Matrix elements of U(2n) generators in a multishell spin-orbit basis. I. The del-operator MEs in a two-shell composite Gelfand-Paldus basis

This is the first in a series of three articles which aimed to derive the matrix elements of the U(2n) generators in a multishell spin-orbit basis. This is a basis appropriate to many-electron systems which have a natural partitioning of the orbital space and where also spin-dependent terms are included in the Hamiltonian. The method is based on a new spin-dependent unitary group approach to the many-electron correlation problem due to Gould and Paldus [M. D. Gould and J. Paldus, J. Chem. Phys. 92, 7394, (1990)]. In this approach, the matrix elements of the U(2n) generators in the U(n) x U(2)-adapted electronic Gelfand basis are determined by the matrix elements of a single Ll(n) adjoint tensor operator called the del-operator, denoted by Delta(j)(i) (1 less than or equal to i, j less than or equal to n). Delta or del is a polynomial of degree two in the U(n) matrix E = [E-j(i)]. The approach of Gould and Paldus 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. Hence, to generalize this approach, we need to obtain formulas for the complete set of adjoint coupling coefficients for the two-shell composite Gelfand-Paldus basis. The nonzero shift coefficients are uniquely determined and may he evaluated by the methods of Gould et al. [see the above reference]. In this article, we define zero-shift adjoint coupling coefficients for the two-shell composite Gelfand-Paldus basis which are appropriate to the many-electron problem. By definition, these are proportional to the corresponding two-shell del-operator matrix elements, and it is shown that the Racah factorization lemma applies. Formulas for these coefficients are then obtained by application of the Racah factorization lemma. The zero-shift adjoint reduced Wigner coefficients required for this procedure are evaluated first. All these coefficients are needed later for the multishell case, which leads directly to the two-shell del-operator matrix elements. Finally, we discuss an application to charge and spin densities in a two-shell molecular system. (C) 1998 John Wiley & Sons.

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.

A relative gradient theory for layered materials

It is possible to remedy certain difficulties with the description of short wave length phenomena and interfacial slip in standard models of a laminated material by considering the bending stiffness of the layers. If the couple or moment stresses are assumed to be proportional to the relative deformation gradient, then the bending effect disappears for vanishing interface slip, and the model correctly reduces to an isotropic standard continuum. In earlier Cosserat-type models this was not the case. Laminated materials of the kind considered here occur naturally as layered rock, or at a different scale, in synthetic layered materials and composites. Similarities to the situation in regular dislocation structures with couple stresses, also make these ideas relevant to single slip in crystalline materials. Application of the theory to a one-dimensional model for layered beams demonstrates agreement with exact results at the extremes of zero and infinite interface stiffness. Moreover, comparison with finite element calculations confirm the accuracy of the prediction for intermediate interfacial stiffness.

Modelling the large deformations in stratified media - the Cosserat continuum approach

Methods employing continuum approximation in describing the deformation of layered materials possess a clear advantage over explicit models, However, the conventional implicit models based on the theory of anisotropic continua suffers from certain difficulties associated with interface slip and internal instabilities. These difficulties can be remedied by considering the bending stiffness of the layers. This implies the introduction of moment (couple) stresses and internal rotations, which leads to a Cosserat-type theory. In the present model, the behaviour of the layered material is assumed to be linearly elastic; the interfaces are assumed to be elastic perfectly plastic. Conditions of slip or no slip at the interfaces are detected by a Coulomb criterion with tension cut off at zero normal stress. The theory is valid for large deformation analysis. The model is incorporated into the finite element program AFENA and validated against analytical solutions of elementary buckling problems in layered medium. A problem associated with buckling of the roof and the floor of a rectangular excavation in jointed rock mass under high horizontal in situ stresses is considered as the main application of the theory. Copyright (C) 1999 John Wiley & Sons, Ltd.

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].

Preliminary experiences with a single-patient trials service in general practice

Objective: To pilot a single-patient trials (SPTs) service in general practice, designed to improve decision-making about long-term medications for chronic conditions. Design: 12-week within-patient, randomised, double-blind, placebo-controlled, crossover comparison of ibuprofen with paracetamol for osteoarthritis, involving three pairs of two-week treatment periods for each participating patient. Setting and patients: Patients attending an academic general practice with a clinical diagnosis of osteoarthritis, with pain of at least a month's duration severe enough to warrant consideration of long-term non-steroidal anti-inflammatory drug (NSAID) use. Main outcome measures: Pain and stiffness; measures of overall arthritis compared with previous fortnight; preference for NSAID at the end of each two-week treatment period; use of escape analgesia; side effects; and management changes as a result of the SPTs. Results: Eight of 14 patients completed SPTs. One was a clear responder to NSAIDs, five were non-responders, and two were indefinite. Of the five who were using NSAIDs before the SPT, two continued and three ceased using them. Clinically useful information assisted decision-making for all eight participants. Medication management changed for six. Conclusions: Single-patient trials can be successfully implemented in general practice and might be a valuable method for GPs to identify patients who respond to medication for chronic stable conditions such as osteoarthritis, in which individual response to medication is variable.

