BN-16, BN-18, BN-19 ,
adimensionnel ou non) (N+1 points comme pour le chier distrib.txt), puis à chaque temps, on enregistre le temps (t = xx ,
Diusion-induced growth of a gas bubble in a viscoelastic uid, Rheol. Acta, vol.30, pp.274283-274293, 1991. ,
On a monte carlo scheme for smoluchowski's equation, 1999. ,
Instantaneous gelation in Smoluchowski???s coagulation equation revisited, Physical Review E, vol.84, issue.1, 2011. ,
DOI : 10.1103/PhysRevE.84.011111
Experimental constraints on degassing and permeability in volcanic conduit ow, Bull Volcanol, vol.67, p.4256, 2005. ,
Bubble growth mechanism in carbon foams, Carbon, vol.43, issue.5, 2005. ,
DOI : 10.1016/j.carbon.2004.11.046
Coupling of viscous and diusive controls on bubble growth during explosive volcanic eruptions, Earth and Planet. Sci. Letters, vol.193, issue.01, pp.4756-4766, 2001. ,
Structural stability of the coalescence, 1995. ,
Heat Conduction Using Green's Functions, Boca Raton, 2011. ,
Mechanisms and dynamics of bubble coalescence in silisic magmas, Bulletin of Volcanology, 2012. ,
Dynamics of diffusive bubble growth and pressure recovery in a bubbly rhyolitic melt embedded in an elastic solid, Journal of Geophysical Research, vol.88, issue.47, pp.7310-7320, 2006. ,
DOI : 10.1029/2005JB004174
Tail distribution of large clusters from the coagulation equation, Journal of Colloid and Interface Science, vol.115, issue.1, pp.2735-2745, 1987. ,
DOI : 10.1016/0021-9797(87)90005-1
Scaling solutions of Smoluchowski's coagulation equation, Journal of Statistical Physics, vol.119, issue.1-2, pp.295329-295339, 1988. ,
DOI : 10.1007/BF01022996
Study of a stochastic particle system associated with the smoluchowski coagulation equation, 2003. ,
Simulation numérique en c++, 2003. ,
Solutions of Smoluchowski's coagulation equation at large cluster sizes, Physica A: Statistical Mechanics and its Applications, vol.145, issue.1-2, pp.1566-1576, 1987. ,
DOI : 10.1016/0378-4371(87)90240-8
A general mathematical survey of the coagulation equation, Topics in Current Aerosol Research, p.201376, 1972. ,
Numerical treatment of the population balance equation using a Spline-Galerkin method, Computers & Chemical Engineering, vol.18, issue.9, pp.775783-775793, 1994. ,
DOI : 10.1016/0098-1354(94)E0007-A
An ecient stochastic algorithm for studying coagulation dynamics and gelation phenomena, SIAM J. Sci. Comput, vol.22, pp.802821-802831, 2000. ,
Stochastic particle approximations for smoluchowski's coagulaion equation, Ann. Appl. Probab, 2001. ,
DOI : 10.1214/aoap/1015345398
URL : http://projecteuclid.org/download/pdf_1/euclid.aoap/1015345398
Numerical resolution of a mono-disperse model of bubble growth in magmas, Applied Mathematical Modelling, vol.36, issue.12, 2012. ,
DOI : 10.1016/j.apm.2012.01.031
URL : https://hal.archives-ouvertes.fr/hal-00544506
(soumis) A nite volume preserving scheme on non-uniform mesches and for multidimensional coalescence Numerical simulation of the smoluchowski equation, Filbet and P. Laurençot, 2004. ,
Theorical considerations for the particle size spectrum of the stratospheric aerosol, J. Meteorol, vol.182, issue.6, p.753759, 1961. ,
Bubble coalescence in rhyolitic melts during decompression from high pressure, Journal of Volcanolgy ang Geothermal Research, vol.166, 2007. ,
Experimental constraints on degassing of magma: isothermal bubble growth during continuous decompression from high pressure, Earth and Planetary Science Letters, vol.168, issue.1-2, pp.201218-201228, 1999. ,
DOI : 10.1016/S0012-821X(99)00051-5
Bubble growth in highly viscous silicate melts during continuous decompression from high pressure, Geochimica et Cosmochimica Acta, vol.64, issue.8, 2000. ,
DOI : 10.1016/S0016-7037(99)00436-6
A scaling cascade model for bubble growth in lavas, Earth Planet. Sci. Lett, vol.139, issue.96, pp.395409-395419, 1996. ,
The viscosity of trachytes, and comparison with basalts, phonolites, and rhyolites, Chemical Geology, vol.213, issue.1-3, 2004. ,
DOI : 10.1016/j.chemgeo.2004.08.032
Coagulation and growth of a multicomponent aerosol, Journal of Colloid and Interface Science, vol.63, issue.3, pp.472479-472489, 1978. ,
