28,755 research outputs found
Higher-Derivative Gravity with Non-minimally Coupled Maxwell Field
We construct higher-derivative gravities with a non-minimally coupled Maxwell
field. The Lagrangian consists of polynomial invariants built from the Riemann
tensor and the Maxwell field strength in such a way that the equations of
motion are second order for both the metric and the Maxwell potential. We also
generalize the construction to involve a generic non-minimally coupled -form
field strength. We then focus on one low-lying example in four dimensions and
construct the exact magnetically-charged black holes. We also construct exact
electrically-charged Lifshitz black holes. We obtain approximate dyonic
black holes for the small coupling constant or small charges. We find that the
thermodynamics based on the Wald formalism disagrees with that derived from the
Euclidean action procedure, suggesting this may be a general situation in
higher-derivative gravities with non-minimally coupled form fields. As an
application in the AdS/CFT correspondence, we study the entropy/viscosity ratio
for the AdS or Lifshitz planar black holes, and find that the exact ratio can
be obtained without having to know the details of the solutions, even for this
higher-derivative theory.Comment: Latex, 23 page
A minimal approach to the scattering of physical massless bosons
Tree and loop level scattering amplitudes which involve physical massless
bosons are derived directly from physical constraints such as locality,
symmetry and unitarity, bypassing path integral constructions. Amplitudes can
be projected onto a minimal basis of kinematic factors through linear algebra,
by employing four dimensional spinor helicity methods or at its most general
using projection techniques. The linear algebra analysis is closely related to
amplitude relations, especially the Bern-Carrasco-Johansson relations for gluon
amplitudes and the Kawai-Lewellen-Tye relations between gluons and graviton
amplitudes. Projection techniques are known to reduce the computation of loop
amplitudes with spinning particles to scalar integrals. Unitarity, locality and
integration-by-parts identities can then be used to fix complete tree and loop
amplitudes efficiently. The loop amplitudes follow algorithmically from the
trees. A range of proof-of-concept examples is presented. These include the
planar four point two-loop amplitude in pure Yang-Mills theory as well as a
range of one loop amplitudes with internal and external scalars, gluons and
gravitons. Several interesting features of the results are highlighted, such as
the vanishing of certain basis coefficients for gluon and graviton amplitudes.
Effective field theories are naturally and efficiently included into the
framework. The presented methods appear most powerful in non-supersymmetric
theories in cases with relatively few legs, but with potentially many loops.
For instance, iterated unitarity cuts of four point amplitudes for
non-supersymmetric gauge and gravity theories can be computed by matrix
multiplication, generalising the so-called rung-rule of maximally
supersymmetric theories. The philosophy of the approach to kinematics also
leads to a technique to control color quantum numbers of scattering amplitudes
with matter.Comment: 65 pages, exposition improved, typos correcte
Probing the halo of Centaurus A: a merger dynamical model for the PN population
Photometry and kinematics of the giant elliptical galaxy NGC~5128
(Centaurus~A) based on planetary nebulae observations (Hui~\etal 1995) are used
to build dynamical models which allow us to infer the presence of a dark matter
halo. To this end, we apply a Quadratic Programming method. Constant
mass-to-light ratio models fail to reproduce the major axis velocity dispersion
measurements at large radii: the profile of this kind of models falls off too
steeply when compared to the observations, clearly suggesting the necessity of
including a dark component in the halo. By assuming a mass-to-light ratio which
is increasing with radius, the model satisfactorily matches the observations.
The total mass for the best fit model is of which
about 50\% is dark matter. However, models with different total masses and dark
halos are also consistent with the data; we estimate that the total mass of
Cen~A within 50~kpc may vary between and
. The best fit model consists of 75\% of stars rotating
around the short axis and 25\% of stars rotating around the long axis .
Finally, the morphology of the projected velocity field is analyzed using
Statler's classification criteria (Statler 1991). We find that the appearance
of our velocity field is compatible with a type 'Nn' or 'Nd'.Comment: 13 pages, uuencoded compressed postscript, without figures. The full
postscript version, including all 14 figures, is available via anonymous ftp
at ftp://naos.rug.ac.be/pub/cena.ps.
