-indium (EGaIn) to completely fill the porous microchannels. In contrast to open channels [M. D. Dickey et al., Adv. Funct. Mater. 18, 1097 (2008)], the flow exhibits a complex unsteady behavior with sudden random length jumps and time stops. However, with appropriate formulation of a suitable mathematical model with the system using (i) the permeability of polydimethylsiloxane to air, (ii) previous descriptions of the nature of the EGaIn surface oxide layer, and (iii) a key probabilistic approach, we show that the average quantities defining the quantumlike flow can be accurately predicted. The proposed probabilistic formulation provides for the first time a description of the dynamics of the surface oxide layer, the breaking and healing characteristic times when EGaIn is driven in a microchannel. Importantly, this work provides a better understanding of complex flow behavior and lays the foundation for future work.

The phase behavior of hard rectangular rods with edge lengths $L$, $D$, and $D$ is studied in a narrow slitlike pore using the Parsons-Lee density functional theory. Using the restricted orientation approximation, we find strong adsorption at the walls with planar ordering, second order uniaxial-biaxial ordering transitions, and first order layering transitions. The layering transition takes place between two fluids having $n$ and $n+1$ layers, where the layer spacing is on the order of $D$. In the case of weak shape anisotropy ($L/D=3$), the coexisting fluids can be either uniaxial or biaxial, while both phases are found to be biaxial for $L/D=6$ and $L/D=9$. Interestingly, even two or more layering transitions can be observed with increasing density at a given shape anisotropy and pore width.

The linear stability analysis of a fluid flow down a slippery inclined plane is carried out when the free surface of the fluid is contaminated by a monolayer of insoluble surfactant. The aim is to extend the earlier study [Samanta et al., J. Fluid Mech. 684, 353 (2011)] for low to high values of the Reynolds number in the presence of an insoluble surfactant. The Orr-Sommerfeld equation (OSE) is derived for infinitesimal disturbances of arbitrary wave numbers. At low Reynolds number, the OSE is solved analytically by using the long-wave analysis, which shows that the critical Reynolds number decreases in the presence of a slippery plane but increases in the presence of an insoluble surfactant. This fact ensures a destabilizing effect of wall slip and a stabilizing effect of insoluble surfactant on the long-wave surface mode. Further, the Chebyshev spectral collocation method is implemented to tackle the OSE equation numerically for an arbitrary value of the Reynolds number, or equivalently, for an arbitrary value of the wave number. At moderate Reynolds number, wall slip exhibits a stabilizing effect on the surface mode as opposed to the result in the long-wave regime, while the insoluble surfactant exhibits a stabilizing effect on the surface mode as in the result of the long-wave regime. On the other hand, at high Reynolds number, both wall slip and insoluble surfactant exhibit a stabilizing effect on the shear mode. Further, it is shown that both surface and shear modes compete with each other to dominate the primary instability once the inclination angle is sufficiently small. In addition, new phase boundaries are identified to differentiate the regimes of surface and shear modes.

The density linear response function for an inhomogeneous system of electrons in equilibrium with an array of fixed ions is considered. Two routes to its evaluation for extreme conditions (e.g., warm dense matter) are considered. The first is from a recently developed short-time kinetic equation; the second is from time-dependent density functional theory. The result from the latter approach agrees with that from kinetic theory in the “adiabatic approximation,” providing support and contextual clarity for each. Both provide a connection to the phenomenological Kubo-Greenwood method for calculating transport properties.

We report a nonlinear phenomenon discovered in the classical problem of thermal convection in rapidly rotating, self-gravitating, internally heated Boussinesq fluid spheres. When linear convective instability (the most unstable mode of convection) is in the form of an axially symmetric, equatorially antisymmetric torsional oscillation, its equatorial symmetry must be broken by nonlinear effects and, consequently, the key properties of the primary solution bifurcating from the instability cannot be predicted on the basis of linear solutions at the onset of convection. We reveal that, when the supercritical Rayleigh number is in the vicinity of its critical value, the primary nonlinear solution is in the form of an axially symmetric, equatorially nonsymmetric, latitudinally propagating spatiotemporal pattern whose amplitude varies periodically, representing an unusual nonlinear phenomenon of thermal convection in rotating fluid spheres.

