Phase diagram of a two-species lattice model with a linear instability

We discuss the properties of a one-dimensional lattice model of a driven system with two species of particles in which the mobility of one species depends on the density of the other. This model was introduced by Lahiri and Ramaswamy (Phys. Rev. Lett., 79, 1150 (1997)) in the context of sedimenting colloidal crystals, and its continuum version was shown to exhibit an instability arising from linear gradient couplings. In this paper we review recent progress in understanding the full phase diagram of the model. There are three phases. In the first, the steady state can be determined exactly along a representative locus using the condition of detailed balance. The system shows phase separation of an exceptionally robust sort, termed strong phase separation, which survives at all temperatures. The second phase arises in the threshold case where the first species evolves independently of the second, but the fluctuations of the first influence the evolution of the second, as in the passive scalar problem. The second species then shows phase separation of a delicate sort, in which long-range order coexists with fluctuations which do not damp down in the large-size limit. This fluctuation-dominated phase ordering is associated with power law decays in cluster size distributions and a breakdown of the Porod law. The third phase is one with a uniform overall density, and along a representative locus the steady state is shown to have product measure form. Density fluctuations are transported by two kinematic waves, each involving both species and coupled at the nonlinear level. Their dissipation properties are governed by the symmetries of these couplings, which depend on the overall densities. In the most interesting case,, the dissipation of the two modes is characterized by different critical exponents, despite the nonlinear coupling.

Thermal instability in a three-dimensional rigid container with prescribed heat flux at lower boundary

The Bénard–Marangoni convection is studied in a three-dimensional container with thermally insulated lateral walls and prescribed heat flux at lower boundary. The upper surface of the incompressible, viscous fluid is assumed to be flat with temperature dependent surface tension. A Galerkin–Tau method with odd and even trial functions satisfying all the essential boundary conditions except the natural boundary conditions at the free surface has been used to solve the problem. The critical Marangoni and Rayleigh numbers are determined for the onset of steady convection as a function of aspect ratios x0 and y0 for the cases of Bénard–Marangoni, pure Marangoni and pure Bénard convections. It is observed that critical parameters are decreasing with an increase in aspect ratios. The flow structures corresponding to the values of the critical parameters are presented in all the cases. It is observed that the critical parameters are higher for case with heat flux prescribed than those corresponding to the case with prescribed temperature. The critical Marangoni number for pure Marangoni convection is higher than critical Rayleigh number corresponding to pure Bénard convection for a given aspect ratio whereas the reverse was observed for two-dimensional infinite layer.

A dynamical instability due to fluid–wall coupling lowers the transition Reynolds number in the flow through a flexible tube

A flow-induced instability in a tube with flexible walls is studied experimentally. Tubes of diameter 0.8 and 1.2 mm are cast in polydimethylsiloxane (PDMS) polymer gels, and the catalyst concentration in these gels is varied to obtain shear modulus in the range 17–550 kPa. A pressure drop between the inlet and outlet of the tube is used to drive fluid flow, and the friction factor $f$ is measured as a function of the Reynolds number $Re$. From these measurements, it is found that the laminar flow becomes unstable, and there is a transition to a more complicated flow profile, for Reynolds numbers as low as 500 for the softest gels used here. The nature of the $f$–$Re$ curves is also qualitatively different from that in the flow past rigid tubes; in contrast to the discontinuous increase in the friction factor at transition in a rigid tube, it is found that there is a continuous increase in the friction factor from the laminar value of $16\ensuremath{/} Re$ in a flexible tube. The onset of transition is also detected by a dye-stream method, where a stream of dye is injected into the centre of the tube. It is found that there is a continuous increase of the amplitude of perturbations at the onset of transition in a flexible tube, in contrast to the abrupt disruption of the dye stream at transition in a rigid tube. There are oscillations in the wall of the tube at the onset of transition, which is detected from the laser scattering off the walls of the tube. This indicates that the coupling between the fluid stresses and the elastic stresses in the wall results in an instability of the laminar flow.

