Stochastic Processes Crossing from Ballistic to Fractional Diffusion with Memory: Exact Results

We address the now classical problem of a diffusion process that crosses over from a ballistic behavior at short times to a fractional diffusion (sub- or super-diffusion) at longer times. Using the standard non-Markovian diffusion equation we demonstrate how to choose the memory kernel to exactly respect the two different asymptotics of the diffusion process. Having done so we solve for the probability distribution function (pdf) as a continuous function which evolves inside a ballistically expanding domain. This general solution agrees for long times with the pdf obtained within the continuous random walk approach but it is much superior to this solution at shorter times where the effect of the ballistic regime is crucial

Using 18O/2H, 3H/3He, 85Kr and CFCs to determine mean residence times and water origin in the Grazer and Leibnitzer Feld groundwater bodies (Austria)

Two groundwater bodies, Grazer Feld and Leibnitzer Feld, with surface areas of 166 and 103 km2 respectively are characterised for the first time by measuring the combination of δ18O/δ2H, 3H/3He, 85Kr, CFC-11, CFC-12 and hydrochemistry in 34 monitoring wells in 2009/2010. The timescales of groundwater recharge have been characterised by 131 δ18O measurements of well and surface water sampled on a seasonal basis. Most monitoring wells show a seasonal variation or indicate variable contributions of the main river Mur (0–30%, max. 70%) and/or other rivers having their recharge areas in higher altitudes. Combined δ18O/δ2H-measurements indicate that 65–75% of groundwater recharge in the unusual wet year of 2009 was from precipitation in the summer based on values from the Graz meteorological station. Monitoring wells downstream of gravel pit lakes show a clear evaporation trend. A boron–nitrate differentiation plot shows more frequent boron-rich water in the more urbanised Grazer Feld and more frequent nitrate-rich water in the more agricultural used Leibnitzer Feld indicating that a some of the nitrate load in the Grazer Feld comes from urban sewer water. Several lumped parameter models based on tritium input data from Graz and monthly data from the river Mur (Spielfeld) since 1977 yield a Mean Residence Time (MRT) for the Mur-water itself between 3 and 4 years in this area. Data from δ18O, 3H/3He measurements at the Wagna lysimeter station supports the conclusion that 90% of the groundwaters in the Grazer Feld and 73% in the Leibnitzer Feld have MRTs of 20 m) with relative thicker unsaturated zones. The young MRT of groundwater from two monitoring wells in the Leibnitzer Feld was confirmed by 85Kr-measurements. Most CFC-11 and CFC-12 concentrations in the groundwater exceed the equilibration concentrations of modern concentrations in water and are therefore unsuitable for dating purposes. An enrichment factor up to 100 compared to atmospheric equilibrium concentrations and the obvious correlation of CFC-12 with SO4, Na, Cl and B in the ground waters of the Grazer Feld suggest that waste water in contact with CFC-containing material above and below ground is the source for the contamination. The dominance of very young groundwater (<5 years) indicates a recent origin of the contamination by nitrate and many other components observed in parts of the groundwater bodies. Rapid measures to reduce those sources are needed to mitigate against further deterioration of these waters

Geometrical restrictions of water diffusion in aqueous protein systems. A study using NMR field-gradient techniques

Geometrical restrictions of water diffusion in different aqueous protein systems were studied using two versions of the NMR field gradient technique. The samples were aqueous systems of bovine serum albumin, gelatin and horse myoglobin at concentrations ranging from diluted solutions to almost dry powders being only partly hydrated. Hydrated protein aerogels were produced by the aid of a special preparation procedure and studied in addition. The experiments referred to the, temperature and concentration dependences of the water diffusion coefficient above and below the free-water freezing temperature. The diffusion coefficient within clusters of overlapping hydration shells is reduced by one order of magnitude compared with that of bulk water. Geometrical restrictions manifest themselves (a) by the obstruction effect observed at low protein concentrations, (b) by the topologically two-dimensional diffusion in the network of overlapping hydration shells, (c) by the percolation threshold appearing at about 15%b.w. water and (d) by the anomalous diffusion behaviour concluded from the protein aerogel study. © 1993 Springer

Diffusion on random site percolation clusters. Theory and NMR microscopy experiments with model objects

