On the smallest scale for the incompressible Navier-Stokes equations

It is proven that for solutions to the two- and three-dimensional incompressible Navier-Stokes equations the minimum scale is inversely proportional to the square root of the Reynolds number based on the kinematic viscosity and the maximum of the velocity gradients. The bounds on the velocity gradients can be obtained for two-dimensional flows, but have to be assumed to be three-dimensional. Numerical results in two dimensions are given which illustrate and substantiate the features of the proof. Implications of the minimum scale result to the decay rate of the energy spectrum are discussed

On the use of intermediate infrared and microwave infrared in weather satellites

Intermediate, and microwave infrared measurements by weather satellite

On the uses of intermediate infrared and microwave infrared in meteorological satellites Third semiannual report

Analysis of Nimbus satellite high resolution infrared radiation grid point data, surface emissivity in intermediate region, and meteorological modeling for microwave stud

On the uses of intermediate infrared and microwave infrared in meteorological satellites Semiannual report

Intermediate infrared and microwave infrared applications in meteorological satellite

Kerr-Schild type initial data for black holes with angular momenta

Generalizing previous work we propose how to superpose spinning black holes in a Kerr-Schild initial slice. This superposition satisfies several physically meaningful limits, including the close and the far ones. Further we consider the close limit of two black holes with opposite angular momenta and explicitly solve the constraint equations in this case. Evolving the resulting initial data with a linear code, we compute the radiated energy as a function of the masses and the angular momenta of the black holes.Comment: 13 pages, 3 figures. Revised version. To appear in Classical and Quantum Gravit

The Initial-Boundary Value Problem in General Relativity

In this article we summarize what is known about the initial-boundary value problem for general relativity and discuss present problems related to it.Comment: 11 pages, 2 figures. Contribution to a special volume for Mario Castagnino's seventy fifth birthda

Binary neutron-star mergers with Whisky and SACRA: First quantitative comparison of results from independent general-relativistic hydrodynamics codes

We present the first quantitative comparison of two independent general-relativistic hydrodynamics codes, the Whisky code and the SACRA code. We compare the output of simulations starting from the same initial data and carried out with the configuration (numerical methods, grid setup, resolution, gauges) which for each code has been found to give consistent and sufficiently accurate results, in particular in terms of cleanness of gravitational waveforms. We focus on the quantities that should be conserved during the evolution (rest mass, total mass energy, and total angular momentum) and on the gravitational-wave amplitude and frequency. We find that the results produced by the two codes agree at a reasonable level, with variations in the different quantities but always at better than about 10%.Comment: Published on Phys. Rev.

On the use of intermediate infrared and microwave infrared in weather satellites First annual report

Microwave infrared sensors in meteorological satellite payloads to obtain additional weather informatio

Constraint-preserving boundary treatment for a harmonic formulation of the Einstein equations

We present a set of well-posed constraint-preserving boundary conditions for a first-order in time, second-order in space, harmonic formulation of the Einstein equations. The boundary conditions are tested using robust stability, linear and nonlinear waves, and are found to be both less reflective and constraint preserving than standard Sommerfeld-type boundary conditions.Comment: 18 pages, 7 figures, accepted in CQ

Introduction to dynamical horizons in numerical relativity

This paper presents a quasi-local method of studying the physics of dynamical black holes in numerical simulations. This is done within the dynamical horizon framework, which extends the earlier work on isolated horizons to time-dependent situations. In particular: (i) We locate various kinds of marginal surfaces and study their time evolution. An important ingredient is the calculation of the signature of the horizon, which can be either spacelike, timelike, or null. (ii) We generalize the calculation of the black hole mass and angular momentum, which were previously defined for axisymmetric isolated horizons to dynamical situations. (iii) We calculate the source multipole moments of the black hole which can be used to verify that the black hole settles down to a Kerr solution. (iv) We also study the fluxes of energy crossing the horizon, which describes how a black hole grows as it accretes matter and/or radiation. We describe our numerical implementation of these concepts and apply them to three specific test cases, namely, the axisymmetric head-on collision of two black holes, the axisymmetric collapse of a neutron star, and a non-axisymmetric black hole collision with non-zero initial orbital angular momentum.Comment: 20 pages, 16 figures, revtex4. Several smaller changes, some didactic content shortene