A treatment of atomic mean square displacement in higher order perturbation theory

A general derivation of the anharmonic coefficients for a periodic lattice invoking the special case of the central force interaction is presented. All of the contributions to mean square displacement (MSD) to order 14 perturbation theory are enumerated. A direct correspondance is found between the high temperature limit MSD and high temperature limit free energy contributions up to and including 0(14). This correspondance follows from the detailed derivation of some of the contributions to MSD. Numerical results are obtained for all the MSD contributions to 0(14) using the Lennard-Jones potential for the lattice constants and temperatures for which the Monte Carlo results were calculated by Heiser, Shukla and Cowley. The Peierls approximation is also employed in order to simplify the numerical evaluation of the MSD contributions. The numerical results indicate the convergence of the perturbation expansion up to 75% of the melting temperature of the solid (TM) for the exact calculation; however, a better agreement with the Monte Carlo results is not obtained when the total of all 14 contributions is added to the 12 perturbation theory results. Using Peierls approximation the expansion converges up to 45% of TM• The MSD contributions arising in the Green's function method of Shukla and Hubschle are derived and enumerated up to and including 0(18). The total MSD from these selected contributions is in excellent agreement with their results at all temperatures. Theoretical values of the recoilless fraction for krypton are calculated from the MSD contributions for both the Lennard-Jones and Aziz potentials. The agreement with experimental values is quite good.

Brillouin spectroscopy : measurement of elastic and photoelastic constants of some alkali holide crystals

The assembly and testing of apparatus for the measurement of elastic and photoelastic constants by Brillouin scattering, using a Fabry-Perot interferometer and with argon ion laser excitation is described. Such measurements are performed on NaCI, KBr and LiF using the A = 488.0 nm laser line. The elastic constants obtained here are in very good agreement with the ultrasonic data for all three materials. The discrepancy between ultrasonic and hypersonic sound velocities which was reported by some authors for KBr and LiF is not confirmed, and the elastic constants obtained for LiF are the most accurate to date. Also, the present photoelastic constants are in good agreement with the data obtained by ultrasonic techniques for all three crystals. The results for the KBr and LiF crystals constitute the first set of photoelastic constants obtained for these materials by Brillouin spectroscopy. Our results for LiF are the best available to date.

Measurement of forces between and within bilayers of neutral phospholipids

Phospholipids in water form lamellar phases made up of alternating layers of water and bimolecular lipid leaflets. Three complementary methods, osmotic, mechanical, and vapour pressures, were used to measure the work of removing water from lamellar phases composed of frozen dipalmitoylphosphatidylcholine ( DPPC ), melted DPPC, egg phosphatidylethanolamine or equimolar mixtures of DPPC and cholesterol ( DPPC/CHOL ), Concurrently the structural changes that resulted from this water removal were measured using X-ray diffraction. The work was divided into that which forces the bilayers together ( F ) and that which compresses the molecules together within the bilayers ( F )# A large repulsive force exists between bilayers composed of each of the lipids studied and this force increases exponentially as bilayer separation is decreased. F is affected by the nature of the head groups, conformation of the acyl chains and heterogeneity of these chains. In general all of the melted phosphatidylcholines ( melted DPPC, egg lecithin and DPPC/CHOL ) have large equilibrium separations in excess water resulting from large repulsive hydration forces between these bilayers. By comparison, egg PE has an increased attractive force, and frozen DPPC has a decreased hydration force; each results in smaller separations in water for these two lipids. The chemical potentials of the water between the bilayers for all these lipids lie on a continuum, indicating that interbilayer water cannot be characterized by two discrete states, usually referred to as "bound" or "non**bound". For all lipids studied a maximum of 25 % of the total work done on the system goes into deforming the bilayers. The method used here viii to separate repulsion from deformation, developed for us by v. A. Parsegian, provides a unique method for the measurement of lateral pressure of a bilayer and its modulus of deformability ( Y ). Lateral pressure is affected by the nature of the head group, conformation and heterogeneity of the acyl chains. For small changes in molecular surface area ( A ) near equilibrium, both melted and frozen DPPC have similar values for the deformability modulus. Thus in this regime it requires about the same force to change the angle of tilt of frozen chains as it does to compress the fluid bilayer. The introduction of cholesterol into bilayers of DPPC reduces dramatically the lateral pressure of the bilayers over a large range of molecular surface areas ( A ). The variation in the magnitude of bilayer repulsion with different phospholipids provides a basis for the mechanism of lipid segregation in mixed lipid systems and suggests that interacting heterogeneous membranes may influence or modulate the composition of the opposing membrane. The measurements of deformabilities of bilayers provides a direct comparison of them with the properties of monolayers.

