Ivan L'Heureux

Dynamical model of oscillatory zoning in plagioclase with nonlinear partition relation

We present a nonlinear dynamical model for oscillatory zoning in plagioclase based on a simple isothermal constitutive undercooling mechanism. A phenomenological partitioning is introduced to relate the concentration of An in the melt at the interface with the concentration in the solid. The non-linearities in the model result from the coupling of the growth velocity with the local An concentration and from the boundary condition at the interface. The consideration of a nonlinear boundary condition is new and generalizes previous nonlinear growth models. It is shown that parameter values exist for which oscillatory solutions are possible via a Hopf bifurcation. As the system is driven further out of equilibrium, the model shows the development of chaotic solutions via a period-doubling sequence.

A new model of periodic precipitation incorporating nucleation, growth and ripening

Abstract We present and solve a one-dimensional model of periodic precipitation which includes nucleation, growth and ripening processes. This model thus generalizes two important models: the prenucleation-based model of Dee and the postnucleation competitive growth model (CGM) of Feeney et al. By tuning a simple phenomenological parameter, our model smoothly bridges the gap between a nucleation-growth dominated regime and one where ripening is active.

Self-organized rhythmic patterns in geochemical systems.

Chemical oscillating patterns are ubiquitous in geochemical systems. Although many such patterns result from systematic variations in the external environmental conditions, it is recognized that some patterns are due to intrinsic self-organized processes in a non-equilibrium nonlinear system with positive feedback. In rocks and minerals, periodic precipitation (Liesegang bands) and oscillatory zoning constitute good examples of patterns that can be explained using concepts from nonlinear dynamics. Generally, as the system parameters exceed some threshold values, the steady (time-independent) state characterizing the system loses its stability. The system then evolves towards other time-dependent solutions (‘attractors’) that may have an oscillatory behaviour or a complex chaotic one. In this review, we describe many of these pattern types taken from a variety of geological environments: eruptive, sedimentary, hydrothermal or metamorphic. One particular example (periodic precipitation of pyrite bands in an evolving sapropel sediment) is presented here for the first time. This will help in convincing the reader that the tools of nonlinear dynamics may be useful to understand the history of our planet.

dSED: a database tool for modeling sediment early diagenesis

Mathematical modeling of sediment early diagenesis always involves choosing and describing a set of chemical reactions and processes that is both self-consistent and sufficient for the problem at hand. This critical choice is always a compromise between describing the systems complexity in all details and using a manageable set of reactions with known or obtainable parameters such as equilibrium and rate constants. We present a database tool for modeling sediment early diagenesis (dSED) that is designed to help modelers and sediment geochemists in this difficult conceptual step. The database should facilitate the development of state-of-the-art spatially continuous reaction-transport models (RTM), as well as simpler interacting-compartment (box) models. It allows one to explore: available kinetic and thermodynamic information, alternative descriptions of the same major processes, different degrees of completeness in description, processes and reactions that could be added or modeled differently, published solutions used by previous workers, and other information. The database is searchable and allows viewing reactions by specific products or reactants, types of processes, or other customized criteria. It operates under Microsoft Access(TM) and can be added to, modified and programmed by the user. The latest version of dSED and its user manual can be downloaded at http://www.science.uottawa.ca/LSSE/dSED.

Impact of seasonal temperature and pressure changes on methane gas production, dissolution, and transport in unfractured sediments

A one‐dimensional reaction‐transport model is used to investigate the dynamics of methane gas in coastal sediments in response to intra‐annual variations in temperature and pressure. The model is applied to data from two shallow water sites in Eckernforde Bay (Germany) characterized by low and high rates of upward fluid advection. At both sites, organic matter is buried below the sulfate‐reducing zone to the methanogenic zone at sufficiently high rates to allow supersaturation of the pore water with dissolved methane and to form a free methane gas phase. The methane solubility concentration varies by similar magnitudes at both study sites in response to bottom water temperature changes and leads to pronounced peaks in the gas volume fraction in autumn when the methanic zone temperature is at a maximum. Yearly hydrostatic pressure variations have comparatively negligible effects on methane solubility. Field data suggest that no free gas escapes to the water column at any time of the year. Although the existence of gas migration cannot be substantiated by direct observation, a speculative mechanism for slow moving gas is proposed here. The model results reveal that free gas migrating upward into the undersaturated pore water will completely dissolve and subsequently be consumed above the free gas depth (FGD) by anaerobic oxidation of methane (AOM). This microbially mediated process maintains methane undersaturation above the FGD. Although the complexities introduced by seasonal changes in temperature lead to different seasonal trends for the depth‐integrated AOM rates and the FGD, both sites adhere to previously developed prognostic indicators for methane fluxes based on the FGD.

