scholarly journals New Perspectives on the Exoplanet Radius Gap from a Mathematica Tool and Visualized Water Equation of State

2021 ◽  
Vol 923 (2) ◽  
pp. 247
Author(s):  
Li Zeng ◽  
Stein B. Jacobsen ◽  
Eugenia Hyung ◽  
Amit Levi ◽  
Chantanelle Nava ◽  
...  
Keyword(s):  
Equation Of State ◽  
Parameter Space ◽  
Equations Of State ◽  
Equilibrium Temperature ◽  
Occurrence Rate ◽  
Astronomical Observations ◽  
Multidimensional Parameter ◽  
Compositional Diversity ◽  
Rocky Planets ◽  
Gaseous Envelopes

Abstract Recent astronomical observations obtained with the Kepler and TESS missions and their related ground-based follow-ups revealed an abundance of exoplanets with a size intermediate between Earth and Neptune (1 R ⊕ ≤ R ≤ 4 R ⊕). A low occurrence rate of planets has been identified at around twice the size of Earth (2 × R ⊕), known as the exoplanet radius gap or radius valley. We explore the geometry of this gap in the mass–radius diagram, with the help of a Mathematica plotting tool developed with the capability of manipulating exoplanet data in multidimensional parameter space, and with the help of visualized water equations of state in the temperature–density (T–ρ) graph and the entropy–pressure (s–P) graph. We show that the radius valley can be explained by a compositional difference between smaller, predominantly rocky planets (<2 × R ⊕) and larger planets (>2 × R ⊕) that exhibit greater compositional diversity including cosmic ices (water, ammonia, methane, etc.) and gaseous envelopes. In particular, among the larger planets (>2 × R ⊕), when viewed from the perspective of planet equilibrium temperature (T eq), the hot ones (T eq ≳ 900 K) are consistent with ice-dominated composition without significant gaseous envelopes, while the cold ones (T eq ≲ 900 K) have more diverse compositions, including various amounts of gaseous envelopes.

SITE-SPECIFIC EQUATIONS OF STATE FOR COASTAL SEA AREAS AND INLAND WATER BODIES

2017 ◽  
Author(s):  
Natalia Andrulionis ◽  
Natalia Andrulionis ◽  
Ivan Zavialov ◽  
Ivan Zavialov ◽  
Elena Kovaleva ◽  
...  
Keyword(s):  
Equation Of State ◽  
Black Sea ◽  
Water Samples ◽  
Equations Of State ◽  
Sea Water ◽  
Ionic Composition ◽  
Water Bodies ◽  
Aral Sea ◽  
The Black Sea ◽  
Coastal Sea

This article presents a new method of laboratory density determination and construction equations of state for marine waters with various ionic compositions and salinities was developed. The validation of the method was performed using the Ocean Standard Seawater and the UNESCO thermodynamic equation of state (EOS-80). Density measurements of water samples from the Aral Sea, the Black Sea and the Issyk-Kul Lake were performed using a high-precision laboratory density meter. The obtained results were compared with the density values calculated for the considered water samples by the EOS-80 equation. It was shown that difference in ionic composition between Standard Seawater and the considered water bodies results in significant inaccuracies in determination of water density using the EOS-80 equation. Basing on the laboratory measurements of density under various salinity and temperature values we constructed a new equation of state for the Aral Sea and the Black Sea water samples and estimated errors for their coefficients.

Application of the Redlich-Kwong-Soave equation of state to the solubility of water in compressed gases

1984 ◽  
Vol 49 (5) ◽  
pp. 1116-1121
Author(s):  
Josef P. Novák ◽  
Jaroslav Matouš ◽  
Petr Pick ◽  
Jiří Pick
Keyword(s):  
Equation Of State ◽  
Binary Systems ◽  
Equations Of State ◽  
Published Data ◽  
Interaction Coefficients

Published data on the solubility of water in compressed gases were employed for calculating the interaction coefficients kij in the Redlich-Kwong-Soave equations of state for binary systems of water with argon, nitrogen, CO2, N2O, CH4, C2H6, or C2H4. With these coefficients, the estimate of the solubility of water in these gases has been improved by more than one order.

scholarly journals Global Well-Posedness of the Ocean Primitive Equations with Nonlinear Thermodynamics

2021 ◽  
Vol 23 (3) ◽  
Author(s):  
Peter Korn
Keyword(s):  
Equation Of State ◽  
Equations Of State ◽  
Boussinesq Equations ◽  
Climate Science ◽  
Rational Functions ◽  
Ocean Dynamics ◽  
Global Ocean ◽  
Primitive Equations ◽  
Well Posedness ◽  
Nonlinear Thermodynamics