‘‘Communication” through the frustrated ground state of a classical triangular Ising antiferromagnet wrapped on a cylinder is studied via reformulation as imaginary-time evolution of a system of fermions on a ring, detailing a breakdown of the ordinary Perron-Frobenius scenario for disordered one-dimensional systems. For instance, constraint of the configuration at one cylinder end allows infinite-range, albeit partial, control of the state. Mutual information between end configurations under open boundary conditions, which measures the strength of the correlations, has an asymptotic decay with a complex dependence on cylinder circumference and spin (anti)periodicity. In some cases, the decay is not even exponential in length, but inverse square.

In many natural systems, attractive coupling together with repulsive coupling plays a vital role in determining their evolutionary dynamics. We investigate the stabilization of amplitude chimera through repulsive coupling in the presence of attractive coupling in a system of nonlocally coupled oscillators. The nonlocal repulsive coupling can facilitate the emergence of stable amplitude chimera even for random initial conditions contrasting with the earlier investigations, where the amplitude chimera was observed just as a transient state and that too for a specific cluster initial conditions. The stability of the observed amplitude chimera is analyzed using Floquet theory. To elucidate the transition among the distinct dynamical states, we find the average number of inhomogeneous oscillators as a function of the coupling strength and show that the transition among the dynamical states exhibits hysteresis. Further, we deduce analytically the critical stability curve that separates the oscillatory (amplitude chimera and traveling wave) states from the death (multi-incoherent oscillation death, cluster chimera death, cluster oscillation death) states. We also analyze the influence of the nonisochronicity parameter and noise on the stable amplitude chimera. We report that the nonisochronicity parameter favors the traveling wave state from incoherent death through the stable amplitude chimera state.

Motivated by recent experimental work on multicomponent lipid membranes supported by colloidal scaffolds, we report an exhaustive theoretical investigation of the equilibrium configurations of binary mixtures on curved substrates. Starting from the Jülicher-Lipowsky generalization of the Canham-Helfrich free energy to multicomponent membranes, we derive a number of exact relations governing the structure of an interface separating two lipid phases on arbitrarily shaped substrates and its stability. We then restrict our analysis to four classes of surfaces of both applied and conceptual interest: the sphere, axisymmetric surfaces, minimal surfaces, and developable surfaces. For each class we investigate how the structure of the geometry and topology of the interface is affected by the shape of the substrate and we make various testable predictions. Our work sheds light on the subtle interaction mechanism between membrane shape and its chemical composition and provides a solid framework for interpreting results from experiments on supported lipid bilayers.

Using laboratory experiments and simplified theoretical arguments, we show that the level of turbulence may reverse the direction of the mean lift on two- and three-dimensional structures with relatively short, deflected splitters. Planar particle image velocimetry and a high-resolution load cell were used to characterize the near wake region and the instantaneous lift of the structures for various geometric configurations, deflection angles and turbulence levels at Reynolds number $\mathrm{Re}=2\times {10}^4$ based on the body width. The possibility of reverse lift may occur within a critical deflection angle, which depends on the splitter length and turbulence level. This particular phenomenon is explained quantitatively with a simple formulation that accounts for the effects of the body geometry and turbulence. The distinctive role of turbulence in structures with splitters provides insight to control hydrodynamic force in various environments.

