Anomalous dynamics of Darcy flow and diffusion through heterogeneous media

This thesis studies diffusion phenomena in heterogeneous media, which includes Darcy flow and diffusive solute transport in geological media. Natural media are heterogeneous at different scales, which induces complexity in diffusion phenomena. The work is centered on the integration of the effects of heterogeneity on Darcy flow and solute diffusion into large scale models. The quantification of the effects of heterogeneity in diffusion phenomena is highly important for a large number of problems such as diffusion and reaction of chemicals and radionuclides in low permeability media, which is essential in subsurface hazardous waste storage problems, CO2 sequestration performance and groundwater management. In a stochastic framework we quantify the effects of heterogeneity in large scale models considering two interrelated strategies that can be called Ôcoefficient approachÕ, which deals with the derivation of effective coefficients to insert in equivalent homogeneous models, and Ôdynamic approachÕ, which deals with the upscaling of the local scale equations and the derivation of large scale formulations which can differ from their local counterparts. Whenever a diffusion process cannot be described in terms of effective coefficient, that behaviour is named anomalous or non-Fickian. Anomalous diffusion behaviours observed experimentally are frequently modelled by effective theories such as fractional diffusion equations, continuous time random walks. One limitation of these models is that often they are rather phenomenological and the relation to the local scale heterogeneity and dynamics may not be clear. In the dynamic approach we derive large scale descriptions that can explain anomalous behaviour and link it with a description of the local scale medium heterogeneity. To this end, we upscale the local scale governing equations using different methods depending on the type of medium heterogeneity. For moderately heterogeneous media we upscale flow equation by stochastic averaging. Starting from the classical flow equation at local scale determined by Darcy's law, we derive an upscaled non-local effective formulation. The non-local effective formulation is compared with its local counterpart by considering the head response for a pulse injection. Numerically, we solve flow and diffusion in heterogeneous media using particle tracking methods. While classical random walk particle tracking is an efficient numerical tool to solve for diffusion problems in moderately heterogeneous media, strong medium contrasts, as encountered in fractured media, render this method inefficient. For highly heterogeneous media efficiency of classical random walk can be increased by the use of the time domain random walk (TDRW) method. We rigorously derive the equivalence of the TDRW algorithm and the diffusion equation and we extend the classical TDRW method to solve diffusion problem in a heterogeneous medium with multi-rate mass transfer properties. Moreover we use the TDRW method in connection with a stochastic model for the heterogeneity in order to upscale heterogeneous diffusion processes. For a certain class of heterogeneity, the upscaled dynamics obey a CTRW. Analytically we upscale diffusion in highly heterogeneous media by using a multicontinuum representation of the media. Using volume and ensemble averaging we derive a multicontinuum model that can explain anomalous diffusion behavior and link it with a suitable local scale description of the medium heterogeneity. Finally, we integrate the multicontinuum model derived in the context of aquifer modelling. We derive a multicontinuum catchment model that can explain anomalous behavior observed in the aquifer dynamics at basin scale. We identify the physical mechanisms that induce anomalous behaviour and we determine the time scales that control its temporal evolution

Temporal scaling of groundwater discharge in dual and multicontinuum catchment models

This paper presents a multicontinuum approach to model fractal temporal scaling of catchment response in hydrological systems. The temporal scaling of discharge is quantified in frequency domain by the transfer function (), which is defined as the ratio between the spectra of catchment response and recharge time series. The transfer function may scale with frequency as ()approximate to-. While the classical linear and Dupuit models predict exponents of =2 and =1, observations indicate scalings with noninteger exponents . Such behaviors have been described by multifractal models, which, however, often lack a relation to the medium characteristics. We revisit and extend the classical linear Dupuit aquifer models and discuss their physical meanings in the light of the resulting aquifer dynamics. On the basis of these classical models, we derive a multicontinuum approach that provides physical recharge models which are able to explain fractal behaviors with exponents 1/2<<2. Furthermore, this approach allows to link the fractal dynamics of the discharge process to the physical aquifer characteristics as reflected in the distribution of storage time scales. We systematically analyze the catchment responses in the proposed multicontinuum models, and identify and quantify the time scales which characterize the dynamics of the catchment response to recharge.Peer ReviewedPostprint (published version

