Sr isotope zoning in plagioclase from Parinacota Volcano (Northern Chile): quantifying magma mixing and crustal contamination

We present analyses of Sr isotope zoning by microdrilling and thermal ionization mass spectrometry in plagioclase crystals from Parinacota volcano (Central Volcanic Zone, northern Chile), which were analysed for major and minor element zoning in a previous study. Although the isotopic range of the bulk-rock samples is small at this volcano (0·7067–0·7070, except for one flow of mafic andesite at 0·7061), significant variations are seen (0·70649–0·70700) within and between plagioclase crystals. A general negative correlation is observed between Sr isotope composition and Sr concentration in the liquid in equilibrium with each plagioclase zone, as calculated from chemical zoning data and partition coefficients. Additional scatter is superimposed on this general trend, indicating a decoupling between isotopic and chemical variations for Sr. In one dacite sample a detailed isotopic profile shows increasing contamination during crystal growth, except for an abrupt decrease correlated with a dissolution surface and interpreted as a recharge event. We apply energy-constrained recharge, assimilation and fractional crystallization modelling to the melt evolution recorded in the chemical and isotopic zoning in this crystal. Results suggest 20% assimilation of the local wall-rock gneiss, at high initial temperatures. The isotopic data confirm the involvement of two contrasting mafic magmas, which are sampled at flank cinder cone vents. One (Lower Ajata) has a low Sr content with high 87Sr/86Sr, the other (Upper Ajata) has a high Sr content with lower 87Sr/86Sr. In some samples from Parinacota, the isotopic composition of plagioclase crystal rims or groundmass crystals is significantly higher than that of the high 87Sr/86Sr mafic magma. In others, where chemical zoning profiles suggest that recharge was from the low 87Sr/86Sr magma, the 87Sr/86Sr of the groundmass and crystal rims is higher than expected. This indicates either additional parent magmas to the two previously identified, or further crustal assimilation, either at lower crustal depths, before crystallization of plagioclase, or just after the last recharge. Our results illustrate the complexity of magma–crust interaction beneath Parinacota, which is likely to be representative of many other Central Andean volcanoes formed on thick crust. Such complex interactions can be revealed by combined study of chemical and isotopic zoning in plagioclase (in a textural petrographic context), despite a small whole-rock isotopic range. The distinct contamination patterns of various samples suggest an important role for the geometry, location and evolution of the magma plumbing system and, in general, variations of the thermal and compositional structure of the crust underneath the volcano

Sr Isotope Zoning in Plagioclase from Parinacota Volcano (Northern Chile): Quantifying Magma Mixing and Crustal Contamination

We present analyses of Sr isotope zoning by microdrilling and thermal ionization mass spectrometry in plagioclase crystals from Parinacota volcano (Central Volcanic Zone, northern Chile), which were analysed for major and minor element zoning in a previous study. Although the isotopic range of the bulk-rock samples is small at this volcano (0·7067-0·7070, except for one flow of mafic andesite at 0·7061), significant variations are seen (0·70649-0·70700) within and between plagioclase crystals. A general negative correlation is observed between Sr isotope composition and Sr concentration in the liquid in equilibrium with each plagioclase zone, as calculated from chemical zoning data and partition coefficients. Additional scatter is superimposed on this general trend, indicating a decoupling between isotopic and chemical variations for Sr. In one dacite sample a detailed isotopic profile shows increasing contamination during crystal growth, except for an abrupt decrease correlated with a dissolution surface and interpreted as a recharge event. We apply energy-constrained recharge, assimilation and fractional crystallization modelling to the melt evolution recorded in the chemical and isotopic zoning in this crystal. Results suggest 20% assimilation of the local wall-rock gneiss, at high initial temperatures. The isotopic data confirm the involvement of two contrasting mafic magmas, which are sampled at flank cinder cone vents. One (Lower Ajata) has a low Sr content with high 87Sr/86Sr, the other (Upper Ajata) has a high Sr content with lower 87Sr/86Sr. In some samples from Parinacota, the isotopic composition of plagioclase crystal rims or groundmass crystals is significantly higher than that of the high 87Sr/86Sr mafic magma. In others, where chemical zoning profiles suggest that recharge was from the low 87Sr/86Sr magma, the 87Sr/86Sr of the groundmass and crystal rims is higher than expected. This indicates either additional parent magmas to the two previously identified, or further crustal assimilation, either at lower crustal depths, before crystallization of plagioclase, or just after the last recharge. Our results illustrate the complexity of magma-crust interaction beneath Parinacota, which is likely to be representative of many other Central Andean volcanoes formed on thick crust. Such complex interactions can be revealed by combined study of chemical and isotopic zoning in plagioclase (in a textural petrographic context), despite a small whole-rock isotopic range. The distinct contamination patterns of various samples suggest an important role for the geometry, location and evolution of the magma plumbing system and, in general, variations of the thermal and compositional structure of the crust underneath the volcan

