7,586 research outputs found
Combined Solar System and rotation curve constraints on MOND
The Modified Newtonian Dynamics (MOND) paradigm generically predicts that the
external gravitational field in which a system is embedded can produce effects
on its internal dynamics. In this communication, we first show that this
External Field Effect can significantly improve some galactic rotation curves
fits by decreasing the predicted velocities of the external part of the
rotation curves. In modified gravity versions of MOND, this External Field
Effect also appears in the Solar System and leads to a very good way to
constrain the transition function of the theory. A combined analysis of the
galactic rotation curves and Solar System constraints (provided by the Cassini
spacecraft) rules out several classes of popular MOND transition functions, but
leaves others viable. Moreover, we show that LISA Pathfinder will not be able
to improve the current constraints on these still viable transition functions.Comment: 13 pages, 7 figures, accepted for publication in MNRA
Basins of attraction in forced systems with time-varying dissipation
We consider dissipative periodically forced systems and investigate cases in
which having information as to how the system behaves for constant dissipation
may be used when dissipation varies in time before settling at a constant final
value. First, we consider situations where one is interested in the basins of
attraction for damping coefficients varying linearly between two given values
over many different time intervals: we outline a method to reduce the
computation time required to estimate numerically the relative areas of the
basins and discuss its range of applicability. Second, we observe that
sometimes very slight changes in the time interval may produce abrupt large
variations in the relative areas of the basins of attraction of the surviving
attractors: we show how comparing the contracted phase space at a time after
the final value of dissipation has been reached with the basins of attraction
corresponding to that value of constant dissipation can explain the presence of
such variations. Both procedures are illustrated by application to a pendulum
with periodically oscillating support.Comment: 16 pages, 13 figures, 7 table
Power computation for the triboelectric nanogenerator
We consider, from a mathematical perspective, the power generated by a
contact-mode triboelectric nanogenerator, an energy harvesting device that has
been well studied recently. We encapsulate the behaviour of the device in a
differential equation, which although linear and of first order, has periodic
coefficients, leading to some interesting mathematical problems. In studying
these, we derive approximate forms for the mean power generated and the current
waveforms, and describe a procedure for computing the Fourier coefficients for
the current, enabling us to show how the power is distributed over the
harmonics. Comparisons with accurate numerics validate our analysis
Quasi-periodic attractors, Borel summability and the Bryuno condition for strongly dissipative systems
We consider a class of ordinary differential equations describing
one-dimensional analytic systems with a quasi-periodic forcing term and in the
presence of damping. In the limit of large damping, under some generic
non-degeneracy condition on the force, there are quasi-periodic solutions which
have the same frequency vector as the forcing term. We prove that such
solutions are Borel summable at the origin when the frequency vector is either
any one-dimensional number or a two-dimensional vector such that the ratio of
its components is an irrational number of constant type. In the first case the
proof given simplifies that provided in a previous work of ours. We also show
that in any dimension , for the existence of a quasi-periodic solution with
the same frequency vector as the forcing term, the standard Diophantine
condition can be weakened into the Bryuno condition. In all cases, under a
suitable positivity condition, the quasi-periodic solution is proved to
describe a local attractor.Comment: 10 page
Modified Baryonic Dynamics: two-component cosmological simulations with light sterile neutrinos
In this article we continue to test cosmological models centred on Modified
Newtonian Dynamics (MOND) with light sterile neutrinos, which could in
principle be a way to solve the fine-tuning problems of the standard model on
galaxy scales while preserving successful predictions on larger scales. Due to
previous failures of the simple MOND cosmological model, here we test a
speculative model where the modified gravitational field is produced only by
the baryons and the sterile neutrinos produce a purely Newtonian field (hence
Modified Baryonic Dynamics). We use two component cosmological simulations to
separate the baryonic N-body particles from the sterile neutrino ones. The
premise is to attenuate the over-production of massive galaxy cluster halos
which were prevalent in the original MOND plus light sterile neutrinos
scenario. Theoretical issues with such a formulation notwithstanding, the
Modified Baryonic Dynamics model fails to produce the correct amplitude for the
galaxy cluster mass function for any reasonable value of the primordial power
spectrum normalisation.Comment: 11 pages, 2 figures. Submitted to JCA
The Galactic potential and the asymmetric distribution of hypervelocity stars
In recent years several hypervelocity stars (HVSs) have been observed in the
halo of our Galaxy. Such HVSs have possibly been ejected from the Galactic
center and then propagated in the Galactic potential up to their current
position. The recent survey for candidate HVSs show an asymmetry in the
kinematics of candidate HVSs (position and velocity vectors), where more
outgoing stars than ingoing stars (i.e. positive Galactocentric velocities vs.
negative ones) are observed. We show that such kinematic asymmetry, which is
likely due to the finite lifetime of the stars and Galactic potential
structure, could be used in a novel method to probe and constrain the Galactic
potential, identify the stellar type of the stars in the survey and estimate
the number of HVSs. Kinematics-independent identification of the stellar types
of the stars in such surveys (e.g. spectroscopic identification) could further
improve these results. We find that the observed asymmetry between ingoing and
outgoing stars favors specific Galactic potential models. It also implies a
lower limit of ~54+-8 main sequence HVSs in the survey sample (>=648+-96 in the
Galaxy), assuming that all of the main sequence stars in the survey originate
from the Galactic center. The other stars in the survey are likely to be hot
blue horizontal branch stars born in the halo rather than stars ejected from
the Galactic center.Comment: 7 pages, 3 figures. Added an appendix. Accepted to Ap
The wedding of modified dynamics and non-exotic dark matter in galaxy clusters
We summarize the status of Modified Newtonian Dynamics (MOND) in galaxy
clusters. The observed acceleration is typically larger than the acceleration
threshold of MOND in the central regions, implying that some dark matter is
necessary to explain the mass discrepancy there. A plausible resolution of this
issue is that the unseen mass in MOND is in the form of ordinary neutrinos with
masses just below the experimentally detectable limit. In particular, we show
that the lensing mass reconstructions of the clusters 1E0657-56 (the bullet
cluster) and Cl0024+17 (the ring) do not pose a new challenge to this scenario.
However, the mass discrepancy for cool X-ray emitting groups, in which
neutrinos cannot cluster, pose a more serious problem, meaning that dark
baryons could present a more satisfactory solution to the problem of unseen
mass in MOND clusters.Comment: to appear in World Scientific, proceedings of DARK 200
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