Anomalous dispersion in correlated porous media: A coupled continuous time random walk approach

We study the causes of anomalous dispersion in Darcy-scale porous media characterized by spatially heterogeneous hydraulic properties. Spatial variability in hydraulic conductivity leads to spatial variability in the flow properties through Darcy's law and thus impacts on solute and particle transport. We consider purely advective transport in heterogeneity scenarios characterized by broad distributions of heterogeneity length scales and point values. Particle transport is characterized in terms of the stochastic properties of equidistantly sampled Lagrangian velocities, which are determined by the flow and conductivity statistics. The persistence length scales of flow and transport velocities are imprinted in the spatial disorder and reflect the distribution of heterogeneity length scales. Particle transitions over the velocity length scales are kinematically coupled with the transition time through velocity. We show that the average particle motion follows a coupled continuous time random walk (CTRW), which is fully parameterized by the distribution of flow velocities and the medium geometry in terms of the heterogeneity length scales. The coupled CTRW provides a systematic framework for the investigation of the origins of anomalous dispersion in terms of heterogeneity correlation and the distribution of heterogeneity point values. Broad distributions of heterogeneity point values and lengths scales may lead to very similar dispersion behaviors in terms of the spatial variance. Their mechanisms, however are very different, which manifests in the distributions of particle positions and arrival times, which plays a central role for the prediction of the fate of dissolved substances in heterogeneous natural and engineered porous materials

Mechanism and stochastic dynamics of transport in Darcy-scale heterogeneous porous media

