Dynamics of the North American continent

The forces that cause deformation of western North America have been debated for decades. Recent studies, primarily based on analysis of crustal stresses in the western United States, have suggested that the deformation of the region is mainly controlled by gravitational potential energy (GPE) variations and boundary loads, with basal tractions due to mantle flow playing a relatively minor role. We address these issues by modelling the deviatoric stress field over western North America from a 3-D finite element mantle circulation model with lateral viscosity variations. Our approach takes into account the contribution from both topography and shallow lithosphere structure (GPE) as well as that from deeper mantle flow in one single model, as opposed to separate lithosphere and circulation models, as has been done so far. In addition to predicting the deviatoric stresses we also jointly fit the constraints of geoid, dynamic topography and plate motion both globally and over North America, in order to ensure that the forces that arise in our models are dynamically consistent. We examine the sensitivity of the dynamic models to different lateral viscosity variations. We find that circulation models that include upper mantle slabs yield a better fit to observed plate velocities. Our results indicate that a model of GPE variations coupled with mantle convection gives the best fit to the observational constraints. We argue that although GPE variations control a large part of the deformation of the western United States, deeper mantle tractions also play a significant role. The average deviatoric stress magnitudes in the western United States range 30-40 MPa. The cratonic region exhibits higher coupling to mantle flow than the rest of the continent. We find that a relatively strong San Andreas fault gives a better fit to the observational constraints, especially that of plate velocity in western North America.

Nonequilibrium noise in electrophoresis: The microion wind

A colloid supported against gravitational settling by means of an imposed electric field behaves, on average, as if it is at equilibrium in a confining potential T. M. Squires, J. Fluid Mech. 443, 403 (2001)]. We show, however, that the effective Langevin equation for the colloid contains a nonequilibrium noise source, proportional to the field, arising from the thermal motion of dissolved ions. The position fluctuations of the colloid show strong, experimentally testable signatures of nonequilibrium behavior, including a highly anisotropic, frequency-dependent ``effective temperature'' obtained from the fluctuation-dissipation ratio.

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.

Clusters, asters, and collective oscillations in chemotactic colloids

The creation of synthetic systems that emulate the defining properties of living matter, such as motility, gradient-sensing, signaling, and replication, is a grand challenge of biomimetics. Such imitations of life crucially contain active components that transform chemical energy into directed motion. These artificial realizations of motility point in the direction of a new paradigm in engineering, through the design of emergent behavior by manipulating properties at the scale of the individual components. Catalytic colloidal swimmers are a particularly promising example of such systems. Here we present a comprehensive theoretical description of gradient-sensing of an individual swimmer, leading controllably to chemotactic or anti-chemotactic behavior, and use it to construct a framework for studying their collective behavior. We find that both the positional and the orientational degrees of freedom of the active colloids can exhibit condensation, signaling formation of clusters and asters. The kinetics of catalysis introduces a natural control parameter for the range of the interaction mediated by the diffusing chemical species. For various regimes in parameter space in the long-ranged limit our system displays precise analogs to gravitational collapse, plasma oscillations, and electrostatic screening. We present prescriptions for how to tune the surface properties of the colloids during fabrication to achieve each type of behavior.

Current kinematics and dynamics of Africa and the East African Rift System

Although the East African Rift System (EARS) is an archetype continental rift, the forces driving its evolution remain debated. Some contend buoyancy forces arising from gravitational potential energy (GPE) gradients within the lithosphere drive rifting. Others argue for a major role of the diverging mantle flow associated with the African Superplume. Here we quantify the forces driving present-day continental rifting in East Africa by (1) solving the depth averaged 3-D force balance equations for 3-D deviatoric stress associated with GPE, (2) inverting for a stress field boundary condition that we interpret as originating from large-scale mantle tractions, (3) calculating dynamic velocities due to lithospheric buoyancy forces, lateral viscosity variations, and velocity boundary conditions, and (4) calculating dynamic velocities that result from the stress response of horizontal mantle tractions acting on a viscous lithosphere in Africa and surroundings. We find deviatoric stress associated with lithospheric GPE gradients are similar to 8-20 MPa in EARS, and the minimum deviatoric stress resulting from basal shear is similar to 1.6 MPa along the EARS. Our dynamic velocity calculations confirm that a force contribution from GPE gradients alone is sufficient to drive Nubia-Somalia divergence and that additional forcing from horizontal mantle tractions overestimates surface kinematics. Stresses from GPE gradients appear sufficient to sustain present-day rifting in East Africa; however, they are lower than the vertically integrated strength of the lithosphere along most of the EARS. This indicates additional processes are required to initiate rupture of continental lithosphere, but once it is initiated, lithospheric buoyancy forces are enough to maintain rifting.

