8 resultados para Continued Fraction Expansion
em Brock University, Canada
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Pictured here from left to right are Jack Miller, Department of Chemistry, R. Misener, Chancellor, R. A. Macleod, Board of Trustees, and actors from the Department of Fine Arts during the sod turning ceremonies in 1982 for the Science Complex expansion to the Mackenzie Chown Complex.
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Built in 1989, Village Residences added more units in 1992.
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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.
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We have calculated the equation of state and the various thermodynamic properties of monatomic fcc crystals by minimizing the Helmholtz free energy derived in the high temperature limit for the quasiharmonic theory, QH, and the lowest-order (cubic and quartic), 'A2, anharmonic terms of the perturbation theory, PT. The total energy in each case is obtained by adding the static energy. The calculation of the thermal properties was carried out for a nearest-neighbour central-force model of the fcc lattice by means of the appropriate thermodynamic relations. We have calculated the lattice constant, the thermal expansion, the coefficient of volume expansion, the specific heat at constant volume and at constant pressure, the isothermal and adiabatic bulk moduli, and the Griineisen parameter, for the rare-gas solids Kr and Xe, and gold. Morse potential and modified Morse potential were each used to represent the atomic interaction for the three fcc materials. For most of the calculated thermodynamic properties from the QH theory, the results for Kr and Xe with the modified Morse potential show an improvement over the results for the Morse potential when compared with the experimental data. However, the results of the 'A 2 equation of state with the modified Morse potential are in good agreement with experiment only in the case of the specific heat at constant volume and at constant pressure. For Au we have calculated the lattice contribution from the QH and 'A 2 PT and the electronic contribution to the thermal properties. The electronic contribution was taken into account by using the free electron model. The results of the thermodynamic properties calculated with the modified Morse potential were similar to those obtained with the Morse potential. U sing the minimized equation of state we also calculated the Mossbauer recoilless fraction for Kr and Xe and the Debye-Waller factor (DWF) for Pb, AI, eu, Ag, and Au. The Mossbauer recoilless fraction was obtained for the above two potentials and Lennard-Jones potential. The L-J potential gives the best agreement with experiment for Kr. No experimental data exists for Xe. At low temperature the calculated DWF results for Pb, AI, and eu show a good agreement with experimental values, but at high temperature the experimental DWF results increase very rapidly. For Ag the computed values were below the expected results at all temperatures. The DWF results of the modified Morse potential for Pb, AI, eu and Ag were slightly better than those of the Morse potential. In the case of Au the calculated values were in poor agreement with experimental results. We have calculated the quasiharmonic phonon dispersion curves for Kr, Xe, eu, Ag, and Au. The calculated and experimental results of the frequencies agree quite well for all the materials except for Au where the longitudinal modes show serious discrepancies with the experimental results. In addition, the two lowest-order anharmonic contributions to the phonon frequency were derived using the Green's function method. The A 2 phonon dispersion curves have been calculated only for eu, and the results were similar to those of the QH dispersion curves. Finally, an expression for the Griineisen parameter "( has been derived from the anharmonic frequencies, and calculated for these materials. The "( results are comparable with those obtained from the thermodynamic definition.
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The site of present-day St. Catharines was settled by 3000 United Empire Loyalists at the end of the 18th century. From 1790, the settlement (then known as "The Twelve") grew as an agricultural community. St. Catharines was once referred to Shipman's Corners after Paul Shipman, owner of a tavern that was an important stagecoach transfer point. In 1815, leading businessman William Hamilton Merritt abandoned his wharf at Queenston and set up another at Shipman's Corners. He became involved in the construction and operation of several lumber and gristmills along Twelve Mile Creek. Shipman's Corners soon became the principal milling site of the eastern Niagara Peninsula. At about the same time, Merritt began to develop the salt springs that were discovered along the river which subsequently gave the village a reputation as a health resort. By this time St. Catharines was the official name of the village; the origin of the name remains obscure, but is thought to be named after Catharine Askin Robertson Hamilton, wife of the Hon. Robert Hamilton, a prominent businessman. Merritt devised a canal scheme from Lake Erie to Lake Ontario that would provide a more reliable water supply for the mills while at the same time function as a canal. He formed the Welland Canal Company, and construction took place from 1824 to 1829. The canal and the mills made St. Catharines the most important industrial centre in Niagara. By 1845, St. Catharines was incorporated as a town, with the town limits extending in 1854. Administrative and political functions were added to St. Catharines in 1862 when it became the county seat of Lincoln. In 1871, construction began on the third Welland Canal, which attracted additional population to the town. As a consequence of continual growth, the town limits were again extended. St. Catharines attained city status in 1876 with its larger population and area. Manufacturing became increasingly important in St. Catharines in the early 1900s with the abundance of hydro-electric power, and its location on important land and water routes. The large increase in population after the 1900s was mainly due to the continued industrialization and urbanization of the northern part of the city and the related expansion of business activity. The fourth Welland Canal was opened in 1932 as the third canal could no longer accommodate the larger ships. The post war years and the automobile brought great change to the urban form of St. Catharines. St. Catharines began to spread its boundaries in all directions with land being added five times during the 1950s. The Town of Merritton, Village of Port Dalhousie and Grantham Township were all incorporated as part of St. Catharines in 1961. In 1970 the Province of Ontario implemented a regional approach to deal with such issues as planning, pollution, transportation and services. As a result, Louth Township on the west side of the city was amalgamated, extending the city's boundary to Fifteen Mile Creek. With its current population of 131,989, St. Catharines has become the dominant centre of the Niagara region. Source: City of St. Catharines website http://www.stcatharines.ca/en/governin/HistoryOfTheCity.asp (January 27, 2011)
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Campus News for Niagara College, August 2002, focusing on the expansion of the Glendale campus for the hospitality and tourism program. The article gives details about the cost of the building, number of students the facility will house and fundraising efforts. Also a photo of the groundbreaking with Donald Ziraldo and several others. The second article on page two is focused on the fundraising efforts for the expansion, specifically the efforts of Donald Ziraldo as the head of the Niagara College Foundation's FutureReady Campaign.
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The Steel Company of Canada (Stelco) was formed in 1910 with the incorporation of the Canada Screw Co. Ltd., the Montreal Rolling Mills Co., the Dominion Wire Manufacturing Co. Ltd., the Hamilton Steel and Iron Co. Ltd., and the Canada Bolt and Nut Co. Ltd. By the 1920s, the company was the largest producer of steel ingots in Canada. The 1930s saw continued success and expansion of the company as Stelco increased its iron and steel capacity by 50 percent. The company continued to prosper throughout the next several decades, with sales revenues exceeding one billion dollars in 1974. In 1980, the company officially changed its name to Stelco, in order to simplify its name in both the French and English language. The company began to experience financial difficulties beginning with the recession in 1982. The troubles persisted for the next 25 years as a result of a decreased demand for steel, labour disputes, and high steel imports. In 2004, Stelco entered bankruptcy protection. By 2007, Stelco had lost $240 million in its first four quarters after emerging from bankruptcy protection. That same year Stelco was purchased by the United States Steel Corp. Despite efforts to restructure the company, bankruptcy was again declared in 2014.