Live Soap: Stability, Order, and Fluctuations in Apolar Active Smectics

We construct a hydrodynamic theory of noisy, apolar active smectics in bulk suspension or on a substrate. Unlike purely orientationally ordered active fluids, active apolar smectics can be dynamically stable in Stokesian bulk suspensions. Smectic order in these systems is quasilong ranged in dimension d = 2 and long ranged in d = 3. We predict reentrant Kosterlitz-Thouless melting to an active nematic in our simplest model in d = 2, a nonzero second-sound speed parallel to the layers in bulk suspensions, and that there are no giant number fluctuations in either case. We also briefly discuss possible instabilities in these systems. DOI: 10.1103/PhysRevLett.110.118102

Yanai waves in the western equatorial Indian Ocean

Observations and models have shown the presence of intraseasonal fluctuations in 20-30-day and 10-20-day bands in the equatorial Indian Ocean west of 60 degrees E (WEIO). Their spatial and temporal structures characterize them as Yanai waves, which we label low-frequency (LFYW) and high-frequency (HFYW) Yanai waves, respectively. We explore the dynamics of these intraseasonal signals, using an ocean general circulation model (Modular Ocean Model) and a linear, continuously stratified model. Yanai waves are forced by the meridional wind tau(y) everywhere in the WEIO most strongly during the monsoon seasons. They are forced both directly in the interior ocean and by reflection of the interior response from the western boundary; interference between the interior and boundary responses results in a complex surface pattern that propagates eastward and has nodes. Yanai waves are also forced by instabilities primarily during June/July in a region offshore from the western boundary (52-55 degrees E). At that time, eddies, generated by barotropic instability of the Southern Gyre, are advected southward to the equator. There, they generate a westward-propagating, cross-equatorial flow field, v(eq), with a wave number/frequency spectrum that fits the dispersion relation of a number of Yanai waves, and these waves are efficiently excited. Typically, Yanai waves associated with several baroclinic modes are excited by both wind and eddy forcing; and typically, they superpose to create beams that carry energy vertically and eastward along ray paths. The same processes generate LFYWs and HFYWs, and hence, their responses are similar; differences are traceable to the property that HFYWs have longer wavelengths than LFYWs for each baroclinic mode.

Hydrodynamics of soft active matter

This review summarizes theoretical progress in the field of active matter, placing it in the context of recent experiments. This approach offers a unified framework for the mechanical and statistical properties of living matter: biofilaments and molecular motors in vitro or in vivo, collections of motile microorganisms, animal flocks, and chemical or mechanical imitations. A major goal of this review is to integrate several approaches proposed in the literature, from semimicroscopic to phenomenological. In particular, first considered are ``dry'' systems, defined as those where momentum is not conserved due to friction with a substrate or an embedding porous medium. The differences and similarities between two types of orientationally ordered states, the nematic and the polar, are clarified. Next, the active hydrodynamics of suspensions or ``wet'' systems is discussed and the relation with and difference from the dry case, as well as various large-scale instabilities of these nonequilibrium states of matter, are highlighted. Further highlighted are various large-scale instabilities of these nonequilibrium states of matter. Various semimicroscopic derivations of the continuum theory are discussed and connected, highlighting the unifying and generic nature of the continuum model. Throughout the review, the experimental relevance of these theories for describing bacterial swarms and suspensions, the cytoskeleton of living cells, and vibrated granular material is discussed. Promising extensions toward greater realism in specific contexts from cell biology to animal behavior are suggested, and remarks are given on some exotic active-matter analogs. Last, the outlook for a quantitative understanding of active matter, through the interplay of detailed theory with controlled experiments on simplified systems, with living or artificial constituents, is summarized.

