Space, diffusion and mobility

Given its origins in traditional dialectology, and given advances in our understanding of the social embedding of language variation, it is paradoxical that space should be one of the categories that has received least attention of all in variationist sociolinguistics. Until recently, space has largely been treated as an empty stage on which sociolinguistic processes are enacted. It has been unexamined, untheorized, and its role in shaping and being shaped by variation and change untested. One function of this chapter, therefore, is to assert that space makes a difference, and to begin, in a very hesitant way, to map out what a geographically informed variation analysis might need to address. It also examines variationist interactions with the related concept of mobility. It might be reasonable to think that human geographers would provide some clues on how to proceed. As we will see, they have engaged in a great deal of soul searching about the goals of their discipline, its very existence as a separate field of enquiry, and the directions it should take. Indeed there are remarkable parallels between the recent history of human geographic thought, and interest in language variation across space. Although space has been undertheorized in variation studies, a number of researchers, from the traditional dialectologists through to those interested in the dialectology of mobility and contact, have, of course, been actively engaged in research on geographical variation and language use. Their work will be contextualized here to highlight both the parallels with theory-building in human geography, but also some of the criticisms of earlier approaches which have fed through to human geography, but remain largely unquestioned in variationist practice. The chapter therefore presents a brief theoretical background to space and mobility, before exemplifying these concepts in variationist research through an examination of, for example, the spatial diffusion of linguistic innovations, the spatial configuration of linguistic boundaries and initial steps to examine the consequences of mobility for variationist research.

Anisotropic diffusion at the field scale in a 4-year multi-tracer diffusion and retention experiment – I: Insights from the experimental data

Abstract Claystones are considered worldwide as barrier materials for nuclear waste repositories. In the Mont Terri underground research laboratory (URL), a nearly 4-year diffusion and retention (DR) experiment has been performed in Opalinus Clay. It aimed at (1) obtaining data at larger space and time scales than in laboratory experiments and (2) under relevant in situ conditions with respect to pore water chemistry and mechanical stress, (3) quantifying the anisotropy of in situ diffusion, and (4) exploring possible effects of a borehole-disturbed zone. The experiment included two tracer injection intervals in a borehole perpendicular to bedding, through which traced artificial pore water (APW) was circulated, and a pressure monitoring interval. The APW was spiked with neutral tracers (HTO, HDO, H2O-18), anions (Br, I, SeO4), and cations (Na-22, Ba-133, Sr-85, Cs-137, Co-60, Eu-152, stable Cs, and stable Eu). Most tracers were added at the beginning, some were added at a later stage. The hydraulic pressure in the injection intervals was adjusted according to the measured value in the pressure monitoring interval to ensure transport by diffusion only. Concentration time-series in the APW within the borehole intervals were obtained, as well as 2D concentration distributions in the rock at the end of the experiment after overcoring and subsampling which resulted in �250 samples and �1300 analyses. As expected, HTO diffused the furthest into the rock, followed by the anions (Br, I, SeO4) and by the cationic sorbing tracers (Na-22, Ba-133, Cs, Cs-137, Co-60, Eu-152). The diffusion of SeO4 was slower than that of Br or I, approximately proportional to the ratio of their diffusion coefficients in water. Ba-133 diffused only into �0.1 m during the �4 a. Stable Cs, added at a higher concentration than Cs-137, diffused further into the rock than Cs-137, consistent with a non-linear sorption behavior. The rock properties (e.g., water contents) were rather homogeneous at the centimeter scale, with no evidence of a borehole-disturbed zone. In situ anisotropy ratios for diffusion, derived for the first time directly from field data, are larger for HTO and Na-22 (�5) than for anions (�3�4 for Br and I). The lower ionic strength of the pore water at this location (�0.22 M) as compared to locations of earlier experiments in the Mont Terri URL (�0.39 M) had no notable effect on the anion accessible pore fraction for Cl, Br, and I: the value of 0.55 is within the range of earlier data. Detailed transport simulations involving different codes will be presented in a companion paper.

Identifiability of diffusion and sorption parameters from in situ diffusion experiments by using simultaneously tracer dilution and claystone data