On the Lagrangian Method for Steady and Unsteady Flow
A new and general Lagrangian formulation of fluid motion is given in which the independent variables are three material functions and a Lagrangian time, which differs for different fluid particles and is distinct from the Eulerian time. For steady flow it requires only three independent variables - the Lagrangian time and two stream functions - in contrast with the conventional Lagrangian formulation which apparently still requires four independent variables for describing a steady flow. This places the Lagrangian formulation for steady flow on the same footing as the Eulerian. For unsteady flow, the new formulation includes the conventional formulation as a special case when the Lagrangian time is identified with the Eulerian time and when the material functions are taken to be the fluid particle's position at some given time. The distinction between the Lagrangian and Eulerian time, however, is found useful in applications, e.g., to problems involving a free boundary
Bifurcation theory applied to aircraft motions
Bifurcation theory is used to analyze the nonlinear dynamic stability characteristics of single-degree-of-freedom motions of an aircraft or a flap about a trim position. The bifurcation theory analysis reveals that when the bifurcation parameter, e.g., the angle of attack, is increased beyond a critical value at which the aerodynamic damping vanishes, a new solution representing finite-amplitude periodic motion bifurcates from the previously stable steady motion. The sign of a simple criterion, cast in terms of aerodynamic properties, determines whether the bifurcating solution is stable (supercritical) or unstable (subcritical). For the pitching motion of a flap-plate airfoil flying at supersonic/hypersonic speed, and for oscillation of a flap at transonic speed, the bifurcation is subcritical, implying either that exchanges of stability between steady and periodic motion are accompanied by hysteresis phenomena, or that potentially large aperiodic departures from steady motion may develop. On the other hand, for the rolling oscillation of a slender delta wing in subsonic flight (wing rock), the bifurcation is found to be supercritical. This and the predicted amplitude of the bifurcation periodic motion are in good agreement with experiments
Bifurcation analysis of aircraft pitching motions near the stability boundary
Bifuraction theory is used to analyze the nonlinear dynamic stability characteristics of an aircraft subject to single degree of freedom pitching-motion perturbations about a large mean angle of attack. The requisite aerodynamic information in the equations of motion is represented in a form equivalent to the response to finite-amplitude pitching oscillations about the mean angle of attack. This information is deduced from the case of infinitesimal-amplitude oscillations. The bifurcation theory analysis reveals that when the mean angle of attack is increased beyond a critical value at which the aerodynamic damping vanishes, new solutions representing finite-amplitude periodic motions bifurcate from the previously stable steady motion. The sign of a simple criterion, cast in terms of aerodynamic properties, determines whether the bifurcating solutions are stable (supercritical) or unstable (subcritical). For flat-plate airfoils flying at supersonic/hypersonic speed, the bifurcation is subcritical, implying either that exchanges of stability between steady and periodic motion are accompanied by hysteresis phenomena, or that potentially large aperiodic departures from steady motion may develop
Unsteady Newton-Busemann flow theory. Part 2: Bodies of revolution
Newtonian flow theory for unsteady flow past oscillating bodies of revolution at very high Mach numbers is completed by adding a centrifugal force correction to the impact pressures. Exact formulas for the unsteady pressure and the stability derivatives are obtained in closed form and are applicable to bodies of revolution that have arbitrary shapes, arbitrary thicknesses, and either sharp or blunt noses. The centrifugal force correction arising from the curved trajectories followed by the fluid particles in unsteady flow cannot be neglected even for the case of a circular cone. With this correction, the present theory is in excellent agreement with experimental results for sharp cones and for cones with small nose bluntness; gives poor agreement with the results of experiments in air for bodies with moderate or large nose bluntness. The pitching motions of slender power-law bodies of revulution are shown to be always dynamically stable according to Newton-Busemann theory
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