Quasi two-dimensional random site percolation model objects were fabricate based on computer generated templates. Samples consisting of two compartments, a reservoir of H$_2$O gel attached to a percolation model object which was initially filled with D$_2$O, were examined with NMR (nuclear magnetic resonance) microscopy for rendering proton spin density maps. The propagating proton/deuteron inter-diffusion profiles were recorded and evaluated with respect to anomalous diffusion parameters. The deviation of the concentration profiles from those expected for unobstructed diffusion directly reflects the anomaly of the propagator for diffusion on a percolation cluster. The fractal dimension of the random walk, $d_w$, evaluated from the diffusion measurements on the one hand and the fractal dimension, $d_f$, deduced from the spin density map of the percolation object on the other permits one to experimentally compare dynamical and static exponents. Approximate calculations of the propagator are given on the basis of the fractional diffusion equation. Furthermore, the ordinary diffusion equation was solved numerically for the corresponding initial and boundary conditions for comparison. The anomalous diffusion constant was evaluated and is compared to the Brownian case. Some ad hoc correction of the propagator is shown to pay tribute to the finiteness of the system. In this way, anomalous solutions of the fractional diffusion equation could experimentally be verified for the first time.Comment: REVTeX, 12 figures in GIF forma

Kohaerenter und inkohaerenter Transport in vivo und in Modellsystemen: ortsaufloesende NMR-Messmethoden und Untersuchung anomaler Eigenschaften

SIGLEAvailable from TIB Hannover: DW 7261 / FIZ - Fachinformationszzentrum Karlsruhe / TIB - Technische InformationsbibliothekDEGerman

Geometrical restrictions of water diffusion in aqueous protein systems. A study using NMR field-gradient techniques

Geometrical restrictions of water diffusion in different aqueous protein systems were studied using two versions of the NMR field gradient technique. The samples were aqueous systems of bovine serum albumin, gelatin and horse myoglobin at concentrations ranging from diluted solutions to almost dry powders being only partly hydrated. Hydrated protein aerogels were produced by the aid of a special preparation procedure and studied in addition. The experiments referred to the, temperature and concentration dependences of the water diffusion coefficient above and below the free-water freezing temperature. The diffusion coefficient within clusters of overlapping hydration shells is reduced by one order of magnitude compared with that of bulk water. Geometrical restrictions manifest themselves (a) by the obstruction effect observed at low protein concentrations, (b) by the topologically two-dimensional diffusion in the network of overlapping hydration shells, (c) by the percolation threshold appearing at about 15%b.w. water and (d) by the anomalous diffusion behaviour concluded from the protein aerogel study. © 1993 Springer

Geometrical restrictions of water diffusion in aqueous protein systems. A study using NMR field-gradient techniques

Geometrical restrictions of water diffusion in different aqueous protein systems were studied using two versions of the NMR field gradient technique. The samples were aqueous systems of bovine serum albumin, gelatin and horse myoglobin at concentrations ranging from diluted solutions to almost dry powders being only partly hydrated. Hydrated protein aerogels were produced by the aid of a special preparation procedure and studied in addition. The experiments referred to the, temperature and concentration dependences of the water diffusion coefficient above and below the free-water freezing temperature. The diffusion coefficient within clusters of overlapping hydration shells is reduced by one order of magnitude compared with that of bulk water. Geometrical restrictions manifest themselves (a) by the obstruction effect observed at low protein concentrations, (b) by the topologically two-dimensional diffusion in the network of overlapping hydration shells, (c) by the percolation threshold appearing at about 15%b.w. water and (d) by the anomalous diffusion behaviour concluded from the protein aerogel study. © 1993 Springer

Geometrical restrictions of water diffusion in aqueous protein systems. A study using NMR field-gradient techniques

Geometrical restrictions of water diffusion in different aqueous protein systems were studied using two versions of the NMR field gradient technique. The samples were aqueous systems of bovine serum albumin, gelatin and horse myoglobin at concentrations ranging from diluted solutions to almost dry powders being only partly hydrated. Hydrated protein aerogels were produced by the aid of a special preparation procedure and studied in addition. The experiments referred to the, temperature and concentration dependences of the water diffusion coefficient above and below the free-water freezing temperature. The diffusion coefficient within clusters of overlapping hydration shells is reduced by one order of magnitude compared with that of bulk water. Geometrical restrictions manifest themselves (a) by the obstruction effect observed at low protein concentrations, (b) by the topologically two-dimensional diffusion in the network of overlapping hydration shells, (c) by the percolation threshold appearing at about 15%b.w. water and (d) by the anomalous diffusion behaviour concluded from the protein aerogel study. © 1993 Springer