Secondary Perturbation Effects in Keplerian Accretion Disks: Elliptical Instability

Origin of turbulence in cold accretion disks, particularly in 3D, which is expected to be hydrodynamic but not magnetohydrodynamic, is a big puzzle. While the flow must exhibit some turbulence in support of the transfer of mass inward and angular momentum outward, according to the linear perturbation theory it should always be stable. We demonstrate that the 3D secondary disturbance to the primarily perturbed disk which exhibits elliptical vortices into the system solves the problem. This result is essentially applicable to the outer region of accretion disks in active galactic nuclei where the gas is significantly cold and neutral in charge and the magnetic Reynolds number is smaller than 10^4.

Interaction anisotropy and shear instability of aspirin polymorphs established by nanoindentation

Nanoindentation is applied to the two polymorphs of aspirin to examine and differentiate their interaction anisotropy and shear instability. Aspirin provides an excellent test system for the technique because: (i) polymorphs I and II exhibit structural similarity in two dimensions, thereby facilitating clear examination of the differences in mechanical response in relation to well-defined differences between the two crystal structures; (ii) single crystals of the metastable polymorph II have only recently become accessible; (iii) shear instability has been proposed for II. Different elastic moduli and hardness values determined for the two polymorphs are correlated with their crystal structures, and the interpretation is supported by measured thermal expansion coefficients. The stress-induced transformation of the metastable polymorph II to the stable polymorph I can be brought about rapidly by mechanical milling, and proceeds via a slip mechanism. This work establishes that nanoindentation provides ``signature'' responses for the two aspirin polymorphs, despite their very similar crystal structures. It also demonstrates the value of the technique to quantify stability relationships and phase transformations in molecular crystals, enabling a deeper understanding of polymorphism in the context of crystal engineering.

Thermal instability and the feedback regulation of hot haloes in clusters, groups and galaxies

We present global multidimensional numerical simulations of the plasma that pervades the dark matter haloes of clusters, groups and massive galaxies (the intracluster medium; ICM). Observations of clusters and groups imply that such haloes are roughly in global thermal equilibrium, with heating balancing cooling when averaged over sufficiently long time- and length-scales; the ICM is, however, very likely to be locally thermally unstable. Using simple observationally motivated heating prescriptions, we show that local thermal instability (TI) can produce a multiphase medium with similar to 104 K cold filaments condensing out of the hot ICM only when the ratio of the TI time-scale in the hot plasma (tTI) to the free-fall time-scale (tff) satisfies tTI/tff? 10. This criterion quantitatively explains why cold gas and star formation are preferentially observed in low-entropy clusters and groups. In addition, the interplay among heating, cooling and TI reduces the net cooling rate and the mass accretion rate at small radii by factors of similar to 100 relative to cooling-flow models. This dramatic reduction is in line with observations. The feedback efficiency required to prevent a cooling flow is similar to 10-3 for clusters and decreases for lower mass haloes; supernova heating may be energetically sufficient to balance cooling in galactic haloes. We further argue that the ICM self-adjusts so that tTI/tff? 10 at all radii. When this criterion is not satisfied, cold filaments condense out of the hot phase and reduce the density of the ICM. These cold filaments can power the black hole and/or stellar feedback required for global thermal balance, which drives tTI/tff? 10. In comparison to clusters, groups have central cores with lower densities and larger radii. This can account for the deviations from self-similarity in the X-ray luminositytemperature () relation. The high-velocity clouds observed in the Galactic halo can be due to local TI producing multiphase gas close to the virial radius if the density of the hot plasma in the Galactic halo is >rsim 10-5 cm-3 at large radii.