DOI : 10.1016/S0021-9797(78)80008-3
Viscosities of hydrous leucogranitic melts : A non-arrhenian model, American Mineralogist, vol.81, p.12971300, 1996. ,
Bubble nucleation in rhyolitic melts: Experiments at high pressure, temperature, and water content, Earth and Planetary Science Letters, vol.122, issue.3-4, pp.267280-267290, 1994. ,
DOI : 10.1016/0012-821X(94)90001-9
Equilibrium and disequilibrium degassing of a phonolite melt (vesuvius ad 79 "white pumice") simulated by decompression experiments, Journal of Volcanology and Geothermal Research, vol.161, p.151164, 2007. ,
Gas content, eruption rate and instabilities of eruption regime in silicic volcanoes, Earth and Planetary Science Letters, vol.102, issue.3-4, pp.413429-413439, 1991. ,
DOI : 10.1016/0012-821X(91)90032-D
Magma ascent at shallow levels. Encyclopedia of volcanoes, p.237245, 2000. ,
Numerical methods for solving two-dimensional aggregation population balance equations, Computers & Chemical Engineering, vol.35, issue.6, 2011. ,
DOI : 10.1016/j.compchemeng.2010.08.002
An ecient numerical technique for solving population balance equation involving aggregation , breakage, growth and nucleation, Powder Technology, 2008. ,
Numerical solution of the smoluchowski kinetik equation and asymptotics of the distribution function, J. Phys. A, vol.63, pp.2025-2039, 1995. ,
On the validity of the coagulation eqution and the nature of runaway growth, Icarus, 2000. ,
A survey of numerical solutions to the coagulation equation, 2001. ,
Experimental study of water degassing from phonolite melts: implications for volatile oversaturation during magmatic ascent, Journal of Volcanology and Geothermal Research, vol.134, issue.1-2, 2004. ,
DOI : 10.1016/j.jvolgeores.2004.01.004
Bubble distributions and dynamics: The expansion-coalescence equation, Journal of Geophysical Research: Solid Earth, vol.50, issue.11, pp.10-1029, 2004. ,
DOI : 10.1007/500445-004-0376-4
URL : https://hal.archives-ouvertes.fr/hal-00711730
A new model of volatile bubble growth in a magmatic system: Isobaric case, Journal of Geophysical Research, vol.3, issue.B4, pp.12208-12218, 2007. ,
DOI : 10.1029/2006JB004872
Bubble growth in rhyolitic melts: experimental and numerical investigation, Bulletin of Volcanology, vol.58, issue.1, pp.19-32, 1996. ,
DOI : 10.1007/s004450050122
On coalescence equations and related models, Modeling and computational methods for kinetic equations, Modeling and Simulation in Science, Engineering ans Technology, p.321356, 2004. ,
DOI : 10.1007/978-0-8176-8200-2_11
Bubble growth during decompression of magma: experimental and theoretical investigation, Journal of Volcanology and Geothermal Research, vol.129, issue.1-3, pp.722-732, 2004. ,
DOI : 10.1016/S0377-0273(03)00229-4
Singularities in the kinetiks of coagulation processes Evolution of coagulating systems, J. Phys. A J. Colloid Interface Sci, vol.14141273, issue.453, pp.33893405-33893415, 1973. ,
Evolution of coagulating systems iii. coagulating mixtures, Journal of Colloid and Interface Science, vol.54, issue.176, pp.10-1016, 1976. ,
Rapid water exsolution, degassing, and bubble collapse observed experimentally in K-phonolite melts, Journal of Volcanology and Geothermal Research, vol.173, issue.3-4, 2008. ,
DOI : 10.1016/j.jvolgeores.2008.01.026
Intermittency, fragmentation, and the Smoluchowski equation, Nuclear Physics B, vol.374, issue.2, pp.327339-327349, 1992. ,
DOI : 10.1016/0550-3213(92)90356-G
Delayed, disequilibrium degassing in rhyolite magma: decompression experiments and implications for explosive volcanism, Earth and Planetary Science Letters, vol.183, issue.3-4, pp.441455-441465, 2000. ,
DOI : 10.1016/S0012-821X(00)00299-5
Decompression experiments as an insight into ascent rates of silisic magmas, Contrib Mineral Petrol, vol.144, p.397415, 2003. ,
Evolution of melt-vapor surface tension in silicic volcanic systems: Experiments with hydrous melts, Journal of Geophysical Research, vol.402, issue.B8, pp.1202-1212, 2005. ,
DOI : 10.1029/2004JB003215
