2,449 research outputs found
Transonic flow theory of airfoils and wings
There are plans to use the supercritical wing on the next generation of commercial aircraft so as to economize on fuel consumption by reducing drag. Computer codes have served well in meeting the consequent demand for new wing sections. The possibility of replacing wind tunnel tests by computational fluid dynamics is discussed. Another approach to the supercritical wing is through shockless airfoils. A novel boundary value problem in the hodograph plane is studied that enables one to design a shockless airfoil so that its pressure distribution very nearly takes on data that are prescribed
Numerical design of shockless airfoils
An attempt is made to indicate and briefly discuss only the most significant achievements of the research. The most successful contribution from the contract was the code for two dimensional analysis of airfoils in transonic flow
Coincidence of length spectra does not imply isospectrality
Penrose--Lifshits mushrooms are planar domains coming in nonisometric pairs
with the same geodesic length spectrum. Recently S. Zelditch raised the
question whether such billiards also have the same eigenvalue spectrum for the
Dirichlet Laplacian (conjecturing ``no''). Here we show that generically (in
the class of smooth domains) the two members of a mushroom pair have different
spectra.Comment: 8 pages, 5 figure
Relic Radiation from an Evaporating Black Hole
We present a non-string-theoretic calculation of the microcanonical entropy
of relic integer-spin Hawking radiation -- at fixed total energy . The only
conserved macroscopic quantity is the total energy (the total energy of the
relic radiation). Data for a boundary-value approach, with massless,
integer-spin perturbations, are set on initial and final space-like
hypersurfaces. In the resulting 1-dimensional statistical-mechanics problem,
the real part of the (complex) time separation at spatial infinity, , is the variable conjugate to the total
energy. We count the number of weak-field configurations on the final
space-like hypersurface with energy . One recovers the Cardy formula and the
Bekenstein-Hawking entropy, if Re(T) is of the order of the black-hole life-
time, leading to a statistical interpretation of black-hole entropy. The
microcanonical entropy includes a logarithmic correction to the black-hole area
law, which is {\it universal} (independent of black-hole parameters). Here, the
discreteness of the energy levels is crucial. This approach is compared with
that of string theory for the transition to the fundamental-string r\'egime in
the final stages of evaporation. The squared coupling, , regulating the
transition to a highly-excited string state and {\it vice versa}, can be
related to the angle, , of complex-time rotation above. The
strong-coupling r\'egime corresponds to a Euclidean black hole, while the
physical limit of a Lorentzian space-time (as ) corresponds to
the weak-coupling r\'egime. This resembles the transition to a highly-excited
string-like state which subsequently decays into massless particles, thereby
avoiding the naked singularity.Comment: To appear in International Journal of Modern Physics
Transonic airfoil codes
Computer codes for the design and analysis of transonic airfoils are considered. The design code relies on the method of complex characteristics in the hodograph plane to construct shockless airfoil. The analysis code uses artificial viscosity to calculate flows with weak shock waves at off-design conditions. Comparisons with experiments show that an excellent simulation of two dimensional wind tunnel tests is obtained. The codes have been widely adopted by the aircraft industry as a tool for the development of supercritical wing technology
Initial Data for General Relativity with Toroidal Conformal Symmetry
A new class of time-symmetric solutions to the initial value constraints of
vacuum General Relativity is introduced. These data are globally regular,
asymptotically flat (with possibly several asymptotic ends) and in general have
no isometries, but a group of conformal isometries. After
decomposing the Lichnerowicz conformal factor in a double Fourier series on the
group orbits, the solutions are given in terms of a countable family of
uncoupled ODEs on the orbit space.Comment: REVTEX, 9 pages, ESI Preprint 12
Time dependence of Bragg forward scattering and self-seeding of hard x-ray free-electron lasers
Free-electron lasers (FELs) can now generate temporally short, high power
x-ray pulses of unprecedented brightness, even though their longitudinal
coherence is relatively poor. The longitudinal coherence can be potentially
improved by employing narrow bandwidth x-ray crystal optics, in which case one
must also understand how the crystal affects the field profile in time and
space. We frame the dynamical theory of x-ray diffraction as a set of coupled
waves in order to derive analytic expressions for the spatiotemporal response
of Bragg scattering from temporally short incident pulses. We compute the
profiles of both the reflected and forward scattered x-ray pulses, showing that
the time delay of the wave is linked to its transverse spatial shift
through the simple relationship , where
is the grazing angle of incidence to the diffracting planes. Finally,
we apply our findings to obtain an analytic description of Bragg forward
scattering relevant to monochromatically seed hard x-ray FELs.Comment: 11 pages, 6 figure
Vacuum Spacetimes with Future Trapped Surfaces
In this article we show that one can construct initial data for the Einstein
equations which satisfy the vacuum constraints. This initial data is defined on
a manifold with topology with a regular center and is asymptotically
flat. Further, this initial data will contain an annular region which is
foliated by two-surfaces of topology . These two-surfaces are future
trapped in the language of Penrose. The Penrose singularity theorem guarantees
that the vacuum spacetime which evolves from this initial data is future null
incomplete.Comment: 19 page
Does the complex deformation of the Riemann equation exhibit shocks?
The Riemann equation , which describes a one-dimensional
accelerationless perfect fluid, possesses solutions that typically develop
shocks in a finite time. This equation is \cP\cT symmetric. A one-parameter
\cP\cT-invariant complex deformation of this equation,
( real), is solved exactly using the
method of characteristic strips, and it is shown that for real initial
conditions, shocks cannot develop unless is an odd integer.Comment: latex, 8 page
Black holes, cosmological singularities and change of signature
There exists a widespread belief that signature type change could be used to
avoid spacetime singularities. We show that signature change cannot be utilised
to this end unless the Einstein equation is abandoned at the suface of
signature type change. We also discuss how to solve the initial value problem
and show to which extent smooth and discontinuous signature changing solutions
are equivalent.Comment: 14pages, Latex, no figur
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