6,966 research outputs found
Fluid-solid transition in hard hyper-sphere systems
In this work we present a numerical study, based on molecular dynamics
simulations, to estimate the freezing point of hard spheres and hypersphere
systems in dimension D = 4, 5, 6 and 7. We have studied the changes of the
Radial Distribution Function (RDF) as a function of density in the coexistence
region. We started our simulations from crystalline states with densities above
the melting point, and moved down to densities in the liquid state below the
freezing point. For all the examined dimensions (including D = 3) it was
observed that the height of the first minimum of the RDF changes in an almost
continuous way around the freezing density and resembles a second order phase
transition. With these results we propose a numerical method to estimate the
freezing point as a function of the dimension D using numerical fits and
semiempirical approaches. We find that the estimated values of the freezing
point are very close to previously reported values from simulations and
theoretical approaches up to D = 6 reinforcing the validity of the proposed
method. This was also applied to numerical simulations for D = 7 giving new
estimations of the freezing point for this dimensionality.Comment: 13 pages, 10 figure
On the liquid-glass transition line in monatomic Lennard-Jones fluids
A thermodynamic approach to derive the liquid-glass transition line in the
reduced temperature vs reduced density plane for a monatomic Lennard-Jones
fluid is presented. The approach makes use of a recent reformulation of the
classical perturbation theory of liquids [M. Robles and M. L\'opez de Haro,
Phys. Chem. Chem. Phys. {\bf 3}, 5528 (2001)] which is at grips with a rational
function approximation for the Laplace transform of the radial distribution
function of the hard-sphere fluid. The only input required is an equation of
state for the hard-sphere system. Within the Mansoori-Canfield/Rasaiah-Stell
variational perturbation theory, two choices for such an equation of state,
leading to a glass transition for the hard-sphere fluid, are considered. Good
agreement with the liquid-glass transition line derived from recent molecular
dynamic simulations [Di Leonardo et al., Phys. Rev. Lett. {\bf 84}, 6054(2000)]
is obtained.Comment: 4 pages, 2 figure
The Einstein-Boltzmann Relation for Thermodynamic and Hydrodynamic Fluctuations
When making the connection between the thermodynamics of irreversible
processes and the theory of stochastic processes through the
fluctuation-dissipation theorem, it is necessary to invoke a postulate of the
Einstein-Boltzmann type. For convective processes hydrodynamic fluctuations
must be included, the velocity is a dynamical variable and although the entropy
cannot depend directly on the velocity, will depend on velocity
variations. Some authors do not include velocity variations in ,
and so have to introduce a non-thermodynamic function which replaces the
entropy and does depend on the velocity. At first sight, it seems that the
introduction of such a function requires a generalisation of the
Einstein-Boltzmann relation to be invoked. We review the reason why it is not
necessary to introduce such a function, and therefore why there is no need to
generalise the Einstein-Boltzmann relation in this way. We then obtain the
fluctuation-dissipation theorem which shows some differences as compared with
the non-convective case. We also show that is a Liapunov
function when it includes velocity fluctuations.Comment: 13 Page
Dual contribution to amplification in the mammalian inner ear
The inner ear achieves a wide dynamic range of responsiveness by mechanically
amplifying weak sounds. The enormous mechanical gain reported for the mammalian
cochlea, which exceeds a factor of 4,000, poses a challenge for theory. Here we
show how such a large gain can result from an interaction between amplification
by low-gain hair bundles and a pressure wave: hair bundles can amplify both
their displacement per locally applied pressure and the pressure wave itself. A
recently proposed ratchet mechanism, in which hair-bundle forces do not feed
back on the pressure wave, delineates the two effects. Our analytical
calculations with a WKB approximation agree with numerical solutions.Comment: 4 pages, 4 figure
Reducing the fine-tuning of gauge-mediated SUSY breaking
Despite their appealing features, models with gauge-mediated supersymmetry
breaking (GMSB) typically present a high degree of fine-tuning, due to the
initial absence of the top trilinear scalar couplings, . In this paper,
we carefully evaluate such a tuning, showing that is worse than per mil in the
minimal model. Then, we examine some existing proposals to generate
term in this context. We find that, although the stops can be made lighter,
usually the tuning does not improve (it may be even worse), with some
exceptions, which involve the generation of at one loop or tree level. We
examine both possibilities and propose a conceptually simplified version of the
latter; which is arguably the optimum GMSB setup (with minimal matter content),
concerning the fine-tuning issue. The resulting fine-tuning is better than one
per mil, still severe but similar to other minimal supersymmetric standard
model constructions. We also explore the so-called "little
problem", i.e. the fact that a large -term is normally accompanied by a
similar or larger sfermion mass, which typically implies an increase in the
fine-tuning. Finally, we find the version of GMSB for which this ratio is
optimized, which, nevertheless, does not minimize the fine-tuning.Comment: 16 pages, 11 figures, 1 appendix. Discussion extended, matches EPJC
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