Matrix elements of U(2n) generators in a multishell spin-orbit basis. III. General formulas

This is the third and final article in a series directed toward the evaluation of the U(2n) generator matrix elements (MEs) in a multishell spin/orbit basis. Such a basis is required for many-electron systems possessing a partitioned orbital space and where spin-dependence is important. The approach taken is based on the transformation properties of the U(2n) generators as an adjoint tensor operator of U(n) x U(2) and application of the Wigner-Eckart theorem. A complete set of adjoint coupling coefficients for the two-shell composite Gelfand-Paldus basis (which is appropriate to the many-electron problem) were obtained in the first and second articles of this series. Ln the first article we defined zero-shift coupling coefficients. These are proportional to the corresponding two-shell del-operator matrix elements. See P. J. Burton and and M. D. Gould, J. Chem. Phys., 104, 5112 (1996), for a discussion of the del-operator and its properties. Ln the second article of the series, the nonzero shift coupling coefficients were derived. Having obtained all the necessary coefficients, we now apply the formalism developed above to obtain the U(2n) generator MEs in a multishell spin-orbit basis. The methods used are based on the work of Gould et al. (see the above reference). (C) 1998 John Wiley & Sons, Inc.

Capillary network models for transport in packed beds: Considerations of pore aspect ratio

The conventional analysis for the estimation of the tortuosity factor for transport in porous media is modified here to account for the effect of pore aspect ratio. Structural models of the porous medium are also constructed for calculating the aspect ratio as a function of porosity. Comparison of the model predictions with the extensive data of Currie (1960) for the effective diffusivity of hydrogen in packed beds shows good agreement with a network model of randomly oriented intersecting pores for porosities upto about 50 percent, which is the region of practical interest. The predictions based on this network model are also found to be in better agreement with the data of Currie than earlier expressions developed for unconsolidated and grainy media.

Modelling fungal growth on surfaces

Fungal growth in time and space at the substrate surface was modelled for a simple system mimicking solid-state fermentation, using a polycarbonate Nucleopore membrane laid over a glucose solution. Biomass production depends on both tip density and the diffusion of glucose within the fungal hyphae. The model predicts early increases in both height and concentration, followed by a period in which the biomass profile moves with a constant wavefront. The rate of increase in height increases as tip diffusivity increases or as the Monod saturation constant for glucose decreases.

In vitro human epidermal and polyethylene membrane penetration and retention of the sunscreen benzophenone-3 from a range of solvents

Purpose. To study epidermal and polyethylene membrane penetration and retention of the sunscreen benzophenone-3 (BP) from a range of single solvent vehicles and evaluate solvent effects on permeability parameters. Methods. The solubility of BP was measured in a number of solvents. Penetration of BP across human epidermis and high density polyethylene (HDPE) membranes was studied from 50% saturated solutions in each solvent. Results. Maximal BP fluxes from the solvents across the two membranes varied widely. Highest fluxes were observed from 90% ethanol (EtOH) for epidermis and from isopropyl myristate (IPM) and C12-15 benzoate alcohols (C12-15 BA) for HDPE membrane. Both the flux and estimated permeability coefficient and skin-vehicle partitioning of BP appeared to be related to the vehicle solubility parameter (delta(v)). The major effects of solvents on BP flux appear to be via changes in BP diffusivity through the membranes. Conclusions. Minimal penetration of sunscreens such as BP is best achieved by choosing vehicles with a delta(v) substantially different to the solubility parameter of the membrane.

Quasispin graded-fermion formalism and gl(m vertical bar n)down arrow osp(m vertical bar n) branching rules

The graded-fermion algebra and quasispin formalism are introduced and applied to obtain the gl(m\n)down arrow osp(m\n) branching rules for the two- column tensor irreducible representations of gl(m\n), for the case m less than or equal to n(n > 2). In the case m < n, all such irreducible representations of gl(m\n) are shown to be completely reducible as representations of osp(m\n). This is also shown to be true for the case m=n, except for the spin-singlet representations, which contain an indecomposable representation of osp(m\n) with composition length 3. These branching rules are given in fully explicit form. (C) 1999 American Institute of Physics. [S0022-2488(99)04410-2].

Scope for further analytical solutions for constant flux infiltration into a semi-infinite soil profile or redistribution in a finite soil profile

[1] We attempt to generate new solutions for the moisture content form of the one-dimensional Richards' [1931] equation using the Lisle [1992] equivalence mapping. This mapping is used as no more general set of transformations exists for mapping the one-dimensional Richards' equation into itself. Starting from a given solution, the mapping has the potential to generate an infinite number of new solutions for a series of nonlinear diffusivity and hydraulic conductivity functions. We first seek new analytical solutions satisfying Richards' equation subject to a constant flux surface boundary condition for a semi-infinite dry soil, starting with the Burgers model. The first iteration produces an existing solution, while subsequent iterations are shown to endlessly reproduce this same solution. Next, we briefly consider the problem of redistribution in a finite-length soil. In this case, Lisle's equivalence mapping is generalized to account for arbitrary initial conditions. As was the case for infiltration, however, it is found that new analytical solutions are not generated using the equivalence mapping, although existing solutions are recovered.

