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 techniques—statistics, global search, parallel computing, variable complexity modeling—that 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 $\bar{u}\bar{d}\bar{d}$ superpotential term. Low energy observables (proton decay, dinucleon decay and $n-\bar{n}$ 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 versio