Eruptive materials of the 2000 eruption of usu volcano, northern japan : Component materials and their temporal change(<special section>the, Bulletin of the Volcanological Society of Japan, vol.47, issue.24, pp.279-288, 2000. ,
Bessel function of integer order Handbook of mathematical functions with formulas, graphs, and mathematical tables, 1972. ,
Kinetic formulation of conservation laws. Oxford lecture series in mathematics and its applications, 2002. ,
Dynamics and energetics of bubble growth in magmas: Analytical formulation and numerical modeling, Journal of Geophysical Research: Solid Earth, vol.80, issue.B8, pp.1822318251-1822318261, 1998. ,
DOI : 10.1029/98JB00906
A numerical model of volcanic eruption mechanisms driven by disequilibrum magma degassing, J. Volcanol, 2005. ,
Dynamics of diusive bubble growth in magmas : Isothermal case, Journal of Geophysical Research, vol.98, issue.B12, pp.2228322307-10, 1993. ,
Solving population balance equations for two-component aggregation by a nite-volume scheme, Chemical Engineering Science, 2007. ,
Study of the growth and motion of graphitic foam bubbles, Carbon, vol.43, issue.15, 2005. ,
DOI : 10.1016/j.carbon.2005.06.044
On the dynamics of phase growth, Chem. Eng. Sci, vol.10, issue.59, pp.113-123, 1959. ,
Linking experimental and natural vesicle texture in vesuvius 79ad white pumice, Journal of Volcanology and Geothermal Research, vol.192, pp.69-84, 2010. ,
Drei Vorträge über Diusion, Brownsche Bewegung und Koagulation von Kolloidteilchen, Physikalische Zeitschrift, vol.17, pp.557-585, 1916. ,
Versuch einer mathematischen Theorie der Koagulationskinetik kolloider Lösungen. Zeitschrift für Physikalische Chemie, 1917. ,
Analytical solutions to simple models of condensation and coalescence. journal of the atmospheric sciences, 037<0612:ASTSMO>2.0.CO, pp.612621-612631, 1980. ,
Steady-State Size Distribution for the Self-Similar Collision Cascade, Icarus, vol.123, issue.2, 1996. ,
DOI : 10.1006/icar.1996.0170
Experimental constraints on the low gas permeability of vesicular magma during decompression, Geophysical Research Letters, vol.56, issue.10, pp.10-1029, 2005. ,
DOI : 10.1029/2005GL022491
Numerical study of nucleation and growth of bubbles in viscous magmas Degassing conditions for permeable silicic magmas : Implications from decompression experiments with constant rates, J. Geophys. Res. Earth and Planetary Science Letters, vol.100, 1995. ,
Particle size distributions in an expanding plume undergoing simultaneously coagulation and condensation, J. Geophys, 1999. ,
Solution of the population balance equation for two-component aggregation by an extended xed pivot technique, Industrial & Engineering Chemistry Research, vol.44, issue.20, pp.78857891-78857901, 2005. ,
Slow bubble growth and dissolution in a viscoelastic uid, 12<2093::AID-APP16>3.0.CO, pp.1097-46282, 1998. ,
Direct simulation of vapor bubble growth, Int. J. Heat and Mass Transf, vol.4197, pp.16551666-16551676, 1998. ,
The viscosity of hydrous dacitic liquids: implications for the rheology of evolving silicic magmas, Bulletin of Volcanology, vol.88, issue.27, pp.185199-185209, 2009. ,
DOI : 10.1007/s00445-008-0217-y
H2O diusion in rhyolitic melts and glasses, Chemical Geology, vol.169, issue.1299, pp.243262-243272, 2000. ,
84 TABLE DES FIGURES 1.28?P28? 28?P fonction dê P a pour la convergence de 1 ,
les courbes se croisent toutes les trois en un point, R = 1, P = 1 + ?. En rouge est représenté P 2, p.60 ,
Données provenant de 13 études) Les 4 champs en vert (cas limites, général et équilibre) font référence à la table 1, Distribution des expériences de laboratoire en termes, p.85 ,
massique" pour le cas monodisperse (gauche) et le cas polydisperse (droite) aux temps t = 0 ,
Sont représentés sur les graphiques, la marginale (gauche) et la marginale "massique" (droite) aux temps t = 0, p.150 ,
85 pour la densité de distribution et la marginale "massique" après post-traitement, p.153 ,
Rayon (gauche) et porosité (droite) en fonction de la pression ambiante, p.159 ,
Rayon (gauche) et porosité (droite) en fonction de la pression ambiante, p.160 ,