AbstractWe consider the hydrostatic Boussinesq equations of global ocean dynamics, also known as the “primitive equations”, coupled to advection–diffusion equations for temperature and salt. The system of equations is closed by an equation of state that expresses density as a function of temperature, salinity and pressure. The equation of state TEOS-10, the official description of seawater and ice properties in marine science of the Intergovernmental Oceanographic Commission, is the most accurate equations of state with respect to ocean observation and rests on the firm theoretical foundation of the Gibbs formalism of thermodynamics. We study several specifications of the TEOS-10 equation of state that comply with the assumption underlying the primitive equations. These equations of state take the form of high-order polynomials or rational functions of temperature, salinity and pressure. The ocean primitive equations with a nonlinear equation of state describe richer dynamical phenomena than the system with a linear equation of state. We prove well-posedness for the ocean primitive equations with nonlinear thermodynamics in the Sobolev space $${{\mathcal {H}}^{1}}$$ H 1 . The proof rests upon the fundamental work of Cao and Titi (Ann. Math. 166:245–267, 2007) and also on the results of Kukavica and Ziane (Nonlinearity 20:2739–2753, 2007). Alternative and older nonlinear equations of state are also considered. Our results narrow the gap between the mathematical analysis of the ocean primitive equations and the equations underlying numerical ocean models used in ocean and climate science.

scholarly journals Measuring the structure and equation of state of polyethylene terephthalate at megabar pressures

2021 ◽  
Vol 11 (1) ◽  
Author(s):  
J. Lütgert ◽  
J. Vorberger ◽  
N. J. Hartley ◽  
K. Voigt ◽  
M. Rödel ◽  
...  
Keyword(s):  
Equation Of State ◽  
Polyethylene Terephthalate ◽  
Density Functional ◽  
Equations Of State ◽  
Md Simulations ◽  
X Ray Diffraction ◽  
Functional Theory ◽  
Shock Hugoniot ◽  
Highly Correlated

AbstractWe present structure and equation of state (EOS) measurements of biaxially orientated polyethylene terephthalate (PET, $$({\hbox {C}}_{10} {\hbox {H}}_8 {\hbox {O}}_4)_n$$ ( C 10 H 8 O 4 ) n , also called mylar) shock-compressed to ($$155 \pm 20$$ 155 ± 20 ) GPa and ($$6000 \pm 1000$$ 6000 ± 1000 ) K using in situ X-ray diffraction, Doppler velocimetry, and optical pyrometry. Comparing to density functional theory molecular dynamics (DFT-MD) simulations, we find a highly correlated liquid at conditions differing from predictions by some equations of state tables, which underlines the influence of complex chemical interactions in this regime. EOS calculations from ab initio DFT-MD simulations and shock Hugoniot measurements of density, pressure and temperature confirm the discrepancy to these tables and present an experimentally benchmarked correction to the description of PET as an exemplary material to represent the mixture of light elements at planetary interior conditions.

Thermodynamic properties of liquid mixtures: Selection of the pure liquid parameter

1974 ◽  
Vol 27 (3) ◽  
pp. 647 ◽  
Author(s):  
DV Fenby ◽  
NF Pasco
Keyword(s):  
Equation Of State ◽  
Thermodynamic Properties ◽  
Equations Of State ◽  
Liquid Mixtures ◽  
Pure Liquid ◽  
Excess Thermodynamic Properties ◽  
Pure Fluids ◽  
Liquid Parameter ◽  
Selection Of

There has recently been a revival of interest in theories of liquid mixtures based on analytic equations of state for pure fluids. We have shown that the method used to determine the parameters of the pure-liquid equation of state has a significant effect on the excess thermodynamic properties obtained from such theories.

scholarly journals Atmospheric speciation of rocky planets from magma ocean outgassing

2020 ◽  
Author(s):  
Tim Lichtenberg ◽  
Dan J. Bower ◽  
Mark Hammond ◽  
Ryan Boukrouche ◽  
Shang-Min Tsai ◽  
...  
Keyword(s):  
Coupled Model ◽  
Initial Distribution ◽  
Occurrence Rate ◽  
Magma Ocean ◽  
Mantle Dynamics ◽  
Mantle Geochemistry ◽  
Prebiotic Chemical ◽  
History Of ◽  
Climatic History ◽  
Rocky Planets

