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.

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.

Effect of age on female choice in the field cricket, Gryllus interger

Female choice is an important element of sexual selection that may vary among females of the same species. Few researchers have investigated the causes of variation in selectivity with respect to potential mates and overall level of motivation toward a stimulus source representative of a mate. This study demonstrates that female age may be one cause of variation in female choice. Females of different ages may have different mate preferences. As females age, they have less time left to reproduce, and their residual reproductive value decreases. This should correspond to a higher reproductive effort which may be represented as increased motivation and/or decreased selectivity. The effect of age on mate choice in Gryllus integer was investigated by using a non-compensating treadmill, called the Kugel, to measure female phonotaxis. Artificially generated male calling songs of varying pulse rates were broadcast in either a singlestimulus or a three-stimulus experimental design. The pulse rates used in the calling song stimuli were 70, 64, 76, 55 and 85 pulses per second. These corresponded to the documented mean pulse rate for the species at the experimental temperature, one standard deviation below and above the mean, and 2.5 standard deviations below and above the mean, respectively. Test females were either 11-14 days or 25-28 days post-ecdysis. Trials usually were conducted two to seven hours into the scotophase. In the single-stimulus experiment, females were presented with stimuli with only one pulse rate. Older females achieved higher vector scores than younger females, indicating that older females are more motivated to mate. Both groups showed little phonotactic response towards 55 or 85 pIs, both of which lie outside the natural range of G. integer calling song at the experimental temperature. Neither group discriminated among the three pulse rates that fell within the natural range of calling song. In the three-stimulus experiment, females were presented with stimuli with one of three pulse rates, 64, 70 or 76 pIs, In alternation. Both age groups had reduced responsiveness in this experiment, perhaps due to an increase in perceived male density. Additionally, younger females responded significantly more to 64 and 70 pIs than to the higher pulse rate, indicating that they are selective with respect to mate choice. Older females did not discriminate among the three pulse rates. Therefore, it was concluded that selectivity decreases with age. A further study was conducted to determine that these effects were due to age and not due to the differing periods without a mating between the two age groups. Again, stimuli were presented in a three-stimulus experimental design. Age was held constant at 28 days and time since last mating varied from 11 to 25 days. Females varyIng in time since last mating did not differ in their responses to the calling song pulse rates. This indicated that the increased motivation and decreased selectivity exhibited In the initial experiments were due to age and not to time without a mating. Neither time of trial nor female weight had an effect upon female phonotaxis. Data are discussed in terms of mate choice, residual reproductive value, and costs of choice.

Effect of diurnal cycling temperatures on cardiovascular- ventilatory function in statically-acclimated rainbow trout, Salmo gairdneri

Four groups of rainbow trout, Salmo gairdneri, were acclimated to 2°, 10°, and 18°e, and to a diurnal temperature cycle (100 ± 4°C). To evaluate the influence of cycling temperatures in terms of an immediate as opposed to acclimatory response various ventilatory-cardiovascular rate functions were observed for trout, either acclimated to cycling temperatures or acclimated to constant temperatures and exposed to a diurnal temperature cycle for the first time (10° ± 4°C for trout acclimated to 10°C; 18°+ 4°C for trout acclimated to l8°e). Gill resistance and the cardiac to ventilatory rate ratio were then calculated. Following a post preparatory recovery period of 36 hr, measurements were made over a 48 hour period with the first 24 hours being at constant temperature in the case of statically-acclimated fish followed by 24 hours under cyclic temperature conditions. Trout exhibited marked changes in oxygen consumption (Vo ) with temp- 2 erature both between acclimation groups, and in response to the diurnal temperature cycle. This increase in oxygen uptake appears to have been achieved by adjustment of ventilatory and, to some extent, cardiovascular activity. Trout exhibited significant changes in ventilatory rate (VR), stroke volume (Vsv), and flow (VG) in response to temperature. Marked changes in cardiac rate were also observed. These findings are discussed in relation to their importance in convective oxygen transport via water and blood at the gills and tissues. Trout also exhibited marked changes in pressure waveforms associated with the action of the resp; ratory pumps with temperature. Mean differenti a 1 pressure increased with temperature as did gill resistance and utilization. This data is discussed in relation to its importance in diffusive oxygen transport and the conditions for gas exchange at the gills. With one exception, rainbow trout were able to respond to changes in oxygen demand and availability associated with changes in temperature by means of adjustments in ventilation, and possibly pafusion, and the conditions for gas exchange at the gills. Trout acclimated to 18°C, however, and exposed to high cyclic temperatures, showed signs of the ventilatory and cardiovascular distress problems commonly associated with low circulating levels of oxygen in the blood. It appears these trout were unable to fully meet the oxygen requirements associated with c~ling temperatures above 18°C. These findings were discussed in relation to possible limitations in the cardiovascular-ventilatory response at high temperatures. The response of trout acclimated to cycling temperatures was generally similar to that for trout acclimated to constant temperatures and exposed to cycling temperatures for the first time. This result suggested that both groups of fish may have been acclimated to a similar thermal range, regardless of the acclimation regime employed. Such a phenomenon would allow trout of either acclimation group to respond equally well to the imposed temperature cycle. Rainbow trout showed no evidence of significant diurnal rhythm in any parameters observed at constant temperatures (2°, 10°, and 18° C), and under a 12/12 light-dark photoperiod regime. This was not taken to indicate an absence of circadian rhythms in these trout, but rather a deficiency in the recording methods used in the study.

