18,081 research outputs found
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
is multiplied by a complex scalar function
. 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 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 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 . 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
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