A director theory for visco-elastic folding instabilities in multilayered rock

A model for finely layered visco-elastic rock proposed by us in previous papers is revisited and generalized to include couple stresses. We begin with an outline of the governing equations for the standard continuum case and apply a computational simulation scheme suitable for problems involving very large deformations. We then consider buckling instabilities in a finite, rectangular domain. Embedded within this domain, parallel to the longer dimension we consider a stiff, layered beam under compression. We analyse folding up to 40% shortening. The standard continuum solution becomes unstable for extreme values of the shear/normal viscosity ratio. The instability is a consequence of the neglect of the bending stiffness/viscosity in the standard continuum model. We suggest considering these effects within the framework of a couple stress theory. Couple stress theories involve second order spatial derivatives of the velocities/displacements in the virtual work principle. To avoid C-1 continuity in the finite element formulation we introduce the spin of the cross sections of the individual layers as an independent variable and enforce equality to the spin of the unit normal vector to the layers (-the director of the layer system-) by means of a penalty method. We illustrate the convergence of the penalty method by means of numerical solutions of simple shears of an infinite layer for increasing values of the penalty parameter. For the shear problem we present solutions assuming that the internal layering is oriented orthogonal to the surfaces of the shear layer initially. For high values of the ratio of the normal-to the shear viscosity the deformation concentrates in thin bands around to the layer surfaces. The effect of couple stresses on the evolution of folds in layered structures is also investigated. (C) 2002 Elsevier Science Ltd. All rights reserved.

Texture alignment in simple shear

We illustrate the flow behaviour of fluids with isotropic and anisotropic microstructure (internal length, layering with bending stiffness) by means of numerical simulations of silo discharge and flow alignment in simple shear. The Cosserat theory is used to provide an internal length in the constitutive model through bending stiffness to describe isotropic microstructure and this theory is coupled to a director theory to add specific orientation of grains to describe anisotropic microstructure. The numerical solution is based on an implicit form of the Material Point Method developed by Moresi et al. [1].

Physiologic parameters that affect pulse transit time difference between the upper and lower limbs in children

Pulse wave velocity (PWV) is a known parameter that is related to arterial distensibility. However, its potential is hampered by the absence of appropriate techniques to estimate it noninvasively. PWV can be used as an assessment of increased arterial stiffness that is linked to systolic hypertension, excess cardiovascular morbidity and mortality.(1,2)

In vivo biological performance of a novel highly bioactive glass-ceramic (Biosilicate (R)): A biomechanical and histomorphometric study in rat tibial defects

This study aimed to investigate bone responses to a novel bioactive fully crystallized glass-ceramic of the quaternary system P(2)O(5)-Na(2)O-CaO-SiO(2) (Biosilicates (R)). Although a previous study demonstrated positive effects of Biosilicate (R) on in vitro bone-like matrix formation, its in vivo effect was not studied yet. Male Wistar rats (n = 40) with tibial defects were used. Four experimental groups were designed to compare this novel biomaterial with a gold standard bioactive material (Bioglass (R) 45S5), unfilled defects and intact controls. A three-point bending test was performed 20 days after the surgical procedure, as well as the histomorphometric analysis in two regions of interest: cortical bone and medullary canal where the particulate biomaterial was implanted. The biomechanical test revealed a significant increase in the maximum load at failure and stiffness in the Biosilicate group (R) (vs. control defects), whose values were similar to uninjured bones. There were no differences in the cortical bone parameters in groups with bone defects, but a great deal of woven bone was present surrounding Biosilicate (R) and Bioglass (R) 45S5 particulate. Although both bioactive materials supported significant higher bone formation; Biosilicate (R) was superior to Bioglass (R) 45S5 in some histomorphometric parameters (bone volume and number of osteoblasts). Regarding bone resorption, Biosilicate (R) group showed significant higher number of osteoclasts per unit of tissue area than defect and intact controls, despite of the non-significant difference in the osteoclastic surface as percentage of bone surface. This study reveals that the fully crystallized Biosilicate (R) has good bone-forming and bone-bonding properties. (C) 2011 Wiley Periodicals, Inc. J Biomed Mater Res Part B: Appl Biomater 978: 139-147, 2011.

