In [1] we formulated and derived the three universal laws governing Near Horizon Extremal Geometries (NHEG). In this work we focus on the Entropy Perturbation Law (EPL) which, similarly to the first law of black hole thermodynamics, relates perturbations of the charges labeling perturbations around a given NHEG to the corresponding entropy perturbation. We show that field perturbations governed...

We consider spherical gravitational perturbations of AdS4 space-time satisfying general boundary conditions at spatial infinity. Using the holographic renormalization method, we compute the energy-momentum tensor and show that it can always be cast in the form of Cotton tensor for a dual boundary metric. In particular, axial and polar perturbations obeying the same boundary conditions for the e...

An interfacial approximation of the streamer stage in the evolution of sparks and lightning can be formulated as a Laplacian growth model regularized by a ’kinetic undercooling’ boundary condition. Using this model we study both the linearized and the full nonlinear evolution of small perturbations of a uniformly translating circle. Within the linear approximation analytical and numerical resul...

We present numerical calculations of the linearized Navier-Stokes equations for axially extended and axially localized spiral structures in the Taylor-Couette system. The eigenvalue surface for spiral vortices with azimuthal wave number M=2 shows significantly more structure than that for vortices with M=0 and 1. Islands are found in parameter space where axially periodic vortex perturbations c...

Burgers vortices are explicit stationary solutions of the Navier-Stokes equations which are often used to describe the vortex tubes observed in numerical simulations of threedimensional turbulence. In this model, the velocity field is a two-dimensional perturbation of a linear straining flow with axial symmetry. The only free parameter is the Reynolds number Re = Γ/ν, where Γ is the total circu...

We study the supergravity solutions describing non-extremal enhançons. There are two branches of solutions: a ‘shell branch’ connected to the extremal solution, and a ‘horizon branch’ which connects to the Schwarzschild black hole at large mass. We show that the shell branch solutions violate the weak energy condition, and are hence unphysical. We investigate linearized perturbations of the hor...

We calculate the linearized metric perturbations in the five dimensional two-brane model of Randall and Sundrum. In a carefully chosen gauge, we write down and decouple Einstein equations for the perturbations and get the final and simple perturbative metric ansatz. This ansatz turns out to be equal to the linear expansion of the metric solution of Charmousis et al. [1]. We show that this ansat...

The linearized wave-equation MVA operator can be used for velocity analysis using both Born and Rytov approximations. The distinction arises from the method used to compute the image perturbations. Both approximations suffer from limitations that limit their practicality: the Born approximation is usable only for small anomalies, while the Rytov approximation requires phase unwrapping. Differen...

1. Introduction. In the linear range a general theory of thermoelasticity based on irreversible thermodynamics was developed and discussed extensively in some earlier work ([3], [4], [9]). It was assumed that the elastic solid is initially in a stress-free equilibrium state at uniform temperature. Completely linearized perturbations in the vicinity of this equilibrium state are then analyzed as...