Comparison of one-dimensional and quasi-one-dimensional Hubbard models from the variational two-electron reduced-density-matrix method

Minimizing the energy of an $N$-electron system as a functional of a two-electron reduced density matrix (2-RDM), constrained by necessary $N$-representability conditions (conditions for the 2-RDM to represent an ensemble $N$-electron quantum system), yields a rigorous lower bound to the ground-state energy in contrast to variational wavefunction methods. We characterize the performance of two sets of approximate constraints, (2,2)-positivity (DQG) and approximate (2,3)-positivity (DQGT) conditions, at capturing correlation in one-dimensional and quasi-one-dimensional (ladder) Hubbard models. We find that, while both the DQG and DQGT conditions capture both the weak and strong correlation limits, the more stringent DQGT conditions improve the ground-state energies, the natural occupation numbers, the pair correlation function, the effective hopping, and the connected (cumulant) part of the 2-RDM. We observe that the DQGT conditions are effective at capturing strong electron correlation effects in both one- and quasi-one-dimensional lattices for both half filling and less-than-half filling

A model for the anisotropic response of fibrous soft tissues using six discrete fibre bundles

The development of accurate constitutive models of fibrous soft-tissues is a challenging problem. Many consider the tissue to be a collection of fibres with a continuous distribution function representing their orientations. A novel discrete fibre model is presented consisting of six weighted fibre bundles. Each bundle is oriented such that they pass through opposing vertices of a regular icosahedron. A novel aspect of the model is the use of simple analytical distribution functions to simulate the undulated collagen fibres. This approach yields a closed form analytical expression for the strain energy function for the collagen fibre bundle that avoids the sometimes costly numerical integration of some statistical distribution functions. The elastin fibres are characterized by a neo-Hookean strain energy function. The model accurately simulates the biaxial stretching of rabbit-skin (error-of-fit 8.7%), the uniaxial stretching of pig-skin (error-of-fit 7.6%), equibiaxial loading of aortic valve cusp (error-of-fit 0.8%), and the simple shear of rat septal myocardium (error-of-fit 9.1%). The proposed model compares favourably with previously published soft-tissue models and alternative methods of representing undulated collagen fibres. The stiffness of collagen fibres predicted by the model ranges from 8.0 MPa to 0.93 GPa. The stiffness of elastin fibres ranges from 2.5 kPa to 154.4 kPa. The anisotropy of model resulting from the representation of the fibre field with a discrete number of fibres is also explored

Stellar Motions in the Polar Ring Galaxy NGC 4650A

We present the first measurement of the stellar kinematics in the polar ring of NGC 4650A. There is well defined rotation, with the stars and gas rotating in the same direction, and with similar amplitude. The gaseous and stellar kinematics suggest an approximately flat rotation curve, providing further support for the hypothesis that the polar material resides in a disk rather than in a ring. The kinematics of the emission line gas at and near the center of the S0 suggests that the polar disk lacks a central hole. We have not detected evidence for two, equal mass, counterrotating stellar polar streams, as is predicted in the resonance levitation model proposed by Tremaine & Yu. A merger seems the most likely explanation for the structure and kinematics of NGC 4650A.Comment: 4 pages, accepted for publication in ApJ Letter

Static versus dynamic loads as an influence on bone remodelling

Bone remodelling activity in the avian ulna was assessed under conditions of disuse alone, disuse with a superimposed continuous compressive load, and disuse interrupted by a short daily period of intermittent loading. The ulna preparation is made by two submetaphyseal osteotomies, the cut ends of the bone being covered with stainless steel caps which, together with the bone they enclosed, are pierced by pins emerging transcutaneously on the dorsal and ventral surfaces of the wing. The 110 mm long undisturbed section of the bone shaft can be protected from functional loading, loaded continuously in compression by joining the pins with springs, or loaded intermittently in compression by engaging the pins in an Instron machine. Similar loads (525 n) were used in both static and dynamic cases engendering similar peak strains at the bone's midshaft (-2000 x 10-6). The intermitent load was applied at a frequency of 1 Hz during a single 100 second period per day as a ramped square wave, with a rate of change of strain during the ramp of 0.01 per second

Improved analytic longitudinal response analysis for axisymmetric launch vehicles. Volume I - Linear analytic model

Improved analytic longitudinal response analysis for axisymmetric launch vehicles - linear mode

Control of bone remodelling by applied dynamic loads

The data showing the relationship between bone mass and peak strain magnitude prepared and submitted for publication. The data from experiments relating remodelling activity with static or dynamic loads were prepared and submitted for publication. Development of programs to relate the location of remodelling activity with he natural and artificial dynamic strain distributions continued. Experiments on the effect of different strain rates on the remodelling response continued

Improved analytic longitudinal response analysis for axisymmetric launch vehicles. Volume II - Computer program description

Improved analytic longitudinal response analysis for axisymmetric launch vehicles - computer program descriptio