Measurement of repulsive forces between charged phospholipid bilayers

Electrostatic forces between membranes containing charged lipids were assumed to play an important role in influencing interactions between membranes long before quantitative measurements of such forces were available. ~ur measurements were designed to measure electrostatic forces between layers of lecithin charged with lipi~s carrying ionizable head groups. These experiments have shown that the interactions between charged lipid bila.yere are dominated by electrostatic forces only at separations greater than 30 A. At smaller separations the repulsion between charged bilayers is dominated by strong hydration forces. The net repulsive force between egg lecithin bilayers containing various amounts of cherged lipids (phosphatidylglycerol (PG) 5,10 ano 50 mole%, phosphatidyli. nosi tol (PI) 10 mole% and sodium oleate (Na-Ol) 3,5 and 10 mole%, where mole% gives the ratio of the number of moles' of .charged lipid to the total number of moles of all lipids present in the sample) was stuoied with the help ('If the osmotic streas technique described by LeNeveu et aI, (1977). Also, the forces between pure PG were j_nvestigated in the same manner. The results have been plotted showing variation of force as a function of bilay- _ er separation dw• All curVes 90 obtained called force curves, were found to be similar in sha.pe, showing two distinct regions, one when dw<.30 A is a region cf very rapid iiivariation of force with separation ( it is the region dominated by hydre,tion force) and second when dw> 40 A is a region of very slow variation of force with separB.tion ( it is the region dominated by the electrostatic force). Between these two regions there exists a transition area in which, in most systems studied, a phase separation of lipids into fractions containing different amounts of charged groups, was observed. A qualitative analysis showed that our results were v/ell described by the simple electrostatic double -le.yer theory. For quantitative agreement between measured and calculated force curves however, the charge density for the calculations had to be taken as half of that given by the number density of charged lipids present in the lecithin bilayers. It is not clear at the moment what causes such low apparent degree of ionization among the charged head groups, and further study is needed in this area.

Molecular dynamics calculation of mean square displacement in alkali metals and rare gas solids and comparison with lattice dynamics

Molec ul ar dynamics calculations of the mean sq ua re displacement have been carried out for the alkali metals Na, K and Cs and for an fcc nearest neighbour Lennard-Jones model applicable to rare gas solids. The computations for the alkalis were done for several temperatures for temperature vol ume a swell as for the the ze r 0 pressure ze ro zero pressure volume corresponding to each temperature. In the fcc case, results were obtained for a wide range of both the temperature and density. Lattice dynamics calculations of the harmonic and the lowe s t order anharmonic (cubic and quartic) contributions to the mean square displacement were performed for the same potential models as in the molecular dynamics calculations. The Brillouin zone sums arising in the harmonic and the quartic terms were computed for very large numbers of points in q-space, and were extrapolated to obtain results ful converged with respect to the number of points in the Brillouin zone.An excellent agreement between the lattice dynamics results was observed molecular dynamics and in the case of all the alkali metals, e~ept for the zero pressure case of CSt where the difference is about 15 % near the melting temperature. It was concluded that for the alkalis, the lowest order perturbation theory works well even at temperat ures close to the melting temperat ure. For the fcc nearest neighbour model it was found that the number of particles (256) used for the molecular dynamics calculations, produces a result which is somewhere between 10 and 20 % smaller than the value converged with respect to the number of particles. However, the general temperature dependence of the mean square displacement is the same in molecular dynamics and lattice dynamics for all temperatures at the highest densities examined, while at higher volumes and high temperatures the results diverge. This indicates the importance of the higher order (eg. ~* ) perturbation theory contributions in these cases.