In situ diffusion experiments are performed in geological formations at underground research laboratories to overcome the limitations of laboratory diffusion experiments and investigate scale effects. Tracer concentrations are monitored at the injection interval during the experiment (dilution data) and measured from host rock samples around the injection interval at the end of the experiment (overcoring data). Diffusion and sorption parameters are derived from the inverse numerical modeling of the measured tracer data. The identifiability and the uncertainties of tritium and Na-22(+) diffusion and sorption parameters are studied here by synthetic experiments having the same characteristics as the in situ diffusion and retention (DR) experiment performed on Opalinus Clay. Contrary to previous identifiability analyses of in situ diffusion experiments, which used either dilution or overcoring data at approximate locations, our analysis of the parameter identifiability relies simultaneously on dilution and overcoring data, accounts for the actual position of the overcoring samples in the claystone, uses realistic values of the standard deviation of the measurement errors, relies on model identification criteria to select the most appropriate hypothesis about the existence of a borehole disturbed zone and addresses the effect of errors in the location of the sampling profiles. The simultaneous use of dilution and overcoring data provides accurate parameter estimates in the presence of measurement errors, allows the identification of the right hypothesis about the borehole disturbed zone and diminishes other model uncertainties such as those caused by errors in the volume of the circulation system and the effective diffusion coefficient of the filter. The proper interpretation of the experiment requires the right hypothesis about the borehole disturbed zone. A wrong assumption leads to large estimation errors. The use of model identification criteria helps in the selection of the best model. Small errors in the depth of the overcoring samples lead to large parameter estimation errors. Therefore, attention should be paid to minimize the errors in positioning the depth of the samples. The results of the identifiability analysis do not depend on the particular realization of random numbers. (C) 2012 Elsevier B.V. All rights reserved.

Increase in hippocampal water diffusion and volume during experimental pneumococcal meningitis is aggravated by bacteremia

BACKGROUND The hippocampus undergoes apoptosis in experimental pneumococcal meningitis leading to neurofunctional deficits in learning and memory function. The aim of the present study was 1) to investigate hippocampal apparent diffusion coefficient (ADC) and volume with MRI during the course of experimental pneumococcal meningitis, 2) to explore the influence of accompanying bacteremia on hippocampal water distribution and volume, 3) and to correlate these findings to the extent of apoptosis in the hippocampus. METHODS Experimental meningitis in rats was induced by intracisternal injection of live pneumococci. The study comprised of four experimental groups. I. Uninfected controls (n = 8); II. Meningitis (n = 11); III. Meningitis with early onset bacteremia by additional i.v. injection of live pneumococci (n = 10); IV. Meningitis with attenuated bacteremia by treatment with serotype-specific anti-pneumococcal antibodies (n = 14). T2 and diffusion weighted MR images were used to analyze changes in hippocampus volume and water diffusion (ADC). The results were correlated to ADC of the cortex, to ventricular volume, and to the extent of hippocampal apoptosis. RESULTS Both ADC and the volume of hippocampus were significantly increased in meningitis rats compared to uninfected controls (Kruskal-Wallis test, p = 0.0001, Dunns Post Test, p < 0.05), and were significantly increased in meningitis rats with an early onset bacteremia as compared to meningitis rats with attenuated bacteremia (p < 0.05). Hippocampal ADC and the volume and size of brain ventricles were positively correlated (Spearman Rank, p < 0.05), whereas no association was found between ADC or volume and the extent of apoptosis (p > 0.05). CONCLUSIONS In experimental meningitis increase in volume and water diffusion of the hippocampus are significantly associated with accompanying bacteremia.

Experimental determination of barium isotope fractionation during diffusion and adsorption processes at low temperatures

Variations in barium (Ba) stable isotope abundances measured in low and high temperature environments have recently received increasing attention. The actual processes controlling Ba isotope fractionation, however, remain mostly elusive. In this study, we present the first experimental approach to quantify the contribution of diffusion and adsorption on mass- dependent Ba isotope fractionation during transport of aqueous Ba2+ ions through a porous medium. Experiments have been carried out in which a BaCl2 solution of known isotopic composition diffused through u-shaped glass tubes filled with silica hydrogel at 10 C and 25 C for up to 201 days. The diffused Ba was highly fractionated by up to -2.15‰ in d137/134Ba, despite the low relative difference in atomic mass. The time-dependent isotope fractionation can be successfully reproduced by a diffusive transport model accounting for mass-dependent differences in the effective diffusivities of the Ba isotope species (D137Ba/D134Ba = (m134/m137)^b). Values of b extracted from the transport model were in the range of 0.010–0.011. Independently conducted batch experiments revealed that adsorption of Ba onto the surface of silica hydrogel favoured the heavier Ba isotopes (a = 1.00015 ± 0.00008). The contribution of adsorption on the overall isotope fractionation in the diffusion experiments, however, was found to be small. Our results contribute to the understanding of Ba isotope fractionation pro- cesses, which is crucial for interpreting natural isotope variations and the assessment of Ba isotope ratios as geochemical proxies.

