579 research outputs found
Sensitivity analysis of chaotic systems using a frequency-domain shadowing approach
We present a frequency-domain method for computing the sensitivities of
time-averaged quantities of chaotic systems with respect to input parameters.
Such sensitivities cannot be computed by conventional adjoint analysis tools,
because the presence of positive Lyapunov exponents leads to exponential growth
of the adjoint variables. The proposed method is based on the least-square
shadowing (LSS) approach [1], that formulates the evaluation of sensitivities
as an optimisation problem, thereby avoiding the exponential growth of the
solution. However, all existing formulations of LSS (and its variants) are in
the time domain and the computational cost scales with the number of positive
Lyapunov exponents. In the present paper, we reformulate the LSS method in the
Fourier space using harmonic balancing. The new method is tested on the
Kuramoto-Sivashinski system and the results match with those obtained using the
standard time-domain formulation. Although the cost of the direct solution is
independent of the number of positive Lyapunov exponents, storage and computing
requirements grow rapidly with the size of the system. To mitigate these
requirements, we propose a resolvent-based iterative approach that needs much
less storage. Application to the Kuramoto-Sivashinski system gave accurate
results with very low computational cost. The method is applicable to large
systems and paves the way for application of the resolvent-based shadowing
approach to turbulent flows. Further work is needed to assess its performance
and scalability
Slowly-rotating compact objects: the nonintegrability of Hartle-Thorne particle geodesics
X-ray astronomy provides information regarding the electromagnetic emission
of active galactic nuclei and X-ray binaries. These events provide details
regarding the astrophysical environment of black holes and stars, and help us
understand gamma-ray bursts. They produce estimates for the maximum mass of
neutron stars and eventually will contribute to the discovery of their equation
of state. Thus, it is crucial to study these configurations to increase the
yield of X-ray astronomy when combined with multimessenger gravitational-wave
astrophysics and black hole shadows. Unfortunately, an exact solution of the
field equations does not exist for neutron stars. Nevertheless, there exist a
variety of approximate compact objects that may characterize massive or neutron
stars. The most studied approximation is the Hartle-Thorne metric that
represents slowly-rotating compact objects, like massive stars, white dwarfs
and neutron stars. Recent investigations of photon orbits and shadows of such
metric revealed that it exhibits chaos close to resonances. Here, we thoroughly
investigate particle orbits around the Hartle-Thorne spacetime. We perform an
exhaustive analysis of bound motion, by varying all parameters involved in the
system. We demonstrate that chaotic regions, known as Birkhoff islands, form
around resonances, where the ratio of the radial and polar frequency of
geodesics, known as the rotation number, is shared throughout the island. This
leads to the formation of plateaus in rotation curves during the most prominent
resonance, which designate nonintegrability. We measure their width and
show how each parameter affects it. The nonintegrability of Hartle-Thorne
metric may affect quasiperiodic oscillations of low-mass X-ray binaries, when
chaos is taken into account, and improve estimates of mass, angular momentum
and multipole moments of astrophysical compact objects.Comment: 12 pages, 5 figure
Bimetric-Affine Quadratic Gravity
Bimetric gravity, is a theory of gravity that posits the existence of two
interacting and dynamical metric tensors. The spectrum of bimetric gravity
consists of a massless and a massive spin-2 particle. The form of the
interactions between the two metrics and is
constrained by requiring absence of the so called Boulware-Deser ghost. In this
work we extend the original bimetric theory to its bimetric-affine counterpart,
in which the two connections, associated with the Ricci scalars, are treated as
independent variables. We examine in detail the case of an additional quadratic
in the Ricci scalar curvature term and we find that
this theory is free of ghosts for a wide range of the interaction parameters,
not excluding the possibility of a Dark Matter interpretation of the massive
spin-2 particle.Comment: matches version to be published in PR
Sensitivity-enhanced generalized polynomial chaos for efficient uncertainty quantification
We present an enriched formulation of the Least Squares (LSQ) regression
method for Uncertainty Quantification (UQ) using generalised polynomial chaos
(gPC). More specifically, we enrich the linear system with additional equations
for the gradient (or sensitivity) of the Quantity of Interest with respect to
the stochastic variables. This sensitivity is computed very efficiently for all
variables by solving an adjoint system of equations at each sampling point of
the stochastic space. The associated computational cost is similar to one