Non-invasive measurement of trigeminal nerve somatosensory evoked potentials

Whiplash injuries are common yet enigmatic to substantiate clinically. Trigeminal somatosensory evoked potentials (TSEPs) were posited as an indicator of trigeminal nerve conduction damage resulting from whiplash. Alternating polarity square-wave current stimuli were applied transcutaneously in the facial region. 379 recorded pilot trials from 27 participants (8 male and 19 female) were utilized to develop a non-invasive recording capability for TSEPs. Stimulus intensity and artifact, cortical recording sites, stimulation electrode design and placement were explored. Statistically significant differences in amplitude of TSEP waveform components at 13, 19 and 27 ms between uninjured and whiplashed participants were noted. Increased stimulus intensity in whiplashed participants was observed to increase TSEP amplitude. The present methodology and hardware are discussed and directions for future advancement of the current process are outlined.

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.

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.

Study of heat capacity measurement methods for small samples

Methods of measuring specific heats of small samples were studied. Three automated methods were explored, two of which have shown promising results. The adiabatic continuous heating method, has provided smooth well behaved data but further work is presently underway to improve on the results obtained so far . The decay method has been success fully implemented demonstrating reasonable agreement with accepted data for a copper test sample.

The measurement of the optical absorption cross section of photosystem 1 and photosystem 2 from whole live cells of porphyridium cruentum, in light state 1 and light state 2

The optical cross section of PS I in whole cells of Porphyridium cruentum (UTEX 161), held in either state 1 or state 2, was determined by measuring the change in absorbance at 820nm, an indication of P700+; the X-section of PS2 was determined by measuring the variable fluorescence, (Fv-Fo)/Fo, from PS2. Both cross-sections were 7 determined by fitting Poisson distribution equations to the light saturation curves obtained with single turnover laser flashes which varied in intensity from zero to a level where maximum yield occurred. Flash wavelengths of 574nm, 626nm, and 668nm were used, energy absorbed by PBS, by PBS and chla, and by chla respectively. There were two populations of both PSi and PS2. A fraction of PSi is associated with PBS, and a fraction of PS2 is free from PBS. On the transition S1->S2, only with PBS-absorbed energy (574nm) did the average X-section of PSi increase (27%), and that of PS2 decrease (40%). The fraction of PSi associated with PBS decreased, from 0.65 to 0.35, and the Xsection of this associated PS 1 increased, from 135±65 A2 to 400±300A2. The cross section of PS2 associated with PBS decreased from 150±50 A2 to 85±45 A2, but the fraction of PS2 associated with PBS, approximately 0.75, did not change significantly. The increase in PSi cross section could not be completely accounted for by postulating that several PSi are associated with a single PBS and that in the transition to state2, fewer PSi share the same number of PBS, resulting in a larger X-section. It is postulated that small changes occur in the attachment of PS2 to PBS causing energy to be diverted to the attached PSi. These experiments support neither the mobile-PBS model of state transitions nor that of spillover. From cross section changes there was no evidence of energy transfer from PS2 to PSi with 668nm light. The decrease in PS2 fluorescence which occurred at this wavelength cannot be explained by energy transfer; another explanation must be sought. No explanation was found for an observed decrease in PSi yield at high flash intensities.

