A continuous time random walk model of transport in variably saturated heterogeneous porous media

We propose a unified physical framework for transport in variably saturated porous media. This approach allows fluid flow and solute migration to be treated as ensemble averages of fluid and solute particles, respectively. We consider the cases of homogeneous and heterogeneous porous materials. Within a fractal mobile-immobile (MIM) continuous time random walk framework, the heterogeneity will be characterized by algebraically decaying particle retention-times. We derive the corresponding (nonlinear) continuum limit partial differential equations and we compare their solutions to Monte Carlo simulation results. The proposed methodology is fairly general and can be used to track fluid and solutes particles trajectories, for a variety of initial and boundary conditions.Comment: 12 pages, 9 figure

Pre-asymptotic corrections to fractional diffusion equations

The motion of contaminant particles through complex environments such as fractured rocks or porous sediments is often characterized by anomalous diffusion: the spread of the transported quantity is found to grow sublinearly in time due to the presence of obstacles which hinder particle migration. The asymptotic behavior of these systems is usually well described by fractional diffusion, which provides an elegant and unified framework for modeling anomalous transport. We show that pre-asymptotic corrections to fractional diffusion might become relevant, depending on the microscopic dynamics of the particles. To incorporate these effects, we derive a modified transport equation and validate its effectiveness by a Monte Carlo simulation.Comment: 6 pages, 3 figure

A model of dispersive transport across sharp interfaces between porous materials

Recent laboratory experiments on solute migration in composite porous columns have shown an asymmetry in the solute arrival time upon reversal of the flow direction, which is not explained by current paradigms of transport. In this work, we propose a definition for the solute flux across sharp interfaces and explore the underlying microscopic particle dynamics by applying Monte Carlo simulation. Our results are consistent with previous experimental findings and explain the observed transport asymmetry. An interpretation of the proposed physical mechanism in terms of a flux rectification is also provided. The approach is quite general and can be extended to other situations involving transport across sharp interfaces.Comment: 4 pages, 4 figure

Usefulness of Linear Mixed-Effects Models to Assess the Relationship between Objective and Subjective Internal Load in Team Sports

Internal load can be objectively measured by heart rate-based models, such as Edwards' summated heart rate zones, or subjectively by session rating of perceived exertion. The relationship between internal loads assessed via heart rate-based models and session rating of perceived exertion is usually studied through simple correlations, although the Linear Mixed Model could represent a more appropriate statistical procedure to deal with intrasubject variability. This study aimed to compare conventional correlations and the Linear Mixed Model to assess the relationships between objective and subjective measures of internal load in team sports. Thirteen male youth beach handball players (15.9 ± 0.3 years) were monitored (14 training sessions; 7 official matches). Correlation coefficients were used to correlate the objective and subjective internal load. The Linear Mixed Model was used to model the relationship between objective and subjective measures of internal load data by considering each player individual response as random effect. Random intercepts were used and then random slopes were added. The likelihood-ratio test was used to compare statistical models. The correlation coefficient for the overall relationship between the objective and subjective internal data was very large (r = 0.74; ρ = 0.78). The Linear Mixed Model using both random slopes and random intercepts better explained (p < 0.001) the relationship between internal load measures. Researchers are encouraged to apply the Linear Mixed Models rather than correlation to analyze internal load relationships in team sports since it allows for the consideration of the individuality of players

Structural analysis of the double-walled copper-steel cryogenic chamber of the ASTAROTH experiment

This document describes the verification process of structural performance of the double- walled copper-steel cryogenic chamber of the ASTAROTH (All Sensitive crysTal ARray with lOw THreshold) experiment and the evaluation of the stresses generated near the thermal bridge connecting the inner and outer wall. The chamber consists of an external AISI 316L stainless steel dewar and an inner double-walled OF (Oxygen Free) copper dewar connected to an AISI 316L stainless steel flanged collar. The results showed that close to the thermal bridge (copper-steel junction) the stresses slightly exceed the YS of copper at the estimated operating temperature (localised strain-hardening condition). On the other hand, the safety coefficient respect to fracture is well above one for both materials. This condition, together with the fact that limited cooling cycles are expected during the operating life of the system, leads to the assumption that a progressive material hardening will occur in this area, thus locally raising the YS limit