Long-time simulations are conducted on a forced three-dimensional (3D) nonlinear viscous gravity-capillary wave equation that describes the surface wave pattern when the forcing moves on the surface of deep water with speeds less than the linear phase speed $c_{\min }=23\mathrm{cm}/\mathrm{s}$. Three different states are identified according to forcing speeds $U$ below $c_{\min }$. At relatively low speeds below a certain speed ($c_1$), a steady circular dimple is observed below the moving forcing. At relatively high speeds above a certain speed ($c_2$), “symmetric” shedding phenomena of 3D depressions are observed behind the moving forcing. At intermediate speeds ($c_1\le U\le c_2$), steady 3D gravity-capillary solitary waves are generated behind the moving forcing and are maintained for some time. After long-time simulations, however, those gravity-capillary solitary waves break up and 3D local depressions are shed asymmetrically behind the moving forcing. In more detail, when the forcing speed ($U$) is very close to $c_1$, the asymmetric shedding is “almost regular” and when the forcing speed ($U$) is very close to $c_2$, the asymmetric shedding is “regular antisymmetric,” after a transient period of an “irregular” asymmetric shedding from the steady state of 3D gravity-capillary solitary waves. On the contrary, for the remaining cases of the entire forcing speeds ($c_1<U<c_2$), the asymmetric shedding is “irregular.”

The magnetorotational instability (MRI) is analyzed using a two fluid model with the effect of spin magnetization in a differentially rotating degenerate electron-ion (e-i) quantum plasma. The electrons are taken to be degenerate, whereas ions are considered as classical owing to their large inertia. The general dispersion relation for spin quantum e-i plasma is derived and a local dispersion relation for MRI is obtained by applying MHD approximations. The obtained MRI criteria is discussed for both magnetized and unmagnetized plasma duly modified by spin correction terms. The instability criteria differ significantly from that reported for the case of classical plasma. Spin magnetization plays a vital role via coupling to the Alfvénic speed and can alter the instability criteria which leads to the transport phenomenon in compact astrophysical objects.

With a statistical measure of distance, we derive a classical uncertainty relation for processes traversing nonequilibrium states both transiently and irreversibly. The geometric uncertainty associated with dynamical histories that we define is an upper bound for the entropy production and flow rates, but it does not necessarily correlate with the shortest distance to equilibrium. For slowly driven systems, we show that our uncertainty lower bounds the rate of energy fluctuations. For a model one-bit memory device, we find that expediting the erasure protocol increases the maximum dissipated heat and geometric uncertainty. A driven version of Onsager's three-state model shows that a set of dissipative, high-uncertainty initial conditions, some of which are near equilibrium, scar the state space.

Transition state theory formally provides a simplifying approach for determining chemical reaction rates and pathways. Given an underlying potential energy surface for a reactive system, one can determine the dividing surface in phase space which separates reactant and product regions, and thereby also these regions. This is often a difficult task, and it is especially demanding for high-dimensional time-dependent systems or when a nonlocal dividing surface is required. Recently, approaches relying on Lagrangian descriptors have been successful at resolving the dividing surface in some of these challenging cases, but this method can also be computationally expensive due to the necessity of integrating the corresponding phase space function. In this paper, we present an alternative method by which time-dependent, locally recrossing-free, and global dividing surfaces can be constructed without the calculation of any auxiliary phase space function, but only from simple dynamical properties close to the energy barrier. Another benefit of this method is its exponential convergence which allows for the determination of high-accuracy dividing surfaces in higher-dimensional systems with relatively small computational effort.

We investigate flexodomains, which are observed in planar layers of certain nematic liquid crystals, when a dc voltage $U$ above a critical value $U_c$ is applied across the layer. They are characterized by stationary stripelike spatial variations of the director in the layer plane with a wave number $p\left(U\right)$. Our experiments for different nematics demonstrate that $p\left(U\right)$ varies almost linearly with $U$ for $U>U_c$. That is confirmed by a numerical analysis of the full nonlinear equations for the director field and the induced electric potential. Beyond this numerical study, we demonstrate that the linearity of $p\left(U\right)$ follows even analytically, when considering a special parameter set first used by Terent'ev and Pikin [Sov. Phys. JETP 56, 587 (1982)]. Their theoretical paper serves until now as the standard reference on the nonlinear analysis of flexodomains, since it has arrived at a linear variation of $p\left(U\right)$ for large $U\gg U_c$. Unfortunately, the corresponding analysis suffers from mistakes, which in a combination led to that result.