A multidimensional measurement approach and analysis of children's motivation for reading, attributional style, and reading achievement

The present study investigates the usefulness of a multi-method approach to the measurement of reading motivation and achievement. A sample of 127 elementary and middle-school children aged 10 to 14 responded to measures of motivation, attributions, and achievement both longitudinally and in a challenging reading context. Novel measures of motivation and attributions were constructed, validated, and utilized to examine the relationship between ~ motivation, attributions, and achievement over a one-year period (Study I). The impact of classroom contexts and instructional practices was also explored through a study of the influence of topic interest and challenge on motivation, attributions, and persistence (Study II), as well as through interviews with children regarding motivation and reading in the classroom (Study III). Creation and validation of novel measures of motivation and attributions supported the use of a self-report measure of motivation in situation-specific contexts, and confirmed a three-factor structure of attributions for reading performance in both hypothetical and situation-specific contexts. A one-year follow up study of children's motivation and reading achievement demonstrated declines in all components of motivation beginning at age 10 through 12, and particularly strong decreases in motivation with the transition to middle school. Past perceived competence for reading predicted current achievement after controlling for past achievement, and showed the strongest relationships with reading-related skills in both elementary and middle school. Motivation and attributions were strongly related, and children with higher motivation Fulmer III displayed more adaptive attributions for reading success and failure. In the context of a developmentally inappropriate challenging reading task, children's motivation for reading, especially in terms of perceived competence, was threatened. However, interest in the story buffered some ofthe negative impacts of challenge, sustaining children's motivation, adaptive attributions, and reading persistence. Finally, children's responses during interviews outlined several emotions, perceptions, and aspects of reading tasks and contexts that influence reading motivation and achievement. Findings revealed that children with comparable motivation and achievement profiles respond in a similar way to particular reading situations, such as excessive challenge, but also that motivation is dynamic and individualistic and can change over time and across contexts. Overall, the present study outlines the importance of motivation and adaptive attributions for reading success, and the necessity of integrating various methodologies to study the dynamic construct of achievement motivation.

Delineation of within-site terroir effects using soil and vine water measurement. Investigation of Cabernet Franc

. The influence of vine water status was studied in commercial vineyard blocks of Vilis vinifera L. cv. Cabernet Franc in Niagara Peninsula, Ontario from 2005 to 2007. Vine performance, fruit composition and vine size of non-irrigated grapevines were compared within ten vineyard blocks containing different soil and vine water status. Results showed that within each vineyard block water status zones could be identified on GIS-generated maps using leaf water potential and soil moisture measurements. Some yield and fruit composition variables correlated with the intensity of vine water status. Chemical and descriptive sensory analysis was performed on nine (2005) and eight (2006) pairs of experimental wines to illustrate differences between wines made from high and low water status winegrapes at each vineyard block. Twelve trained judges evaluated six aroma and flavor (red fruit, black cherry, black current, black pepper, bell pepper, and green bean), thr~e mouthfeel (astringency, bitterness and acidity) sensory attributes as well as color intensity. Each pair of high and low water status wine was compared using t-test. In 2005, low water status (L WS) wines from Buis, Harbour Estate, Henry of Pelham (HOP), and Vieni had higher color intensity; those form Chateau des Charmes (CDC) had high black cherry flavor; those at RiefEstates were high in red fruit flavor and at those from George site was high in red fruit aroma. In 2006, low water status (L WS) wines from George, Cave Spring and Morrison sites were high in color intensity. L WS wines from CDC, George and Morrison were more intense in black cherry aroma; LWS wines from Hernder site were high in red fruit aroma and flavor. No significant differences were found from one year to the next between the wines produced from the same vineyard, indicating that the attributes of these wines were maintained almost constant despite markedly different conditions in 2005 and 2006 vintages. Partial ii Least Square (PLS) analysis showed that leaf \}' was associated with red fruit aroma and flavor, berry and wine color intensity, total phenols, Brix and anthocyanins while soil moisture was explained with acidity, green bean aroma and flavor as well as bell pepper aroma and flavor. In another study chemical and descriptive sensory analysis was conducted on nine (2005) and eight (2006) medium water status (MWS) experimental wines to illustrate differences that might support the sub-appellation system in Niagara. The judges evaluated the same aroma, flavor, and mouthfeel sensory attributes as well as color intensity. Data were analyzed using analysis of variance (ANOVA), principal component analysis (PCA) and discriminate analysis (DA). ANOV A of sensory data showed regional differences for all sensory attributes. In 2005, wines from CDC, HOP, and Hemder sites showed highest. r ed fruit aroma and flavor. Lakeshore and Niagara River sites (Harbour, Reif, George, and Buis) wines showed higher bell pepper and green bean aroma and flavor due to proximity to the large bodies of water and less heat unit accumulation. In 2006, all sensory attributes except black pepper aroma were different. PCA revealed that wines from HOP and CDC sites were higher in red fruit, black currant and black cherry aroma and flavor as well as black pepper flavor, while wines from Hemder, Morrison and George sites were high in green bean aroma and flavor. ANOV A of chemical data in 2005 indicated that hue, color intensity, and titratable acidity (TA) were different across the sites, while in 2006, hue, color intensity and ethanol were different across the sites. These data indicate that there is the likelihood of substantial chemical and sensory differences between clusters of sub-appellations within the Niagara Peninsula iii

