Effect of Power Law Rheology of Surroundings on the Gravitational Instability of a Viscous Layer

2013 ◽  
pp. 216-223
Author(s):  
A. T. Ismail-Zadeh ◽  
H. Huppert
Keyword(s):  
Power Law ◽  
Gravitational Instability ◽  
Viscous Layer

scholarly journals The role of interstellar filaments in the origin of the stellar initial mass function: Insights from Herschel observations

2015 ◽  
Vol 11 (A29B) ◽  
pp. 708-708
Author(s):  
Philippe André ◽  
Vera Könyves ◽  
Arabindo Roy ◽  
Doris Arzoumanian
Keyword(s):  
Power Law ◽  
Gravitational Instability ◽  
Mass Function ◽  
Mass Scale ◽  
Initial Mass Function ◽  
Initial Mass ◽  
Critical Threshold ◽  
Stellar Initial Mass Function ◽  
The Imf

AbstractThe origin of the stellar initial mass function (IMF) is one of the most debated issues in astrophysics. Two major features of the IMF are 1) a fairly robust power-law slope at the high-mass end (Salpeter 1955), and 2) a broad peak around ~ 0.3 M⊙ corresponding to a characteristic stellar mass scale (cf. Elmegreen et al. 2008). In recent years, the dominant theoretical model proposed to account for these features has been the “gravo-turbulent fragmentation” picture (e.g., Hennebelle & Chabrier 2008; Hopkins 2012) whereby the properties of interstellar turbulence lead to the Salpeter power law and gravity sets the characteristic mass scale (Jeans mass). We discuss modifications to this picture based on extensive submillimeter continuum imaging observations of nearby molecular clouds with the Herschel Space Observatory which emphasize the importance of filamentary geometry (André et al. 2010; Könyves et al. 2015). The Herschel results point to the key role of the quasi-universal filamentary structure pervading the cold interstellar medium and support a scenario in which star formation occurs in two main steps (cf. André et al. 2014): first, the dissipation of kinetic energy in large-scale turbulent MHD flows generates ~ 0.1 pc-wide filaments (Arzoumanian et al. 2011) in the cold ISM; second, the densest filaments grow and fragment into prestellar cores (and ultimately protostars) by gravitational instability above a critical threshold ~ 16 M⊙/pc in mass per unit length or ~ 160 M⊙/pc2 in gas surface density (AV ∼ 8). In our observationally-driven scenario, the dense cores making up the peak of the prestellar core mass function (CMF) - likely responsible for the peak of the IMF - result from gravitational fragmentation of filaments near the critical threshold for global gravitational instability. The power-law tail of the CMF/IMF arises from the growth of the Kolmogorov-like power spectrum of initial density fluctuations [P(k) ∝ k−1.6±0.3] measured along Herschel filaments (Roy et al. 2015), in agreement with the model by Inutsuka (2001), and from the power-law distribution of line masses observed for supercritical filaments.

Analysis of power law assumptions for short-period comets and Kuiper bodies

1999 ◽  
Vol 173 ◽  
pp. 289-293 ◽  
Author(s):  
J.R. Donnison ◽  
L.I. Pettit
Keyword(s):  
Power Law ◽  
Pareto Distribution ◽  
Limited Data ◽  
Short Period ◽  
Probability Plots ◽  
Exponential Probability

AbstractA Pareto distribution was used to model the magnitude data for short-period comets up to 1988. It was found using exponential probability plots that the brightness did not vary with period and that the cut-off point previously adopted can be supported statistically. Examination of the diameters of Trans-Neptunian bodies showed that a power law does not adequately fit the limited data available.

