On the equation of state and atomic mean square displacement of crystals

We have presented a Green's function method for the calculation of the atomic mean square displacement (MSD) for an anharmonic Hamil toni an . This method effectively sums a whole class of anharmonic contributions to MSD in the perturbation expansion in the high temperature limit. Using this formalism we have calculated the MSD for a nearest neighbour fcc Lennard Jones solid. The results show an improvement over the lowest order perturbation theory results, the difference with Monte Carlo calculations at temperatures close to melting is reduced from 11% to 3%. We also calculated the MSD for the Alkali metals Nat K/ Cs where a sixth neighbour interaction potential derived from the pseudopotential theory was employed in the calculations. The MSD by this method increases by 2.5% to 3.5% over the respective perturbation theory results. The MSD was calculated for Aluminum where different pseudopotential functions and a phenomenological Morse potential were used. The results show that the pseudopotentials provide better agreement with experimental data than the Morse potential. An excellent agreement with experiment over the whole temperature range is achieved with the Harrison modified point-ion pseudopotential with Hubbard-Sham screening function. We have calculated the thermodynamic properties of solid Kr by minimizing the total energy consisting of static and vibrational components, employing different schemes: The quasiharmonic theory (QH), ).2 and).4 perturbation theory, all terms up to 0 ().4) of the improved self consistent phonon theory (ISC), the ring diagrams up to o ().4) (RING), the iteration scheme (ITER) derived from the Greens's function method and a scheme consisting of ITER plus the remaining contributions of 0 ().4) which are not included in ITER which we call E(FULL). We have calculated the lattice constant, the volume expansion, the isothermal and adiabatic bulk modulus, the specific heat at constant volume and at constant pressure, and the Gruneisen parameter from two different potential functions: Lennard-Jones and Aziz. The Aziz potential gives generally a better agreement with experimental data than the LJ potential for the QH, ).2, ).4 and E(FULL) schemes. When only a partial sum of the).4 diagrams is used in the calculations (e.g. RING and ISC) the LJ results are in better agreement with experiment. The iteration scheme brings a definitive improvement over the).2 PT for both potentials.

Optimization of trial wave functions for use in quantum Monte Carlo with application to LiH

Methods for both partial and full optimization of wavefunction parameters are explored, and these are applied to the LiH molecule. A partial optimization can be easily performed with little difficulty. But to perform a full optimization we must avoid a wrong minimum, and deal with linear-dependency, time step-dependency and ensemble-dependency problems. Five basis sets are examined. The optimized wavefunction with a 3-function set gives a variational energy of -7.998 + 0.005 a.u., which is comparable to that (-7.990 + 0.003) 1 of Reynold's unoptimized \fin ( a double-~ set of eight functions). The optimized wavefunction with a double~ plus 3dz2 set gives ari energy of -8.052 + 0.003 a.u., which is comparable with the fixed-node energy (-8.059 + 0.004)1 of the \fin. The optimized double-~ function itself gives an energy of -8.049 + 0.002 a.u. Each number above was obtained on a Bourrghs 7900 mainframe computer with 14 -15 hrs CPU time.

Phonon dispersion curves and atomic mean square displacement for several fcc and bcc materials

The atomic mean square displacement (MSD) and the phonon dispersion curves (PDC's) of a number of face-centred cubic (fcc) and body-centred cubic (bcc) materials have been calclllated from the quasiharmonic (QH) theory, the lowest order (A2 ) perturbation theory (PT) and a recently proposed Green's function (GF) method by Shukla and Hiibschle. The latter method includes certain anharmonic effects to all orders of anharmonicity. In order to determine the effect of the range of the interatomic interaction upon the anharmonic contributions to the MSD we have carried out our calculations for a Lennard-Jones (L-J) solid in the nearest-neighbour (NN) and next-nearest neighbour (NNN) approximations. These results can be presented in dimensionless units but if the NN and NNN results are to be compared with each other they must be converted to that of a real solid. When this is done for Xe, the QH MSD for the NN and NNN approximations are found to differ from each other by about 2%. For the A2 and GF results this difference amounts to 8% and 7% respectively. For the NN case we have also compared our PT results, which have been calculated exactly, with PT results calculated using a frequency-shift approximation. We conclude that this frequency-shift approximation is a poor approximation. We have calculated the MSD of five alkali metals, five bcc transition metals and seven fcc transition metals. The model potentials we have used include the Morse, modified Morse, and Rydberg potentials. In general the results obtained from the Green's function method are in the best agreement with experiment. However, this improvement is mostly qualitative and the values of MSD calculated from the Green's function method are not in much better agreement with the experimental data than those calculated from the QH theory. We have calculated the phonon dispersion curves (PDC's) of Na and Cu, using the 4 parameter modified Morse potential. In the case of Na, our results for the PDC's are in poor agreement with experiment. In the case of eu, the agreement between the tlleory and experiment is much better and in addition the results for the PDC's calclliated from the GF method are in better agreement with experiment that those obtained from the QH theory.

