Stochastic modelling and simulations for solute transport in porous media

A stochastic model for solute transport in aquifers is studied based on the concepts of stochastic velocity and stochastic diffusivity. By applying finite difference techniques to the spatial variables of the stochastic governing equation, a system of stiff stochastic ordinary differential equations is obtained. Both the semi-implicit Euler method and the balanced implicit method are used for solving this stochastic system. Based on the Karhunen-Loeve expansion, stochastic processes in time and space are calculated by means of a spatial correlation matrix. Four types of spatial correlation matrices are presented based on the hydraulic properties of physical parameters. Simulations with two types of correlation matrices are presented.

On the construction of correlation functions for the integrable supersymmetric fermion models

We review the recent progress on the construction of the determinant representations of the correlation functions for the integrable supersymmetric fermion models. The factorizing F-matrices (or the so-called F-basis) play an important role in the construction. In the F-basis, the creation (and the annihilation) operators and the Bethe states of the integrable models are given in completely symmetric forms. This leads to the determinant representations of the scalar products of the Bethe states for the models. Based on the scalar products, the determinant representations of the correlation functions may be obtained. As an example, in this review, we give the determinant representations of the two-point correlation function for the U-q(gl(2 vertical bar 1)) (i.e. q-deformed) supersymmetric t-J model. The determinant representations are useful for analyzing physical properties of the integrable models in the thermodynamical limit.

Correlation of habitual physical activity levels with flow mediated dilation of the brachial artery in 5-10 year old children

Endothelial dysfunction is an early key event of atherogenesis. Both fitness level and exercise intervention have been shown to positively influence endothelial function. In a cross-sectional study of 47 children, the relationship between habitual physical activity and flow-mediated dilation (FMD) of the brachial artery was explored. Habitual physical activity levels (PALs) were assessed using a validated stable isotope technique, and FMD of the brachial artery was measured via high-resolution ultrasound. The results showed that habitual physical activity significantly correlated with FMD (r=0.39, P=0.007), and remained the most influential variable on dilation in multivariate analysis. Although both fitness level and exercise intervention have previously been shown to positively influence FMD, this is the first time that a relationship with normal PALs has been investigated, especially, at such a young age. These data support the concept that physical activity exerts its protective effect on cardiovascular health via the endothelium and add further emphasis to the importance of physical activity in childhood.

Twisted quantum affine superalgebra Uq[gl(m|n)(2)] and new Uq[osp(m|n)] invariant R-matrices

The minimal irreducible representations of U-q[gl(m|n)], i.e. those irreducible representations that are also irreducible under U-q[osp(m|n)] are investigated and shown to be affinizable to give irreducible representations of the twisted quantum affine superalgebra U-q[gl(m|n)((2))]. The U-q[osp(m|n)] invariant R-matrices corresponding to the tensor product of any two minimal representations are constructed, thus extending our twisted tensor product graph method to the supersymmetric case. These give new solutions to the spectral-dependent graded Yang-Baxter equation arising from U-q[gl(m|n)((2))], which exhibit novel features not previously seen in the untwisted or non-super cases.

Correlation between carbon isotope discrimination and transpiration efficiency in lines of the C-4 species Sorghum bicolor in the glasshouse and the field

Transpiration efficiency, W, the ratio of plant carbon produced to water transpired and carbon isotope discrimination of leaf dry matter, Delta(d)' were measured together on 30 lines of the C-4 species, Sorghum bicolor in the glasshouse and on eight lines grown in the field. In the glasshouse, the mean W observed was 4.9 mmol C mol(-1) H2O and the range was 0.8 mmol C mol(-1) H2O The mean Delta(d) was 3.0 parts per thousand and the observed range was 0.4 parts per thousand. In the field, the mean W was lower at 2.8 mmol C mol H2O and the mean Delta(d) was 4.6 parts per thousand. Significant positive correlations between W and Delta(d) were observed for plants grown in the glasshouse and in the field. The observed correlations were consistent with theory, opposite to those for C-4 species, and showed that variation in Delta(d) was an integrated measure of long-term variation in the ratio of intercellular to ambient CO2 partial pressure, p(i)/p(a). Detailed gas exchange measurements of carbon isotope discrimination during CO2 uptake, Delta(A) and p(i)/p(a) were made on leaves of eight S. bicolor lines. The observed relationship between Delta(A) and p(i)/p(a) was linear with a negative slope of 3.7 parts per thousand in Delta(A) for a unit change in p(i)/p(a). The slope of this linear relationship between Delta(A) and p(i)/p(a) in C-4 species is dependent on the leakiness of the CO2 concentrating mechanism of the C pathway, We estimated the leakiness (defined as the fraction of CO2 released in the bundle sheath by C-4 acid decarboxylations, which is lost by leakage) to be 0.2. We conclude that, although variation in Delta(d) observed in the 30 lines of S. bicolor is smaller than that commonly observed in C-4 species, it also reflects variation in transpiration efficiency, W. Among the eight lines examined in detail and in the environments used, there was considerable genotype x environment interaction.

