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Stability Study of a Longitudinal Dispersivity Identification Method (1993)

Pisani, Stefano ; Tosi, Nicola

Oxford, UK : Blackwell Publishing Ltd

Ground water 31 (1993), S. 0

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ISSN: 1745-6584

Source: Blackwell Publishing Journal Backfiles 1879-2005

Topics: Energy, Environment Protection, Nuclear Power Engineering , Geosciences

Notes: The knowledge of the value of longitudinal dispersivity is very important in the simulation of solute transport. Therefore, a method for the identification of longitudinal dispersivity in a solute transport laboratory experiment was developed. The solute was assumed to be ideal and the medium isotropic and homogeneous, with a one-dimensional geometry. The sensitivity of the inversion method to a uniform random noise in porosity, which accounts for possible heterogeneities of the medium, and to concentration measurement errors, which are always present in a laboratory experiment, was analyzed. This analysis is necessary to estimate the reliability of the method. Then, supposing the concentration error distributed according to a Gaussian with zero mean, the probability distribution of the relative identification error was computed as a function of the standard deviation of the Gaussian. The mean value of the relative identification error was found to be positive, due to the nonlinearity of the identification algorithm.

Type of Medium: Electronic Resource

URL: http://dx.doi.org/10.1111/j.1745-6584.1993.tb00835.x

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2

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Two Methods for the Laboratory Identification of Transversal Dispersivity (1994)

Pisani, Stefano ; Tosi, Nicola

Oxford, UK : Blackwell Publishing Ltd

Ground water 32 (1994), S. 0

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ISSN: 1745-6584

Source: Blackwell Publishing Journal Backfiles 1879-2005

Topics: Energy, Environment Protection, Nuclear Power Engineering , Geosciences

Notes: The experimental identification of transversal dispersivity in the laboratory is not a very developed subject; the authors herein propose two methods for identifying transversal dispersivity in laboratory experiments, based on the analytical solution of a continuous, point-like, injection of a nonreactive solute in a flow tank packed with a homogeneous porous medium. The solute transport is supposedly two-dimensional, whereas the hydraulic flow is monodimensional with a uniform velocity.Each identification method is based on the measurement of concentration in pairs of points. In the first method the points are taken along lines normal to the direction of the fluid flow, with one of the two points set on the central axis of the flow tank. In the second method the two measurement points are placed on lines passing through the solute injection point.The stability of the two methods, with respect to concentration measurement errors, is analyzed to assess the reliability of the transversal dispersivity estimate. Furthermore, the two methods are found to be sensitive to variations of the concentrations.

Type of Medium: Electronic Resource

URL: http://dx.doi.org/10.1111/j.1745-6584.1994.tb00660.x

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3

Electronic Resource

A technique to test finite difference schemes to model some geophysical processes in a geological structure (1992)

Ponzini, Giansilvio ; Tosi, Nicola

Springer

Mathematical geology 24 (1992), S. 499-537

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ISSN: 1573-8868

Keywords: earth's heat flow ; geological modeling ; finite difference schemes ; model validation

Source: Springer Online Journal Archives 1860-2000

Topics: Geosciences , Mathematics

Notes: Abstract A preliminary problem to solve in the set-up of a mathematical model simulating a geophysical process is the choice of a suitable discrete scheme to approximate the governing differential equations. This paper presents a simple technique to test finite difference schemes used in the modeling of geophysical processes occurring in a geological structure. This technique consists in generating analytical solutions similar to the ones characterizing a geophysical process, given general information on some relevant parameters. Useful information for the choice of the discrete scheme to employ in the mathematical model simulating the original geophysical process can be obtained from the comparison between the analytical solution and the approximated numerical solutions generated by means of different discrete schemes. Two classes of numerical examples approximating the differential equation that governs the steady state earth's heat flow have been treated using three different finite differences schemes. The first class of examples deals with media whose phenomenological parameters vary as continuous space functions; the second class, instead, deals with media whose phenomenological parameters vary as discontinuous space functions. The finite difference schemes that have been utilized are: Centered Finite Difference Scheme (CDS), Arithmetic Mean Scheme (AMS), and Harmonic Mean Scheme (HMS). The numerical simulations showed that: the CDS may yield physically inconsistent solutions if the lattice internodal distance is too large, but in case of phenomenological parameters varying as a continuous function, this pitfall can be avoided increasing the lattice node refinement. In case of phenomenological parameters varying as a discontinuous function, instead, the CDS may yield physically inconsistent solutions for any lattice-node refinement. The HMS produced good results for both classes of examples showing to be a scheme suitable to model situations like these.

Type of Medium: Electronic Resource

URL: http://dx.doi.org/10.1007/BF00890532

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Origin and evolution of the atmospheres of early Venus, Earth and Mars (2018)

Lammer, Helmut ; Zerkle, Aubrey L. ; Gebauer, Stefanie ; [et al.]