Hearing in Mice by GSR Audiometry: II. Magnitude of Unconditioned GSR as a Function of Intensity and Frequency Interactions

1968 ◽  
Vol 11 (1) ◽  
pp. 169-178 ◽  
Author(s):  
Alan Gill ◽  
Charles I. Berlin
Keyword(s):  
Power Law ◽  
Response Magnitude ◽  
Single Units ◽  
Spectral Content ◽  
Hearing Sensitivity ◽  
Subjective Magnitude ◽  
Orderly Fashion ◽  
Viiith Nerve

The unconditioned GSR’s elicited by tones of 60, 70, 80, and 90 dB SPL were largest in the mouse in the ranges around 10,000 Hz. The growth of response magnitude with intensity followed a power law (10 .17 to 10 .22 , depending upon frequency) and suggested that the unconditioned GSR magnitude assessed overall subjective magnitude of tones to the mouse in an orderly fashion. It is suggested that hearing sensitivity as assessed by these means may be closely related to the spectral content of the mouse’s vocalization as well as to the number of critically sensitive single units in the mouse’s VIIIth nerve.

How Useful is the Power Law of Practice for Recognizing Practice in Concentration Tests?

2007 ◽  
Vol 23 (3) ◽  
pp. 157-165 ◽  
Author(s):  
Carmen Hagemeister
Keyword(s):  
Logistic Regression ◽  
Reaction Time ◽  
Power Law ◽  
Error Rate ◽  
Reaction Times ◽  
Practice Effect ◽  
Practice Effects ◽  
Rate Decrease ◽  
Small Practice

Abstract. When concentration tests are completed repeatedly, reaction time and error rate decrease considerably, but the underlying ability does not improve. In order to overcome this validity problem this study aimed to test if the practice effect between tests and within tests can be useful in determining whether persons have already completed this test. The power law of practice postulates that practice effects are greater in unpracticed than in practiced persons. Two experiments were carried out in which the participants completed the same tests at the beginning and at the end of two test sessions set about 3 days apart. In both experiments, the logistic regression could indeed classify persons according to previous practice through the practice effect between the tests at the beginning and at the end of the session, and, less well but still significantly, through the practice effect within the first test of the session. Further analyses showed that the practice effects correlated more highly with the initial performance than was to be expected for mathematical reasons; typically persons with long reaction times have larger practice effects. Thus, small practice effects alone do not allow one to conclude that a person has worked on the test before.

Inverse Power Law Behavior in a Memory Scanning Experiment

2006 ◽  
Author(s):  
Gerardo Ramirez ◽  
Sonia Perez ◽  
John G. Holden
Keyword(s):  
Power Law ◽  
Inverse Power ◽  
Memory Scanning ◽  
Inverse Power Law

Saturation mechanism and generated viscosity in gravito-turbulent accretion disks

2020 ◽  
Vol 640 ◽  
pp. A53
Author(s):  
L. Löhnert ◽  
S. Krätschmer ◽  
A. G. Peeters
Keyword(s):  
Growth Rate ◽  
Numerical Simulations ◽  
Accretion Disks ◽  
Gravitational Instability ◽  
Turbulent Viscosity ◽  
Radial Distance ◽  
Maximum Growth ◽  
Wave Number ◽  
Radiative Cooling ◽  
Mixing Length

Here, we address the turbulent dynamics of the gravitational instability in accretion disks, retaining both radiative cooling and irradiation. Due to radiative cooling, the disk is unstable for all values of the Toomre parameter, and an accurate estimate of the maximum growth rate is derived analytically. A detailed study of the turbulent spectra shows a rapid decay with an azimuthal wave number stronger than ky−3, whereas the spectrum is more broad in the radial direction and shows a scaling in the range kx−3 to kx−2. The radial component of the radial velocity profile consists of a superposition of shocks of different heights, and is similar to that found in Burgers’ turbulence. Assuming saturation occurs through nonlinear wave steepening leading to shock formation, we developed a mixing-length model in which the typical length scale is related to the average radial distance between shocks. Furthermore, since the numerical simulations show that linear drive is necessary in order to sustain turbulence, we used the growth rate of the most unstable mode to estimate the typical timescale. The mixing-length model that was obtained agrees well with numerical simulations. The model gives an analytic expression for the turbulent viscosity as a function of the Toomre parameter and cooling time. It predicts that relevant values of α = 10−3 can be obtained in disks that have a Toomre parameter as high as Q ≈ 10.

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