Aerothermal modeling program, phase 1

Aerothermal submodels used in analytical combustor models are analyzed. The models described include turbulence and scalar transport, gaseous full combustion, spray evaporation/combustion, soot formation and oxidation, and radiation. The computational scheme is discussed in relation to boundary conditions and convergence criteria. Also presented is the data base for benchmark quality test cases and an analysis of simple flows

Gravitational wave energy spectrum of a parabolic encounter

We derive an analytic expression for the energy spectrum of gravitational waves from a parabolic Keplerian binary by taking the limit of the Peters and Matthews spectrum for eccentric orbits. This demonstrates that the location of the peak of the energy spectrum depends primarily on the orbital periapse rather than the eccentricity. We compare this weak-field result to strong-field calculations and find it is reasonably accurate (~10%) provided that the azimuthal and radial orbital frequencies do not differ by more than ~10%. For equatorial orbits in the Kerr spacetime, this corresponds to periapse radii of rp > 20M. These results can be used to model radiation bursts from compact objects on highly eccentric orbits about massive black holes in the local Universe, which could be detected by LISA.Comment: 5 pages, 3 figures. Minor changes to match published version; figure 1 corrected; references adde

Multiple jet impingement heat transfer characteristic: Experimental investigation of in-line and staggered arrays with crossflow

Heat transfer characteristics were obtained for configurations designed to model the impingement cooled midchord region of air cooled gas turbine airfoils. The configurations tested were inline and staggered two-dimensional arrays of circular jets with ten spanwise rows of holes. The cooling air was constrained to exit in the chordwise direction along the channel formed by the jet orifice plate and the heat transfer surface. Tests were run for chordwise jet hole spacings of five, ten, and fifteen hole diameters; spanwise spacings of four, six, and eight diameters; and channel heights of one, two, three, and six diameters. Mean jet Reynolds numbers ranged from 5000 to 50,000. The thermal boundary condition at the heat transfer test surface was isothermal. Tests were run for sets of geometrically similar configurations of different sizes. Mean and chordwise resolved Nusselt numbers were determined utilizing a specially constructed test surface which was segmented in the chordwise direction

Electromagnetic vortex lines riding atop null solutions of the Maxwell equations

New method of introducing vortex lines of the electromagnetic field is outlined. The vortex lines arise when a complex Riemann-Silberstein vector $({\bm E} + i{\bm B})/\sqrt{2}$ is multiplied by a complex scalar function $\phi$. Such a multiplication may lead to new solutions of the Maxwell equations only when the electromagnetic field is null, i.e. when both relativistic invariants vanish. In general, zeroes of the $\phi$ function give rise to electromagnetic vortices. The description of these vortices benefits from the ideas of Penrose, Robinson and Trautman developed in general relativity.Comment: NATO Workshop on Singular Optics 2003 To appear in Journal of Optics

Geometric phases and hidden local gauge symmetry

The analysis of geometric phases associated with level crossing is reduced to the familiar diagonalization of the Hamiltonian in the second quantized formulation. A hidden local gauge symmetry, which is associated with the arbitrariness of the phase choice of a complete orthonormal basis set, becomes explicit in this formulation (in particular, in the adiabatic approximation) and specifies physical observables. The choice of a basis set which specifies the coordinate in the functional space is arbitrary in the second quantization, and a sub-class of coordinate transformations, which keeps the form of the action invariant, is recognized as the gauge symmetry. We discuss the implications of this hidden local gauge symmetry in detail by analyzing geometric phases for cyclic and noncyclic evolutions. It is shown that the hidden local symmetry provides a basic concept alternative to the notion of holonomy to analyze geometric phases and that the analysis based on the hidden local gauge symmetry leads to results consistent with the general prescription of Pancharatnam. We however note an important difference between the geometric phases for cyclic and noncyclic evolutions. We also explain a basic difference between our hidden local gauge symmetry and a gauge symmetry (or equivalence class) used by Aharonov and Anandan in their definition of generalized geometric phases.Comment: 25 pages, 1 figure. Some typos have been corrected. To be published in Phys. Rev.

Screening of charged singularities of random fields

Many types of point singularity have a topological index, or 'charge', associated with them. For example the phase of a complex field depending on two variables can either increase or decrease on making a clockwise circuit around a simple zero, enabling the zeros to be assigned charges of plus or minus one. In random fields we can define a correlation function for the charge-weighted density of singularities. In many types of random fields, this correlation function satisfies an identity which shows that the singularities 'screen' each other perfectly: a positive singularity is surrounded by an excess of concentration of negatives which exactly cancel its charge, and vice-versa. This paper gives a simple and widely applicable derivation of this result. A counterexample where screening is incomplete is also exhibited.Comment: 12 pages, no figures. Minor revision of manuscript submitted to J. Phys. A, August 200

The Schwinger SU(3) construction - I: Multiplicity problem and relation to induced representations

The Schwinger oscillator operator representation of SU(3) is analysed with particular reference to the problem of multiplicity of irreducible representations. It is shown that with the use of an $Sp(2,R)$ unitary representation commuting with the SU(3) representation, the infinity of occurrences of each SU(3) irreducible representation can be handled in complete detail. A natural `generating representation' for SU(3), containing each irreducible representation exactly once, is identified within a subspace of the Schwinger construction; and this is shown to be equivalent to an induced representation of SU(3).Comment: Latex, 25 page

Topological quantum phase transition and the Berry phase near the Fermi surface in hole-doped quantum wells

We propose a topological quantum phase transition for quantum states with different Berry phases in hole-doped III-V semiconductor quantum wells with bulk and structure inversion asymmetry. The Berry phase of the occupied Bloch states can be characteristic of topological metallic states. It is found that the adjustment of thickness of the quantum well may cause a transition of Berry phase in two-dimensional hole gas. Correspondingly, the jump of spin Hall conductivity accompanies the change of the Berry phase. This property is robust against the impurity potentials in the system. Experimental detection of this topological quantum phase transition is discussed

Dynamical diffraction in sinusoidal potentials: uniform approximations for Mathieu functions

Eigenvalues and eigenfunctions of Mathieu's equation are found in the short wavelength limit using a uniform approximation (method of comparison with a `known' equation having the same classical turning point structure) applied in Fourier space. The uniform approximation used here relies upon the fact that by passing into Fourier space the Mathieu equation can be mapped onto the simpler problem of a double well potential. The resulting eigenfunctions (Bloch waves), which are uniformly valid for all angles, are then used to describe the semiclassical scattering of waves by potentials varying sinusoidally in one direction. In such situations, for instance in the diffraction of atoms by gratings made of light, it is common to make the Raman-Nath approximation which ignores the motion of the atoms inside the grating. When using the eigenfunctions no such approximation is made so that the dynamical diffraction regime (long interaction time) can be explored.Comment: 36 pages, 16 figures. This updated version includes important references to existing work on uniform approximations, such as Olver's method applied to the modified Mathieu equation. It is emphasised that the paper presented here pertains to Fourier space uniform approximation

Nodal domains on quantum graphs

We consider the real eigenfunctions of the Schr\"odinger operator on graphs, and count their nodal domains. The number of nodal domains fluctuates within an interval whose size equals the number of bonds $B$. For well connected graphs, with incommensurate bond lengths, the distribution of the number of nodal domains in the interval mentioned above approaches a Gaussian distribution in the limit when the number of vertices is large. The approach to this limit is not simple, and we discuss it in detail. At the same time we define a random wave model for graphs, and compare the predictions of this model with analytic and numerical computations.Comment: 19 pages, uses IOP journal style file