Bounds on the growth of high Sobolev norms of solutions to 2D Hartree Equations

In this paper, we consider Hartree-type equations on the two-dimensional torus and on the plane. We prove polynomial bounds on the growth of high Sobolev norms of solutions to these equations. The proofs of our results are based on the adaptation to two dimensions of the techniques we previously used to study analogous problems on $S^1$, and on $\mathbb{R}$.Comment: 38 page

Semiclassical Propagation of Coherent States for the Hartree equation

In this paper we consider the nonlinear Hartree equation in presence of a given external potential, for an initial coherent state. Under suitable smoothness assumptions, we approximate the solution in terms of a time dependent coherent state, whose phase and amplitude can be determined by a classical flow. The error can be estimated in $L^2$ by C \sqrt {\var}, \var being the Planck constant. Finally we present a full formal asymptotic expansion

Rate of Convergence Towards Hartree Dynamics

We consider a system of N bosons interacting through a two-body potential with, possibly, Coulomb-type singularities. We show that the difference between the many-body Schr\"odinger evolution in the mean-field regime and the effective nonlinear Hartree dynamics is at most of the order 1/N, for any fixed time. The N-dependence of the bound is optimal.Comment: 26 page

Instabilities in Zakharov Equations for Laser Propagation in a Plasma

F.Linares, G.Ponce, J-C.Saut have proved that a non-fully dispersive Zakharov system arising in the study of Laser-plasma interaction, is locally well posed in the whole space, for fields vanishing at infinity. Here we show that in the periodic case, seen as a model for fields non-vanishing at infinity, the system develops strong instabilities of Hadamard's type, implying that the Cauchy problem is strongly ill-posed

Density of State in a Complex Random Matrix Theory with External Source

The density of state for a complex $N\times N$ random matrix coupled to an external deterministic source is considered for a finite N, and a compact expression in an integral representation is obtained.Comment: 7 pages, late

Abstract cluster expansion with applications to statistical mechanical systems

We formulate a general setting for the cluster expansion method and we discuss sufficient criteria for its convergence. We apply the results to systems of classical and quantum particles with stable interactions

A sharp condition for scattering of the radial 3d cubic nonlinear Schroedinger equation

We consider the problem of identifying sharp criteria under which radial $H^1$ (finite energy) solutions to the focusing 3d cubic nonlinear Schr\"odinger equation (NLS) $i\partial_t u + \Delta u + |u|^2u=0$ scatter, i.e. approach the solution to a linear Schr\"odinger equation as $t\to \pm \infty$. The criteria is expressed in terms of the scale-invariant quantities $\|u_0\|_{L^2}\|\nabla u_0\|_{L^2}$ and $M[u]E[u]$, where $u_0$ denotes the initial data, and $M[u]$ and $E[u]$ denote the (conserved in time) mass and energy of the corresponding solution $u(t)$. The focusing NLS possesses a soliton solution $e^{it}Q(x)$, where $Q$ is the ground-state solution to a nonlinear elliptic equation, and we prove that if $M[u]E[u]<M[Q]E[Q]$ and $\|u_0\|_{L^2}\|\nabla u_0\|_{L^2} < \|Q\|_{L^2}\|\nabla Q\|_{L^2}$, then the solution $u(t)$ is globally well-posed and scatters. This condition is sharp in the sense that the soliton solution $e^{it}Q(x)$, for which equality in these conditions is obtained, is global but does not scatter. We further show that if $M[u]E[u] \|Q\|_{L^2}\|\nabla Q\|_{L^2}$, then the solution blows-up in finite time. The technique employed is parallel to that employed by Kenig-Merle \cite{KM06a} in their study of the energy-critical NLS

Singularity Formation in 2+1 Wave Maps

We present numerical evidence that singularities form in finite time during the evolution of 2+1 wave maps from spherically equivariant initial data of sufficient energy.Comment: 5 pages, 3 figure