&lt;p&gt;The earliest atmospheres of rocky planets originate from extensive volatile release during one or more magma ocean epochs that occur during primary and late-stage assembly of the planet (1). These epochs represent the most extreme cycling of volatiles between the interior and atmosphere in the history of a planet, and establish the initial distribution of the major volatile elements (C, H, N, O, S) between different chemical reservoirs that subsequently evolve via geological cycles. Crucially, the erosion or recycling of primary atmospheres bear upon the nature of the long-lived secondary atmospheres that will be probed with current and future observing facilities (2). Furthermore, the chemical speciation of the atmosphere arising from magma ocean processes can potentially be probed with present-day observations of tidally-locked rocky super-Earths (3). The speciation in turn strongly influences the climatic history of rocky planets, for instance the occurrence rate of planets that are locked in long-term runaway greenhouse states (4). We will present an integrated framework to model the build-up of the earliest atmospheres from magma ocean outgassing using a coupled model of mantle dynamics and atmospheric evolution. We consider the diversity of atmospheres that can arise for a range of initial planetary bulk compositions, and show how even small variations in volatile abundances can result in dramatically different atmospheric compositions and affect earliest mantle geochemistry and atmospheric speciation relevant for surficial prebiotic chemical environments (5). Only through the lense of coupled evolutionary models of terrestrial interiors and atmospheres can we begin to deconvolve the imprint of formation from that of evolution, with consequences for how we interpret the diversity revealed by astrophysical observables, and their relation to the earliest planetary conditions of our home world.&lt;/p&gt; &lt;div class=&quot;&quot;&gt;&lt;em&gt;References&lt;/em&gt;&lt;/div&gt; &lt;ol&gt; &lt;li&gt;Bower, D. J., Kitzmann, D., Wolf, A. S., et al. (2019). Astron. Astrophys. 631, A103.&lt;/li&gt; &lt;li&gt;Bonati, I., Lichtenberg, T., Bower, D. J., et al. (2019). Astron. Astrophys. 621, A125.&lt;/li&gt; &lt;li&gt;Kreidberg, L., Koll, D. D., Morley, C., et al. (2019). Nature 573, 87-90.&lt;/li&gt; &lt;li&gt;Hamano, K., Abe, Y., Genda, H. (2013). Nature 497, 607-610.&lt;/li&gt; &lt;li&gt;Sasselov, D. D., Grotzinger, J. P., Sutherland, J. D. (2020). Sci. Adv. 6, eaax3419.&lt;/li&gt; &lt;/ol&gt;

The theory of rubber elasticity

1976 ◽  
Vol 351 (1666) ◽  
pp. 397-406 ◽  
Keyword(s):  
Equation Of State ◽  
Statistical Mechanics ◽  
Equations Of State ◽  
Rubber Elasticity ◽  
Elastic Behaviour ◽  
Excluded Volume ◽  
Simple Pattern ◽  
Dynamical Approach ◽  
Equilibrium Approach ◽  
The Future

It is argued that since statistical mechanics has developed in two ways, the dynamical approach of Boltzmann and the equilibrium approach of Gibbs, both should be valuable in rubber elasticity. It is shown that this is indeed the case, and the generality of these approaches allows one to study the problem in greater depth than hitherto. In particular, damping terms in the elastic behaviour of rubber can be calculated, and also the effect of entanglements and excluded volume on the equation of state. It is noticeable that although the calculated equations of state are quite complex, they do not fit into a simple pattern of invariants. The future for these developments is briefly discussed.

scholarly journals The Compositional Diversity of Low-Mass Exoplanets

2019 ◽  
Vol 47 (1) ◽  
pp. 141-171 ◽  
Author(s):  
Daniel Jontof-Hutter
Keyword(s):  
Bulk Composition ◽  
Diverse Range ◽  
Kepler Mission ◽  
Low Mass ◽  
Orbital Periods ◽  
Gaseous Atmospheres ◽  
The Masses ◽  
Compositional Diversity ◽  
Rocky Planets ◽  
Observational Techniques

Low-mass planets have an extraordinarily diverse range of bulk compositions, from primarily rocky worlds to those with deep gaseous atmospheres. As techniques for measuring the masses of exoplanets advance the field toward the regime of rocky planets, from ultrashort orbital periods to Venus-like distances, we identify the bounds on planet compositions, where sizes and incident fluxes inform bulk planet properties. In some cases, the precision of measurement of planet masses and sizes is approaching the theoretical uncertainties in planet models. An emerging picture explains aspects of the diversity of low-mass planets, although some problems remain: Do extreme low-density, low-mass planets challenge models of atmospheric mass loss? Are planet sizes strictly separated by bulk composition? Why do some stellar characterizations differ between observational techniques? With the Transiting Exoplanet Survey Satellite ( TESS) mission, low-mass exoplanets around the nearest stars will soon be discovered and characterized with unprecedented precision, permitting more detailed planetary modeling and atmospheric characterization of low-mass exoplanets than ever before. ▪ Following the Kepler mission, studies of exoplanetary compositions have entered the terrestrial regime. ▪ Low-mass planets have an extraordinary range of compositions, from Earth-like mixtures of rock and metal to mostly tenuous gas. ▪ The TESS mission will discover low-mass planets that can be studied in more detail than ever before.

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