Nonlinear preconditioning for efficient and accurate interface capturing in simulation of multicomponent compressible flows

Single fluid schemes that rely on an interface function for phase identification in multicomponent compressible flows are widely used to study hydrodynamic flow phenomena in several diverse applications. Simulations based on standard numerical implementation of these schemes suffer from an artificial increase in the width of the interface function owing to the numerical dissipation introduced by an upwind discretization of the governing equations. In addition, monotonicity requirements which ensure that the sharp interface function remains bounded at all times necessitate use of low-order accurate discretization strategies. This results in a significant reduction in accuracy along with a loss of intricate flow features. In this paper we develop a nonlinear transformation based interface capturing method which achieves superior accuracy without compromising the simplicity, computational efficiency and robustness of the original flow solver. A nonlinear map from the signed distance function to the sigmoid type interface function is used to effectively couple a standard single fluid shock and interface capturing scheme with a high-order accurate constrained level set reinitialization method in a way that allows for oscillation-free transport of the sharp material interface. Imposition of a maximum principle, which ensures that the multidimensional preconditioned interface capturing method does not produce new maxima or minima even in the extreme events of interface merger or breakup, allows for an explicit determination of the interface thickness in terms of the grid spacing. A narrow band method is formulated in order to localize computations pertinent to the preconditioned interface capturing method. Numerical tests in one dimension reveal a significant improvement in accuracy and convergence; in stark contrast to the conventional scheme, the proposed method retains its accuracy and convergence characteristics in a shifted reference frame. Results from the test cases in two dimensions show that the nonlinear transformation based interface capturing method outperforms both the conventional method and an interface capturing method without nonlinear transformation in resolving intricate flow features such as sheet jetting in the shock-induced cavity collapse. The ability of the proposed method in accounting for the gravitational and surface tension forces besides compressibility is demonstrated through a model fully three-dimensional problem concerning droplet splash and formation of a crownlike feature. (C) 2014 Elsevier Inc. All rights reserved.

Chern-Simons vortices and holography

In this paper, based on the AdS(4)/CFT3 duality, we have explored the precise connection between the abelian Chern-Simons (CS) Higgs model in (2 + 1) dimensions to that with its dual gravitational counterpart living in one higher dimension. It has been observed that theU(1) current computed at the boundary of the AdS(4) could be expressed as the local function of the vortex solution that has the remarkable structural similarity to that with the Ginzburg-Landau (GL) type local expression for the current associated with the Maxwell-CS type vortices in (2 + 1) dimensions. In order to explore this duality a bit further we have also computed the coherence length as well as the magnetic penetration depth associated with these vortices. Finally using the knowledge of both the coherence length as well as the magnetic penetration depth we have computed the Ginzburg-Landau coefficient for the Maxwell-CS type vortices in (2 + 1) dimensions.

Hall viscosity to entropy ratio in higher derivative theories

In this paper based on the basic principles of gauge/gravity duality we compute the hall viscosity to entropy ratio in the presence of various higher derivative corrections to the dual gravitational description embedded in an asymptotically AdS(4) space time. As the first step of our analysis, considering the back reaction we impose higher derivative corrections to the abelian gauge sector of the theory where we notice that the ratio indeed gets corrected at the leading order in the coupling. Considering the probe limit as a special case we compute this leading order correction over the fixed background of the charged black brane solution. Finally we consider higher derivative (R-2) correction to the gravity sector of the theory where we notice that the above ratio might get corrected at the sixth derivative level.

On entanglement entropy functionals in higher-derivative gravity theories

In arXiv:1310.5713 1] and arXiv:1310.6659 2] a formula was proposed as the entanglement entropy functional for a general higher-derivative theory of gravity, whose lagrangian consists of terms containing contractions of the Riemann tensor. In this paper, we carry out some tests of this proposal. First, we find the surface equation of motion for general four-derivative gravity theory by minimizing the holographic entanglement entropy functional resulting from this proposed formula. Then we calculate the surface equation for the same theory using the generalized gravitational entropy method of arXiv:1304.4926 3]. We find that the two do not match in their entirety. We also construct the holographic entropy functional for quasi-topological gravity, which is a six-derivative gravity theory. We find that this functional gives the correct universal terms. However, as in the R-2 case, the generalized gravitational entropy method applied to this theory does not give exactly the surface equation of motion coming from minimizing the entropy functional.