A simple model of flow patterns in overpressured sedimentary basins with heat transport and fracturing

Overpressure zones in sedimentary basins are defined as sediments where the fluid pore pressure is substantially higher than hydrostatic. Chief among the causes for the formation of overpressure is the rapid deposition of low-permeablity sediments so that compaction and dewatering are inhibited. This results in the support of the overlying material in part by the fluid, rather than by grain to grain contact. Many overpressure zones also have associated geothermal anomalies whereby the geotherms are hotter than normal. In this paper, we present a one-dimensional model of overpressure generation and dissipation, with hydraulic fracture. The fluid flow is coupled to the fluid temperature field and to the motion of the solid sediment matrix. Compacted coordinates are introduced to decouple the fluid velocity and temperature from the solid matrix velocity. Using a maximum sedimentation rate of 1 km Myr−1 and a hydraulic conductivity at the top of the layer equal to 5×10−12 m s−1, 3 km of partially compacted sediment are deposited in 5 Myr, generating an overpressure of 0.81 of the lithostatic pressure at the bottom of the sediment layer. An undercompaction of 19% relative to normally compacted sediment is developed at a final depth of 3.66 km by the end of sedimentation. Dissipation of the overpressure takes place on a timescale of the order of 40 Myr. The equilibrium temperature generates thermal gradients in excess of 38°C km−1 at shallow depths. Fast sedimentation rate and high permeability in the fractured state favor oscillating behavior and propagation of fracture waves. Overpressure zones may constitute a proximal source of hydrothermal fluids for the genesis of ore deposits in sedimentary basins.

Nonlinear Geophysics: Why We Need It

Few geoscientists would deny that effects are often sensitively dependent on causes, or that their amplification is commonly so strong as to give rise to qualitatively new “emergent” properties, or that geostructures are typically embedded one within another in a hierarchy. Starting in the 1980s, a growing number felt the need to underline the absolute importance of such nonlinearity through workshops and conferences. Building on this, the European Geosciences Union (EGU) organized a nonlinear processes (NP) section in 1990; AGU established a nonlinear geophysics (NG) focus group in 1997; and both unions began collaborating on an academic journal, Nonlinear Processes in Geophysics, in 1994.

Mechanism and duration of banding in Mississippi Valley‐type sphalerite

We present a new quantitative model of mm-scale Fe-Zn banding in sphalerite Mississippi-Valley type ore deposits. The banded sphalerite is typically intergrown with dendritic galena in cm-scale clusters. We show that this pattern may arise due to a combined effect of geochemical reactions, crystal growth, dissolution, and ripening in far-from-equilibrium conditions. The simulated patterns are due to a self-propagating sequence of growth and dissolution events (so called coarsening wave). One of the surprising results is the geologically short time scale of the pattern formation.

Two-dimensional model of banding pattern formation in minerals by means of coarsening waves: Mississippi Valley-type sphalerite

Abstract We present for the first time a two-dimensional quantitative model of mm-scale Fe–Zn banding in ZnS ore mineral sphalerite. Banded ring-like compositional pattern is shown to arise due to a self-propagating sequence of growth and dissolution (so-called coarsening wave). Conditions for generating and preserving such a pattern are discussed.

EXPERIMENTAL EVIDENCE FOR DICHOTOMOUS NOISE-INDUCED STATES IN A BISTABLE INTERFERENCE FILTER

Abstract Noise-induced transitions in a ZnSe interference filter subjected to Markovian dichotomous fluctuations in the incident power the experimentally detected and investigated for various noise-correlation times. The results are qualitatively consistent with theoretical expectations.