This study reports an opposing effect of curvature on the interfacial heat transfer, which implies a monotonic increase in the temperature jump over a convex surface and, conversely, a monotonic decrease in the temperature jump over a concave surface, as the curvature of the surface increases. The study shows that this effect is present at both gas-solid and liquid-solid interfaces. The curvature dependence of the interfacial thermal conductance is also investigated and the opposing effect is elucidated by the change in the thermal conductivity of the fluid-solid interface.

In this paper, we study the clap and fling motion of insect flights by applying an inviscid vortex shedding model. We describe separated vortices from the edges of two wings by vortex sheets and extend the model to the two bodies with symmetry. The model demonstrates sucking of leading edge vortices between the wings in the fling process. Remarkably, leading edge vortices move forward and backward as the wings close and open in the clap and fling process. We also calculate lift and drag coefficients of the wings. The numerical results show that the shedding rates at the edges increase at the rotational and acceleration phases of the fling process, which generate a large lift. When the full clap and fling stroke is taken, lift of the model dramatically increases at the rotational phase, which is much larger than results of Navier-Stokes simulations of low and moderate Reynolds numbers. This result suggests the use of the Weis-Fogh mechanism for larger insects flying at high Reynolds numbers.

We analyze the final state sensitivity of nonlocal networks with respect to initial conditions of their units. By changing the initial conditions of a single network unit, we perturb an initially synchronized state. Depending on the perturbation strength, we observe the existence of two possible network long-term states: (i) The network neutralizes the perturbation effects and returns to its synchronized configuration. (ii) The perturbation leads the network to an alternative desynchronized state. By computing uncertainty exponents of a two-dimensional cross section of the state space, we find the existence of fractal basin boundaries separating synchronized solutions from desynchronized ones. We attribute these features to an unstable chaotic set in which trajectories persist for times indefinitely long in the network.

A thermodynamic integration (TI) scheme is presented that allows us to compute the free energy of grain boundaries (GBs) in crystals from an atomistic computer simulation. Unlike previous approaches, the method can be applied at arbitrary temperatures and allows for a systematic extrapolation to the thermodynamic limit. It is applied to a $\mathrm{\Sigma }11$ GB in a face-centered-cubic Lennard-Jones crystal. At a constant density, the GB free energy shows a nonmonotonic temperature dependence with a maximum at about half the melting temperature, and the GB changes from a rigid to a rough interface with distinct finite-size scaling above this temperature.

Brownian ratchets are small-scale systems which rectify thermal fluctuations to produce a net current of particles. They have inspired many models of molecular motors that perform transport in the noisy environment of living cells. For the most common ratchet systems, this rectification is achieved by means of the switching of a periodic and spatially asymmetric potential (flashing ratchets) or by means of a rocking force (rocking ratchets). The rectification mechanism can be applied without information on the state of the system (open-loop ratchets) or using information on the state of the system (feedback or closed-loop ratchets). In order to characterize the transport, the most used quantity is the mean velocity of the center of mass of the system. However, another important transport attribute that has not received much attention is its quality. Here we analyze the quality of transport by studying the coherence and reproducibility of the transport induced by several representative open- and closed-loop rectification protocols under the maximum mean velocity conditions. We find that for few-particle systems, the best protocol is the rocked feedback protocol, producing the transport of particles with the highest coherence and reproducibility per distance traveled at the maximum mean velocity, while for larger systems it is overtaken by its open-loop counterpart. Our results also show that protocols with similar maximum mean velocities can have quite different coherences and reproducibilities. This highlights the importance of studying the reliability of rectified transport to develop performant synthetic rectification devices. These contributions to the emerging field of reliable transport in noisy environments are expected also to provide insight into the performance of natural molecular motors.