Dynamics and fracture of ligaments from a droplet on a vibrating surface

A droplet residing on a vibrating surface and in the pressure antinode of an asymmetric standing wave can spread radially outward and atomize. In this work, proper orthogonal decomposition through high speed imaging is shown to predict the likelihood of atomization for various viscous fluids based on prior information in the droplet spreading phase. Capillary instabilities are seen to affect ligament rupture. Viscous dissipation plays an important role in determining the wavelength of the most unstable mode during the inception phase of the ligaments. However, the highest ligament capillary number achieved was less than 1, and the influence of viscosity in the ligament growth and breakup phases is quite minimal. It is inferred from the data that the growth of a typical ligament is governed by a balance between the inertial force obtained from the inception phase and capillary forces. By including the effect of acoustic pressure field around the droplet, the dynamics of the ligament growth phase is revealed and the ligament growth profiles for different fluids are shown to collapse on a straight line using a new characteristic time scale.

The problem of clear air turbulence: Changing perspectives in the understanding of the phenomenon

Due to rapid improvements in on-board instrumentation and atmospheric observation systems, in most cases, aircraft are able to steer clear of regions of adverse weather. However, they still encounter unexpected bumpy flight conditions in regions away from storms and clouds. This is the phenomenon of clear air turbulence (CAT), which has been a challenge to our understanding as well as efforts at prediction. While most of such cases result in mild discomfort, a few cases can be violent leading to serious injuries to passengers and damage to the aircraft. The underlying physical mechanisms have been sought to be explained in terms of fluid dynamic instabilities and waves in the atmosphere. The main mechanisms which have been proposed are: (i) Kelvin-Helmholtz instability of shear layers, (ii) waves generated from flow over mountains, (iii) inertia-gravity waves from clouds and other sources, (iv) spontaneous imbalance theory and (v) horizontal vortex tubes. This has also undergone a change over the years. We present an overview of the mechanisms proposed and their implications for prediction.

Jeans instability criterion modified by external tidal field

The well-known Jeans criterion describes the onset of instabilities in an infinite, homogeneous, self-gravitating medium supported by pressure. Most realistic astrophysical systems, however, are not isolated - instead they are under the influence of an external field such as the tidal field due to a neighbour. Here, we do a linear perturbation analysis for a system in an external field and obtain a generalized dispersion relation that depends on the wavenumber, the sound speed and also the magnitude of the tidal field. A typical, disruptive tidal field is shown to make the system more stable against perturbations, and results in a higher effective Jeans wavelength. The minimum mass that can become unstable is then higher (super-Jeans) than the usual Jeans mass. Conversely, in a compressive tidal field, perturbations can grow even when the mass is lower (sub-Jeans). This approach involving the inclusion of tidal field opens up a new way of looking at instabilities in gravitating systems. The treatment is general and the simple analytical form of the modified Jeans criterion obtained makes it easily accessible.

Energy Loss in the Impact of Elastic Spheres on a Rigid Half-Space in Presence of Adhesion

Adhesion can cause energy losses in asperities or particles coming into dynamic contact resulting in frictional dissipation, even if the deformation occurring is purely elastic. Such losses are of special significance in impact of nanoparticles and friction between surfaces under low contact pressure to hardness ratio. The objective of this work is to study the effect of adhesion during the normal impact of elastic spheres on a rigid half-space, with an emphasis on understanding the mechanism of energy loss. We use finite element method for modeling the impact phenomenon, with the adhesion due to van der Waals force and the short-range repulsion included as body forces distributed over the volume of the sphere. This approach, in contrast with commonly used surface force approximation, helps to model the interactions in a more precise way. We find that the energy loss in impact of elastic spheres is negligible unless there are adhesion-induced instabilities. Significant energy loss through elastic stress waves occurs due to jump-to-contact and jump-out-of-contact instabilities and can even result in capture of the elastic sphere on the half-space.

