Statistical theory of thermal instability

By A. Illarionov, I. Igumenshchev. 1997

A new statistical approach is presented to study the thermal instability of an optically thin unmagnetized plasma. In the framework of this approach the time evolution of the mass distribution function over temperature ϕ(T) is calculated. Function ϕ(T) characterizes the statistical properties of the multiphase medium of arbitrarily spaced three-dimensional structure of arbitrary (small or large) temperature perturbations. We construct our theory under the isobarical condition (P = constant over space), which is satisfied in the short-wavelength limit of the perturbations. The developed theory is illustrated for the case of the thermal instability of a slowly expanding interstellar cloud (smooth scenario). Numerical solutions of equations of the statistical theory are constructed and compared with hydrodynamical solutions. The results of both approaches are identical in the short-wavelength range when the isobarity condition is satisfied. Also the limits of applicability of the statistical theory are estimated. The possible evolution of the initial spectrum of perturbations is discussed. The proposed theory and numerical models can be relevant to the formation of the two-phase medium in the ∼ 1 pc region around quasars. Then small warm (T ≃ 104 K) clouds are formed as the result of thermal instability in an expanded gas fragment, which is a product of either star–star or star–accretion disc collision.

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

Citations in the corpus

Composite quantile regression and the oracle Model Selection Theory (2008, background): “Fan and Li (2006) gave a comprehensive overview of recent advances in variable selection.”
ON THE ADAPTIVE ELASTIC-NET WITH A DIVERGING NUMBER OF PARAMETERS (2009, background): “Variable selection is fundamentally important for knowledge discovery with high-dimensional data [Fan and Li (2006)] and it could greatly enhance the prediction performance of the ﬁtted model.”
Asymptotic properties of bridge estimators in sparse high-dimensional regression models (2008, background): “For any given γ > 0, the value β̂n that minimizes (1) is called a bridge estimator [Frank and Friedman (1993) and Fu (1998)]. The bridge estimator includes two important special cases. When γ = 2, it is the familiar ridge estimator [Hoerl and Kennard (1970)]. When γ = 1, it is the LASSO estimator [T”
Bayesian variable selection for high dimensional generalized linear models : Convergence rates of the fitted densities (2007, methodology): “In contrast to these frequentist approaches based on optimization, the Bayesian method considered here has the attractive capability of presenting several likely models together with the corresponding posterior probabilities.”
Robust rank correlation based screening (2010, methodology): “To further improve estimation efficiency, Fan and Lv (2008) suggested a two-stage procedure. First, SIS is used as a fast but crude method of reducing the ultra-high dimensionality to a relatively large scale that is smaller than or equal to the sample size n; then, a more sophisticated technique ca”
On the “degrees of freedom” of the lasso (2007, unknown): “The Annals of Statistics 2007, Vol. 35, No. 5, 2173–2192 DOI: 10.1214/009053607000000127 © Institute of Mathematical Statistics, 2007”