16,586 research outputs found
Dynamics of Black Hole Pairs I: Periodic Tables
Although the orbits of comparable mass, spinning black holes seem to defy
simple decoding, we find a means to decipher all such orbits. The dynamics is
complicated by extreme perihelion precession compounded by spin-induced
precession. We are able to quantitatively define and describe the fully three
dimensional motion of comparable mass binaries with one black hole spinning and
expose an underlying simplicity. To do so, we untangle the dynamics by
capturing the motion in the orbital plane. Our results are twofold: (1) We
derive highly simplified equations of motion in a non-orthogonal orbital basis,
and (2) we define a complete taxonomy for fully three-dimensional orbits. More
than just a naming system, the taxonomy provides unambiguous and quantitative
descriptions of the orbits, including a determination of the zoom-whirliness of
any given orbit. Through a correspondence with the rationals, we are able to
show that zoom-whirl behavior is prevalent in comparable mass binaries in the
strong-field regime. A first significant conclusion that can be drawn from this
analysis is that all generic orbits in the final stages of inspiral under
gravitational radiation losses are characterized by precessing clovers with few
leaves and that no orbit will behave like the tightly precessing ellipse of
Mercury. The gravitational waveform produced by these low-leaf clovers will
reflect the natural harmonics of the orbital basis -- harmonics that,
importantly, depend only on radius. The significance for gravitational wave
astronomy will depend on the number of windings the pair executes in the
strong-field regime and could be more conspicuous for intermediate mass pairs
than for stellar mass pairs.Comment: 19 pages, lots of figure
Liquidity and Market Structure
Market liquidity is modeled as being determined by the demand and supply of immediacy. Exogenous liquidity events coupled with the risk of delayed trade create a demand for immediacy. Market makers supply immediacy by their continuous presence. and willingness to bear risk during the time period between the arrival of final buyers and sellers. In the long run the number of market makers adjusts to equate the supply and demand for immediacy. This determine the equilibrium level of liquidity in the market. The lower is the autocorrelation in rates of return, the higher is the equilibrium level of liquidity.
Polynomial Response Surface Approximations for the Multidisciplinary Design Optimization of a High Speed Civil Transport
Surrogate functions have become an important tool in multidisciplinary design optimization to deal with noisy functions, high computational cost, and the practical difficulty of integrating legacy disciplinary computer codes. A combination of mathematical, statistical, and engineering techniques, well known in other contexts, have made polynomial surrogate functions viable for MDO. Despite the obvious limitations imposed by sparse high fidelity data in high dimensions and the locality of low order polynomial approximations, the success of the panoply of techniques based on polynomial response surface approximations for MDO shows that the implementation details are more important than the underlying approximation method (polynomial, spline, DACE, kernel regression, etc.). This paper surveys some of the ancillary techniquesâstatistics, global search, parallel computing, variable complexity modelingâthat augment the construction and use of polynomial surrogates
F-15 flight flutter test program
The modes to be observed during the F-15 flight flutter test program were selected on the basis of the results of analytical studies, wind tunnel tests, and ground vibration tests. The modes (both symmetrical and antisymmetrical) tracked on this basis were: fin first bending, fin torsion, fin tip roll, stabilator bending, stabilator pitch, boom lateral bending, boom torsion, boom vertical bending, wing first bending, wing second bending, wing first torsion, outer wing torsion, and aileron rotation. Data obtained for these various modes were evaluated in terms of damping versus airspeed at 1525 m (5000 ft), damping versus altitude at the cross-section Mach numbers (to extrapolate to the damping value to be expected at sea level), and flutter boundaries on the basis of flutter margin of various modal pairs representing potential flutter mechanisms. Results of these evaluations are summarized in terms of minimum predicted flutter margin for the various mechanisms
MFV SUSY: A Natural Theory for R-Parity Violation
We present an alternative approach to low-energy supersymmetry. Instead of
imposing R-parity we apply the minimal flavor violation (MFV) hypothesis to the
R-parity violating MSSM. In this framework, which we call MFV SUSY, squarks can
be light and the proton long lived without producing missing energy signals at
the LHC. Our approach differs from that of Nikolidakis and Smith in that we
impose holomorphy on the MFV spurions. The resulting model is highly
constrained and R-parity emerges as an accidental approximate symmetry of the
low-energy Lagrangian. The size of the small R-parity violating terms is
determined by the flavor parameters, and in the absence of neutrino masses
there is only one renormalizable R-parity violating interaction: the
baryon-number violating superpotential term. Low energy
observables (proton decay, dinucleon decay and oscillation) pose
only mild constraints on the parameter space. LHC phenomenology will depend on
whether the LSP is a squark, neutralino, chargino or slepton. If the LSP is a
squark it will have prompt decays, explaining the non-observation of events
with missing transverse energy at the LHC.Comment: 41 pages, 14 figures; v3: minor corrections, matches published
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