Formation of Prestellar Cores via Non-Isothermal Gas Fragmentation

Sheet-like clouds are common in turbulent gas and perhaps form via collisions between turbulent gas flows. Having examined the evolution of an isothermal shocked slab in an earlier contribution, in this work we follow the evolution of a sheet-like cloud confined by (thermal) pressure and gas in it is allowed to cool. The extant purpose of this endeavour is to study the early phases of core-formation. The observed evolution of this cloud supports the conjecture that molecular clouds themselves are three-phase media (comprising viz. a stable cold and warm medium, and a third thermally unstable medium), though it appears, clouds may evolve in this manner irrespective of whether they are gravitationally bound. We report, this sheet fragments initially due to the growth of the thermal instability (TI) and some fragments are elongated, filament-like. Subsequently, relatively large fragments become gravitationally unstable and sub-fragment into smaller cores. The formation of cores appears to be a three stage process: first, growth of the TI leads to rapid fragmentation of the slab; second, relatively small fragments acquire mass via gas-accretion and/or merger and third, sufficiently massive fragments become susceptible to the gravitational instability and sub-fragment to form smaller cores. We investigate typical properties of clumps (and smaller cores) resulting from this fragmentation process. Findings of this work support the suggestion that the weak velocity field usually observed in dense clumps and smaller cores is likely seeded by the growth of dynamic instabilities. Simulations were performed using the smooth particle hydrodynamics algorithm.

The cold mode: a phenomenological model for the evolution of density perturbations in the intracluster medium

Cool cluster cores are in global thermal equilibrium but are locally thermally unstable. We study a non-linear phenomenological model for the evolution of density perturbations in the intracluster medium (ICM) due to local thermal instability and gravity. We have analysed and extended a model for the evolution of an overdense blob in the ICM. We find two regimes in which the overdense blobs can cool to thermally stable low temperatures. One for large t(cool)/t(ff) (t(cool) is the cooling time and t(ff) is the free-fall time), where a large initial overdensity is required for thermal runaway to occur; this is the regime which was previously analysed in detail. We discover a second regime for t(cool)/t(ff) less than or similar to 1 (in agreement with Cartesian simulations of local thermal instability in an external gravitational field), where runaway cooling happens for arbitrarily small amplitudes. Numerical simulations have shown that cold gas condenses out more easily in a spherical geometry. We extend the analysis to include geometrical compression in weakly stratified atmospheres such as the ICM. With a single parameter, analogous to the mixing length, we are able to reproduce the results from numerical simulations; namely, small density perturbations lead to the condensation of extended cold filaments only if t(cool)/t(ff) less than or similar to 10.

Nonlinear constraints on gravity from entanglement

Using the positivity of relative entropy arising from the Ryu-Takayanagi formula for spherical entangling surfaces, we obtain constraints at the nonlinear level for the gravitational dual. We calculate the Green's function necessary to compute the first order correction to the entangling surface and use this to find the relative entropy for non-constant stress tensors in a derivative expansion. We show that the Einstein value satisfies the positivity condition, while the multidimensional parameter space away from it gets constrained.

Stability of Filaments in Star-Forming Clouds and the Formation of Prestellar Cores in Them

The exact process(es) that generate(s) dense filaments which then form prestellar cores within them is unclear. Here we study the formation of a dense filament using a relatively simple set-up of a pressure-confined, uniform-density cylinder. We examine if its propensity to form a dense filament and further, to the formation of prestellar cores along this filament, bears on the gravitational state of the initial volume of gas. We report a radial collapse leading to the formation of a dense filamentary cloud is likely when the initial volume of gas is at least critically stable (characterised by the approximate equality between the mass line-density for this volume and its maximum value). Though self-gravitating, this volume of gas, however, is not seen to be in free-fall. This post-collapse filament then fragments along its length due to the growth of a Jeans-like instability to form prestellar cores. We suggest dense filaments in typical star-forming clouds classified as gravitationally super-critical under the assumption of: (i) isothermality when in fact, they are not, and (ii) extended radial profiles as against pressure-truncated, that significantly over-estimates their mass line-density, are unlikely to experience gravitational free-fall. The radial density and temperature profile derived for this post-collapse filament is consistent with that deduced for typical filamentary clouds mapped in recent surveys of nearby star-forming regions.

Hydrodynamics from scalar black branes

In this paper, using the Gauge/gravity duality techniques, we explore the hydrodynamic regime of a very special class of strongly coupled QFTs that come up with an emerging UV length scale in the presence of a negative hyperscaling violating exponent. The dual gravitational counterpart for these QFTs consists of scalar dressed black brane solutions of exactly integrable Einstein-scalar gravity model with Domain Wall (DW) asymptotics. In the first part of our analysis we compute the R-charge diffusion for the boundary theory and find that (unlike the case for the pure AdS (4) black branes) it scales quite non trivially with the temperature. In the second part of our analysis, we compute the eta/s ratio both in the non extremal as well as in the extremal limit of these special class of gauge theories and it turns out to be equal to 1/4 pi in both the cases. These results therefore suggest that the quantum critical systems in the presence of (negative) hyperscaling violation at UV, might fall under a separate universality class as compared to those conventional quantum critical systems with the usual AdS (4) duals.