Application of [Lambda] to the fourth perturbation theory in calculating the equation of state of rare gas solids and fcc metals

We have calculated the thermodynamic properties of monatomic fcc crystals from the high temperature limit of the Helmholtz free energy. This equation of state included the static and vibrational energy components. The latter contribution was calculated to order A4 of perturbation theory, for a range of crystal volumes, in which a nearest neighbour central force model was used. We have calculated the lattice constant, the coefficient of volume expansion, the specific heat at constant volume and at constant pressure, the adiabatic and the isothermal bulk modulus, and the Gruneisen parameter, for two of the rare gas solids, Xe and Kr, and for the fcc metals Cu, Ag, Au, Al, and Pb. The LennardJones and the Morse potential were each used to represent the atomic interactions for the rare gas solids, and only the Morse potential was used for the fcc metals. The thermodynamic properties obtained from the A4 equation of state with the Lennard-Jones potential, seem to be in reasonable agreement with experiment for temperatures up to about threequarters of the melting temperature. However, for the higher temperatures, the results are less than satisfactory. For Xe and Kr, the thermodynamic properties calculated from the A2 equation of state with the Morse potential, are qualitatively similar to the A 2 results obtained with the Lennard-Jones potential, however, the properties obtained from the A4 equation of state are in good agreement with experiment, since the contribution from the A4 terms seem to be small. The lattice contribution to the thermal properties of the fcc metals was calculated from the A4 equation of state, and these results produced a slight improvement over the properties calculated from the A2 equation of state. In order to compare the calculated specific heats and bulk moduli results with experiment~ the electronic contribution to thermal properties was taken into account~ by using the free electron model. We found that the results varied significantly with the value chosen for the number of free electrons per atom.

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.

Task-Dependent Oscillatory Brain Activity During Oculomotor Delayed Response Task

This study used three Oculomotor Delayed Response (ODR) tasks to investigate the unique cognitive demands during the delay period. Changes in alpha power were used to index cognitive efforts during the delay period. Continuous EEGs from 25 healthy young adults (18-34 years) were recorded using dense electrode array. The data was analyzed by 6-cycle Morlet wavelet decompositions in the frequency range of 2-30 Hz to create time- frequency decompositions for four midline electrode sites. The 99% confidence intervals using the bootstrapped 20% trimmed mean of the 10 Hz frequency were used to examine the differences among conditions. Compared to two Memory conditions (Match and Non-Match), Control condition yielded significant differences in all frequencies over the entire trial period, suggesting a cognitive state difference. Compared to Match condition, the Non–Match condition had lower alpha activity during the delay period at each midline electrode site reflecting the higher cognitive effort required.

Force potentiation as a modulator of contractile performance: Implications for control of skeletal muscle force and energetics of work

This thesis investigated the modulation of dynamic contractile function and energetics of work by posttetanic potentiation (PTP). Mechanical experiments were conducted in vitro using software-controlled protocols to stimulate/determine contractile function during ramp shortening, and muscles were frozen during parallel incubations for biochemical analysis. The central feature of this research was the comparison of fast hindlimb muscles from wildtype and skeletal myosin light chain kinase knockout (skMLCK-/-) mice that does not express the primary mechanism for PTP: myosin regulatory light chain (RLC) phosphorylation. In contrast to smooth/cardiac muscles where RLC phosphorylation is indispensable, its precise physiological role in skeletal muscle is unclear. It was initially determined that tetanic potentiation was shortening speed dependent, and this sensitivity of the PTP mechanism to muscle shortening extended the stimulation frequency domain over which PTP was manifest. Thus, the physiological utility of RLC phosphorylation to augment contractile function in vivo may be more extensive than previously considered. Subsequent experiments studied the contraction-type dependence for PTP and demonstrated that the enhancement of contractile function was dependent on force level. Surprisingly, in the absence of RLC phosphorylation, skMLCK-/- muscles exhibited significant concentric PTP; consequently, up to ~50% of the dynamic PTP response in wildtype muscle may be attributed to an alternate mechanism. When the interaction of PTP and the catchlike property (CLP) was examined, we determined that unlike the acute augmentation of peak force by the CLP, RLC phosphorylation produced a longer-lasting enhancement of force and work in the potentiated state. Nevertheless, despite the apparent interference between these mechanisms, both offer physiological utility and may be complementary in achieving optimal contractile function in vivo. Finally, when the energetic implications of PTP were explored, we determined that during a brief period of repetitive concentric activation, total work performed was ~60% greater in wildtype vs. skMLCK-/- muscles but there was no genotype difference in High-Energy Phosphate Consumption or Economy (i.e. HEPC: work). In summary, this thesis provides novel insight into the modulatory effects of PTP and RLC phosphorylation, and through the observation of alternative mechanisms for PTP we further develop our understanding of the history-dependence of fast skeletal muscle function.