Springer

In: Astronomy and Astrophysics Review. 2018; 26(1): 2. Published 2018 May 10. doi: 10.1007/s00159-018-0108-y.

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Publication Date: 2018-05-10

Print ISSN: 0935-4956

Electronic ISSN: 1432-0754

Topics: Physics

Published by Springer

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The habitability of stagnant-lid Earths around dwarf stars (2019)

Godolt, Mareike ; Tosi, Nicola ; Stracke, Barbara ; [et al.]

EDP Sciences

In: Astronomy and Astrophysics. 2019; 625: A12. Published 2019 Apr 30. doi: 10.1051/0004-6361/201834658.

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Publication Date: 2019-04-30

Description: Context. The habitability of a planet depends on various factors, such as the delivery of water during its formation, the co-evolution of the interior and the atmosphere, and the stellar irradiation which changes in time. Aims. Since an unknown number of rocky extrasolar planets may operate in a one-plate convective regime, i.e. without plate tectonics, our aim is to understand the conditions under which planets in such a stagnant-lid regime may support habitable surface conditions. Understanding the interaction of the planetary interior and outgassing of volatiles in combination with the evolution of the host star is crucial to determining the potential habitability. M-dwarf stars in particular possess a high-luminosity pre-main sequence phase that endangers the habitability of planets around them via water loss. We therefore explore the potential of secondary outgassing from the planetary interior to rebuild a water reservoir allowing for habitability at a later stage. Methods. We compute the boundaries of the habitable zone around M-, K-, G-, and F-dwarf stars using a 1D cloud-free radiative-convective climate model accounting for the outgassing history of CO2 and H2O from an interior evolution and outgassing model for different interior compositions and stellar luminosity evolutions. Results. The outer edge of the habitable zone strongly depends on the amount of CO2 outgassed from the interior, while the inner edge is mainly determined via the stellar irradiation, as soon as a sufficiently large water reservoir has been outgassed. A build-up of a secondary surface and atmospheric water reservoir for planets around M-dwarf stars is possible even after severe water loss during the high-luminosity pre-main sequence phase as long as some water has been retained within the mantle. For small mantle water reservoirs, between 62 and 125 ppm, a time delay in outgassing from the interior permits such a secondary water reservoir build-up especially for early and mid-M dwarfs because their pre-main sequence lifetimes are shorter than the outgassing timescale. Conclusions. We show that Earth-like stagnant-lid planets allow for habitable surface conditions within a continuous habitable zone that is dependent on interior composition. Secondary outgassing from the interior may allow for habitability of planets around M-dwarf stars after severe water loss during the high-luminosity pre-main sequence phase by rebuilding a surface water reservoir.

Print ISSN: 0004-6361

Electronic ISSN: 1432-0746

Topics: Physics

Published by EDP Sciences

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Carbon cycling and interior evolution of water-covered plate tectonics and stagnant-lid planets (2019)

Höning, Dennis ; Tosi, Nicola ; Spohn, Tilman

EDP Sciences

In: Astronomy and Astrophysics. 2019; 627: A48. Published 2019 Jul 01. doi: 10.1051/0004-6361/201935091.

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Publication Date: 2019-07-01

Description: Aims. The long-term carbon cycle for planets with a surface entirely covered by oceans works differently from that of the present-day Earth because inefficient erosion leads to a strong dependence of the weathering rate on the rate of volcanism. In this paper, we investigate the long-term carbon cycle for these planets throughout their evolution. Methods. We built box models of the long-term carbon cycle based on CO2 degassing, seafloor-weathering, metamorphic decarbonation, and ingassing and coupled them with thermal evolution models of plate tectonics and stagnant-lid planets. Results. The assumed relationship between the seafloor-weathering rate and the atmospheric CO2 or the surface temperature strongly influences the climate evolution for both tectonic regimes. For a planet with plate tectonics, the atmospheric CO2 partial pressure is characterized by an equilibrium between ingassing and degassing and depends on the temperature gradient in subduction zones affecting the stability of carbonates. For a stagnant lid planet, partial melting and degassing are always accompanied by decarbonation, such that the combined carbon content of the crust and atmosphere increases with time. While the initial mantle temperature on planets with plate tectonics only affects the early evolution, it influences the evolution of the surface temperature of stagnant-lid planets for much longer. Conclusions. For both tectonic regimes, mantle cooling results in a decreasing atmospheric CO2 partial pressure. For a planet with plate tectonics this is caused by an increasing fraction of subduction zones that avoid crustal decarbonation, and for stagnant-lid planets this is caused by an increasing decarbonation depth. This mechanism may partly compensate for the increase of the surface temperature due to increasing solar luminosity with time, and thereby contribute to keeping planets habitable in the long-term.

Print ISSN: 0004-6361

Electronic ISSN: 1432-0746

Topics: Physics

Published by EDP Sciences

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