Ionic regulation in goldfish, Carassius auratus, acclimated to constant and diurnally-cycling temperature conditions

The effects of a diurnal sine-wave temperature cycle (250 +- 5° C) on the wa terI-e etc r o1 yt est a t us 0 f gol df1' Sh , Carassius auratus, was assessed through determination of Na+, K+, Mg2+, Ca2+, Cl- and water content in plasma, Red blood cells and muscle tissue. Animals were also acclimated to o 0 0 static temperatures (20 C, 25 c, 30 C) corresponding to the high, low and mid-ooint temperatures of the cycle. All groups were sampled at 03:00, 09:00, 15:00 and 21:00 hr. Hemoglobin content and packed cell volume, as well as electrolyte and 'water levels were determined for each animal and red cell ion concentrations and ion : hemoglobin ratios estimated. Cycled animals were distinct from those at constant temperatures in several respects. Hematological parameters were elevated above those of animals at constant temperature and were, on a diurnal basis, more stable. Red blood cell electrolyte levels varied in an adaptively appropriate fashion to cycle temperatures. This was not the case in the constant temperature groups_ Under the cycling regime, plasma ion levels were more diurnally stable than those of constant temperature fish. Although muscle parameters in cycled fish exhibited more fluctuation than was observed in plasma, these also tended to be relatively more stable than was the caseErythrocytic data are discussed in terms of their effects on hemoglobin-oxygen affinity while plasma and muscle observations were considered from the standpoint of overall water-electrolyte balance. In general, cycled fish appeared to be capable of stabilizing overall body fluid composition, while simultaneously effecting adaptively-appropriate modifications in the erythrocytic ionic microenvironment of hemoglobin. The sometimes marked diurnal variability of water-electrolyte status in animals held at constant temperature as opposed to the conservation of cycled fish suggests that this species is, in some fashion, programmed for regulation in a thermally-fluctuating environment. If this interpretation is valid and a phenomenon of general occurrence, some earlier studies involving constant acclimation of eurythermal species normally occupying habitats which vary in temperature on a daily basis may require reconsideration. at constant temperature.

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.

