1,243 research outputs found
Thermodynamics and collapse of self-gravitating Brownian particles in D dimensions
We address the thermodynamics (equilibrium density profiles, phase diagram,
instability analysis...) and the collapse of a self-gravitating gas of Brownian
particles in D dimensions, in both canonical and microcanonical ensembles. In
the canonical ensemble, we derive the analytic form of the density scaling
profile which decays as f(x)=x^{-\alpha}, with alpha=2. In the microcanonical
ensemble, we show that f decays as f(x)=x^{-\alpha_{max}}, where \alpha_{max}
is a non-trivial exponent. We derive exact expansions for alpha_{max} and f in
the limit of large D. Finally, we solve the problem in D=2, which displays
rather rich and peculiar features
Kinetic theory of point vortices: diffusion coefficient and systematic drift
We develop a kinetic theory for point vortices in two-dimensional
hydrodynamics. Using standard projection operator technics, we derive a
Fokker-Planck equation describing the relaxation of a ``test'' vortex in a bath
of ``field'' vortices at statistical equilibrium. The relaxation is due to the
combined effect of a diffusion and a drift. The drift is shown to be
responsible for the organization of point vortices at negative temperatures. A
description that goes beyond the thermal bath approximation is attempted. A new
kinetic equation is obtained which respects all conservation laws of the point
vortex system and satisfies a H-theorem. Close to equilibrium this equation
reduces to the ordinary Fokker-Planck equation.Comment: 50 pages. To appear in Phys. Rev.
Generalized thermodynamics and Fokker-Planck equations. Applications to stellar dynamics, two-dimensional turbulence and Jupiter's great red spot
We introduce a new set of generalized Fokker-Planck equations that conserve
energy and mass and increase a generalized entropy until a maximum entropy
state is reached. The concept of generalized entropies is rigorously justified
for continuous Hamiltonian systems undergoing violent relaxation. Tsallis
entropies are just a special case of this generalized thermodynamics.
Application of these results to stellar dynamics, vortex dynamics and Jupiter's
great red spot are proposed. Our prime result is a novel relaxation equation
that should offer an easily implementable parametrization of geophysical
turbulence. This relaxation equation depends on a single key parameter related
to the skewness of the fine-grained vorticity distribution. Usual
parametrizations (including a single turbulent viscosity) correspond to the
infinite temperature limit of our model. They forget a fundamental systematic
drift that acts against diffusion as in Brownian theory. Our generalized
Fokker-Planck equations may have applications in other fields of physics such
as chemotaxis for bacterial populations. We propose the idea of a
classification of generalized entropies in classes of equivalence and provide
an aesthetic connexion between topics (vortices, stars, bacteries,...) which
were previously disconnected.Comment: Submitted to Phys. Rev.
Relaxation equations for two-dimensional turbulent flows with a prior vorticity distribution
Using 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
[Ellis, Haven, Turkington, Nonlin., 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 provide a
small-scale parametrization of 2D turbulence or serve as numerical algorithms
to compute maximum entropy states with appropriate constraints. We perform
numerical simulations of these relaxation equations in order to illustrate
geometry induced phase transitions in geophysical flows.Comment: 21 pages, 9 figure
Introducing pattern graph rewriting in novel spatial aggregation procedures for a class of traffic assignment models
In this study two novel spatial aggregation methods are presented compatible with a class of traffic assignment models. Both methods are formalized using a category theoretical approach. While this type of formalization is new to the field of transport, it is well known in other fields that require tools to allow for reasoning on complex structures. The method presented stems from a method originally developed to deal with quantum physical processes. The first benefit of adopting this formalization technique is that it provides an intuitive graphical representation while having a rigorous mathematical underpinning. Secondly, it bears close resemblances to regular expressions and functional programming techniques giving insights in how to potentially construct solvers (i.e. algorithms). The aggregation methods proposed in this paper are compatible with traffic assignment procedures utilising a path travel time function consisting out of two components, namely (i) a flow invariant component representing free flow travel time, and (ii) a flow dependent component representing queuing delays. By exploiting the fact that, in practice, most large scale networks only have a small portion of the network exhibiting queuing delays, this method aims at decomposing the network into a constant free flowing part to compute once and a, much smaller, demand varying delay part that requires recomputation across demand scenarios. It is demonstrated that under certain conditions this procedure is lossless. On top of the decomposition method, a path set reduction method is proposed. This method reduces the path set to the minimal path set which further decreases computational cost. A large scale case study is presented to demonstrate the proposed methods can reduce computation times to less than 5% of the original without loss of accuracy
