73 research outputs found
Core-halo distribution in the Hamiltonian Mean-Field Model
We study a paradigmatic system with long-range interactions: the Hamiltonian
Mean-Field Model (HMF). It is shown that in the thermodynamic limit this model
does not relax to the usual equilibrium Maxwell-Boltzmann distribution.
Instead, the final stationary state has a peculiar core-halo structure. In the
thermodynamic limit, HMF is neither ergodic nor mixing. Nevertheless, we find
that using dynamical properties of Hamiltonian systems, it is possible to
quantitatively predict both the spin distribution and the velocity distribution
functions in the final stationary state, without any adjustable parameters. We
also show that HMF undergoes a non-equilibrium first-order phase transition
between paramagnetic and ferromagnetic states
Statistical Mechanics of Unbound Two Dimensional Self-Gravitating Systems
We study, using both theory and molecular dynamics simulations, the
relaxation dynamics of a microcanonical two dimensional self-gravitating
system. After a sufficiently large time, a gravitational cluster of N particles
relaxes to the Maxwell-Boltzmann distribution. The time to reach the
thermodynamic equilibrium, however, scales with the number of particles. In the
thermodynamic limit, at fixed total mass, equilibrium state is
never reached and the system becomes trapped in a non-ergodic stationary state.
An analytical theory is presented which allows us to quantitatively described
this final stationary state, without any adjustable parameters
Microcanonical Analysis of Exactness of the Mean-Field Theory in Long-Range Interacting Systems
Classical spin systems with nonadditive long-range interactions are studied
in the microcanonical ensemble. It is expected that the entropy of such a
system is identical to that of the corresponding mean-field model, which is
called "exactness of the mean-field theory". It is found out that this
expectation is not necessarily true if the microcanonical ensemble is not
equivalent to the canonical ensemble in the mean-field model. Moreover,
necessary and sufficient conditions for exactness of the mean-field theory are
obtained. These conditions are investigated for two concrete models, the
\alpha-Potts model with annealed vacancies and the \alpha-Potts model with
invisible states.Comment: 23 pages, to appear in J. Stat. Phy
Collisionless relaxation in gravitational systems: From violent relaxation to gravothermal collapse
Theory and simulations are used to study collisionless relaxation of a
gravitational -body system. It is shown that when the initial one particle
distribution function satisfies the virial condition -- potential energy is
minus twice the kinetic energy -- the system quickly relaxes to a metastable
state described {\it quantitatively} by the Lynden-Bell distribution with a
cutoff. If the initial distribution function does not meet the virial
requirement, the system undergoes violent oscillations, resulting in a partial
evaporation of mass. The leftover particles phase separate into a core-halo
structure. The theory presented allows us to quantitatively predict the amount
and the distribution of mass left in the central core, without any adjustable
parameters. On a longer time scale collisionless relaxation
leads to a gravothermal collapse
Phase transitions of quasistationary states in the Hamiltonian Mean Field model
The out-of-equilibrium dynamics of the Hamiltonian Mean Field (HMF) model is
studied in presence of an externally imposed magnetic field h. Lynden-Bell's
theory of violent relaxation is revisited and shown to adequately capture the
system dynamics, as revealed by direct Vlasov based numerical simulations in
the limit of vanishing field. This includes the existence of an
out-of-equilibrium phase transition separating magnetized and non magnetized
phases. We also monitor the fluctuations in time of the magnetization, which
allows us to elaborate on the choice of the correct order parameter when
challenging the performance of Lynden-Bell's theory. The presence of the field
h removes the phase transition, as it happens at equilibrium. Moreover, regions
with negative susceptibility are numerically found to occur, in agreement with
the predictions of the theory.Comment: 6 pages, 7 figure
Controlling chaos in wave-particle interactions
We analyze the behavior of a relativistic particle moving under the influence
of a uniform magnetic field and a stationary electrostatic wave. We work with a
set of pulsed waves that allows us to obtain an exact map for the system. We
also use a method of control for near-integrable Hamiltonians that consists in
the addition of a small and simple control term to the system. This control
term creates invariant tori in phase space that prevent chaos from spreading to
large regions and make the controlled dynamics more regular. We show
numerically that the control term just slightly modifies the system but is able
to drastically reduce chaos with a low additional cost of energy. Moreover, we
discuss how the control of chaos and the consequent recovery of regular
trajectories in phase space are useful to improve regular particle
acceleration.Comment: 8 pages, 2 figures. Published in Physical Review
Fast Retinal Vessel Detection and Measurement Using Wavelets and Edge Location Refinement
The relationship between changes in retinal vessel morphology and the onset and progression of diseases such as diabetes, hypertension and retinopathy of prematurity (ROP) has been the subject of several large scale clinical studies. However, the difficulty of quantifying changes in retinal vessels in a sufficiently fast, accurate and repeatable manner has restricted the application of the insights gleaned from these studies to clinical practice. This paper presents a novel algorithm for the efficient detection and measurement of retinal vessels, which is general enough that it can be applied to both low and high resolution fundus photographs and fluorescein angiograms upon the adjustment of only a few intuitive parameters. Firstly, we describe the simple vessel segmentation strategy, formulated in the language of wavelets, that is used for fast vessel detection. When validated using a publicly available database of retinal images, this segmentation achieves a true positive rate of 70.27%, false positive rate of 2.83%, and accuracy score of 0.9371. Vessel edges are then more precisely localised using image profiles computed perpendicularly across a spline fit of each detected vessel centreline, so that both local and global changes in vessel diameter can be readily quantified. Using a second image database, we show that the diameters output by our algorithm display good agreement with the manual measurements made by three independent observers. We conclude that the improved speed and generality offered by our algorithm are achieved without sacrificing accuracy. The algorithm is implemented in MATLAB along with a graphical user interface, and we have made the source code freely available
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