Solute transport in heterogeneous porous media in general exhibits anomalous behaviors, in the sense that it is characterized by features that cannot be explained in terms of traditional models based on the advection-dispersion equation with constant effective coefficients. Signatures of anomalous transport are the non-linear temporal growth of the variance of solute concentration, non- Gaussian density profiles and heavy-tailed breakthrough curves. Understanding and predicting transport behavior in groundwater systems is crucial for several environmental and industrial applications, including groundwater management and risk assessment for nuclear waste repositories. The complexity of this task lies in the intrinsic multi-scale heterogeneity of geological formations and in the large amount of degrees of freedom. Hence, the predictive description of transport requires a process of upscaling that is based on measurable medium and flow attributes. The time domain random walk (TDRW) and continuous time random walk (CTRW) approaches provide suitable frameworks for transport upscaling. In this thesis, we identify different mechanisms that induce anomalous transport and we quantify their impact on transport attributes. We propose average transport models that can be parameterized in terms of flow and medium properties. Among the mechanisms that induce non-Fickian behaviors, a pivotal role is played by the heterogeneity of the flow field, which is directly linked to medium disorder. Due to its importance, the impact of advective heterogeneity is studied throughout the thesis, alongside with other mechanisms. First, we consider solute trapping due to physical or chemical heterogeneity, which we parameterize in terms of a constant trapping rate and a distribution of return times. We observe three distinct transport regimes that are linked to characteristic trapping time scales. At early times, transport is advection- controlled until particles start to get trapped. Then, the increasing distance between mobile and immobile particles gives rise to a superdiffusive regime which finally evolves towards a trapping-controlled regime. Second, we study transport in correlated porous media. We show that particle motion describes a coupled CTRW that is parameterized in terms of the distribution of flow velocity and length scales. We show that disorder and correlation may lead to similar behaviors in terms of displacement moments, but the difference between these mechanisms is manifest in the distributions of particle positions and arrival times. Next, we study the relationship between flow and transport properties and the impact of different injection conditions on transport. To this end, the relationship between Eulerian and Lagrangian velocities is investigated. Lagrangian statistics evolves to a steady-state that depends on the injection conditions. We study the velocity organization in Darcy flows and we develop a CTRW model for transport that is parameterized in terms of flow and medium attributes only. This CTRW accounts for non-stationarity through Markovian velocity models. We study the impact of advective heterogeneity by considering different disorder scenarios. Finally, we quantify the impact of diffusion in layered and fibrous heterogeneous media by considering two disorder scenarios characterized by quenched random velocities and quenched retardation properties, respectively. These mechanisms lead to different, dimension-dependent disorder samplings that give rise to dual transport processes in space and time. Specifically, transport describes correlated Lévy flights in the random velocity model and correlated CTRWs in the random retardation model.El transporte de solutos en medios heterogéneos porosos exhibe comportamientos anómalos, que se caracteriza por rasgos que no pueden ser explicados en términos de modelos tradicionales basados en la ecuación de advección-dispersión con coeficientes efectivos constantes. Las características del transporte anómalo son el crecimiento temporal no lineal de la varianza de la concentración de soluto, los perfiles de densidad no gausianos y la curvas de llegada con colas pronunciadas. Entender y predecir el comportamiento del transporte en hidrología subterránea es crucial para aplicaciones ambientales e industriales, como la gestión de aguas subterráneas o la evaluación de riesgos en repositorios de residuos nucleares. La complejidad de estas tareas se debe a la heterogeneidad intrínseca en múltiples escalas de las formaciones geológicas y del gran número de grados de libertad. Por lo tanto, una descripción predictiva del transporte requiere un proceso de upscaling basado en propiedades medibles del medio y el flujo para el que los modelos time domain random walk (TDRW) y continuous time random walk (CTRW) proporcionan un marco adecuado. En esta tesis, se identifican los mecanismos que inducen transporte anómalo y se cuantifica su impacto en el transporte. Se proponen modelos de transporte parametrizados en términos de las propiedades del medio y el flujo. Entre los mecanismos que inducen comportamientos no fickianos, la heterogeneidad del flujo, relacionada con el desorden del medio, desempeña un papel fundamental. Por lo tanto, su impacto se estudia junto con los de otros mecanismos a lo largo de toda la tesis. Primero, se considera el atrapamiento de soluto debido a heterogeneidades físicas o químicas parametrizadas en términos de un ratio de atrapamiento constante y una distribución de tiempos de retorno. Se observan tres regímenes de transporte relacionados con las escalas temporales características del atrapamiento. A tiempos pequeños, el transporte está controlado por la advección hasta que las partículas comienzan a ser atrapadas. A continuación el incremento de la distancia entre partículas móviles e inmóviles origina un régimen superdifusivo que finalmente evoluciona hacia un régimen controlado por el atrapamiento. Después, se estudia el transporte en medios correlacionados en los que el movimiento de las partículas es descrito por un CTRW acoplado parametrizado según la distribución de velocidades del flujo y de las escalas espaciales. El desorden y la correlación generan comportamientos similares en los momentos del desplazamiento de las partículas, pero diferentes en las distribución de posiciones y de tiempos de llegada. A continuación, se estudia la relación entre flujo y transporte bajo diferentes condiciones de inyección, a través de las velocidades eulerianas y lagrangianas. La estadística lagrangiana evoluciona hacia un estado estacionario que depende de los modos de inyección. Se estudia la organización de las velocidades en flujos de Darcy y se desarrolla un CTRW para el transporte que se parametriza solo en términos de las propiedades del medio y del flujo. Este CTRW considera la no estacionariedad a través de modelos de velocidad markovianos. El impacto de la heterogeneidad advectiva se estudia considerando diferentes escenarios de desorden. Finalmente, se cuantifica el impacto de la difusión en medios heterogéneos estratificados considerando dos escenarios de heterogeneidad que se caracterizan respectivamente por velocidades y propiedades de retraso aleatorias. Estos mecanismos originan diferentes muestreos del desorden que generan procesos de transportes duales en tiempo y espacio. El transporte describe un Lévy flight correlacionado en el modelo de velocidades aleatorias y un CTRW correlacionado en el modelo de retraso

Mechanism and stochastic dynamics of transport in Darcy-scale heterogeneous porous media

