14,177 research outputs found
Symplectic Microgeometry II: Generating functions
We adapt the notion of generating functions for lagrangian submanifolds to
symplectic microgeometry. We show that a symplectic micromorphism always admits
a global generating function. As an application, we describe hamiltonian flows
as special symplectic micromorphisms whose local generating functions are the
solutions of Hamilton-Jacobi equations. We obtain a purely categorical
formulation of the temporal evolution in classical mechanics.Comment: 27 pages, 1 figur
Equilibrium Configuration of Black Holes and the Inverse Scattering Method
The inverse scattering method is applied to the investigation of the
equilibrium configuration of black holes. A study of the boundary problem
corresponding to this configuration shows that any axially symmetric,
stationary solution of the Einstein equations with disconnected event horizon
must belong to the class of Belinskii-Zakharov solutions. Relationships between
the angular momenta and angular velocities of black holes are derived.Comment: LaTeX, 14 pages, no figure
Geometric quantization of Hamiltonian actions of Lie algebroids and Lie groupoids
We construct Hermitian representations of Lie algebroids and associated
unitary representations of Lie groupoids by a geometric quantization procedure.
For this purpose we introduce a new notion of Hamiltonian Lie algebroid
actions. The first step of our procedure consists of the construction of a
prequantization line bundle. Next, we discuss a version of K\"{a}hler
quantization suitable for this setting. We proceed by defining a
Marsden-Weinstein quotient for our setting and prove a ``quantization commutes
with reduction'' theorem. We explain how our geometric quantization procedure
relates to a possible orbit method for Lie groupoids. Our theory encompasses
the geometric quantization of symplectic manifolds, Hamiltonian Lie algebra
actions, actions of families of Lie groups, foliations, as well as some general
constructions from differential geometry.Comment: 40 pages, corrected version 11-01-200
Charged Rotating Black Holes in Equilibrium
Axially symmetric, stationary solutions of the Einstein-Maxwell equations
with disconnected event horizon are studied by developing a method of explicit
integration of the corresponding boundary-value problem. This problem is
reduced to non-leaner system of algebraic equations which gives relations
between the masses, the angular momenta, the angular velocities, the charges,
the distance parameters, the values of the electromagnetic field potential at
the horizon and at the symmetry axis. A found solution of this system for the
case of two charged non-rotating black holes shows that in general the total
mass depends on the distance between black holes. Two-Killing reduction
procedure of the Einstein-Maxwell equations is also discussed.Comment: LaTeX 2.09, no figures, 15 pages, v2, references added, introduction
section slightly modified; v3, grammar errors correcte
Template-based Gravitational-Wave Echoes Search Using Bayesian Model Selection
The ringdown of the gravitational-wave signal from a merger of two black
holes has been suggested as a probe of the structure of the remnant compact
object, which may be more exotic than a black hole. It has been pointed out
that there will be a train of echoes in the late-time ringdown stage for
different types of exotic compact objects. In this paper, we present a
template-based search methodology using Bayesian statistics to search for
echoes of gravitational waves. Evidence for the presence or absence of echoes
in gravitational-wave events can be established by performing Bayesian model
selection. The Occam factor in Bayesian model selection will automatically
penalize the more complicated model that echoes are present in
gravitational-wave strain data because of its higher degree of freedom to fit
the data. We find that the search methodology was able to identify
gravitational-wave echoes with Abedi et al.'s echoes waveform model about 82.3%
of the time in simulated Gaussian noise in the Advanced LIGO and Virgo network
and about 61.1% of the time in real noise in the first observing run of
Advanced LIGO with significance. Analyses using this method are
performed on the data of Advanced LIGO's first observing run, and we find no
statistical significant evidence for the detection of gravitational-wave
echoes. In particular, we find combined evidence of the three events
in Advanced LIGO's first observing run. The analysis technique developed in
this paper is independent of the waveform model used, and can be used with
different parametrized echoes waveform models to provide more realistic
evidence of the existence of echoes from exotic compact objects.Comment: 16 pages, 6 figure
Rapid method for determination of antimicrobial susceptibilities pattern of urinary bacteria
Method determines bacterial sensitivity to antimicrobial agents by measuring level of adenosine triphosphate remaining in the bacteria. Light emitted during reaction of sample with a mixture of luciferase and luciferin is measured
Excitation Thresholds for Nonlinear Localized Modes on Lattices
Breathers are spatially localized and time periodic solutions of extended
Hamiltonian dynamical systems. In this paper we study excitation thresholds for
(nonlinearly dynamically stable) ground state breather or standing wave
solutions for networks of coupled nonlinear oscillators and wave equations of
nonlinear Schr\"odinger (NLS) type. Excitation thresholds are rigorously
characterized by variational methods. The excitation threshold is related to
the optimal (best) constant in a class of discr ete interpolation inequalities
related to the Hamiltonian energy. We establish a precise connection among ,
the dimensionality of the lattice, , the degree of the nonlinearity
and the existence of an excitation threshold for discrete nonlinear
Schr\"odinger systems (DNLS).
We prove that if , then ground state standing waves exist if
and only if the total power is larger than some strictly positive threshold,
. This proves a conjecture of Flach, Kaldko& MacKay in
the context of DNLS. We also discuss upper and lower bounds for excitation
thresholds for ground states of coupled systems of NLS equations, which arise
in the modeling of pulse propagation in coupled arrays of optical fibers.Comment: To appear in Nonlinearit
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