The effects of an acute bout of whole-body vibration on pulse wave velocity in individuals with SCI

Cardiovascular disease is a leading cause of mortality in the spinal cord injured (SCI) population. Reduced arterial compliance is a cardiovascular risk factor and whole body vibration (WBV) has be en shown to improve arterial compliance in able-bodied individuals. The study investigated the effect of an acute session ofWBV on arterial compliance as measured by pulse wave velocity (PWV). On separate days, arm, leg and aortic PWV were measured pre- and post- a 45 minute session of passive stance (PS) and WBV. The WBV was intermittent with a set frequency of 45Hz and amplitude of O.6mm. There was no condition by time effect when comparing PWV after WBV and PS. Following WBV, aortic (928.6±127.7 vs. 901.1±96.6cm/sec), leg (1035.2±113.8 vs.l099.8±114.2cm/sec) and arm PWV (1118.9±119.8 vs. 1181.1±124.4cm/s) did not change. As such, WBV did not reduce arterial compliance, however future research with protocol modifications is recommended.

Square Root Finding In Graphs

Abstract: Root and root finding are concepts familiar to most branches of mathematics. In graph theory, H is a square root of G and G is the square of H if two vertices x,y have an edge in G if and only if x,y are of distance at most two in H. Graph square is a basic operation with a number of results about its properties in the literature. We study the characterization and recognition problems of graph powers. There are algorithmic and computational approaches to answer the decision problem of whether a given graph is a certain power of any graph. There are polynomial time algorithms to solve this problem for square of graphs with girth at least six while the NP-completeness is proven for square of graphs with girth at most four. The girth-parameterized problem of root fining has been open in the case of square of graphs with girth five. We settle the conjecture that recognition of square of graphs with girth 5 is NP-complete. This result is providing the complete dichotomy theorem for square root finding problem.

Some Travelling Wave Solutions of KdV-Burgers Equation

In this paper we study the extended Tanh method to obtain some exact solutions of KdV-Burgers equation. The principle of the Tanh method has been explained and then apply to the nonlinear KdV- Burgers evolution equation. A finnite power series in tanh is considered as an ansatz and the symbolic computational system is used to obtain solution of that nonlinear evolution equation. The obtained solutions are all travelling wave solutions.

Design of Resistivity Instrumentation for a He3 Cryostat and its Application to the Charge Density Wave Superconductor CuxTiSe2

Fermi patches in quasi-two dimensional charge density waves (CDW) have not described the connection to superconductivity (SC) according to theory adequately at this point in time. The connection between CDW and SC in the quasi-two dimensional material CuxTiSe2 is an interesting one which might reveal mechanisms in unconventional superconductors. A previous Brock graduate student grew crystals of CuxTiSe2. The precise doping of the samples was not known. In order to determine the doping parameter x in CuxTiSe2, a sensitive resistivity measurement system was necessary. A new resistivity measurement system was designed and implemented utilizing an Infrared Labs HDL-10 He3 cryostat. By comparing with data from the literature, doping of two samples was investigated using the new measurement system and a Quantum Design Magnetic Property Measurement System (MPMS). Methods for determining the doping revealed that the old resistivity system would not be able to determine the CDW transition temperature of highly doped samples or doping for elongated samples due to electronic noise. Doping in one sample was found to be between x=0.06 and x=0.065. Values of doping in the second sample had a discrepancy but could be explained by incorrect sample orientation.

License no. 144 of season 1872/73 made out to S.D. Woodruff for 36 square miles in berth no. 192

License no. 144 of season 1872/73 made out to S.D. Woodruff for 36 square miles in berth no. 192. This document is slightly torn and stained along the right hand side. This does not affect the text, April 7, 1873.

License no. 145 of season 1872/73 made out to S.D. Woodruff for 35 ¾ square miles in berth no. 198

License no. 145 of season 1872/73 made out to S.D. Woodruff for 35 ¾ square miles in berth no. 198, April 7, 1873.

License no. 67 of season 1873/74 made out to S.D. Woodruff for 36 square miles in berth no. 192

License no. 67 of season 1873/74 made out to S.D. Woodruff for 36 square miles in berth no. 192, June 13, 1873

License no. 68 of season 1873/74 made out to S.D. Woodruff for 35 ¾ square miles in berth no. 198

License no. 68 of season 1873/74 made out to S.D. Woodruff for 35 ¾ square miles in berth no. 198, June 13, 1873.

License no. 11 of season 1874/75 made out to S.D. Woodruff for 35 ¾ square miles in berth no. 198

License no. 11 of season 1874/75 made out to S.D. Woodruff for 35 ¾ square miles in berth no. 198, May 20, 1874.

License no. 5 of season 1875/76 made out to S.D. Woodruff for 36 square miles in berth no. 192

License no. 5 of season 1875/76 made out to S.D. Woodruff for 36 square miles in berth no. 192, June 1, 1875.

License no. 2 of season 1886/87 made out to S.D. Woodruff for 36 square miles in berth no. 192

License no. 2 of season 1886/87 made out to S.D. Woodruff for 36 square miles in berth no. 192, May 15, 1876.