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 static and diurnally-cycling temperature acclimations on thermal tolerances of rainbow trout, Salmo gairdneri

:ofiedian lethal temperatures ( LT50' s ) were determined for rainbow trout, Salmo gairdnerii, acclimated for a minimum of 21 days at 5 c onstant temperatures between 4 and 20 0 C. and 2 diel temperature fluctuations ( sinewave curves of amplitudes ± 4 and ± 7 0 C. about a mean temperature of 12 0 C. ) . Twenty-four-, 48-, and 96-hour LT50 estimates were c alculated f ollowing standard flow-through aquatic bioassay techniques and probi t transformation of mortality data. The phenomenon of delayed thermal mortality was also investigated. Shifts in upper incipient lethal temperature occurred as a result of previous thermal conditioning. It was shown that increases in constant acclimation temperature result in proportional l inear increases in thermal tolerances. The increase i n estimated 96-hour LT50's was approximately 0.13 0 c. X 1 0 C:1 between 8 and 20 0 C. The effect of acclimation to both cyclic temperature regimes was an increase in LT50 to values between the mean and maximum constant equivalent daily temperatures of the cycles. Twenty-four-, 48-, and 96-hour LT50 estimates of both cycles corresponded approximately to the LT50 values of the 16 0 C. c onstant temperature equivalent . This increase i n thermal tolerance was further demonstrated by the delayed thermal mortality experiments . Cycle amplitudes appeared to i nfluence thermal resistance through alterations in initi al mortality since mortality patterns characteristic of base temperature acclimations re-appeared after approximately 68 hours exposure to test temperatures for the 12 + 4 0 C. group, whereas mortality patterns stabilized and remained constant for a period greater than 192 hours with the larger therma l cycle ( 12 + 7 0 C. ). NO s ignificant corre lations between s pecimen weight and time-to-death was apparent. Data are discussed in relation to the establishment of thermal criteria for important commercial and sport fishes , such as the salmonids , as is the question whether previously reported values on lethal temperature s may have been under estimated.

The role of water in determining structure and function of macromolecules and macromolecular assemblies /

The interaction of biological molecules with water is an important determinant of structural properties both in molecular assemblies, and in conformation of individual macromolecules. By observing the effects of manipulating the activity of water (which can be accomplished by limiting its concentration or by adding additional solutes, "osmotic stress"), one can learn something about intrinsic physical properties of biological molecules as well as measure an energetic contribution of closely associated water molecules to overall equilibria in biological reactions. Here two such studies are reported. The first of these examines several species of lysolipid which, while present in relatively low concentrations in biomembranes, have been shown to affect many cellular processes involving membrane-protein or membrane-membrane interactions. Monolayer elastic constants were determined by combining X-ray diffraction and the osmotic stress technique. Spontaneous radii of curvature of lysophosphatidylcholines were determined to be positive and in the range +30A to +70A, while lysophosphatidylethanolamines proved to be essentially flat. Neither lysolipid significantly affected the bending modulus of the monolayer in which it was incorporated. The second study examines the role of water in theprocess of polymerization of actin into filaments. Water activity was manipulated by adding osmolytes and the effect on the equilibrium dissociation constant (measured as the criticalmonomer concentration) was determined. As water activity was decreased, the critical concentration was reduced for Ca-actin but not for Mg-actin, suggesting that 10-12 fewer water molecules are associated with Ca-actin in the polymerized state. Thisunexpectedly small amount of water is discussed in the context of the common structural motif of a nucleotide binding cleft.

Foraging ecology and parental care of common terns (Sterna hirundo) nesting in Windermere Basin, Lake Ontario

