Loading atom lasers by collectivity-enhanced optical pumping

The effect of collectivity on the loading of an atom laser via optical pumping is discussed. In our model, atoms in a beam are laser-excited and subsequently spontaneously decay into a trapping state. We consider the case of sufficiently high particle density in the beam such that the spontaneous emission is modified by the particle interaction. We show that the collective effects lead to a better population of the trapping state over a wide range of system parameters, and that the second order correlation function of the atoms can be controlled by the applied laser field.Comment: 5 pages, 7 figure

Positivity and optimization for semi-algebraic functions

We describe algebraic certificates of positivity for functions belonging to a finitely generated algebra of Borel measurable functions, with particular emphasis to algebras generated by semi-algebraic functions. In which case the standard global optimization problem with constraints given by elements of the same algebra is reduced via a natural change of variables to the better understood case of polynomial optimization. A collection of simple examples and numerical experiments complement the theoretical parts of the article.Comment: 20 page

A micromechanics based constitutive model for fibre reinforced cementitious composites

A new constitutive model for fibre reinforced cementitious composites based on micromechanical solutions is proposed. The model employs a two-phase composite based on the Eshelby matrix-inclusion solution and the Mori-Tanaka homogenization scheme and also simulates directional microcracking. An exterior point Eshelby based criterion is employed to model crack-initiation in the matrix-inclusion interface. Microcrack surfaces are assumed to be rough and able to regain contact under both normal and shear displacements. Fibres are included into the formulation in both cracked and uncracked conditions. Once cracks start to develop, the crack-bridging action of fibres is simulated using a local constitutive equation that accounts for the debonding and pull-out of fibre groups with different orientations. It is shown that the combination of the rough microcrack and fibre-bridging sub-models allows microcracking behaviour deriving from both tensile and compressive loads to be modelled in a unified manner. This ability to model tensile and compressive behaviour using the same micromechanical mechanisms is considered to be a particularly attractive feature of the formulation, which removes the need for multi-parameter triaxial yield surfaces and evolution functions that bedevil many competitor models. The model is successfully validated using a series of examples based on experimental test data

Sound propagation in a solid through a screen of cylindrical scatterers

The propagation of SH waves in a solid containing a screen of line-like scatterers is investigated. When the scatterers are uniformly distributed, the amplitudes of the coherent waves inside and outside the screen are evaluated in closed form. In the analysis, multiple scattering effects are taken into account within the context of a first-order approximation. A Global Closure Assumption is proposed, which yields an effective wavenumber identical to that of Waterman and Truell. The scatterers can be fibers of circular or elliptical cross-sections; they can also be two-dimensional cracks with slit-like or elliptical cross-sections. Specific analytical and numerical results are presented for flat cracks and empty cavities of circular cross-sections. In those two cases, figures are presented to illustrate the variations of the reflection and transmission coefficients as functions of frequency and of scatterer concentration. The crack and cavity results, respectively, are compared with those of earlier works

Computation and visualization of Casimir forces in arbitrary geometries: non-monotonic lateral forces and failure of proximity-force approximations

We present a method of computing Casimir forces for arbitrary geometries, with any desired accuracy, that can directly exploit the efficiency of standard numerical-electromagnetism techniques. Using the simplest possible finite-difference implementation of this approach, we obtain both agreement with past results for cylinder-plate geometries, and also present results for new geometries. In particular, we examine a piston-like problem involving two dielectric and metallic squares sliding between two metallic walls, in two and three dimensions, respectively, and demonstrate non-additive and non-monotonic changes in the force due to these lateral walls.Comment: Accepted for publication in Physical Review Letters. (Expected publication: Vol. 99 (8) 2007

Asymptotic Stability for a Class of Metriplectic Systems

Using the framework of metriplectic systems on $\R^n$ we will describe a constructive geometric method to add a dissipation term to a Hamilton-Poisson system such that any solution starting in a neighborhood of a nonlinear stable equilibrium converges towards a certain invariant set. The dissipation term depends only on the Hamiltonian function and the Casimir functions