Renormalization group analysis of the Reynolds stress transport equation

The pressure velocity correlation and return to isotropy term in the Reynolds stress transport equation are analyzed using the Yakhot-Orszag renormalization group. The perturbation series for the relevant correlations, evaluated to lowest order in the epsilon-expansion of the Yakhot-Orszag theory, are infinite series in tensor product powers of the mean velocity gradient and its transpose. Formal lowest order Pade approximations to the sums of these series produce a fast pressure strain model of the form proposed by Launder, Reece, and Rodi, and a return to isotropy model of the form proposed by Rotta. In both cases, the model constant are computed theoretically. The predicted Reynolds stress ratios in simple shear flows are evaluated and compared with experimental data. The possibility is discussed of driving higher order nonlinear models by approximating the sums more accurately

Casimir-Polder forces, boundary conditions and fluctuations

We review different aspects of the atom-atom and atom-wall Casimir-Polder forces. We first discuss the role of a boundary condition on the interatomic Casimir-Polder potential between two ground-state atoms, and give a physically transparent interpretation of the results in terms of vacuum fluctuations and image atomic dipoles. We then discuss the known atom-wall Casimir-Polder force for ground- and excited-state atoms, using a different method which is also suited for extension to time-dependent situations. Finally, we consider the fluctuation of the Casimir-Polder force between a ground-state atom and a conducting wall, and discuss possible observation of this force fluctuation.Comment: 5 page

Enhanced van der Waals interaction at interfaces

Using a recently obtained (general) formula for the interaction energy between an excited and a ground-state atom (Sherkunov Y 2007 Phys. Rev. A 75 012705), we consider the interaction energy between two such atoms near the interface between two media. We demonstrate that under the circumstances of the resonant coupling of the excited atom to the surface polariton mode of a vacuum-medium system the nonretarded atom*-atom interaction energy can be enhanced by (several) orders of magnitude in comparison with the van der Waals interaction energy of the two isolated atoms.Comment: 8 pages, 5 figures, local-field corrections included and improved presentatio

Saddle Points and Stark Ladders: Exact Calculations of Exciton Spectra in Superlattices

A new, exact method for calculating excitonic absorption in superlattices is described. It is used to obtain high resolution spectra showing the saddle point exciton feature near the top of the miniband. The evolution of this feature is followed through a series of structures with increasing miniband width. The Stark ladder of peaks produced by an axial electric field is investigated, and it is shown that for weak fields the line shapes are strongly modified by coupling to continuum states, taking the form of Fano resonances. The calculated spectra, when suitably broadened, are found to be in good agreement with experimental results.Comment: 9 pages Revtex v3.0, followed by 4 uuencoded postscript figures, SISSA-CM-94-00

Elliptic Flow, Initial Eccentricity and Elliptic Flow fluctuations in Heavy Ion Collisions at RHIC

We present measurements of elliptic flow and event-by-event fluctuations established by the PHOBOS experiment. Elliptic flow scaled by participant eccentricity is found to be similar for both systems when collisions with the same number of participants or the same particle area density are compared. The agreement of elliptic flow between Au+Au and Cu+Cu collisions provides evidence that the matter is created in the initial stage of relativistic heavy ion collisions with transverse granularity similar to that of the participant nucleons. The event-by-event fluctuation results reveal that the initial collision geometry is translated into the final state azimuthal particle distribution, leading to an event-by-event proportionality between the observed elliptic flow and initial eccentricity.Comment: To appear in the proceedings of the Lake Louise Winter Institute 2007. The proceedings of the institute will be published by World Scientifi

Environments of Redshift Survey Compact Groups of Galaxies

Redshift Survey Compact Groups (RSCGs) are tight knots of N >= 3 galaxies selected from the CfA2+SSRS2 redshift survey. The selection is based on physical extent and association in redshift space alone. We measured 300 new redshifts of fainter galaxies within 1 h^{-1} Mpc of 14 RSCGs to explore the relationship between RSCGs and their environments. 13 of 14 RSCGs are embedded in overdense regions of redshift space. The systems range from a loose group of 5 members to an Abell cluster. The remaining group, RSCG 64, appears isolated. RSCGs are isolated and distinct from their surroundings to varying degrees, as are the Hickson Compact Groups. Among the 13 embedded RSCGs, 3 are distinct from their general environments (RSCG 9, RSCG 11 and RSCG 85).Comment: 35 pages, including 10 figures and 5 tables, accepted for publication in the Astronomical Journa