U-q[(sl(2)over-cap vertical bar 1)] vertex operators, screen currents, and correlation functions at an arbitrary level

Bosonized q-vertex operators related to the four-dimensional evaluation modules of the quantum affine superalgebra U-q[sl((2) over cap\1)] are constructed for arbitrary level k=alpha, where alpha not equal 0,-1 is a complex parameter appearing in the four-dimensional evaluation representations. They are intertwiners among the level-alpha highest weight Fock-Wakimoto modules. Screen currents which commute with the action of U-q[sl((2) over cap/1)] up to total differences are presented. Integral formulas for N-point functions of type I and type II q-vertex operators are proposed. (C) 2000 American Institute of Physics. [S0022-2488(00)00608-3].

Mesoionic pyridopyrimidinylium and pyridooxazinylium olates and non-mesoionic pyridopyrimidinones. Structures in the solid state, solution, and matrices

X-Ray crystal structures, C-13 NMR spectra and theoretical calculations (B3LYP/6-31G*) are reported for the mesoionic (zwitterionic) pyridopyrimidinylium- and pyridooxazinyliumolates 2a, 3a and 5a,b as well as the enol ether 11b and the enamine 11c. The 1-NH compounds like 1a, 2a and 3a exist in the mesoionic form in the crystal and in solution, but the OH tautomers such as 1b and 2b dominate in the gas phase as revealed by the Ar matrix IR spectra in conjunction with DFT calculations. All data indicate that the mesoionic compounds can be regarded as intramolecular pyridine-ketene zwitterions (cf. 16 --> 17) with a high degree of positive charge on the pyridinium nitrogen, a long pyridinium N-CO bond (ca. 1.44-1.49 Angstrom), and normal C=O double bonds (ca. 1.22 Angstrom). All mesoionic compounds exhibit a pronounced tilting of the olate C=O groups (the C=O groups formally derived from a ketene) towards the pyridinium nitrogen, giving NCO angles of 110-118 degrees. Calculations reveal a hydrogen bond with 6-CH, analogous to what is found in ketene-pyridine zwitterions and the C3O2-pyridine complex. The 2-OH tautomers of type 1b, 2b, and 11 also show a high degree of zwitterionic character as indicated by the canonical structures 11 12.

Variation in mortality rates in Australia: correlation with Indigenous status, remoteness and socio-economic deprivation

Background The aim of this study was to study ecological correlations between age-adjusted all-cause mortality rates in Australian statistical divisions and (1) the proportion of residents that self-identify as Indigenous, (2) remoteness, and (3) socio-economic deprivation. Methods All-cause mortality rates for 57 statistical divisions were calculated and directly standardized to the 1997 Australian population in 5-year age groups using Australian Bureau of Statistics (ABS) data. The proportion of residents who self-identified as Indigenous was obtained from the 1996 Census. Remoteness was measured using ARIA (Accessibility and Remoteness Index for Australia) values. Socioeconomic deprivation was measured using SEIFA (Socio-Economic index for Australia) values from the ABS. Results Age-standardized all-cause mortality varies twofold from 5.7 to 11.3 per 1000 across Australian statistical divisions. Strongest correlation was between Indigenous status and mortality (r = 0.69, p < 0.001). correlation between remoteness and mortality was modest (r = 0.39, p = 0.002) as was correlation between socio-economic deprivation and mortality (r = -0.42, p = 0.001). Excluding the three divisions with the highest mortality, a multiple regression model using the logarithm of the adjusted mortality rate as the dependent variable showed that the partial correlation (and hence proportion of the variance explained) for Indigenous status was 0.03 (9 per cent; p = 0.03), for SEIFA score was -0.17 (3 per cent; p = 0.22); and for remoteness was -0.22 (5 per cent; p = 0.13). Collectively, the three variables studied explain 13 per cent of the variability in mortality. Conclusions Ecological correlation exists between all-cause mortality, Indigenous status, remoteness and disadvantage across Australia. The strongest correlation is with indigenous status, and correlation with all three characteristics is weak when the three statistical divisions with the highest mortality rates are excluded. intervention targeted at these three statistical divisions could reduce much of the variability in mortality in Australia.