The relationships among chick feeding, size and type of prey item, and foraging time away from the brood have not been well studied in seabirds. This study investigated spatial and temporal patterns of foraging and chick-provisioning among 23 radio-tagged male common terns nesting at Hamilton Harbour, Lake Ontario during 1991 and 1992. Telemetry data were collected concurrently with behavioural observations from an elevated blind. Terns fitted with transmitters did not differ from controls with respect to either brood attendance, patterns of chick mortality, species and size distributions of prey delivered to offspring, or chick-provisioning rates. There was a clear separation of parental roles: males were primarily responsible for feeding chicks while females allocated more time to brood attendance. The prey species most commonly delivered to chicks by adults were rainbow smelt (Osmerus mordax) and alewife (A/osa pseudoharengus), followed in importance by larval fish, emerald shiner (Notropis antherinoides), salmonids, and fathead minnows (Pimepha/es prome/as). The relative proportions of various fish speCies delivered to chicks by males differed over the course of each breeding season, and there was also much variability in species composition of prey between years. Sizes of prey delivered to chicks also differed between sampling periods. The modal size of fish brought to chicks during Peak 1991 was 1.5 bill lengths, while the majority of prey in Late 1991 were small larval fish. The reverse trend occurred in 1992 when small fish were delivered to chicks predominantly during the Peak nesting period. During periods when predominantly small fish were delivered to chicks, the foraging activity of radio-tagged males was concentrated within a two kilometer radius of the colony. The observed variation in prey composition and foraging locations during the study likely reflects temporal variation in the availability of prey in the vicinity of the colony. Males delivered fish to chicks at a constant rate, while females 4 increased their feeding frequency over the first six to ten brood days. The mean length of fish delivered to chicks by adults increased significantly with increasing chick age. As a group, within each nesting period, transmittered males either foraged predominantly in the same directional bearing (north during Peak 1991, south during Late 1992), or concentrated foraging activity in the immediate vicinity of the colony (Late 1991, Peak 1992). However, individual radio-tagged males exhibited unique and predictable foraging patterns, often favouring specific locations within these areas and differing in their secondary foraging patterns. Overall, the Lake Ontario shoreline between NCB Bay" (3.5 km south of colony) and the lift bridge canal (4 km north of colony) was the foraging area used most frequently by radiotagged males during the chick-rearing period. Foraging patterns of transmittered males at Windermere Basin are similar to patterns of peak-nesting common terns, but differ from those of late-nesters, at a nearby colony (Port Colborne, Lake Erie). Differences between the foraging patterns of late-nesting terns at these colonies likely reflect differences in annual patterns of fish availability between the two locations. No relationship was found between foraging proficiency of adults and survival of offspring. Stochastic factors, such as predation by black-crowned nightherons (Nycticorax nycticorax) and adverse weather conditions during the early stages of chick rearing, may be more important determinants of common tern breeding success than parental quality or fish availability.

The reliability of an isometric test based on constant perception of effort

To date there is no documented procedure to extrapolate findings of an isometric nature to a whole body performance setting. The purpose of this study was to quantify the reliability of perceived exertion to control neuromuscular output during an isometric contraction. 21 varsity athletes completed a maximal voluntary contraction and a 2 min constant force contraction at both the start and end of the study. Between pre and post testing all participants completed a 2 min constant perceived exertion contraction once a day for 4 days. Intra-class correlation coefficient (R=O.949) and standard error of measurement (SEM=5.12 Nm) concluded that the isometric contraction was reliable. Limits of agreement demonstrated only moderate initial reliability, yet with smaller limits towards the end of 4 training sessions. In conclusion, athlete's na"ive to a constant effort isometric contraction will produce reliable and acceptably stable results after 1 familiarization sessions has been completed.

“You Know What I Mean?”- Language and Cultural Retention in Luso-Canadian Mothers in the Greater Toronto Area

The Portuguese community is one of the largest diasporic groups in the Greater Toronto Area and the choice of retention and transmission of language and culture to Luso-Canadians is crucial to the development and sustainability of the community. The overall objective of this study is to learn about the factors that influence Luso-Canadian mothers’ inclination to teach Portuguese language and cultural retention to their children. To explore this topic I employed a qualitative research design that included in-depth interviews conducted in 2012 with six Luso-Canadian mothers. Three central arguments emerged from the findings. First, Luso-Canadian mothers interviewed posses a pronounced desire for their children to succeed academically, and to provide opportunities that their children that they did not have. Second, five of the mothers attempt to achieve this mothering objective partly by disconnecting from their Portuguese roots, and by disassociating their children from the Portuguese language and culture. Third, the disconnection they experience and enact is influenced by the divisions evident in the Portuguese community in the GTA that divides regions and hierarchically ranks dialects, and groups. I conclude that the children in these households inevitably bear the prospects of maintaining a vibrant Portuguese community in the GTA and I propose that actions by the community in ranking dialects influence mothers’ decisions about transmitting language and culture to their children.

Canada’s new Open Access Policy: what does it mean for Brock researchers?

Presentation at Brock Library Spring Symposium 2015: What's really going on?