40,366 research outputs found
Out-of-equilibrium phase re-entrance(s) in long-range interacting systems
No full textSystems with long-range interactions display a short-time relaxation toward quasistationary states (QSSs) whose lifetime increases with system size. The application of Lynden-Bell’s theory of “violent relaxation” to the Hamiltonian Mean Field model leads to the prediction of out-of-equilibrium first- and second-order phase transitions between homogeneous (zero magnetization) and inhomogeneous (nonzero magnetization) QSSs, as well as an interesting phenomenon of phase re-entrances. We compare these theoretical predictions with direct N-body numerical simulations. We confirm the existence of phase re-entrance in the typical parameter range predicted from Lynden-Bell’s theory, but also show that the picture is more complicated than initially thought. In particular, we exhibit the existence of secondary re-entrant phases: we find unmagnetized states in the theoretically magnetized region as well as persisting magnetized states in the theoretically unmagnetized region. We also report the existence of a region with negative specific heats for QSSs both in the numerical and analytical caloric curves
Dynamical and thermodynamical stability of two-dimensional flows: variational principles and relaxation equations
No full textWe review and connect different variational principles that have been proposed to settle the dynamical and thermodynamical stability of two-dimensional incompressible and inviscid flows governed by the 2D Euler equation. These variational principles involve functionals of a very wide class that go beyond the usual Boltzmann functional. We provide relaxation equations that can be used as numerical algorithms to solve these optimization problems. These relaxation equations have the form of nonlinear mean field Fokker-Planck equations associated with generalized “entropic”
functionals [P.H. Chavanis, Eur. Phys. J. B 62, 179 (2008)]
Negative Specific Heat in the Canonical Statistical Ensemble
No full textAccording to thermodynamics, the specific heat of Boltzmannian short-range interacting systems is a positive quantity. Less intuitive properties are instead displayed by systems characterized by long-range interactions. In that case, the sign of specific heat depends on the considered statistical ensemble: Negative specific heat can be found in isolated systems, which are studied in the framework of the microcanonical ensemble; on the other hand, it is generally recognized that a positive specific heat should always be measured in systems in contact with a thermal bath, for which the canonical ensemble is the appropriate one. We demonstrate that the latter assumption is not generally true: One can, in principle, measure negative specific heat also in the canonical ensemble if the system under scrutiny is non-Boltzmannian and/or out-of-equilibrium
A 2 h periodic variation in the low-mass X-ray binary Ser X-1
No full textSpectroscopy of the low-mass X-ray binary Ser X-1 using the Gran Telescopio Canarias have revealed a ?2 h periodic variability that is present in the three strongest emission lines. We tentatively interpret this variability as due to orbital motion, making it the first indication of the orbital period of Ser X-1. Together with the fact that the emission lines are remarkably narrow, but still resolved, we show that a main-sequence K dwarf together with a canonical 1.4 M? neutron star gives a good description of the system. In this scenario, the most likely place for the emission lines to arise is the accretion disc, instead of a localized region in the binary (such as the irradiated surface or the stream-impact point), and their narrowness is due instead to the low inclination (?10°) of Ser X-1
On the lifetime of metastable states in self-gravitating systems
No full textWe discuss the physical basis of the statistical
mechanics of self-gravitating systems. We show the correspondance
between statistical mechanics methods based on the evaluation of
the density of states and partition function and thermodynamical
methods based on the optimization of a thermodynamical potential
(entropy or free energy). We address the question of the
thermodynamic limit of self-gravitating systems, the justification
of the mean-field approximation, the validity of the saddle point
approximation near the transition point, the lifetime of metastable
states and the fluctuations in isothermal spheres. In particular,
we emphasize the tremendously long lifetime of metastable states of
self-gravitating systems which increases exponentially with the
number of particles N except in the vicinity of the critical
point. More specifically, using an adaptation of the Kramers
formula justified by a kinetic theory, we show that the lifetime of
a metastable state scales as in microcanonical
ensemble and in canonical ensemble, where and are the barriers of entropy and free energy
per particle respectively. The physical
caloric curve must take these metastable states (local entropy
maxima) into account. As a result, it becomes multi-valued and
leads to microcanonical phase transitions and “dinosaur's necks”
(Chavanis [CITE], [arXiv:astroph/0205426
Classification of robust isolated vortices in two-dimensional hydrodynamics
No full textWe determine solutions of the Euler equation
representing isolated vortices (monopoles,
dipoles) in an infinite domain, for arbitrary values of
energy, circulation, angular momentum and impulse. A linear
relationship between vorticity and stream function is
assumed inside the vortex (while the flow is irrotational
outside). The emergence of
these solutions in a turbulent flow is justified by the
statistical mechanics of continuous
vorticity fields. The additional restriction of mixing to a
‘maximum-entropy bubble’,
due to kinetic constraints, is assumed. The linear
relationship between vorticity and
stream function is obtained from the statistical theory in
the limit of strong mixing
(when constraints are weak). In this limit, maximizing
entropy becomes equivalent to
a kind of enstrophy minimization. New stability criteria
are investigated and imply
in particular that, in most cases, the vorticity must be
continuous (or slightly discontinuous) at the vortex boundary.