Local and Global Casimir Energies for a Semitransparent Cylindrical Shell

The local Casimir energy density and the global Casimir energy for a massless scalar field associated with a $\lambda\delta$-function potential in a 3+1 dimensional circular cylindrical geometry are considered. The global energy is examined for both weak and strong coupling, the latter being the well-studied Dirichlet cylinder case. For weak-coupling,through $\mathcal{O}(\lambda^2)$, the total energy is shown to vanish by both analytic and numerical arguments, based both on Green's-function and zeta-function techniques. Divergences occurring in the calculation are shown to be absorbable by renormalization of physical parameters of the model. The global energy may be obtained by integrating the local energy density only when the latter is supplemented by an energy term residing precisely on the surface of the cylinder. The latter is identified as the integrated local energy density of the cylindrical shell when the latter is physically expanded to have finite thickness. Inside and outside the delta-function shell, the local energy density diverges as the surface of the shell is approached; the divergence is weakest when the conformal stress tensor is used to define the energy density. A real global divergence first occurs in $\mathcal{O}(\lambda^3)$, as anticipated, but the proof is supplied here for the first time; this divergence is entirely associated with the surface energy, and does {\em not} reflect divergences in the local energy density as the surface is approached.Comment: 28 pages, REVTeX, no figures. Appendix added on perturbative divergence

Sub-leading contributions to the black hole entropy in the brick wall approach

[Abridged] We compute the canonical entropy of a quantum scalar field around static and spherically symmetric black holes through the brick wall approach at the higher orders (in fact, up to the sixth order in \hbar) in the WKB approximation. We explicitly show that the brick wall model generally predicts corrections to the Bekenstein-Hawking entropy in all spacetime dimensions. In four dimensions, we find that the corrections to the Bekenstein-Hawking entropy are of the form (A^n \log A), while, in six dimensions, the corrections behave as (A^m + A^n \log A), where A denotes the area of the black hole event horizon, and (m, n) < 1. We compare our results with the corrections to the Bekenstein-Hawking entropy that have been obtained through the other approaches in the literature, and discuss the implications.Comment: 21 pages, Revtex 4; Final verson - 22 pages, References added, Accepted in Phys. Rev.

A review of residual stress analysis using thermoelastic techniques

Thermoelastic Stress Analysis (TSA) is a full-field technique for experimental stress analysis that is based on infra-red thermography. The technique has proved to be extremely effective for studying elastic stress fields and is now well established. It is based on the measurement of the temperature change that occurs as a result of a stress change. As residual stress is essentially a mean stress it is accepted that the linear form of the TSA relationship cannot be used to evaluate residual stresses. However, there are situations where this linear relationship is not valid or departures in material properties due to manufacturing procedures have enabled evaluations of residual stresses. The purpose of this paper is to review the current status of using a TSA based approach for the evaluation of residual stresses and to provide some examples of where promising results have been obtained

Thermodynamic Scaling of the Viscosity of Van Der Waals, H-Bonded, and Ionic Liquids

Viscosities and their temperature, T, and volume, V, dependences are reported for 7 molecular liquids and polymers. In combination with literature viscosity data for 5 other liquids, we show that the superpositioning of relaxation times for various glass-forming materials when expressed as a function of TV^g, where the exponent g is a material constant, can be extended to the viscosity. The latter is usually measured to higher temperatures than the corresponding relaxation times, demonstrating the validity of the thermodynamic scaling throughout the supercooled and higher T regimes. The value of g for a given liquid principally reflects the magnitude of the intermolecular forces (e.g., steepness of the repulsive potential); thus, we find decreasing g in going from van der Waals fluids to ionic liquids. For strongly H-bonded materials, such as low molecular weight polypropylene glycol and water, the superpositioning fails, due to the non-trivial change of chemical structure (degree of H-bonding) with thermodynamic conditions.Comment: 16 pages 7 figure