MS

thesisA new conductivity model, the Generalized Effective Medium Theory of Induced Polarization (GEMTIP) is tested with complex resistivity data and detailed mineralogy of porphyry system rock samples. The induced polarization (IP) effects are important phenomena for EM exploration. GEMTIP represents an expansion of the rock properties used for electromagnetic modeling of bulk apparent resistivity. The new model includes, mineral type, mineral size, mineral conductivity and other petrographic information. Rocks containing disseminated sulfides from porphyry systems are chosen as a good analog to the testing of the spherical grain analytic solution of GEMTIP. GEMTIP predicts the same trend in peak IP response as function of grain size for both chalcopyrite and pyrite containing synthetic rocks as a previous study, study. Inversion routines are developed and tested using synthetic data to recover the two empirical variables from recorded complex resistivity data. The two empirical variables are surface polarizability (a) and the decay coefficient (C). For three porphyry system rock samples, detailed geologic analysis using optical mineralogy, and X-ray tomography is conducted to determine GEMTIP model inputs. Sulfides in the rock samples exhibited a range of forms including near perfect cubes, stacked cubes, rounded, and complex amorphous forms. The sizes of sulfides varied from less than 0.01 mm to over 2 mm in radius. Measured surface area and surface area to volume ratios for each sample do not match the computed values assuming uniform spherical grains. Complex resistivity values are calculated from recorded EM data from 0.0156 Hz to 9216 Hz. Using the observed mineralogical data the GEMTIP model was able to fit the recorded complex resistivity data for the three samples with a the inclusion of an empirical factor to account for the difference in measured and computed spherical surface area reenforcing the role of surface area in the IP effect. Successful GEMTIP modeling of the rock samples provided insight into controlling factors of the IP effect. Forward geophysical modeling of copper porphyry systems is accomplished using geologic inputs from rock-scale to deposit-scale. For deposit scale modeling an Integral Equation method Electromagnetic forward modeling code IBCEM3DIP, developed by the Consortium for Electromagnetic Modeling and Inversion (CEMI) is used. A new interface to allow modeling of geometrically complex geologic systems was developed for the IBCEM3DIP code. The GEMTIP conductivity model was incorporated into IBCEM3DIP. Both the rock type and associated electric properties and mineralogical properties (approximate) are used for synthetic data creation. Using the new interface and developed Simplified Porphry Model as a template the effect of deposit-scale changes in sulfide distribution are tested on synthetic IP data. Although differences in the apparent resistivity data are subtle, changes in sulfide distribution strongly influence the apparent phase data. This highlights the importance of IP data and its use for mineral disrimination. With advances in the understanding of the IP effect through GEMTIP, forward modeling and inversion, detection and discrimination capability will improve for porphyry systems and other geologic targets, leading to greater efficiency in mineral exploration

Food Quality in Producer-Grazer Models: A Generalized Analysis

Stoichiometric constraints play a role in the dynamics of natural populations, but are not explicitly considered in most mathematical models. Recent theoretical works suggest that these constraints can have a significant impact and should not be neglected. However, it is not yet resolved how stoichiometry should be integrated in population dynamical models, as different modeling approaches are found to yield qualitatively different results. Here we investigate a unifying framework that reveals the differences and commonalities between previously proposed models for producer-grazer systems. Our analysis reveals that stoichiometric constraints affect the dynamics mainly by increasing the intraspecific competition between producers and by introducing a variable biomass conversion efficiency. The intraspecific competition has a strongly stabilizing effect on the system, whereas the variable conversion efficiency resulting from a variable food quality is the main determinant for the nature of the instability once destabilization occurs. Only if the food quality is high an oscillatory instability, as in the classical paradox of enrichment, can occur. While the generalized model reveals that the generic insights remain valid in a large class of models, we show that other details such as the specific sequence of bifurcations encountered in enrichment scenarios can depend sensitively on assumptions made in modeling stoichiometric constraints.Comment: Online appendixes include

Stochastic models (cooperative and non-cooperative) for NMR analysis of the hetero-association of aromatic molecules in aqueous solution

Stochastic cooperative (STOCH-C) and non-cooperative (STOCH-NC) models have been developed for NMR analysis of the hetero-association of aromatic compounds in solution, in order to take into account all physically meaningful association reactions of molecules in which there are no limitations on the lengths of the aggregates and complexes. These algorithmical approaches are compared with previously published basic (BASE) and generalized (GEN) analytical statistical thermodynamical models of hetero-association of biologically active aromatic molecules using the same sets of published NMR data measured under the same solution conditions (0.1 M phosphate buffer, pD = 7.1, T = 298 K). It is shown that, within experimental errors, the BASE analytical model may be used to describe molecular systems characterized by relatively small contributions of hetero-association reactions, whereas the GEN model may be applied to hetero-association reactions of any aromatic compound with different self-association properties. The STOCH-C computational algorithm enabled the effect on hetero-association of the interactions of molecules with different cooperativity parameters of self-association to be estimated for the first time and it is proposed that the algorithm for the stochastic models has great potential for detailed investigation and understanding of the interactions of aromatic molecules in solution

General analysis of mathematical models for bone remodeling

Bone remodeling is regulated by pathways controlling the interplay of osteoblasts and osteoclasts. In this work, we apply the method of generalized modelling to systematically analyse a large class of models of bone remodeling. Our analysis shows that osteoblast precursors can play an important role in the regulation of bone remodeling. Further, we find that the parameter regime most likely realized in nature lies very close to bifurcation lines, marking qualitative changes in the dynamics. Although proximity to a bifurcation facilitates adaptive responses to changing external conditions, it entails the danger of losing dynamical stability. Some evidence implicates such dynamical transitions as a potential mechanism leading to forms of Paget's disease

Quasichemical Models of Multicomponent Nonlinear Diffusion

Diffusion preserves the positivity of concentrations, therefore, multicomponent diffusion should be nonlinear if there exist non-diagonal terms. The vast variety of nonlinear multicomponent diffusion equations should be ordered and special tools are needed to provide the systematic construction of the nonlinear diffusion equations for multicomponent mixtures with significant interaction between components. We develop an approach to nonlinear multicomponent diffusion based on the idea of the reaction mechanism borrowed from chemical kinetics. Chemical kinetics gave rise to very seminal tools for the modeling of processes. This is the stoichiometric algebra supplemented by the simple kinetic law. The results of this invention are now applied in many areas of science, from particle physics to sociology. In our work we extend the area of applications onto nonlinear multicomponent diffusion. We demonstrate, how the mechanism based approach to multicomponent diffusion can be included into the general thermodynamic framework, and prove the corresponding dissipation inequalities. To satisfy thermodynamic restrictions, the kinetic law of an elementary process cannot have an arbitrary form. For the general kinetic law (the generalized Mass Action Law), additional conditions are proved. The cell--jump formalism gives an intuitively clear representation of the elementary transport processes and, at the same time, produces kinetic finite elements, a tool for numerical simulation.Comment: 81 pages, Bibliography 118 references, a review paper (v4: the final published version