Infiltration from surface and buried point sources: The average wetting water content

The assumption in analytical solutions for flow from surface and buried point sources of an average water content, (θ) over bar, behind the wetting front is examined. Some recent work has shown that this assumption fitted some field data well. Here we calculated (θ) over bar using a steady state solution based on the work by Raats [1971] and an exponential dependence of the diffusivity upon the water content. This is compared with a constant value of (θ) over bar calculated from an assumption of a hydraulic conductivity at the wetting front of 1 mm day(-1) and the water content at saturation. This comparison was made for a wide range of soils. The constant (θ) over bar generally underestimated (θ) over bar at small wetted radii and overestimated (θ) over bar at large radii. The crossover point between under and overestimation changed with both soil properties and flow rate. The largest variance occurred for coarser texture soils at low-flow rates. At high-flow rates in finer-textured soils the use of a constant (θ) over bar results in underestimation of the time for the wetting front to reach a particular radius. The value of (θ) over bar is related to the time at which the wetting front reaches a given radius. In coarse-textured soils the use of a constant value of (θ) over bar can result in an error of the time when the wetting front reaches a particular radius, as large as 80% at low-flow rates and large radii.

Eigenvalues of Casimir invariants for unitary irreps of Uq(gl(m vertical bar n))

A fully explicit formula for the eigenvalues of Casimir invariants for U-q(gl(m/n)) is given which applies to all unitary irreps. This is achieved by making some interesting observations on atypicality indices for irreps occurring in the tensor product of unitary irreps of the same type. These results have applications in the determination of link polynomials arising from unitary irreps of U-q(gl(m/n)).

Electron paramagnetic resonance of Ni(II) doped tris(ethylenediamine)zinc(II) dinitrate

Variable temperature electron paramagnetic resonance spectra of tris(ethylenediamine)zinc(II) dinitrate single crystals doped with NI(II) have been measured. The host crystal undergoes a trigonal to monoclinic phase transition at 146 K. Above the transition temperature the zero field splitting tensor is axially symmetric with D = -0.831 cm(-1) and below it becomes rhombic with D = -0.785 cm(-1), E = -0.088 cm(-1). The low temperature spectrum is characterised by the pattern repeating every 60 degrees when the crystal is rotated about the high temperature c axis. The analysis shows that the Zn(II) site retains a C-2 symmetry axis and that the distortion away from the D-3 site symmetry observed for high temperatures is small, the principal axes being tilted by 2.6 degrees. This implies that the phase transition involves the flipping of the C-C backbone in one of the ethylenediamine ligands of the complex, resulting in a A delta delta delta to Lambda delta delta lambda type conformational change.

Twisted quantum affine superalgebra U-q[sl(2/2)((2))], U-q[osp(2/2)] invariant R-matrices and a new integrable electronic model

We describe the twisted affine superalgebra sl(2\2)((2)) and its quantized version U-q[sl(2\2)((2))]. We investigate the tensor product representation of the four-dimensional grade star representation for the fixed-point sub superalgebra U-q[osp(2\2)]. We work out the tensor product decomposition explicitly and find that the decomposition is not completely reducible. Associated with this four-dimensional grade star representation we derive two U-q[osp(2\2)] invariant R-matrices: one of them corresponds to U-q [sl(2\2)(2)] and the other to U-q [osp(2\2)((1))]. Using the R-matrix for U-q[sl(2\2)((2))], we construct a new U-q[osp(2\2)] invariant strongly correlated electronic model, which is integrable in one dimension. Interestingly this model reduces in the q = 1 limit, to the one proposed by Essler et al which has a larger sl(2\2) symmetry.

White matter microstructure underlying default mode network connectivity in the human brain

Resting state functional magnetic resonance imaging (fMRI) reveals a distinct network of correlated brain function representing a default mode state of the human brain The underlying structural basis of this functional connectivity pattern is still widely unexplored We combined fractional anisotropy measures of fiber tract integrity derived from diffusion tensor imaging (DTI) and resting state fMRI data obtained at 3 Tesla from 20 healthy elderly subjects (56 to 83 years of age) to determine white matter microstructure e 7 underlying default mode connectivity We hypothesized that the functional connectivity between the posterior cingulate and hippocampus from resting state fMRI data Would be associated with the white matter microstructure in the cingulate bundle and fiber tracts connecting posterior cingulate gyrus With lateral temporal lobes, medial temporal lobes, and precuneus This was demonstrated at the p<0001 level using a voxel-based multivariate analysis of covariance (MANCOVA) approach In addition, we used a data-driven technique of joint independent component analysis (ICA) that uncovers spatial pattern that are linked across modalities. It revealed a pattern of white matter tracts including cingulate bundle and associated fiber tracts resembling the findings from the hypothesis-driven analysis and was linked to the pattern of default mode network (DMN) connectivity in the resting state fMRI data Out findings support the notion that the functional connectivity between the posterior cingulate and hippocampus and the functional connectivity across the entire DMN is based oil distinct pattern of anatomical connectivity within the cerebral white matter (C) 2009 Elsevier Inc All rights reserved