Temporal and spatial scaling of hydraulic response to recharge in fractured aquifers: Insights from a frequency domain analysis

International audienceQuantification of the recharge in fractured aquifers is particularly challenging because of the multiscale heterogeneity and the range of temporal scales involved. Here we investigate the hydraulic response to recharge of a fractured aquifer, using a frequency domain approach. Transfer functions are calculated in a range of temporal scales from 1 day up to a few years, for a fractured crystalline-rock aquifer located in Ploemeur (S Brittany, France), using recharge and groundwater level fluctuations as input and output respectively. The spatial variability of the response to recharge (characteristic response time, amplitude, temporal scaling) is analyzed for 10 wells sampling the different compartments of the aquifer. Some of the transfer functions follow the linear reservoir model behavior. On the contrary, others display a temporal scaling at high frequency that cannot be represented by classic models. Large-scale hydraulic parameters, estimated from the low-frequency response, are compared with those estimated from hydraulic tests at different scales. The variability of transmissivity and storage coefficient tends to decrease with scale, and the average estimates converge toward the highest values at large scale. The small-scale variability of diffusivities, which implies the existence of a range of characteristic temporal scales associated with different pathways, is suggested to be at the origin of the unconventional temporal scaling of the hydraulic response to recharge at high frequenc

Male breast cancer in BRCA1 and BRCA2 mutation carriers: pathology data from the Consortium of Investigators of Modifiers of BRCA1/2

Background BRCA1 and, more commonly, BRCA2 mutations are associated with increased risk of male breast cancer (MBC). However, only a paucity of data exists on the pathology of breast cancers (BCs) in men with BRCA1/2 mutations. Using the largest available dataset, we determined whether MBCs arising in BRCA1/2 mutation carriers display specific pathologic features and whether these features differ from those of BRCA1/2 female BCs (FBCs). Methods We characterised the pathologic features of 419 BRCA1/2 MBCs and, using logistic regression analysis, contrasted those with data from 9675 BRCA1/2 FBCs and with population-based data from 6351 MBCs in the Surveillance, Epidemiology, and End Results (SEER) database. Results Among BRCA2 MBCs, grade significantly decreased with increasing age at diagnosis (P = 0.005). Compared with BRCA2 FBCs, BRCA2 MBCs were of significantly higher stage (P for trend = 2 × 10−5) and higher grade (P for trend = 0.005) and were more likely to be oestrogen receptor–positive [odds ratio (OR) 10.59; 95 % confidence interval (CI) 5.15–21.80] and progesterone receptor–positive (OR 5.04; 95 % CI 3.17–8.04). With the exception of grade, similar patterns of associations emerged when we compared BRCA1 MBCs and FBCs. BRCA2 MBCs also presented with higher grade than MBCs from the SEER database (P for trend = 4 × 10−12). Conclusions On the basis of the largest series analysed to date, our results show that BRCA1/2 MBCs display distinct pathologic characteristics compared with BRCA1/2 FBCs, and we identified a specific BRCA2-associated MBC phenotype characterised by a variable suggesting greater biological aggressiveness (i.e., high histologic grade). These findings could lead to the development of gender-specific risk prediction models and guide clinical strategies appropriate for MBC management