Studies on the wobble mode stability of a three-wheeled vehicle

A wobble instability is one of the major problems of a three-wheeled vehicle commonly used in India, and these instabilities are of great interest to industry and academia. In this paper, we studied this instability using a multi-body dynamic model and with experiments conducted on a prototype three-wheeled vehicle on a test track. The multi-body dynamic model of a three-wheeled vehicle is developed using the commercial software ADAMS/Car. In an initial model, all components including main structures such as the frame, the steering column and the rear forks are assumed to be rigid bodies. A linear eigenvalue analysis, which is carried out at different speeds, reveals a mode that has predominantly a steering oscillation, also called a wobble mode, with a frequency of around 5-6Hz. The analysis results shows that the damping of this mode is low but positive up to the maximum speed of the three-wheeled vehicle. However, the experimental study shows that the mode is unstable at speeds below 8.33m/s. To predict and study this instability in detail, a more refined model of the three-wheeled vehicle, with flexibilities of three important bodies, was constructed in ADAMS/Car. With flexible bodies, three modes of a steering oscillation were observed. Two of these are well damped and the other is lightly damped with negative damping at lower speeds. Simulation results with flexibility incorporated show a good match with the instability observed in the experimental studies. Further, we investigated the effect of each flexible body and found that the flexibility of the steering column is the major contributor for wobble instability and is similar to the wheel shimmy problem in aircraft.

On the absence of shear cracking and grain boundary cavitation in secondary tensile regions of Ti-6Al-4V-0.1B alloy during hot (alpha plus beta)-compression

Deformation instabilities, such as shear cracking and grain boundary cavitation, which are observed in the secondary tensile region of Ti-6Al-4V alloy during compressive deformation in the (+)-phase field, do not form in Ti-6Al-4V-0.1B alloy when processed under the same conditions. This has been attributed to the microstructural modifications, e.g. the absence of grain boundary and adjacent grain boundary retained layers and a lower proportion of 90(o)-misoriented -colonies that occur with boron addition.

Experimental analysis of shape deformation of evaporating droplet using Legendre polynomials

Experiments involving heating of liquid droplets which are acoustically levitated, reveal specific modes of oscillations. For a given radiation flux, certain fluid droplets undergo distortion leading to catastrophic bag type breakup. The voltage of the acoustic levitator has been kept constant to operate at a nominal acoustic pressure intensity, throughout the experiments. Thus the droplet shape instabilities are primarily a consequence of droplet heating through vapor pressure, surface tension and viscosity. A novel approach is used by employing Legendre polynomials for the mode shape approximation to describe the thermally induced instabilities. The two dominant Legendre modes essentially reflect (a) the droplet size reduction due to evaporation, and (b) the deformation around the equilibrium shape. Dissipation and inter-coupling of modal energy lead to stable droplet shape while accumulation of the same ultimately results in droplet breakup. (C) 2013 Elsevier B.V. All rights reserved.

Local stability of a gravitating filament: a dispersion relation

Filamentary structures are ubiquitous in astrophysics and are observed at various scales. On a cosmological scale, matter is usually distributed along filaments, and filaments are also typical features of the interstellar medium. Within a cosmic filament, matter can contract and form galaxies, whereas an interstellar gas filament can clump into a series of bead-like structures that can then turn into stars. To investigate the growth of such instabilities, we derive a local dispersion relation for an idealized self-gravitating filament and study some of its properties. Our idealized picture consists of an infinite self-gravitating and rotating cylinder with pressure and density related by a polytropic equation of state. We assume no specific density distribution, treat matter as a fluid, and use hydrodynamics to derive the linearized equations that govern the local perturbations. We obtain a dispersion relation for axisymmetric perturbations and study its properties in the (kR, kz) phase space, where kR and kz are the radial and longitudinal wavenumbers, respectively. While the boundary between the stable and unstable regimes is symmetrical in kR and kz and analogous to the Jeans criterion, the most unstable mode displays an asymmetry that could constrain the shape of the structures that form within the filament. Here the results are applied to a fiducial interstellar filament, but could be extended for other astrophysical systems, such as cosmological filaments and tidal tails.

