Monte Carlo study of the XY-model on quasi-periodic lattices

Monte Carlo Simulations were carried out using a nearest neighbour ferromagnetic XYmodel, on both 2-D and 3-D quasi-periodic lattices. In the case of 2-D, both the unfrustrated and frustrated XV-model were studied. For the unfrustrated 2-D XV-model, we have examined the magnetization, specific heat, linear susceptibility, helicity modulus and the derivative of the helicity modulus with respect to inverse temperature. The behaviour of all these quatities point to a Kosterlitz-Thouless transition occuring in temperature range Te == (1.0 -1.05) JlkB and with critical exponents that are consistent with previous results (obtained for crystalline lattices) . However, in the frustrated case, analysis of the spin glass susceptibility and EdwardsAnderson order parameter, in addition to the magnetization, specific heat and linear susceptibility, support a spin glass transition. In the case where the 'thin' rhombus is fully frustrated, a freezing transition occurs at Tf == 0.137 JlkB , which contradicts previous work suggesting the critical dimension of spin glasses to be de > 2 . In the 3-D systems, examination of the magnetization, specific heat and linear susceptibility reveal a conventional second order phase transition. Through a cumulant analysis and finite size scaling, a critical temperature of Te == (2.292 ± 0.003) JI kB and critical exponents of 0:' == 0.03 ± 0.03, f3 == 0.30 ± 0.01 and I == 1.31 ± 0.02 have been obtained.

Particle swarm optimization for two-connected networks with bounded rings

The Two-Connected Network with Bounded Ring (2CNBR) problem is a network design problem addressing the connection of servers to create a survivable network with limited redirections in the event of failures. Particle Swarm Optimization (PSO) is a stochastic population-based optimization technique modeled on the social behaviour of flocking birds or schooling fish. This thesis applies PSO to the 2CNBR problem. As PSO is originally designed to handle a continuous solution space, modification of the algorithm was necessary in order to adapt it for such a highly constrained discrete combinatorial optimization problem. Presented are an indirect transcription scheme for applying PSO to such discrete optimization problems and an oscillating mechanism for averting stagnation.

Anharmonic Helmholtz free energy to O(lambdaâ ´) in the non- leading term approximation /|nby Leslie Wilk. -- 260 St. Catharines, Ont. : [s. n.],

Expressions for the anharmonic Helmholtz free energy contributions up to o( f ) ,valid for all temperatures, have been obtained using perturbation theory for a c r ystal in which every atom is on a site of inversion symmetry. Numerical calculations have been carried out in the high temperature limit and in the non-leading term approximation for a monatomic facecentred cubic crystal with nearest neighbour c entralforce interactions. The numbers obtained were seen to vary by a s much as 47% from thos e obtai.ned in the leading term approximati.on,indicating that the latter approximati on is not in general very good. The convergence to oct) of the perturbation series in the high temperature limit appears satisfactory.

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.

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.

On the path integral formulation and the evaluation of quantum statistical averages

Four problems of physical interest have been solved in this thesis using the path integral formalism. Using the trigonometric expansion method of Burton and de Borde (1955), we found the kernel for two interacting one dimensional oscillators• The result is the same as one would obtain using a normal coordinate transformation, We next introduced the method of Papadopolous (1969), which is a systematic perturbation type method specifically geared to finding the partition function Z, or equivalently, the Helmholtz free energy F, of a system of interacting oscillators. We applied this method to the next three problems considered• First, by summing the perturbation expansion, we found F for a system of N interacting Einstein oscillators^ The result obtained is the same as the usual result obtained by Shukla and Muller (1972) • Next, we found F to 0(Xi)f where A is the usual Tan Hove ordering parameter* The results obtained are the same as those of Shukla and Oowley (1971), who have used a diagrammatic procedure, and did the necessary sums in Fourier space* We performed the work in temperature space• Finally, slightly modifying the method of Papadopolous, we found the finite temperature expressions for the Debyecaller factor in Bravais lattices, to 0(AZ) and u(/K/ j,where K is the scattering vector* The high temperature limit of the expressions obtained here, are in complete agreement with the classical results of Maradudin and Flinn (1963) .

Sediment genotoxicity and its relationship to the frequency of chironomid labial plate deformities

Sediment samples were taken from seven locations in the WeIland River in December 1986 and April 1987. The DMSO extracts of these sediment samples showed a significant (pbounded by an industrialized area were slightly toxic according to -the alkaline phosphatase inhib_ii~ion component of the 50S chromotest analyses. The toxicity of these samples was only evident once they had been activated by the 59 (liver extract) mixture.