Solute transport in heterogeneous porous media in general exhibits anomalous behaviors, in the sense that it is characterized by features that cannot be explained in terms of traditional models based on the advection-dispersion equation with constant effective coefficients. Signatures of anomalous transport are the non-linear temporal growth of the variance of solute concentration, non- Gaussian density profiles and heavy-tailed breakthrough curves. Understanding and predicting transport behavior in groundwater systems is crucial for several environmental and industrial applications, including groundwater management and risk assessment for nuclear waste repositories. The complexity of this task lies in the intrinsic multi-scale heterogeneity of geological formations and in the large amount of degrees of freedom. Hence, the predictive description of transport requires a process of upscaling that is based on measurable medium and flow attributes. The time domain random walk (TDRW) and continuous time random walk (CTRW) approaches provide suitable frameworks for transport upscaling. In this thesis, we identify different mechanisms that induce anomalous transport and we quantify their impact on transport attributes. We propose average transport models that can be parameterized in terms of flow and medium properties. Among the mechanisms that induce non-Fickian behaviors, a pivotal role is played by the heterogeneity of the flow field, which is directly linked to medium disorder. Due to its importance, the impact of advective heterogeneity is studied throughout the thesis, alongside with other mechanisms. First, we consider solute trapping due to physical or chemical heterogeneity, which we parameterize in terms of a constant trapping rate and a distribution of return times. We observe three distinct transport regimes that are linked to characteristic trapping time scales. At early times, transport is advection- controlled until particles start to get trapped. Then, the increasing distance between mobile and immobile particles gives rise to a superdiffusive regime which finally evolves towards a trapping-controlled regime. Second, we study transport in correlated porous media. We show that particle motion describes a coupled CTRW that is parameterized in terms of the distribution of flow velocity and length scales. We show that disorder and correlation may lead to similar behaviors in terms of displacement moments, but the difference between these mechanisms is manifest in the distributions of particle positions and arrival times. Next, we study the relationship between flow and transport properties and the impact of different injection conditions on transport. To this end, the relationship between Eulerian and Lagrangian velocities is investigated. Lagrangian statistics evolves to a steady-state that depends on the injection conditions. We study the velocity organization in Darcy flows and we develop a CTRW model for transport that is parameterized in terms of flow and medium attributes only. This CTRW accounts for non-stationarity through Markovian velocity models. We study the impact of advective heterogeneity by considering different disorder scenarios. Finally, we quantify the impact of diffusion in layered and fibrous heterogeneous media by considering two disorder scenarios characterized by quenched random velocities and quenched retardation properties, respectively. These mechanisms lead to different, dimension-dependent disorder samplings that give rise to dual transport processes in space and time. Specifically, transport describes correlated Lévy flights in the random velocity model and correlated CTRWs in the random retardation model.El transporte de solutos en medios heterogéneos porosos exhibe comportamientos anómalos, que se caracteriza por rasgos que no pueden ser explicados en términos de modelos tradicionales basados en la ecuación de advección-dispersión con coeficientes efectivos constantes. Las características del transporte anómalo son el crecimiento temporal no lineal de la varianza de la concentración de soluto, los perfiles de densidad no gausianos y la curvas de llegada con colas pronunciadas. Entender y predecir el comportamiento del transporte en hidrología subterránea es crucial para aplicaciones ambientales e industriales, como la gestión de aguas subterráneas o la evaluación de riesgos en repositorios de residuos nucleares. La complejidad de estas tareas se debe a la heterogeneidad intrínseca en múltiples escalas de las formaciones geológicas y del gran número de grados de libertad. Por lo tanto, una descripción predictiva del transporte requiere un proceso de upscaling basado en propiedades medibles del medio y el flujo para el que los modelos time domain random walk (TDRW) y continuous time random walk (CTRW) proporcionan un marco adecuado. En esta tesis, se identifican los mecanismos que inducen transporte anómalo y se cuantifica su impacto en el transporte. Se proponen modelos de transporte parametrizados en términos de las propiedades del medio y el flujo. Entre los mecanismos que inducen comportamientos no fickianos, la heterogeneidad del flujo, relacionada con el desorden del medio, desempeña un papel fundamental. Por lo tanto, su impacto se estudia junto con los de otros mecanismos a lo largo de toda la tesis. Primero, se considera el atrapamiento de soluto debido a heterogeneidades físicas o químicas parametrizadas en términos de un ratio de atrapamiento constante y una distribución de tiempos de retorno. Se observan tres regímenes de transporte relacionados con las escalas temporales características del atrapamiento. A tiempos pequeños, el transporte está controlado por la advección hasta que las partículas comienzan a ser atrapadas. A continuación el incremento de la distancia entre partículas móviles e inmóviles origina un régimen superdifusivo que finalmente evoluciona hacia un régimen controlado por el atrapamiento. Después, se estudia el transporte en medios correlacionados en los que el movimiento de las partículas es descrito por un CTRW acoplado parametrizado según la distribución de velocidades del flujo y de las escalas espaciales. El desorden y la correlación generan comportamientos similares en los momentos del desplazamiento de las partículas, pero diferentes en las distribución de posiciones y de tiempos de llegada. A continuación, se estudia la relación entre flujo y transporte bajo diferentes condiciones de inyección, a través de las velocidades eulerianas y lagrangianas. La estadística lagrangiana evoluciona hacia un estado estacionario que depende de los modos de inyección. Se estudia la organización de las velocidades en flujos de Darcy y se desarrolla un CTRW para el transporte que se parametriza solo en términos de las propiedades del medio y del flujo. Este CTRW considera la no estacionariedad a través de modelos de velocidad markovianos. El impacto de la heterogeneidad advectiva se estudia considerando diferentes escenarios de desorden. Finalmente, se cuantifica el impacto de la difusión en medios heterogéneos estratificados considerando dos escenarios de heterogeneidad que se caracterizan respectivamente por velocidades y propiedades de retraso aleatorias. Estos mecanismos originan diferentes muestreos del desorden que generan procesos de transportes duales en tiempo y espacio. El transporte describe un Lévy flight correlacionado en el modelo de velocidades aleatorias y un CTRW correlacionado en el modelo de retraso.Postprint (published version

