121 research outputs found
Solvable model of a self-gravitating system
We introduce and discuss an effective model of a self-gravitating system
whose equilibrium thermodynamics can be solved in both the microcanonical and
the canonical ensemble, up to a maximization with respect to a single variable.
Such a model can be derived from a model of self-gravitating particles confined
on a ring, referred to as the self-gravitating ring (SGR) model, allowing a
quantitative comparison between the thermodynamics of the two models. Despite
the rather crude approximations involved in its derivation, the effective model
compares quite well with the SGR model. Moreover, we discuss the relation
between the effective model presented here and another model introduced by
Thirring forty years ago. The two models are very similar and can be considered
as examples of a class of minimal models of self-gravitating systems.Comment: 21 pages, 6 figures; submitted to JSTAT for the special issue on
long-range interaction
Energy landscape and phase transitions in the self-gravitating ring model
We apply a recently proposed criterion for the existence of phase
transitions, which is based on the properties of the saddles of the energy
landscape, to a simplified model of a system with gravitational interactions,
referred to as the self-gravitating ring model. We show analytically that the
criterion correctly singles out the phase transition between a homogeneous and
a clustered phase and also suggests the presence of another phase transition,
not previously known. On the basis of the properties of the energy landscape we
conjecture on the nature of the latter transition
On a microcanonical relation between continuous and discrete spin models
A relation between a class of stationary points of the energy landscape of
continuous spin models on a lattice and the configurations of a Ising model
defined on the same lattice suggests an approximate expression for the
microcanonical density of states. Based on this approximation we conjecture
that if a O(n) model with ferromagnetic interactions on a lattice has a phase
transition, its critical energy density is equal to that of the n = 1 case,
i.e., a system of Ising spins with the same interactions. The conjecture holds
true in the case of long-range interactions. For nearest-neighbor interactions,
numerical results are consistent with the conjecture for n=2 and n=3 in three
dimensions. For n=2 in two dimensions (XY model) the conjecture yields a
prediction for the critical energy of the Berezinskij-Kosterlitz-Thouless
transition, which would be equal to that of the two-dimensional Ising model. We
discuss available numerical data in this respect.Comment: 5 pages, no figure
Geometry of the energy landscape of the self-gravitating ring
We study the global geometry of the energy landscape of a simple model of a
self-gravitating system, the self-gravitating ring (SGR). This is done by
endowing the configuration space with a metric such that the dynamical
trajectories are identified with geodesics. The average curvature and curvature
fluctuations of the energy landscape are computed by means of Monte Carlo
simulations and, when possible, of a mean-field method, showing that these
global geometric quantities provide a clear geometric characterization of the
collapse phase transition occurring in the SGR as the transition from a flat
landscape at high energies to a landscape with mainly positive but fluctuating
curvature in the collapsed phase. Moreover, curvature fluctuations show a
maximum in correspondence with the energy of a possible further transition,
occurring at lower energies than the collapse one, whose existence had been
previously conjectured on the basis of a local analysis of the energy landscape
and whose effect on the usual thermodynamic quantities, if any, is extremely
weak. We also estimate the largest Lyapunov exponent of the SGR using
the geometric observables. The geometric estimate always gives the correct
order of magnitude of and is also quantitatively correct at small
energy densities and, in the limit , in the whole homogeneous
phase.Comment: 20 pages, 12 figure
Topological origin of the phase transition in a mean-field model
We argue that the phase transition in the mean-field XY model is related to a
particular change in the topology of its configuration space. The nature of
this topological transition can be discussed on the basis of elementary Morse
theory using the potential energy per particle V as a Morse function. The value
of V where such a topological transition occurs equals the thermodynamic value
of V at the phase transition and the number of (Morse) critical points grows
very fast with the number of particles N. Furthermore, as in statistical
mechanics, also in topology the way the thermodynamic limit is taken is
crucial.Comment: REVTeX, 5 pages, with 1 eps figure included. Some changes in the
text. To appear in Physical Review Letter
The NY-Ålesund TurbulencE Fiber Optic eXperiment (NYTEFOX): investigating the Arctic boundary layer, Svalbard
