Equation of state for all phases. Part 1.—Basic isothermal equation

1976 ◽  
Vol 72 (0) ◽  
pp. 273 ◽  
Author(s):  
E. A. Seibold
Keyword(s):  
Equation Of State ◽  
Isothermal Equation

An isothermal equation of state for solids

2004 ◽  
Vol 350 (4) ◽  
pp. 375-388 ◽  
Author(s):  
Papiya Bose Roy ◽  
Sushil Bose Roy
Keyword(s):  
Equation Of State ◽  
Isothermal Equation

scholarly journals Importance of radiative effects in gap opening by planets in protoplanetary disks

2020 ◽  
Vol 637 ◽  
pp. A50 ◽  
Author(s):  
Alexandros Ziampras ◽  
Wilhelm Kley ◽  
Cornelis P. Dullemond
Keyword(s):  
Equation Of State ◽  
Energy Equation ◽  
Protoplanetary Disks ◽  
Class Ii ◽  
Radiative Effects ◽  
Gap Opening ◽  
Isothermal Equation ◽  
Spiral Arm

Recent ALMA observations revealed concentric annular structures in several young class-II objects. In an attempt to produce the rings and gaps in some of these systems, they have been modeled numerically with a single embedded planet assuming a locally isothermal equation of state. This is often justified by observations targeting the irradiation-dominated outer regions of disks (approximately 100 au). We test this assumption by conducting hydrodynamics simulations of embedded planets in thin locally isothermal and radiative disks that mimic the systems HD 163296 and AS 209 in order to examine the effect of including the energy equation in a seemingly locally isothermal environment as far as planet–disk interaction is concerned. We find that modeling such disks with an ideal equation of state makes a difference in terms of the number of produced rings and the spiral arm contrast in the disk. Locally isothermal disks produce sharper annular or azimuthal features and overestimate a single planet’s gap-opening capabilities by producing multiple gaps. In contrast, planets in radiative disks carve a single gap for typical disk parameters. Consequently, for accurate modeling of planets with semimajor axes up to about 100 au, radiative effects should be taken into account even in seemingly locally isothermal disks. In addition, for the case of AS 209, we find that the primary gap is significantly different between locally isothermal and radiative models. Our results suggest that multiple planets are required to explain the ring-rich structures in such systems.

scholarly journals Quasi-hydrostatic equation of state of silicon up to 1 megabar at ambient temperature

2019 ◽  
Vol 9 (1) ◽  
Author(s):  
Simone Anzellini ◽  
Michael T. Wharmby ◽  
Francesca Miozzi ◽  
Annette Kleppe ◽  
Dominik Daisenberger ◽  
...  
Keyword(s):  
Equation Of State ◽  
Room Temperature ◽  
Uniaxial Stress ◽  
Sample Volume ◽  
X Ray Diffraction ◽  
Experimental Conditions ◽  
X Ray ◽  
Pressure Medium ◽  
Diamond Anvil ◽  
Isothermal Equation

Abstract The isothermal equation of state of silicon has been determined by synchrotron x-ray diffraction experiments up to 105.2 GPa at room temperature using diamond anvil cells. A He-pressure medium was used to minimize the effect of uniaxial stress on the sample volume and ruby, gold and tungsten pressure gauges were used. Seven different phases of silicon have been observed along the experimental conditions covered in the present study.

An Isothermal Equation of State of Solid

2001 ◽  
Vol 226 (1) ◽  
pp. 125-132 ◽  
Author(s):  
Papiya Bose Roy ◽  
Sushil Bose Roy
Keyword(s):  
Equation Of State ◽  
Isothermal Equation

New isothermal equation of state of solids applied to high pressures

Pramana ◽  
2003 ◽  
Vol 61 (4) ◽  
pp. 753-757 ◽  
Author(s):  
Piyush Kuchhal ◽  
Narsingh Dass
Keyword(s):  
Equation Of State ◽  
High Pressures ◽  
Isothermal Equation

scholarly journals Isothermal equation of state and phase stability of Fe5 Si3 up to 96 GPa and 3000 K

2017 ◽  
Vol 122 (6) ◽  
pp. 4328-4335 ◽  
Author(s):  
C. McGuire ◽  
D. Santamaria-Pérez ◽  
A. Makhluf ◽  
A. Kavner
Keyword(s):  
Equation Of State ◽  
Phase Stability ◽  
Isothermal Equation

scholarly journals Larson–Penston Self-similar Gravitational Collapse

2021 ◽  
Author(s):  
Yan Guo ◽  
Mahir Hadžić ◽  
Juhi Jang
Keyword(s):  
Equation Of State ◽  
Numerical Integration ◽  
Gravitational Collapse ◽  
Similar Solution ◽  
Newtonian Gravity ◽  
Asymptotically Flat ◽  
Self Similar Solution ◽  
Self Similar ◽  
Isothermal Equation

AbstractUsing numerical integration, in 1969 Penston (Mon Not R Astr Soc 144:425–448, 1969) and Larson (Mon Not R Astr Soc 145:271–295, 1969) independently discovered a self-similar solution describing the collapse of a self-gravitating asymptotically flat fluid with the isothermal equation of state $$p=k\varrho $$ p = k ϱ , $$k>0$$ k > 0 , and subject to Newtonian gravity. We rigorously prove the existence of such a Larson–Penston solution.

A New Isothermal Equation of State for Solids

2009 ◽  
Vol 64 (1-2) ◽  
pp. 54-58
Author(s):  
Quan Liu
Keyword(s):  
Equation Of State ◽  
Critical Analysis ◽  
Short Range ◽  
Rare Gas ◽  
Volume Data ◽  
Volume Dependence ◽  
Short Range Force ◽  
Good Accordance ◽  
Isothermal Equation ◽  
Range Force

A new isothermal equation of state (EOS) for solids is derived by starting from the theory of lattice potential and using an analytical function for the volume dependence of the short-range force constant. A critical analysis of the isothermal EOSs: Murnaghan EOS, Vinet EOS, and the new EOS derived here, is presented by investigating the pressure-volume data for rare gas solids, metals and minerals. It is found that the results obtained from the new EOS are in good accordance with the corresponding values obtained from the Vinet EOS and with experimental data for all the solids up to very large compressions. On the other hand, the Murnaghan EOS is less successful at high pressure in most cases.

scholarly journals Dynamics of the inner edge of the dead zone in protoplanetary disks

2013 ◽  
Vol 8 (S299) ◽  
pp. 157-158
Author(s):  
Julien Faure ◽  
Sebastien Fromang ◽  
Henrik Latter
Keyword(s):  
Equation Of State ◽  
Numerical Simulations ◽  
Rossby Wave ◽  
Dead Zone ◽  
Vortex Formation ◽  
Protoplanetary Disks ◽  
Natural Consequence ◽  
Wave Instability ◽  
Turbulent Dissipation ◽  
Isothermal Equation

AbstractIn protoplanetary disks, the inner boundary between an MRI active and inactive region has recently been suggested to be a promising site for planet formation. A set of numerical simulations has indeed shown that vortex formation mediated by the Rossby wave instability is a natural consequence of the disk dynamics at that location. However, such models have so far considered only the case of an isothermal equation of state, while the complex thermodynamics is at the heart of how this region works. Using the Godunov code Ramses, we have performed 3D global numerical simulations of protoplanetary disks that relax the isothermal hypothesis. We find that, at the interface, the disk thermodynamics and the turbulent dynamics are intimately entwined, because of the importance of turbulent dissipation and thermal ionisation.

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