Advanced bearing study. Part 2: Bearing tests

Tests of ball bearings of various material combinations in liquid hydroge

Parental separation and children's educational attainment: heterogeneity and rare and common educational outcomes

While the association between parental separation and children’s lower educational achievements is a robust finding, the evidence regarding its heterogeneity across social groups is mixed. Some studies show that socioeconomically advantaged families manage to shelter their pupils from the consequences of parental break-up, while others find the opposite. We contribute to this debate and sketch a structural theory of the heterogeneity of the consequences associated to parental separation on children's educational outcomes. We argue that the separation penalty and its heterogeneity across social backgrounds differ depending on the selectivity of a given educational outcome. In particular, the smallest penalty will be observed for very rare and very common outcomes. The rarity of an educational outcome depends on pupils’ social background, which might produce the observed heterogeneity even if the separation penalty itself is equal across parental social background. We investigate the heterogeneity of the consequences of separation by parents’ education in Spain on two children’s outcomes. One outcome (enrolment in tertiary education) is rare for children in low educated families, while the other (retaking in primary and secondary education) is rare for children in highly educated families. The results show that the penalty associated to parental separation for retaking a year in primary and secondary education is larger for children of low educated mothers. No heterogeneity is found for enrolment in tertiary education.Während der Zusammenhang zwischen elterlicher Trennung und geringeren Bildungserfolgen der Kinder als belastbares Forschungsergebnis gilt, ist die Evidenz bezüglich ihrer Heterogenität über die sozialen Gruppen hinweg uneinheitlich. Einige Studien zeigen auf, dass sozioökonomisch bessergestellte Familien es schaffen, ihre Kinder im Schulalter vor den Folgen elterlicher Trennung abzuschirmen, während andere Studien dies verneinen. Wir tragen zu dieser Debatte bei, indem wir eine Strukturtheorie der Heterogenität der mit der der elterlichen Trennung assoziierten Konsequenzen für den Bildungsergebnisse der Kinder skizzieren. Wir argumentieren, dass die Bildungseinbußen aufgrund der Trennung und deren Heterogenität über die sozialen Hintergründe hinweg in Abhängigkeit von der Selektivität des jeweiligen Bildungsergebnisses unterscheiden. Insbesondere gilt, dass die geringsten Einbußen für sehr seltene und für sehr verbreitete Ergebnisse beobachtet werden. Die Seltenheit eines Bildungsergebnisses hängt vom sozialen Hintergrund der Schüler ab, der wiederum die beobachtete Heterogenität hervorbringen könnte; dies selbst dann, wenn die Einbußen aufgrund der Trennung über den sozialen Hintergrund der Eltern hinweg gleich sind. Wir untersuchen die Heterogenität der Trennungsfolgen anhand der elterlichen Bildung für zwei Ergebnisse für Kinder in Spanien: Eines dieser Ergebnisse - Besuch einer Einrichtung des tertiären Bildungssektors - tritt für Kinder in Familien mit niedriger Bildung selten auf, während das andere - Klassenwiederholung im Primär- und Sekundärschulsektor - für Kinder aus höher gebildeten Familien selten ist. Die Ergebnisse zeigen, dass die Bildungseinbußen, die mit der elterlichen Trennung in Verbindung gebracht werden - das Sitzenbleiben in der Elementar- und Sekundarschule - für die Kinder von Müttern mit niedriger Bildung größer sind. Für den Besuch des tertiären Bildungssektors wurde keine Heterogenität gefunden