NEGOTIATING GENDER ACCOUNTABILITY ACROSS CONTEXTS: THE CASE OF THE FORMER COLLEGE ATHLETE

Thesis (Ph.D.) - Indiana University, Department of Sociology/Arts and Sciences, 2024The purpose of this dissertation is to uncover the nuanced ways individuals make sense of shifting gender accountability norms as they transition out of a unique social context and into broader U.S. society. This dissertation examines how 84 former Division I college athletes use the socialization they acquired through college sport in their lives once they are no longer student-athletes. I ask: When is being a former college athlete utilized as an asset, and when is it seen as a liability? How does race and gender impact these choices? I use the case study of former Division I college athletes to investigate three key things. First, to explore how women and men translate the skillset acquired in the previous context of college athletics to their current workplace context that associates such skills with the masculine-typed ideal worker image. Second, to uncover the degree to which women and men can use a gendered status marker to their advantage at work. Third, to explore the extent to which broader cultural gender norms impede or facilitate the maintenance of one’s athletic identity—a social identity cultivated and rewarded by all genders in the college athletics context, still seen as masculine by broader U.S. society. Results show all former student-athletes use the social skills learned through college athletics in their work life today, but men can benefit from these skills to a greater degree than women because they more directly embody the ideal worker image. Respondents are more likely to use their college athlete credential in workplace contexts that share similar values and norms as college athletics. These workplace contexts are more likely to be predominantly white and men-dominated spaces than not. Thus, unsurprisingly, white men were more likely than Black men and Black and White women to use their athlete credential to their advantage at work. Furthermore, I find men have a smoother transition to recreational sporting life than women because broader gender norms continue to view athletics as a predominantly man-centric activity. I argue the case of the former D1 college athlete serves as an appropriate site to explore the ways in which people use or reject social practices previously learned in an overarchingly masculine institution as they navigate the contexts surrounding work and sport in their lives today

NEGOTIATING GENDER ACCOUNTABILITY ACROSS CONTEXTS: THE CASE OF THE FORMER COLLEGE ATHLETE

Thesis (Ph.D.) - Indiana University, Sociology/College of Arts and Sciences, 2024The purpose of this dissertation is to uncover the nuanced ways individuals make sense of shifting gender accountability norms as they transition out of a unique social context and into broader U.S. society. This dissertation examines how 84 former Division I college athletes use the socialization they acquired through college sport in their lives once they are no longer student-athletes. I ask: When is being a former college athlete utilized as an asset, and when is it seen as a liability? How does race and gender impact these choices? I use the case study of former Division I college athletes to investigate three key things. First, to explore how women and men translate the skillset acquired in the previous context of college athletics to their current workplace context that associates such skills with the masculine-typed ideal worker image. Second, to uncover the degree to which women and men can use a gendered status marker to their advantage at work. Third, to explore the extent to which broader cultural gender norms impede or facilitate the maintenance of one’s athletic identity—a social identity cultivated and rewarded by all genders in the college athletics context, still seen as masculine by broader U.S. society. Results show all former student-athletes use the social skills learned through college athletics in their work life today, but men can benefit from these skills to a greater degree than women because they more directly embody the ideal worker image. Respondents are more likely to use their college athlete credential in workplace contexts that share similar values and norms as college athletics. These workplace contexts are more likely to be predominantly white and men-dominated spaces than not. Thus, unsurprisingly, white men were more likely than Black men and Black and White women to use their athlete credential to their advantage at work. Furthermore, I find men have a smoother transition to recreational sporting life than women because broader gender norms continue to view athletics as a predominantly man-centric activity. I argue the case of the former D1 college athlete serves as an appropriate site to explore the ways in which people use or reject social practices previously learned in an overarchingly masculine institution as they navigate the contexts surrounding work and sport in their lives today

Large scale behavior of Flow in Heterogeneous Media

EGU General Assembly 2011, 3-8 Abril 2011, Viena (Austria)Spatial heterogeneity of hydraulic conductivity can lead to anomalous behaviour in the pressure response to hydraulic stimulation. The classical interpretation framework of Theis, based on a homogeneous bi-dimensional equivalent medium is well known, but cannot describe the anomalous pressure behavior observed in nature. In order to explain anomalous behaviours with a physical meaningful model we considered a double permeability model. The model is constituted by two layers characterized by different hydraulic parameters, which constitute the mobile and immobile zone. Unlike the Barenblatt model (1960), which assumes quasi-steady pressure distribution in the mobile and immobile zone, we choose a non-equilibrium approach of kinetic pressure exchange between mobile and immobile zones. We obtain a temporally non-local governing equation for the hydraulic head that can model observed sub-diffusive drawdown behavior. We compare our model to the Theis model (1935) and the fractional flow models by Barker (1988) and Acuna and Yortsos (1995). We derive solutions for 1, 2 and 3 dimensions and apply them to the experimental data of pumping tests performed in a highly fractured aquifer (La Borgne, 2004). The Theis model clearly fails to explain the observed hydraulic variation, in particular the sub-diffusive trend of drawdown. The proposed double permeability model can explain the data of the drowdawn curves and the evolution of the characteristic drawdown time and the characteristic drawdown amplitude with the distance from the pumping well.Peer reviewe