Lattice Green Function (at 0) for the 4d Hypercubic Lattice

The generating function for recurrent Polya walks on the four dimensional hypercubic lattice is expressed as a Kampe-de-Feriet function. Various properties of the associated walks are enumerated.Comment: latex, 5 pages, Res. Report 1

Minimax studies

Effect of nonzero initial conditions on selection of minimax controllers for large launch vehicles and extremal bounded amplitude bounded rate inputs to linear system

Long-term field and laboratory leaching tests of cemented radioactive wastes

Experiments with real and simulated radioactive cementitious wasteforms were set up to compare the leaching behaviour of cementitious wasteforms containing nuclear power plant operational waste in field and laboratory test conditions. Experiments revealed that the average annual Cs-137 leach rate in deionised water was about thirty-five times greater compared with the measured average value for the 1st year of the field test. Cumulative leached fraction of Cs-137 for 1st year (3.74%) was close to values reported in literature for similar laboratory experiments in deionised water, however more than two orders of magnitude higher than the 1st year leached fraction of Cs-137 in the repository test (0.01%). Therefore, to compare field and laboratory test results, a scaling factor is required in order to account for surface to volume factor difference, multiplied by a temperature factor and a leach rate decrease coefficient related to the ground water composition. (C) 2011 Elsevier B.V. All rights reserved

Effects of oil and natural or synthetic vitamin E on ruminal and milk fatty acid profiles in cows receiving a high-starch diet

Among trans fatty acids, trans-10,cis-12 CLA has negative effects on cow milk fat production and can affect human health. In high-yielding dairy cows, a shift from the trans-11 to the trans-10 pathway of biohydrogenation (BH) can occur in the rumen of cows receiving high-concentrate diets, especially when the diet is supplemented with unsaturated fat sources. In some but not all experiments, vitamin E has been shown to control this shift. To ascertain the effects of vitamin E on this shift of BH pathway, 2 studies were conducted. The first study explored in vitro the effects of addition of natural (RRR-α-tocopherol acetate) and synthetic (dl-α-tocopherol acetate) vitamin E. Compared with control and synthetic vitamin E, the natural form resulted in a greater trans-10/trans-11 ratio; however, the effect was very low, suggesting that vitamin E was neither a limiting factor for rumen BH nor a modulator of the BH pathway. An in vivo study investigated the effect of natural vitamin E (RRR-α-tocopherol) on this shift and subsequent milk fat depression. Six rumenfistulated lactating Holstein cows were assigned to a 2 × 2 crossover design. Cows received 20-kg DM of a control diet based on corn silage with 22% of wheat, and after 2 wk of adaptation, the diet was supplemented with 600 g of sunflower oil for 2 more weeks. During the last week of this 4-wk experimental period, cows were divided into 2 groups: an unsupplemented control group and a group receiving 11 g of RRR-α-tocopherol acetate per day. A trans-10 shift of ruminal BH associated with milk fat depression due to oil supplementation of a high-wheat diet was observed, but vitamin E supplementation of dairy cows did not result in a reversal toward a trans-11 BH pathway, and did not restore milk fat content

Green's function of a finite chain and the discrete Fourier transform

A new expression for the Green's function of a finite one-dimensional lattice with nearest neighbor interaction is derived via discrete Fourier transform. Solution of the Heisenberg spin chain with periodic and open boundary conditions is considered as an example. Comparison to Bethe ansatz clarifies the relation between the two approaches.Comment: preprint of the paper published in Int. J. Modern Physics B Vol. 20, No. 5 (2006) 593-60

Exact parent Hamiltonians of bosonic and fermionic Moore-Read states on lattices and local models

We introduce a family of strongly-correlated spin wave functions on arbitrary spin-1/2 and spin-1 lattices in one and two dimensions. These states are lattice analogues of Moore-Read states of particles at filling fraction 1/q, which are non-Abelian Fractional Quantum Hall states in 2D. One parameter enables us to perform an interpolation between the continuum limit, where the states become continuum Moore-Read states of bosons (odd q) and fermions (even q), and the lattice limit. We show numerical evidence that the topological entanglement entropy stays the same along the interpolation for some of the states we introduce in 2D, which suggests that the topological properties of the lattice states are the same as in the continuum, while the 1D states are critical states. We then derive exact parent Hamiltonians for these states on lattices of arbitrary size. By deforming these parent Hamiltonians, we construct local Hamiltonians that stabilize some of the states we introduce in 1D and in 2D.Comment: 15 pages, 7 figure