The NY-Ålesund TurbulencE Fiber Optic eXperiment (NYTEFOX) was a field experiment at the
Ny-Ålesund Arctic site (78.9◦ N, 11.9◦ E) and yielded a unique meteorological data set. These data describe the
distribution of heat, airflows, and exchange in the Arctic boundary layer for a period of 14 d from 26 February
to 10 March 2020. NYTEFOX is the first field experiment to investigate the heterogeneity of airflow and its
transport of temperature, wind, and kinetic energy in the Arctic environment using the fiber-optic distributed
sensing (FODS) technique for horizontal and vertical observations. FODS air temperature and wind speed were
observed at a spatial resolution of 0.127 m and a temporal resolution of 9 s along a 700 m horizontal array at
1 m above ground level (a.g.l.) and along three 7 m vertical profiles. Ancillary data were collected from three
sonic anemometers and an acoustic profiler (minisodar; sodar is an acronym for “sound detection and ranging”)
yielding turbulent flow statistics and vertical profiles in the lowest 300 m a.g.l., respectively. The observations
from this field campaign are publicly available on Zenodo (https://doi.org/10.5281/zenodo.4756836, Huss et al.,
2021) and supplement the meteorological data set operationally collected by the Baseline Surface Radiation
Network (BSRN) at Ny-Ålesund, Svalbard
Topological aspects of geometrical signatures of phase transitions
Certain geometric properties of submanifolds of configuration space are
numerically investigated for classical lattice phi^4 models in one and two
dimensions. Peculiar behaviors of the computed geometric quantities are found
only in the two-dimensional case, when a phase transition is present. The
observed phenomenology strongly supports, though in an indirect way, a recently
proposed topological conjecture about a topology change of the configuration
space submanifolds as counterpart of a phase transition.Comment: REVTEX file, 4 pages, 5 figure
Geometric dynamical observables in rare gas crystals
We present a detailed description of how a differential geometric approach to
Hamiltonian dynamics can be used for determining the existence of a crossover
between different dynamical regimes in a realistic system, a model of a rare
gas solid. Such a geometric approach allows to locate the energy threshold
between weakly and strongly chaotic regimes, and to estimate the largest
Lyapunov exponent. We show how standard mehods of classical statistical
mechanics, i.e. Monte Carlo simulations, can be used for our computational
purposes. Finally we consider a Lennard Jones crystal modeling solid Xenon. The
value of the energy threshold turns out to be in excellent agreement with the
numerical estimate based on the crossover between slow and fast relaxation to
equilibrium obtained in a previous work by molecular dynamics simulations.Comment: RevTeX, 19 pages, 6 PostScript figures, submitted to Phys. Rev.
Riemannian theory of Hamiltonian chaos and Lyapunov exponents
This paper deals with the problem of analytically computing the largest
Lyapunov exponent for many degrees of freedom Hamiltonian systems. This aim is
succesfully reached within a theoretical framework that makes use of a
geometrization of newtonian dynamics in the language of Riemannian geometry. A
new point of view about the origin of chaos in these systems is obtained
independently of homoclinic intersections. Chaos is here related to curvature
fluctuations of the manifolds whose geodesics are natural motions and is
described by means of Jacobi equation for geodesic spread. Under general
conditions ane effective stability equation is derived; an analytic formula for
the growth-rate of its solutions is worked out and applied to the
Fermi-Pasta-Ulam beta model and to a chain of coupled rotators. An excellent
agreement is found the theoretical prediction and the values of the Lyapunov
exponent obtained by numerical simulations for both models.Comment: RevTex, 40 pages, 8 PostScript figures, to be published in Phys. Rev.
E (scheduled for November 1996
Chaos in effective classical and quantum dynamics
We investigate the dynamics of classical and quantum N-component phi^4
oscillators in the presence of an external field. In the large N limit the
effective dynamics is described by two-degree-of-freedom classical Hamiltonian
systems. In the classical model we observe chaotic orbits for any value of the
external field, while in the quantum case chaos is strongly suppressed. A
simple explanation of this behaviour is found in the change in the structure of
the orbits induced by quantum corrections. Consistently with Heisenberg's
principle, quantum fluctuations are forced away from zero, removing in the
effective quantum dynamics a hyperbolic fixed point that is a major source of
chaos in the classical model.Comment: 6 pages, RevTeX, 5 figures, uses psfig, changed indroduction and
conclusions, added reference
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