Association between symptom severity and internal capsule volume in obsessive-compulsive disorder

Neurobiological models support an involvement of white matter tracts in the pathophysiology of obsessive-compulsive disorder (OCD), but there has been little systematic evaluation of white matter volumes in OCD using magnetic resonance imaging (MRI). We investigated potential differences in the volume of the cingulum bundle (CB) and anterior limb of internal capsule (ALIC) in OCD patients (n = 19) relative to asymptomatic control subjects (n = 15). White matter volumes were assessed using a 1.5T MRI scanner. Between-group comparisons were carried out after spatial normalization and image segmentation using optimized voxel-based morphometry. Correlations between regional white matter volumes in OCD subjects and symptom severity ratings were also investigated. We found significant global white matter reductions in OCD patients compared to control subjects. The voxel-based search for regional abnormalities (with covariance for total white matter volumes) showed no specific white matter volume deficits in brain portions predicted a priori to be affected in OCD (CB and ALIC). However, large clusters of significant positive correlation with OCD severity scores were found bilaterally on the ALIC. These findings provide evidence of OCD-related ALIC abnormalities and suggest a connectivity dysfunction within frontal-striatal-thalamic-cortical circuits. Further studies are warranted to better define the role of such white matter alterations in the pathophysiology of OCD, and may provide clues for a more effectively targeting of neurosurgical treatments for OCD. (C) 2009 Elsevier Ireland Ltd. All rights reserved.

The Cholinergic System in Mild Cognitive Impairment and Alzheimer`s Disease: An In Vivo MRI and DTI study

Few studies have investigated in vivo changes of the cholinergic basal forebrain in Alzheimer`s disease (AD) and amnestic mild cognitive impairment (MCI), an at risk stage of AD. Even less is known about alterations of cortical projecting fiber tracts associated with basal forebrain atrophy. In this study, we determined regional atrophy within the basal forebrain in 21 patients with AD and 16 subjects with MCI compared to 20 healthy elderly subjects using deformation-based morphometry of MRI scans. We assessed effects of basal forebrain atrophy on fiber tracts derived from high-resolution diffusion tensor imaging (DTI) using tract-based spatial statistics. We localized significant effects relative to a map of cholinergic nuclei in MRI standard space as determined from a postmortem brain. Patients with AD and MCI subjects showed reduced volumes in basal forebrain areas corresponding to anterior medial and lateral, intermediate and posterior nuclei of the Nucleus basalis of Meynert (NbM) as well as in the diagonal band of Broca nuclei (P < 0.01). Effects in MCI subjects were spatially more restricted than in AD, but occurred at similar locations. The volume of the right antero-lateral NbM nucleus was correlated with intracortical projecting fiber tract integrity such as the corpus callosum, cingulate, and the superior longitudinal, inferior longitudinal, inferior fronto-occipital, and uncinate fasciculus (P < 0.05, corrected for multiple comparisons). Our findings suggest that a multimodal MRI-DTI approach is supportive to determine atrophy of cholinergic nuclei and its effect on intracortical projecting fiber tracts in AD. Hum Brain Mapp 32: 1349-1362, 2011. (C) 2010 Wiley-Liss, Inc.

Altered gray matter morphometry and resting-state functional and structural connectivity in social anxiety disorder

In social anxiety disorder (SAD), impairments in limbic/paralimbic structures are associated with emotional dysregulation and inhibition of the medial prefrontal cortex (MPFq. Little is known, however, about alterations in limbic and frontal regions associated with the integrated morphometric, functional, and structural architecture of SAD. Whether altered gray matter volume is associated with altered functional and structural connectivity in SAD. Three techniques were used with 18 SAD patients and 18 healthy controls: voxel-based morphometry; resting-state functional connectivity analysis; and diffusion tensor imaging tractography. SAD patients exhibited significantly decreased gray matter volumes in the right posterior inferior temporal gyrus (ITG) and right parahippocampal/hippocampal gyrus (PHG/HIP). Gray matter volumes in these two regions negatively correlated with the fear factor of the Liebowitz Social Anxiety Scale. In addition, we found increased functional connectivity in SAD patients between the right posterior ITG and the left inferior occipital gyrus, and between the right PHF/HIP and left middle temporal gyms. SAD patients had increased right MPFC volume, along with enhanced structural connectivity in the genu of the corpus callosum. Reduced limbic/paralimbic volume, together with increased resting-state functional connectivity, suggests the existence of a compensatory mechanism in SAD. Increased MPFC volume, consonant with enhanced structural connectivity, suggests a long-time overgeneralization of structural connectivity and a role of this area in the mediation of clinical severity. Overall, our results may provide a valuable basis for future studies combining morphometric, functional and anatomical data in the search for a comprehensive understanding of the neural circuitry underlying SAD. (C) 2011 Elsevier B.V. All rights reserved.