Modelling of cold-formed purlin-sheeting systems .2. Simplified model

A number of theoretical and experimental investigations have been made into the nature of purlin-sheeting systems over the past 30 years. These systems commonly consist of cold-formed zed or channel section purlins, connected to corrugated sheeting. They have proven difficult to model due to the complexity of both the purlin deformation and the restraint provided to the purlin by the sheeting. Part 1 of this paper presented a non-linear elasto plastic finite element model which, by incorporating both the purlin and the sheeting in the analysis, allowed the interaction between the two components of the system to be modelled. This paper presents a simplified version of the first model which has considerably decreased requirements in terms of computer memory, running time and data preparation. The Simplified Model includes only the purlin but allows for the sheeting's shear and rotational restraints by modelling these effects as springs located at the purlin-sheeting connections. Two accompanying programs determine the stiffness of these springs numerically. As in the Full Model, the Simplified Model is able to account for the cross-sectional distortion of the purlin, the shear and rotational restraining effects of the sheeting, and failure of the purlin by local buckling or yielding. The model requires no experimental or empirical input and its validity is shown by its goon con elation with experimental results. (C) 1997 Elsevier Science Ltd.

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.

Beneficial Effect of Creatine Supplementation in Knee Osteoarthritis

NEVES JR., M., B. GUALANO, H. ROSCHEL, R. FULLER, F. B. BENATTI, A. L. DE SA PINTO, F. R. LIMA, R. M. PEREIRA, A. H. LANCHA JR., E. BONFA. Beneficial Effect of Creatine Supplementation in Knee Osteoarthritis. Med. Sci. Sports Exerc., Vol. 43, No. 8, pp. 1538-1543, 2011. Introduction: The aim of this study was to investigate the efficacy of creatine (CR) supplementation combined with strengthening exercises in knee osteoarthritis (OA). Methods: A randomized, double-blind, placebo-controlled trial was performed. Postmenopausal women with knee OA were allocated to receive either CR (20 g.d(-1) for 1 wk and 5 g.d(-1) thereafter) or placebo (PL) and were enrolled in a lower limb resistance training program. They were assessed at baseline (PRE) and after 12 wk (POST). The primary outcome was the physical function as measured by the timed-stands test. Secondary outcomes included lean mass, quality of life, pain, stiffness, and muscle strength. Results: Physical function was significantly improved only in the CR group (P = 0.006). In addition, a significant between-group difference was observed (CR: PRE = 15.7 +/- 1.4, POST = 18.1 +/- 1.8; PL: PRE = 15.0 +/- 1.8, POST = 15.2 +/- 1.2; P = 0.004). The CR group also presented improvements in physical function and stiffness subscales as evaluated by the Western Ontario and McMaster Universities Osteoarthritis Index (P = 0.005 and P = 0.024, respectively), whereas the PL group did not show any significant changes in these parameters (P > 0.05). In addition, only the CR group presented a significant improvement in lower limb lean mass (P = 0.04) as well as in quality of life (P = 0.01). Both CR and PL groups demonstrated significant reductions in pain (P G 0.05). Similarly, a main effect for time revealed an increase in leg-press one-repetition maximum (P = 0.005) with no significant differences between groups (P = 0.81). Conclusions: CR supplementation improves physical function, lower limb lean mass, and quality of life in postmenopausal women with knee OA undergoing strengthening exercises.

Effects of high-intensity aerobic interval training vs. moderate exercise on hemodynamic, metabolic and neuro-humoral abnormalities of young normotensive women at high familial risk for hypertension

Exercise training has an important role in the prevention and treatment of hypertension, but its effects on the early metabolic and hemodynamic abnormalities observed in normotensive offspring of hypertensive parents (FH+) have not been studied. We compared high-intensity interval (aerobic interval training, AIT) and moderate-intensity continuous exercise training (CMT) with regard to hemodynamic, metabolic and hormonal variables in FH+ subjects. Forty-four healthy FH+ women (25.0+/-4.4 years) randomized to control (ConFH+) or to a three times per week equal-volume AIT (80-90% of VO(2MAX)) or CMT (50-60% of VO(2MAX)) regimen, and 15 healthy women with normotensive parents (ConFH-; 25.3+/-3.1 years) had their hemodynamic, metabolic and hormonal variables analyzed at baseline and after 16 weeks of follow-up. Ambulatorial blood pressure (ABP), glucose and cholesterol levels were similar among all groups, but the FH+ groups showed higher insulin, insulin sensitivity, carotid-femoral pulse wave velocity (PWV), norepinephrine and endothelin-1 (ET-1) levels and lower nitrite/ nitrate (NOx) levels than ConFH- subjects. AIT and CMT were equally effective in improving ABP (P<0.05), insulin and insulin sensitivity (P<0.001); however, AIT was superior in improving cardiorespiratory fitness (15 vs. 8%; P<0.05), PWV (P<0.01), and BP, norepinephrine, ET-1 and NOx response to exercise (P<0.05). Exercise intensity was an important factor in improving cardiorespiratory fitness and reversing hemodynamic, metabolic and hormonal alterations involved in the pathophysiology of hypertension. These findings may have important implications for the exercise training programs used for the prevention of inherited hypertensive disorder. Hypertension Research (2010) 33, 836-843; doi:10.1038/hr.2010.72; published online 7 May 2010