Then, the vortex radius is automatically determined
by the integral constraints and we can obtain a classification
of isolated vortices
such as monopoles and dipoles (rotating or translating) in
terms of a single control
parameter. This article generalizes the classification
obtained in a bounded domain
by Chavanis & Sommeria (1996).</jats:p
Statistical mechanics of Fofonoff flows in an oceanic basin
No full textWe study the minimization of potential enstrophy at fixed circulation and energy in an oceanic basin with arbitrary topography. For illustration, we consider a rectangular basin and a linear topography h=by which represents either a real bottom topography or the β-effect appropriate to oceanic situations. Our minimum enstrophy principle is motivated by different arguments of statistical mechanics reviewed in the article. It leads to steady states of the quasigeostrophic (QG) equations characterized by a linear relationship between potential vorticity q and stream function ψ. For low values of the energy, we recover Fofonoff flows [J. Mar. Res. 13, 254 (1954)] that display a strong westward jet. For large values of the energy, we obtain geometry induced phase transitions between monopoles and dipoles similar to those found by Chavanis and Sommeria [J. Fluid Mech. 314, 267 (1996)] in the absence of topography. In the presence of topography, we recover and confirm the results obtained by Venaille and Bouchet [Phys. Rev. Lett. 102, 104501 (2009)] using a different formalism. In addition, we introduce relaxation equations towards minimum potential enstrophy states and perform numerical simulations to illustrate the phase transitions in a rectangular oceanic basin with linear topography (or β-effect). Copyright EDP Sciences, SIF, Springer-Verlag Berlin Heidelberg 2011
Relaxation equations for two-dimensional turbulent flows with a prior vorticity distribution
No full textUsing a Maximum Entropy Production Principle (MEPP), we derive a new type of relaxation equations for two-dimensional turbulent flows in the case where a prior vorticity distribution is prescribed instead of the Casimir constraints [R. Ellis, K. Haven, B. Turkington, Nonlinearity 15, 239 (2002)]. The particular case of a Gaussian prior is specifically treated in connection to minimum enstrophy states and Fofonoff flows. These relaxation equations are compared with other relaxation equations proposed by Robert and Sommeria [Phys. Rev. Lett. 69, 2776 (1992)] and Chavanis [Physica D 237, 1998 (2008)]. They can serve as numerical algorithms to compute maximum entropy states and minimum enstrophy states with appropriate constraints. We perform numerical simulations of these relaxation equations in order to illustrate geometry induced phase transitions in geophysical flows. Copyright EDP Sciences, SIF, Springer-Verlag Berlin Heidelberg 2010
Efficient p-Multigrid Based Solvers for Isogeometric Analysis on Multipatch Geometries
No full textIsogeometric Analysis can be considered as the natural extension of the Finite Element Method (FEM) to higher-order spline based discretizations simplifying the treatment of complex geometries with curved boundaries. Finding a solution of the resulting linear systems of equations efficiently remains, however, a challenging task. Recently, p-multigrid methods have been considered [18], in which a multigrid hierarchy is constructed based on different approximation orders p instead of mesh widths h as it would be the case in classical h-multigrid schemes [8]. The use of an Incomplete LU-factorization as a smoother within the p-multigrid method has shown to lead to convergence rates independent of both h and p for single patch geometries [19]. In this paper, the focus lies on the application of the aforementioned p-multigrid method on multipatch geometries having a C0-continuous coupling between the patches. The use of ILUT as a smoother within p-multigrid methods leads to convergence rates that are essentially independent of h and p, but depend mildly on the number of patches.Green Open Access added to TU Delft Institutional Repository ‘You share, we take care!’ – Taverne project https://www.openaccess.nl/en/you-share-we-take-care Otherwise as indicated in the copyright section: the publisher is the copyright holder of this work and the author uses the Dutch legislation to make this work public.Numerical Analysi
Going Beyond Counting First Authors in Author Co-citation Analysis
No full textThe present study examines one of the fundamental aspects of author co-citation analysis (ACA) - the way co-citation
counts are defined. Co-citation counting provides the data on which all subsequent statistical analyses and mappings
are based, and we compare ACA results based on two different types of co-citation counting - the traditional type that
only counts the first one among a cited work's authors on the one hand and a non-traditional type that takes into
account the first 5 authors of a cited work on the other hand. Results indicate that the picture produced through this non-traditional author co-citation counting contains more coherent author groups and is therefore considerably clearer. However, this picture represents fewer specialties in the research field being studied than that produced through the traditional first-author co-citation counting when the same number of top-ranked authors is selected and analyzed. Reasons for these effects are discussed
- …
