On the constants in a Kato inequality for the Euler and Navier-Stokes equations

We continue an analysis, started in [10], of some issues related to the incompressible Euler or Navier-Stokes (NS) equations on a d-dimensional torus T^d. More specifically, we consider the quadratic term in these equations; this arises from the bilinear map (v, w) -> v . D w, where v, w : T^d -> R^d are two velocity fields. We derive upper and lower bounds for the constants in some inequalities related to the above bilinear map; these bounds hold, in particular, for the sharp constants G_{n d} = G_n in the Kato inequality | < v . D w | w >_n | <= G_n || v ||_n || w ||^2_n, where n in (d/2 + 1, + infinity) and v, w are in the Sobolev spaces H^n, H^(n+1) of zero mean, divergence free vector fields of orders n and n+1, respectively. As examples, the numerical values of our upper and lower bounds are reported for d=3 and some values of n. When combined with the results of [10] on another inequality, the results of the present paper can be employed to set up fully quantitative error estimates for the approximate solutions of the Euler/NS equations, or to derive quantitative bounds on the time of existence of the exact solutions with specified initial data; a sketch of this program is given.Comment: LaTeX, 39 pages. arXiv admin note: text overlap with arXiv:1007.4412 by the same authors, not concerning the main result

An investigation of nodal structures and the construction of trial wave functions

The factors influencing the quality of the nodal surfaces, namely, the atomic basis set, the single-particle orbitals, and the configurations included in the wave-function expansion, are examined for a few atomic and molecular systems. The following empirical rules are found: the atomic basis set must be fairly large, complete active space and natural orbitals are usually better than Hartree-Fock orbitals, multiconfiguration expansions perform better than single-determinant wave functions, but only few configurations are effective and their choice is suggested by symmetry considerations, while too long determinantal expansions spoil the nodal surfaces. These rules allow us to reduce the nodal error and to compute the best fixed node-diffusion Monte Carlo energies for a series of dimers of first-row atoms

Quantum Monte Carlo estimators for the positron-electron annihilation rate in bound and low-energy scattering states

Variational and exact estimators for the positron-electron annihilation rate in bound states of systems containing a positron in the framework of quantum Monte Carlo methods are presented. The modification needed to compute the effective number of electrons Z(eff) when scattering states are concerned is also discussed. The algorithms are tested against four cases for which close to exact results are available, finding an overall good agreement. The systems are Ps(-), PsH, and the s-wave scattering component of e(+)H and e(+)He

From Connectivity to Advanced Internet Services: A Comprehensive Review of Small Satellites Communications and Networks

Recently the availability of innovative and affordable COTS (Commercial Off The Shelf) technological solutions and the ever improving results of microelectronics and microsystems technologies have enabled the design of ever smaller yet ever more powerful satellites. The emergence of very capable small satellites heralds an era of new opportunities in the commercial space market. Initially applied only to scientific missions, earth observation and remote sensing, small satellites are now being deployed to support telecommunications services. This review paper examines the operational features of small satellites that contribute to their success. An overview of recent advances and development trends in the field of small satellites is provided, with a special focus on telecommunication aspects such as the use of higher frequency bands, optical communications, new protocols, and advanced architectures

A class of Poisson-Nijenhuis structures on a tangent bundle

Equipping the tangent bundle TQ of a manifold with a symplectic form coming from a regular Lagrangian L, we explore how to obtain a Poisson-Nijenhuis structure from a given type (1,1) tensor field J on Q. It is argued that the complete lift of J is not the natural candidate for a Nijenhuis tensor on TQ, but plays a crucial role in the construction of a different tensor R, which appears to be the pullback under the Legendre transform of the lift of J to co-tangent manifold of Q. We show how this tangent bundle view brings new insights and is capable also of producing all important results which are known from previous studies on the cotangent bundle, in the case that Q is equipped with a Riemannian metric. The present approach further paves the way for future generalizations.Comment: 22 page