432 research outputs found
Chemically Reactive Solute Distribution in a Steady MHD Boundary Layer Flow over a Stretching Surface
The paper is concerned to find the distribution of the chemically reactant solute in the MHD flow of an electrically conducting viscous incompressible fluid over a stretching surface. The first order chemical reaction and the variable solute distribution along the surface are taken into consideration. The governing partial differential equations along with appropriate boundary conditions for flow field and reactive solute are transformed into a set of non-linear self-similar ordinary differential equations by using scaling group of transformations. An exact analytic solution is obtained for the velocity field. Using this velocity field, we obtain numerical solution for the reactant concentration field. It reveals from the study that the values of concentration profile enhances with the increase of the magnetic field and decreases with increase of Schmidt number as well as the reaction rate parameter. Most importantly, when the solute distribution along the surface increases then the concentration profile decreases
Causality and the AdS Dirichlet problem
The (planar) AdS Dirichlet problem has previously been shown to exhibit
superluminal hydrodynamic sound modes. This problem is defined by bulk
gravitational dynamics with Dirichlet boundary conditions imposed on a rigid
timelike cut-off surface. We undertake a careful examination of this set-up and
argue that, in most cases, the propagation of information between points on the
Dirichlet hypersurface is nevertheless causal with respect to the induced light
cones. In particular, the high-frequency dynamics is causal in this sense.
There are however two exceptions and both involve boundary gravitons whose
propagation is not constrained by the Einstein equations. These occur in i)
AdS, where the boundary gravitons generally do not respect the induced
light cones on the boundary, and ii) Rindler space, where they are related to
the infinite speed of sound in incompressible fluids. We discuss implications
for the fluid/gravity correspondence with rigid Dirichlet boundaries and for
the black hole membrane paradigm.Comment: 29 pages, 5 figures. v2: added refs. v3: minor clarification
Hydrodynamics from charged black branes
We extend the recent work on fluid-gravity correspondence to charged
black-branes by determining the metric duals to arbitrary charged fluid
configuration up to second order in the boundary derivative expansion. We also
derive the energy-momentum tensor and the charge current for these
configurations up to second order in the boundary derivative expansion. We find
a new term in the charge current when there is a bulk Chern-Simons interaction
thus resolving an earlier discrepancy between thermodynamics of charged
rotating black holes and boundary hydrodynamics. We have also confirmed that
all our expressions are covariant under boundary Weyl-transformations as
expected.Comment: 0+ 31 Pages; v2: 0+33 pages, typos corrected and new sections (in
appendix) added; v3:published versio
Discussion on a possible neutrino detector located in India
We have identified some important and worthwhile physics opportunitites with
a possible neutrino detector located in India. Particular emphasis is placed on
the geographical advantage with a stress on the complimentary aspects with
respect to other neutrino detectors already in operation.Comment: 9 pages; arXiv copy of published proceedings contributio
Wilsonian Approach to Fluid/Gravity Duality
The problem of gravitational fluctuations confined inside a finite cutoff at
radius outside the horizon in a general class of black hole geometries
is considered. Consistent boundary conditions at both the cutoff surface and
the horizon are found and the resulting modes analyzed. For general cutoff
the dispersion relation is shown at long wavelengths to be that of a
linearized Navier-Stokes fluid living on the cutoff surface. A cutoff-dependent
line-integral formula for the diffusion constant is derived. The
dependence on is interpreted as renormalization group (RG) flow in the
fluid. Taking the cutoff to infinity in an asymptotically AdS context, the
formula for reproduces as a special case well-known results derived
using AdS/CFT. Taking the cutoff to the horizon, the effective speed of sound
goes to infinity, the fluid becomes incompressible and the Navier-Stokes
dispersion relation becomes exact. The resulting universal formula for the
diffusion constant reproduces old results from the membrane
paradigm. Hence the old membrane paradigm results and new AdS/CFT results are
related by RG flow. RG flow-invariance of the viscosity to entropy ratio is shown to follow from the first law of thermodynamics together with
isentropy of radial evolution in classical gravity. The ratio is expected to
run when quantum gravitational corrections are included.Comment: 34 pages, harvmac, clarified boundary conditio
Nonlinear Hydrodynamics from Flow of Retarded Green's Function
We study the radial flow of retarded Green's function of energy-momentum
tensor and -current of dual gauge theory in presence of generic higher
derivative terms in bulk Lagrangian. These are first order non-linear Riccati
equations. We solve these flow equations analytically and obtain second order
transport coefficients of boundary plasma. This way of computing transport
coefficients has an advantage over usual Kubo approach. The non-linear equation
turns out to be a linear first order equation when we study the Green's
function perturbatively in momentum. We consider several examples including
term and generic four derivative terms in bulk. We also study the flow
equations for -charged black holes and obtain exact expressions for second
order transport coefficients for dual plasma in presence of arbitrary chemical
potentials. Finally we obtain higher derivative corrections to second order
transport coefficients of boundary theory dual to five dimensional gauge
supergravity.Comment: Version 2, reference added, typos correcte
Thermalization from gauge/gravity duality: Evolution of singularities in unequal time correlators
We consider a gauge/gravity dual model of thermalization which consists of a
collapsing thin matter shell in asymptotically Anti-de Sitter space. A central
aspect of our model is to consider a shell moving at finite velocity as
determined by its equation of motion, rather than a quasi-static approximation
as considered previously in the literature. By applying a divergence matching
method, we obtain the evolution of singularities in the retarded unequal time
correlator , which probes different stages of the thermalization. We
find that the number of singularities decreases from a finite number to zero as
the gauge theory thermalizes. This may be interpreted as a sign of decoherence.
Moreover, in a second part of the paper, we show explicitly that the thermal
correlator is characterized by the existence of singularities in the complex
time plane. By studying a quasi-static state, we show the singularities at real
times originate from contributions of normal modes. We also investigate the
possibility of obtaining complex singularities from contributions of
quasi-normal modes.Comment: 35 pages, 4 figure
From Navier-Stokes To Einstein
We show by explicit construction that for every solution of the
incompressible Navier-Stokes equation in dimensions, there is a uniquely
associated "dual" solution of the vacuum Einstein equations in
dimensions. The dual geometry has an intrinsically flat timelike boundary
segment whose extrinsic curvature is given by the stress tensor of
the Navier-Stokes fluid. We consider a "near-horizon" limit in which
becomes highly accelerated. The near-horizon expansion in gravity is shown to
be mathematically equivalent to the hydrodynamic expansion in fluid dynamics,
and the Einstein equation reduces to the incompressible Navier-Stokes equation.
For , we show that the full dual geometry is algebraically special Petrov
type II. The construction is a mathematically precise realization of
suggestions of a holographic duality relating fluids and horizons which began
with the membrane paradigm in the 70's and resurfaced recently in studies of
the AdS/CFT correspondence.Comment: 15 pages, 2 figures, typos correcte
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