A lossless spatial aggregation procedure for a class of capacity constrained traffic assignment models incorporating point queues
In this paper two novel spatial aggregation procedures are proposed. A network aggregation procedure based on a travel time delay decomposition method and a zonal aggregation procedure based on a path redistribution scheme. The effectiveness of these procedures lies in the fact that they, unlike existing aggregation methods, exploit available information regarding the application context and the characteristics of the adopted traffic assignment procedure. The context considered involves all applications that require path and inter-zonal travel times as output. A typical example of such applications are quick-scan methods, which have become increasing popular in recent years. The proposed procedures are compatible with a class of traffic assignment procedures incorporating (residual) point queues. Furthermore, one can choose to combine network aggregation with zonal aggregation to increase the effectiveness of the procedure. Results are demonstrated via theoretical examples as well as a large-scale case study. In the case study it is shown that network loading times can be reduced to as little as 4% of the original situation without suffering any information loss
An efficient eventâbased algorithm for solving first order dynamic network loading problems
In this paper we will present a novel solution algorithm for the Generalised Link Transmission Model (G-LTM). It will utilise a truly event based approach supporting the generation of exact results, unlike its time discretised counterparts. Furthermore, it can also be configured to yield approximate results, when this approach is adopted its computational complexity decreases dramatically. It will be demonstrated on a theoretical as well as a real world network that when utilising fixed periods of stationary demands to mimic departure time demand fluctuations, this novel approach can be efficient while maintaining a high level of result accuracy. The link model is complemented by a generic node model formulation yielding a proper generic first order DNL solution algorithm
Non locality, closing the detection loophole and communication complexity
It is shown that the detection loophole which arises when trying to rule out
local realistic theories as alternatives for quantum mechanics can be closed if
the detection efficiency is larger than
where is the dimension of the entangled system. Furthermore it is argued
that this exponential decrease of the detector efficiency required to close the
detection loophole is almost optimal. This argument is based on a close
connection that exists between closing the detection loophole and the amount of
classical communication required to simulate quantum correlation when the
detectors are perfect.Comment: 4 pages Latex, minor typos correcte
Does quantum nonlocality irremediably conflict with Special Relativity?
We reconsider the problem of the compatibility of quantum nonlocality and the
requests for a relativistically invariant theoretical scheme. We begin by
discussing a recent important paper by T. Norsen [arXiv:0808.2178] on this
problem and we enlarge our considerations to give a general picture of the
conceptually relevant issue to which this paper is devoted.Comment: 18 pages, 1 figur
Dynamical stability of infinite homogeneous self-gravitating systems: application of the Nyquist method
We complete classical investigations concerning the dynamical stability of an
infinite homogeneous gaseous medium described by the Euler-Poisson system or an
infinite homogeneous stellar system described by the Vlasov-Poisson system
(Jeans problem). To determine the stability of an infinite homogeneous stellar
system with respect to a perturbation of wavenumber k, we apply the Nyquist
method. We first consider the case of single-humped distributions and show
that, for infinite homogeneous systems, the onset of instability is the same in
a stellar system and in the corresponding barotropic gas, contrary to the case
of inhomogeneous systems. We show that this result is true for any symmetric
single-humped velocity distribution, not only for the Maxwellian. If we
specialize on isothermal and polytropic distributions, analytical expressions
for the growth rate, damping rate and pulsation period of the perturbation can
be given. Then, we consider the Vlasov stability of symmetric and asymmetric
double-humped distributions (two-stream stellar systems) and determine the
stability diagrams depending on the degree of asymmetry. We compare these
results with the Euler stability of two self-gravitating gaseous streams.
Finally, we determine the corresponding stability diagrams in the case of
plasmas and compare the results with self-gravitating systems
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