solution of the direct problem. For the selection of the sampling points, we
apply a greedy algorithm which is based on the pivoted QR decomposition of the
measurement matrix. We call the new approach sensitivity-enhanced generalised
polynomial chaos, or se-gPC. We apply the method to several test cases to test
accuracy and convergence with increasing chaos order, including an aerodynamic
case with stochastic parameters. The method is found to produce accurate
estimations of the statistical moments using the minimum number of sampling
points. The computational cost scales as , instead of
of the standard LSQ formulation, where is the number of stochastic
variables and the chaos order. The solution of the adjoint system of
equations is implemented in many computational mechanics packages, thus the
infrastructure exists for the application of the method to a wide variety of
engineering problems
Bimetric Starobinsky model
The bimetric theory of gravity is an extension of general relativity that
describes a massive spin- particle in addition to the standard massless
graviton. The theory is based on two dynamical metric tensors with their
interactions constrained by requiring the absence of the so-called
Boulware-Deser ghost. It has been realized that the quantum interactions of
matter fields with gravity are bound to generate modifications to the standard
Einstein-Hilbert action such as quadratic curvature terms. Such a quadratic
Ricci scalar term is present in the so-called Starobinsky model which has been
proven to be rather robust in its inflationary predictions. In the present
article we study a generalization of the Starobinsky model within the bimetric
theory and find that its inflationary behavior stays intact while keeping all
consistency requirements of the bimetric framework. The interpretation of the
massive spin-2 particle as dark matter remains a viable scenario, as in
standard bigravity.Comment: 7 pages, 3 figures, title slightly edited, matches published versio
Geodesics and gravitational waves in chaotic extreme-mass-ratio inspirals: the curious case of Zipoy-Voorhees black-hole mimickers
Due to the growing capacity of gravitational-wave astronomy and black-hole
imaging, we will soon be able to emphatically decide if astrophysical objects
lurking in galactic centers are black holes. Sgr A*, one of the most prolific
astronomical radio sources in our galaxy, is the focal point for tests of
general relativity. Current mass and spin constraints predict that the central
object of the Milky Way is supermassive and slowly rotating, thus can be
conservatively modeled as a Schwarzschild black hole. The well-established
presence of accretion disks and astrophysical environments around supermassive
objects can deform their geometry and complicate their observational scientific
yield. Here, we study extreme-mass-ratio binaries comprised of a minuscule
secondary object inspiraling onto a supermassive Zipoy-Voorhees compact object;
the simplest exact solution of general relativity that describes a static,
spheroidal deformation of Schwarzschild spacetime. We examine geodesics of
prolate and oblate deformations for generic orbits and reevaluate the
non-integrability of Zipoy-Voorhees spacetime through the existence of resonant
islands in the orbital phase space. By including radiation loss with
post-Newtonian techniques, we evolve stellar-mass secondary objects around a
supermassive Zipoy-Voorhees primary and find clear imprints of
non-integrability in these systems. The peculiar structure of the primary,
allows for, not only typical single crossings of transient resonant islands,
that are well-known for non-Kerr objects, but also inspirals that traverse
through several islands, in a brief period of time, that lead to multiple
glitches in the gravitational-wave frequency evolution of the binary. The
detectability of glitches with future spaceborne detectors can, therefore,
narrow down the parameter space of exotic solutions that, otherwise, can cast
identical shadows with black holes.Comment: 16 pages, 7 figures, minor revision, accepted for publication in
General Relativity and Gravitation, abstract minimally trimmed due to arxiv
limitation
Electron spin relaxation of N@C60 in CS2
We examine the temperature dependence of the relaxation times of the
molecules N@C60 and N@C70 (which comprise atomic nitrogen trapped within a
carbon cage) in liquid CS2 solution. The results are inconsistent with the
fluctuating zero field splitting (ZFS) mechanism, which is commonly invoked to
explain electron spin relaxation for S > 1/2 spins in liquid solution, and is
the mechanism postulated in the literature for these systems. Instead, we find
a clear Arrhenius temperature dependence for N@C60, indicating the spin
relaxation is driven primarily by an Orbach process. For the asymmetric N@C70
molecule, which has a permanent non-zero ZFS, we resolve an additional
relaxation mechanism caused by the rapid reorientation of its ZFS. We also
report the longest coherence time (T2) ever observed for a molecular electron
spin, being 0.25 ms at 170K.Comment: 6 pages, 6 figures V2: Updated to published versio
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