Reply to the comment on V.A. Antonov and B.P. Kondrat’ev’s paper “On the magnitude of the earth’s inner core displacement”

Антонов, В. А.; Kondrat'ev, B. P.

doi:10.1134/s1069351306010101

Cited by 10 publications

(16 citation statements)

References 2 publications

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“…The same is true for a uniformly rotating viscous disks (Lynden-Bell & Pringle 1974). A somewhat more elaborate discussion on viscous disks can be found in Gammie (1996) and Antonov & Kondratyev (1995). All this implies that the Toomre criterion for stability of an inviscid disk Q := c s κ πGΣ > 1 (6) (where Q is called the Toomre parameter and κ is the epicyclic frequency 2 ; Toomre 1964; Goldreich & Lynden-Bell 1965) is not a valid criterion for stability in viscous disks.…”

Section: Gravitational Instability In Self-gravitating Accretion Disksmentioning

confidence: 66%

A Gravitational Instability-driven Viscosity in Self-gravitating Accretion Disks

Duschl¹,

Britsch²

2006

ApJ

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Section: Gravitational Instability In Self-gravitating Accretion Disksmentioning

confidence: 66%

A Gravitational Instability-driven Viscosity in Self-gravitating Accretion Disks

Duschl¹,

Britsch²

2006

ApJ

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“…Vortexes of two fundamentally different types are used for describing a highly swirling flow of gas in a channel [3][4][5].…”

Section: Mathematical Simulationmentioning

confidence: 99%

The structure of gasdynamic flow in a supersonic separator of natural gas

Malyshkina

2008

High Temp

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Results are given of calculations of flow within the two-dimensional Euler model of supersonic swirling flow of gas in a supersonic separator of natural gas. The formulation of the problem is given, numerical experiment is performed, and the basic parameters of gas flow (velocity components, pressure, and so on) are obtained as functions of radius. The process of relaxation of flow to steady state with the formation of shock wave is considered, and the shock wave structure is determined. The behavior of gasdynamic parameters is analyzed under conditions of separation in the region of shock wave and behind it.

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“…The standard statistical physics textbooks thus conclude that rigourously speaking there is no phase transitions in finite systems. However, as we have already mentioned, first for self-gravitating objects [2,26,31,69,70,71,72,73] and then in small systems [3,15,30,48,36,74,75,76,79,81] it was shown that phase transitions might be associated with the occurrence of negative microcanonical heat capacities. This can be generalized to the occurence of an inverted curvature of the thermodynamic potential of any ensemble keeping at least one extensive variable A L not orthogonal to the order parameter 7 [36,83].…”

Section: Phase Transitions In Finite Systemsmentioning

confidence: 99%

“…Moreover, such inequivalences may survive at the thermodynamic limit if forces are long ranged as for self gravitating objects [3,4]. In fact the characteristic of phase transitions in finite systems, and in particular the occurrence of a negative heat capacity, have first been discussed in the astrophysical context [2,31,26,69,70,71,72,73]. Since these pioneering works in astrophysics, an abundant literature is focused on the understanding of phase transition in small systems from a general point of view [15,30,36,74,75,76,77,78,79] or in the mean-field context [4,80] or for some specific systems such as metallic clusters [48,68] or nuclei [81] and even DNA [82].…”

Section: Definitions Of Phase Transitions In Finite Systemsmentioning

confidence: 99%

Phase Transitions in Finite Systems using Information Theory

Chomaz

Gulminelli²

2008

AIP Conference Proceedings

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Abstract. In this paper, we present the issues we consider as essential as far as the statistical mechanics of finite systems is concerned. In particular, we emphasis our present understanding of phase transitions in the framework of information theory. Information theory provides a thermodynamically-consistent treatment of finite, open, transient and expanding systems which are difficult problems in approaches using standard statistical ensembles.As an example, we analyze is the problem of boundary conditions, which in the framework of information theory must also be treated statistically. We recall that out of the thermodynamical limit the different ensembles are not equivalent and in particular they may lead to dramatically different equation of states, in the region of a first order phase transition. We recall the recent progresses achieved in the understanding of first-order phase transition in finite systems: the equivalence between the Yang-Lee theorem and the occurrence of bimodalities in the intensive ensemble and the presence of inverted curvatures of the thermodynamic potential of the associated extensive ensemble. We come back to the concept of order parameters and to the role of constraints on order parameters in order to predict the expected signature of first-order phase transition: in absence of any constraint (intensive ensemble) bimobality of the event distribution is expected while an inverted curvature of the thermodynamic potential is expected at a fixe value of the order parameter (extensive ensemble) in between the phases (coexistence zone). We stress that this discussion is not restricted to the possible occurrence of negative specific heat, but can also include negative compressibility's and negative susceptibilities, and in fact any curvature anomaly of the thermodynamic potential.

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Reply to the comment on V.A. Antonov and B.P. Kondrat’ev’s paper “On the magnitude of the earth’s inner core displacement”

Cited by 10 publications

References 2 publications

A Gravitational Instability-driven Viscosity in Self-gravitating Accretion Disks

A Gravitational Instability-driven Viscosity in Self-gravitating Accretion Disks

The structure of gasdynamic flow in a supersonic separator of natural gas

Phase Transitions in Finite Systems using Information Theory

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