LOCAL TWO-DIMENSIONAL PARTICLE-IN-CELL SIMULATIONS OF THE COLLISIONLESS MAGNETOROTATIONAL INSTABILITY

The magnetorotational instability (MRI) is a crucial mechanism of angular momentum transport in a variety of astrophysical accretion disks. In systems accreting at well below the Eddington rate, such as the central black hole in the Milky Way (Sgr A*), the plasma in the disk is essentially collisionless. We present a nonlinear study of the collisionless MRI using first-principles particle-in-cell plasma simulations. We focus on local two-dimensional (axisymmetric) simulations, deferring more realistic three-dimensional simulations to future work. For simulations with net vertical magnetic flux, the MRI continuously amplifies the magnetic field, B, until the Alfven velocity, v(A), is comparable to the speed of light, c (independent of the initial value of v(A)/c). This is consistent with the lack of saturation of MRI channel modes in analogous axisymmetric MHD simulations. The amplification of the magnetic field by the MRI generates a significant pressure anisotropy in the plasma (with the pressure perpendicular to B being larger than the parallel pressure). We find that this pressure anisotropy in turn excites mirror modes and that the volume-averaged pressure anisotropy remains near the threshold for mirror mode excitation. Particle energization is due to both reconnection and viscous heating associated with the pressure anisotropy. Reconnection produces a distinctive power-law component in the energy distribution function of the particles, indicating the likelihood of non-thermal ion and electron acceleration in collisionless accretion disks. This has important implications for interpreting the observed emission-from the radio to the gamma-rays-of systems such as Sgr A*.

Projecting low-dimensional chaos from spatiotemporal dynamics in a model for plastic instability

We investigate the possibility of projecting low-dimensional chaos from spatiotemporal dynamics of a model for a kind of plastic instability observed under constant strain rate deformation conditions. We first discuss the relationship between the spatiotemporal patterns of the model reflected in the nature of dislocation bands and the nature of stress serrations. We show that at low applied strain rates, there is a one-to-one correspondence with the randomly nucleated isolated bursts of mobile dislocation density and the stress drops. We then show that the model equations are spatiotemporally chaotic by demonstrating the number of positive Lyapunov exponents and Lyapunov dimension scale with the system size at low and high strain rates. Using a modified algorithm for calculating correlation dimension density, we show that the stress-strain signals at low applied strain rates corresponding to spatially uncorrelated dislocation bands exhibit features of low-dimensional chaos. This is made quantitative by demonstrating that the model equations can be approximately reduced to space-independent model equations for the average dislocation densities, which is known to be low-dimensionally chaotic. However, the scaling regime for the correlation dimension shrinks with increasing applied strain rate due to increasing propensity for propagation of the dislocation bands.

Stochastically driven instability in rotating shear flows

The origin of hydrodynamic turbulence in rotating shear flows is investigated, with particular emphasis on the flows whose angular velocity decreases but whose specific angular momentum increases with the increasing radial coordinate. Such flows are Rayleigh stable, but must be turbulent in order to explain the observed data. Such a mismatch between the linear theory and the observations/experiments is more severe when any hydromagnetic/magnetohydrodynamic instability and then the corresponding turbulence therein is ruled out. This work explores the effect of stochastic noise on such hydrodynamic flows. We essentially concentrate on a small section of such a flow, which is nothing but a plane shear flow supplemented by the Coriolis effect. This also mimics a small section of an astrophysical accretion disc. It is found that such stochastically driven flows exhibit large temporal and spatial correlations of perturbation velocities and hence large energy dissipations of perturbation, which presumably generate the instability. A range of angular velocity (Omega) profiles of the background flow, starting from that of a constant specific angular momentum (lambda = Omega r(2); r being the radial coordinate) to a constant circular velocity (v(phi) = Omega r), is explored. However, all the background angular velocities exhibit identical growth and roughness exponents of their perturbations, revealing a unique universality class for the stochastically forced hydrodynamics of rotating shear flows. This work, to the best of our knowledge, is the first attempt to understand the origin of instability and turbulence in three-dimensional Rayleigh stable rotating shear flows by introducing additive noise to the underlying linearized governing equations. This has important implications to resolve the turbulence problem in astrophysical hydrodynamic flows such as accretion discs.

Influence of system size on spatiotemporal dynamics of a model for plastic instability: Projecting low-dimensional and extensive chaos