Diffusion-weighted MR imaging of native and transplanted kidneys

Applications of diffusion-weighted (DW) magnetic resonance (MR) imaging outside the brain have gained increasing importance in recent years. Owing to technical improvements in MR imaging units and faster sequences, the need for noninvasive imaging without contrast medium administration, mainly in patients with renal insufficiency, can be met successfully by applying this technique. DW MR imaging is quantified by the apparent diffusion coefficient (ADC), which provides information on diffusion and perfusion simultaneously. By using a biexponential fitting process of the DW MR imaging data, these two entities can be separated, because this type of fitting process can serve as an estimate of both the perfusion fraction and the true diffusion coefficient. DW MR imaging can be applied for functional evaluation of the kidneys in patients with acute or chronic renal failure. Impairment of renal function is accompanied by a decreased ADC. Acute ureteral obstruction leads to perfusion and diffusion changes in the affected kidney, and renal artery stenosis results in a decreased ADC. In patients with pyelonephritis, diffuse or focal changes in signal intensity are seen on the high-b-value images, with increased signal intensity corresponding to low signal intensity on the ADC map. The feasibility and reproducibility of DW MR imaging in patients with transplanted kidneys have already been demonstrated, and initial results seem to be promising for the assessment of allograft deterioration. Overall, performance of renal DW MR imaging, presuming that measurements are of high quality, will further boost this modality, particularly for early detection of diffuse renal conditions, as well as more accurate characterization of focal renal lesions.

Functional evaluation of transplanted kidneys with diffusion-weighted and BOLD MR imaging: initial experience

PURPOSE: To prospectively evaluate feasibility and reproducibility of diffusion-weighted (DW) and blood oxygenation level-dependent (BOLD) magnetic resonance (MR) imaging in patients with renal allografts, as compared with these features in healthy volunteers with native kidneys. MATERIALS AND METHODS: The local ethics committee approved the study protocol; patients provided written informed consent. Fifteen patients with a renal allograft and in stable condition (nine men, six women; age range, 20-67 years) and 15 age- and sex-matched healthy volunteers underwent DW and BOLD MR imaging. Seven patients with renal allografts were examined twice to assess reproducibility of results. DW MR imaging yielded a total apparent diffusion coefficient including diffusion and microperfusion (ADC(tot)), as well as an ADC reflecting predominantly pure diffusion (ADC(D)) and the perfusion fraction. R2* of BOLD MR imaging enabled the estimation of renal oxygenation. Statistical analysis was performed, and analysis of variance was used for repeated measurements. Coefficients of variation between and within subjects were calculated to assess reproducibility. RESULTS: In patients, ADC(tot), ADC(D), and perfusion fraction were similar in the cortex and medulla. In volunteers, values in the medulla were similar to those in the cortex and medulla of patients; however, values in the cortex were higher than those in the medulla (P < .05). Medullary R2* was higher than cortical R2* in patients (12.9 sec(-1) +/- 2.1 [standard deviation] vs 11.0 sec(-1) +/- 0.6, P < .007) and volunteers (15.3 sec(-1) +/- 1.1 vs 11.5 sec(-1) +/- 0.5, P < .0001). However, medullary R2* was lower in patients than in volunteers (P < .004). Increased medullary R2* was paralleled by decreased diffusion in patients with allografts. A low coefficient of variation in the cortex and medulla within subjects was obtained for ADC(tot), ADC(D), and R2* (<5.2%), while coefficient of variation within subjects was higher for perfusion fraction (medulla, 15.1%; cortex, 8.6%). Diffusion and perfusion indexes correlated significantly with serum creatinine concentrations. CONCLUSION: DW and BOLD MR imaging are feasible and reproducible in patients with renal allografts.

In-situ diffusion of HTO, 22Na+, Cs+ and I- in Opalinus Clay at the Mont Terri underground rock laboratory

The diffusion properties of the Opalinus Clay were studied in the underground research laboratory at Mont Terri (Canton Jura, Switzerland) and the results were compared with diffusion data measured in the laboratory on small-scale samples. The diffusion of HTO, Na-22(+), Cs+ and I- were investigated for a period of 10 months. The diffusion equipment used in the field experiment was designed in such a way that a solution of tracers was circulated through a sintered metal screen placed at the end of a borehole drilled in the formation. The concentration decrease caused by the diffusion of tracers into the rock could be followed with time and allowed first estimations of the effective diffusion coefficient. After 10 months, the diffusion zone was over-cored and the tracer profiles measured. From these profiles, effective diffusion coefficients and rock capacity factors Could be extracted by applying a two-dimensional transport model including diffusion and sorption. The simulations were done with the reactive transport code CRUNCH. In addition, results obtained from through-diffusion experiments oil small-sized samples with HTO, Cl-36(-) and Na-22(+) are presented and compared with the in situ data. In all cases. excellent agreement between the two data sets exists. Results for Cs+ indicated five times higher diffusion rates relative to HTO. Corresponding laboratory diffusion measurements are still lacking. However. our Cs+ data are in qualitative agreement wish through-diffusion data for Callovo-Oxfordian argillite rock samples. which also indicate significantly higher effective diffusivities for Cs+ relative to HTO.