Effective Q Criterion for Disk Stability in an External Potential

The standard Q criterion (with Q > 1) describes the stability against local, axisymmetric perturbations in a disk supported by rotation and random motion. Most astrophysical disks, however, are under the influence of an external gravitational potential, which can significantly affect their stability. A typical example is a galactic disk embedded in a dark matter halo. Here, we do a linear perturbation analysis for a disk in an external potential and obtain a generalized dispersion relation and the effective stability criterion. An external potential, such as that due to the dark matter halo concentric with the disk, contributes to the unperturbed rotational field and significantly increases its stability. We obtain the values for the effective Q parameter for the Milky Way and for a low surface brightness galaxy, UGC 7321. We find that in each case the stellar disk by itself is barely stable and it is the dark matter halo that stabilizes the disk against local, axisymmetric gravitational instabilities. Thus, the dark matter halo is necessary to ensure local disk stability. This result has been largely missed so far because in practice the Q parameter for a galactic disk is obtained using the observed rotational field that already includes the effect of the halo

EFFECTIVE Q CRITERION FOR DISK STABILITY IN AN EXTERNAL POTENTIAL

standard Q criterion (with Q > 1) describes the stability against local, axisymmetric perturbations in a disk supported by rotation and random motion. Most astrophysical disks, however, are under the influence of an external gravitational potential, which can significantly affect their stability. A typical example is a galactic disk embedded in a dark matter halo. Here, we do a linear perturbation analysis for a disk in an external potential and obtain a generalized dispersion relation and the effective stability criterion. An external potential, such as that due to the dark matter halo concentric with the disk, contributes to the unperturbed rotational field and significantly increases its stability. We obtain the values for the effective Q parameter for the Milky Way and for a low surface brightness galaxy, UGC 7321. We find that in each case the stellar disk by itself is barely stable and it is the dark matter halo that stabilizes the disk against local, axisymmetric gravitational instabilities. Thus, the dark matter halo is necessary to ensure local disk stability. This result has been largely missed so far because in practice the Q parameter for a galactic disk is obtained using the observed rotational field that already includes the effect of the halo.

Nonlinear viscoelasticity of entangled wormlike micellar fluid under large-amplitude oscillatory shear: Role of elastic Taylor-Couette instability

The role of elastic Taylor-Couette flow instabilities in the dynamic nonlinear viscoelastic response of an entangled wormlike micellar fluid is studied by large-amplitude oscillatory shear (LAOS) rheology and in situ polarized light scattering over a wide range of strain and angular frequency values, both above and below the linear crossover point. Well inside the nonlinear regime, higher harmonic decomposition of the resulting stress signal reveals that the normalized third harmonic I-3/I-1 shows a power-law behavior with strain amplitude. In addition, I-3/I-1 and the elastic component of stress amplitude sigma(E)(0) show a very prominent maximum at the strain value where the number density (n(v)) of the Taylor vortices is maximum. A subsequent increase in applied strain (gamma) results in the distortions of the vortices and a concomitant decrease in n(v), accompanied by a sharp drop in I-3 and sigma(E)(0). The peak position of the spatial correlation function of the scattered intensity along the vorticity direction also captures the crossover. Lissajous plots indicate an intracycle strain hardening for the values of gamma corresponding to the peak of I-3, similar to that observed for hard-sphere glasses.

Temperature-dependent stability of stacking faults in Al, Cu and Ni: first-principles analysis

We present comparative analysis of microscopic mechanisms relevant to plastic deformation of the face-centered cubic (FCC) metals Al, Cu, and Ni, through determination of the temperature-dependent free energies of intrinsic and unstable stacking faults along 1 (1) over bar 0] and 1 (2) over bar 1] on the (1 1 1) plane using first-principles density-functional-theory-based calculations. We show that vibrational contribution results in significant decrease in the free energy of barriers and intrinsic stacking faults (ISFs) of Al, Cu, and Ni with temperature, confirming an important role of thermal fluctuations in the stability of stacking faults (SFs) and deformation at elevated temperatures. In contrast to Al and Ni, the vibrational spectrum of the unstable stacking fault (USF1 (2) over bar 1]) in Cu reveals structural instabilities, indicating that the energy barrier (gamma(usf)) along the (1 1 1)1 (2) over bar 1] slip system in Cu, determined by typical first-principles calculations, is an overestimate, and its commonly used interpretation as the energy release rate needed for dislocation nucleation, as proposed by Rice (1992 J. Mech. Phys. Solids 40 239), should be taken with caution.