This work is a continuation of our efforts to quantify the irregular scalar stress signals from the Ananthakrishna model for the Portevin-Le Chatelier instability observed under constant strain rate deformation conditions. Stress related to the spatial average of the dislocation activity is a dynamical variable that also determines the time evolution of dislocation densities. We carry out detailed investigations on the nature of spatiotemporal patterns of the model realized in the form of different types of dislocation bands seen in the entire instability domain and establish their connection to the nature of stress serrations. We then characterize the spatiotemporal dynamics of the model equations by computing the Lyapunov dimension as a function of the drive parameter. The latter scales with the system size only for low strain rates, where isolated dislocation bands are seen, and at high strain rates, where fully propagating bands are seen. At intermediate applied strain rates corresponding to the partially propagating bands, the Lyapunov dimension exhibits two distinct slopes, one for small system sizes and another for large. This feature is rationalized by demonstrating that the spatiotemporal patterns for small system sizes are altered from the partially propagating band types to isolated burst type. This in turn allows us to reconfirm that low-dimensional chaos is projected from the stress signals as long as there is a one-to-one correspondence between the bursts of dislocation bands and the stress drops. We then show that the stress signals in the regime of partially to fully propagative bands have features of extensive chaos by calculating the correlation dimension density. We also show that the correlation dimension density also depends on the system size. A number of issues related to the system size dependence of the Lyapunov dimension density and the correlation dimension density are discussed.

Crow instability in unitary Fermi gas

In this paper, we investigate the initiation and subsequent evolution of Crow instability in an inhomogeneous unitary Fermi gas using zero-temperature Galilei-invariant nonlinear Schrodinger equation. Considering a cigar-shaped unitary Fermi gas, we generate the vortex-antivortex pair either by phase-imprinting or by moving a Gaussian obstacle potential. We observe that the Crow instability in a unitary Fermi gas leads to the decay of the vortex-antivortex pair into multiple vortex rings and ultimately into sound waves.

A multifold reduction in the transition Reynolds number, and ultra-fast mixing, in a micro-channel due to a dynamical instability induced by a soft wall

A dynamical instability is observed in experimental studies on micro-channels of rectangular cross-section with smallest dimension 100 and 160 mu m in which one of the walls is made of soft gel. There is a spontaneous transition from an ordered, laminar flow to a chaotic and highly mixed flow state when the Reynolds number increases beyond a critical value. The critical Reynolds number, which decreases as the elasticity modulus of the soft wall is reduced, is as low as 200 for the softest wall used here (in contrast to 1200 for a rigid-walled channel) The instability onset is observed by the breakup of a dye-stream introduced in the centre of the micro-channel, as well as the onset of wall oscillations due to laser scattering from fluorescent beads embedded in the wall of the channel. The mixing time across a channel of width 1.5 mm, measured by dye-stream and outlet conductance experiments, is smaller by a factor of 10(5) than that for a laminar flow. The increased mixing rate comes at very little cost, because the pressure drop (energy requirement to drive the flow) increases continuously and modestly at transition. The deformed shape is reconstructed numerically, and computational fluid dynamics (CFD) simulations are carried out to obtain the pressure gradient and the velocity fields for different flow rates. The pressure difference across the channel predicted by simulations is in agreement with the experiments (within experimental errors) for flow rates where the dye stream is laminar, but the experimental pressure difference is higher than the simulation prediction after dye-stream breakup. A linear stability analysis is carried out using the parallel-flow approximation, in which the wall is modelled as a neo-Hookean elastic solid, and the simulation results for the mean velocity and pressure gradient from the CFD simulations are used as inputs. The stability analysis accurately predicts the Reynolds number (based on flow rate) at which an instability is observed in the dye stream, and it also predicts that the instability first takes place at the downstream converging section of the channel, and not at the upstream diverging section. The stability analysis also indicates that the destabilization is due to the modification of the flow and the local pressure gradient due to the wall deformation; if we assume a parabolic velocity profile with the pressure gradient given by the plane Poiseuille law, the flow is always found to be stable.

Spark plasma sintering may lead to phase instability and inferior mechanical properties: A case study with TiB2

In contrast to the widely reported beneficial aspects of spark plasma sintering in developing materials with better properties, we report here two interesting aspects recorded with difficult-to-sinter titanium diboride: (a) in situ formation of second phase (TiB) and (b) inferior hardness (by similar to 30%) and elastic modulus (by similar to 20%) for spark plasma sintered TiB2, with respect to hot pressed TiB2. The formation of TiB is discussed with reference to the enhanced reaction kinetics in the presence of pulsed electric field. (C) 2013 Acta Materialia Inc. Published by Elsevier Ltd. All rights reserved.

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.