Measurement of growth in the lichen Rhizocarpon geographicum using a new photographic technique

Lichenologists and users of lichenometry have long used calipers or photogrammetry to measure the growth of crustose lichens. Now, digital photography and popular computer software provide methodological alternatives. This thesis developed and tested a new methodology for tracking change and growth of the lichen, Rhizocarpon geographicum. Adobe Photoshop CS3 Extended software and a photographic time series (1996,2003,2006 and 2007) were used to measure thallus diameter, area, prothallus width and areolae area in 115 small R. geographicum thalli (0.53-1049.88 mm2 ). Measures of 8 diameters per thallus showed that change in diameter was highly variable and is a weak index of growth. Thallus area was a reliable measure of growth (power correlation, R2 = 0.89). Rapid, highly irregular growth occurred in small thalli «30 mm2 ), and steady, uniform growth occurred in larger thalli (>30 mm2 ). This new methodology is tedious but can potentially generate accurate and precise measures for even the tiniest of lichens.

VOCATIONAL INTERESTS: CONSTRUCT VALIDITY AND MEASUREMENT

This dissertation addressed several questions relevant to vocational interests and personality characteristics, examining (a) the roles of personality, vocational interests, and sexual fantasies in defining a general factor of Masculinity/Femininity (M/F) (Study 1), (b) the validity of a new measure of vocational interests (Study 2), and (c) the individual difference characteristics that discriminate between students in various academic majors, and that predict academic outcomes (Study 3). In Study 1, vocational interests, personality, and sexual fantasies were examined to find whether these variables would yield a general Masculinity/Femininity (M/F) factor, and whether that factor would still emerge when controlling for participant sex. The results of Study 1 revealed that a general factor of M/F did emerge. When sex was removed, the loadings of vocational interests decreased from high to very low, suggesting that the link of vocational interests with other indicators of M/F is mainly due to sex differences in these variables. The purpose of Study 2 was to validate the Oregon Vocational Interest Scales (ORVIS), a new public domain vocational interests questionnaire designed to measure eight vocational interest scales. ORVIS scores obtained in a college and community sample were compared with those of two personality measures and two cognitive ability tests. Results from this study showed that the ORVIS scales were reliable and showed good construct validity. The purpose of Study 3, using the ORVIS along with the HEXACO-PI and tests of cognitive ability, was to examine the individual difference characteristics of students in different academic majors, and to use the congruence between a student's academic major and vocational interests as a predictor of academic outcomes, such as GPA, academic major change, and satisfaction with major. The results of Study 3 revealed that students in different academic majors show theoretically meaningful differences in personality, abilities, and interests. Conscientiousness and math ability were found to be the best predictors of academic outcomes. However, congruence between major and interests did not add significant predictive validity to any of these outcomes beyond personality and ability. Together, these three studies show the role of vocational interests in defming MlF and in predicting various academic outcomes.

Statement of finals of the marsh lands main drain as near as can be estimated until its completion and final measurement

Statement of finals of the marsh lands main drain as near as can be estimated until its completion and final measurement. This is signed by Fred Holmes, July 9, 1857.