Wilsonian Approach to Fluid/Gravity Duality

The problem of gravitational fluctuations confined inside a finite cutoff at radius $r=r_c$ 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 $r_c$ 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 $D(r_c)$ is derived. The dependence on $r_c$ is interpreted as renormalization group (RG) flow in the fluid. Taking the cutoff to infinity in an asymptotically AdS context, the formula for $D(\infty)$ 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 $D(horizon)$ 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 $\eta /s$ 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

Motion and Interaction of Magnetic Dislocations in Alternating Magnetic Field

Abstract The behavior of magnetic dislocations (MDs) in an alternating harmonic magnetic field in iron garnets has been experimentally investigated. The results are presented for single-crystal plates in which the drift of domain walls is observed in fields of sound frequencies. It is found that MDs in a stripe domain structure are able to move not only along but also across domain walls. A pairwise interaction between magnetic dislocations when they approach each other to distances on the order of the sizes of the cores of MDs is revealed. The processes of the annihilation, mutual passing of magnetic dislocations through each other and overtaking are found. The features of the dynamic behavior of MDs are explained using a mechanism based on the presence of vertical Bloch lines in a structure of domain walls. MDs are formed at nucleation centers, and their nucleation field is lower than the drift-starting field, which corresponds to previously proposed dislocational mechanism of the drift. The dependencies of quantitative parameters of the drift and MDs on amplitude and frequency of the pumping field are determined. The behavior of MDs should be considered when analyzing the mechanisms for magnetization and temperature-dependent phase transitions in magnetic layers

Unidirectional motion of magnetic domain walls: The experiment and numerical simulation

The results of study of unidirectional motion of topologically different domain structures under the influence of periodic bipolar and unipolar magnetic field pulses applied perpendicular to the sample plane of (111) iron garnet single crystal plate are presented. The response of the domain structure to the field pulses was studied by direct observations utilizing the stroboscopic technique. Experimentally obtained dependences of the speed of unidirectional motion of stripe domains on the parameters of external bipolar pulsed magnetic field are compared with the results of numerical simulations. © Published under licence by IOP Publishing Ltd.Ministry of Science and Higher Education of the Russian Federation: 3.6121.2017The work was performed within the framework of the basic part of the state assignment of the Ministry of Science and Higher Education of the Russian Federation (project 3.6121.2017)

Restricting SBH Ambiguity via Restriction Enzymes

Abstract. The expected number of n-base long sequences consistent with a given SBH spectrum grows exponentially with n, which severely limits the potential range of applicability of SBH even in an error-free setting. Restriction enzymes (RE) recognize specific patterns and cut the DNA molecule at all locations of that pattern. The output of a restriction assay is the set of lengths of the resulting fragments. By augmenting the SBH spectrum with the target string’s RE spectrum, we can eliminate much of the ambiguity of SBH. In this paper, we build on [20] to enhance the resolving power of restriction enzymes. We give a hardness result for the SBH+RE problem, and supply improved heuristics for the existing backtracking algorithm. We prove a lower bound on the number restric-tion enzymes required for unique reconstruction, and show experimental results that are not far from this bound.

From Navier-Stokes To Einstein

We show by explicit construction that for every solution of the incompressible Navier-Stokes equation in $p+1$ dimensions, there is a uniquely associated "dual" solution of the vacuum Einstein equations in $p+2$ dimensions. The dual geometry has an intrinsically flat timelike boundary segment $\Sigma_c$ whose extrinsic curvature is given by the stress tensor of the Navier-Stokes fluid. We consider a "near-horizon" limit in which $\Sigma_c$ 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 $p=2$, 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