Gender and socioeconomic inequalities in health and wellbeing across age in France and Switzerland

There is increasing evidence that wellbeing is unequally distributed across sociodemographic groups in contemporary societies. However, less is known about the divergence across social groups of trajectories of wellbeing across age groups. This issue is of great relevance in contexts characterised by changing population structures and growing imbalances across and within generations, and in which ensuring that everyone has the opportunity to have a happy and healthy life course is a primary welfare goal. In this study, we investigate wellbeing trends in France and Switzerland across age, gender, and socioeconomic status groups. We use two household surveys (the Sant´e et Itin´eraires Professionnels and the Swiss Household Panel) to compare the unfolding inequalities in health and wellbeing across age groups in two rich countries. We view wellbeing as multidimensional, following the literature highlighting the importance of considering dierent dimensions and measures of wellbeing. Thus, we investigate a number of outcomes, including dierent measures of physical and mental health, as well as of relational wellbeing, using a linear regression model and a linear probability model. Our findings show interesting country and dimension-specific heterogeneities in the development of health and wellbeing over age. While our results indicate that there are gender and educational inequalities in both Switzerland and France, and that gender inequalities in mental health accumulate with age in both countries, we also find that educational inequalities in health and wellbeing remain rather stable across age groups

The causal effect of the great recession on childlessness of white American women

Published: 13 November 2015Many studies have documented a negative association between macroeconomic indicators and fertility in times of economic crisis. These studies are based on research designs that do not allow for excluding that the observed association is driven by confounders. The aim of the present paper is to estimate the causal effect of the Great Recession on cohorts’ childlessness in the United States. We apply a difference-in-difference approach to the probability of childlessness in two pseudo-cohorts of white women who entered the age of 34–36 years old being childless before the crisis, in 2004, and at the onset of the crisis, in 2007. Our identification strategy relies on the assumption that these two adjacent cohorts of women differ only because the latter cohort lived some critical years of reproductive life during the Great Recession period. We then study how many childless women aged 34–36 had a child when they were 37–39, between the years 2004 and 2007 for the control group and between the years 2007 and 2010 for the treatment group. We argue that an increase of childlessness at the age 37–39 is likely to lead to an increase in permanent childlessness, since major catch-up processes are unlikely after age 40. We replicate the analysis on two datasets: the American Community Survey and the Fertility Supplement of the Current Population Survey. Our findings suggest that the Great Recession has had a positive, though mild, effect on childlessness of white women at about the age of 40 in the US

Spread-ing Uncertainty, Shrinking Birth Rates: A Natural Experiment for Italy

Many previous studies have documented the procyclicality of fertility to business cycles or labour market indicators in Western countries. However, part of the recent fertility decline witnessed since the Great Recession has been left unexplained by traditional measures. The present study advances the notion that birth postponement might have accelerated in response to rising uncertainty, which fuelled negative expectations and declining levels of confidence about the future. To provide empirical support for the causal effect of perceived uncertainty on birth rates, we focus on Italy’s sovereign debt crisis of 2011–2012 as a natural experiment. Perceived uncertainty is measured using Google trends for the term ‘spread’—which acted as somewhat of a barometer for the crisis both in the media and everyday conversations—to capture the general public’s degree of concern about the stability of Italian public finances. A regression discontinuity in time identifies the effect of perceived uncertainty on birth rates in Italy as a drop between 1.5% and 5%, depending on model specification

Monitoring of fatigue crack growth in composite adhesively bonded joints using Fiber Bragg Gratings

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