Thermodynamic properties and Debye-Waller factor of fee materials

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.

Geochemistry and petrogenesis of the McElroy and Larder Lake assemblages, Abitibi Greenstone Belt, Northeastern Ontario

The McElroy and Larder Lake assemblages, located in the southern Abitibi Greenstone Belt are two late Archean metavolcanic sequences having markedly contrasting physical characteristics arid are separated from one another by a regional fault. An assemblage is an informal term which describes stratified volcanic and/or sedimentary rock units built during a specific time period in a similar depositional or volcanic setting and are commonly bounded by faults, unconformities or intrusions. The petrology and petrogenesis of these assemblages have been investigated to determine if a genetic link exists between the two adjacent assemblages. The McElroy assemblage is homoclinal sequence of evolved massive and pillowed fl.ows, which except for the basal unit represents a progressively fractionated volcanic pile. From the base to the top of the assemblage the lithologies include Fe-tholeiitic, dendritic flows; komatiite basaltic, ultramafic flows; Mg-tholeiitic, leucogabbro; Mg-tholeiitic, massive flows and Fe-tholeiitic, pillowed flows. Massive flows range from coarse grained to aphanitic and are commonly plagioclase glomerophyric. The Larder Lake assemblage consists of komatiitic, Mg-rich and Fe-rich tholeiitic basalts, structurally disrupted by folds and faults. Tholeiitic rocks in the Larder Lake assemblage range from aphanitic to coarse grained massive and pillowed flows. Komatiitic flows contain both spinifex and massive textures. Geochemical variability within both assemblages is attributed to different petrogenetic histories. The lithologies of the McElroy assemblage were derived by partial melting of a primitive mantle source followed by various degrees of crystal fractionation. Partial melting of a primitive mantle source generated the ultramafic flows and possibly other flows in the assemblage. Fractionation of ultramafic flows may have also produced the more evolved McElroy lithologies. The highly evolved, basal, dendritic flow may represent the upper unit 3 of a missing volcanic pile in which continued magmatism generated the remaining McElroy lithologies. Alternatively, the dendritic flows may represent a primary lava derived from a low degree (10-15%) partial melt of a primitive mantle source which was followed by continued partial melting to generate the ultramafic flows. The Larder Lake lithologies were derived by partial melting of a komatiitic source followed by gabbroic fractionation. The tectonic environment for both assemblages is interpreted to be an oceanic arc setting. The McElroy assemblage lavas were generated in a mature back arc setting whereas the Larder Lake lithologies were produced during the early stages of komatiitc crust subduction. This setting is consistent with previous models involving plate tectonic processes for the generation of other metavolcanic assemblages in the Abitibi Greenstone Belt.

Grant of Permission for lease of military lands from Sir Robert Prescott to Thomas Clark, 1798-1801.

Transcript (original spelling and grammar retained): By His Excellency Robert Prescott Esquire, Captain General and Governor in Chief in and over His Majestys Provinces of Upper and Lower Canada, General and Commander in Chief of all His Majesty’s forces in the Provinces of Upper and Lower Canada, Nova Scotia, New Brunswick and their several Dependencies and in the Island of Newfoundland &ca. &ca. &ca. I do hereby authorise and permit Thomas Clark of Queenstown in the County of Lincoln in the Province of Upper Canada merchant to take possession of all that Lot, piece and parcel of Land (being part of the land reserved by his Majesty for Military purposes) situate, lying and being at Queenstown in the Township of Newark, in the Home District in the said Province of Upper Canada, bounded and abutted as follows, that is to say beginning at the Distance of two Chains and ninety links from the South East End of his Majesty’s Store House, the said distance being measured along the Bank up Stream, thence South thirty nine degrees and an half West one Chain and fifty links thence south fifty degrees and an half East one Chain and thirty links thence North thirty nine degrees and an half East to the Edge of the Bank and from thence along the Bank to the place of beginning, containing thirty one perches and one hundred and twenty five square links and to occupy and hold the said Lot, piece and parcel of Land during pleasure subject nevertheless to the provisoes and Conditions herein after contained, that is to say. First on condition that it shall and may be lawful to and for His Majesty his Heirs and Successors and to and for the Commander in Chief of His Majesty Forces for the time being and to and for the Officer commanding his Majesty’s Forces in Upper Canada for the time being and to and for either of them to determine and make void this present permission to occupy during pleasure the said Lot, Piece or Parcel of Land above described at any time hereafter whenever he or they shall see fit so to do without any compensation or indemnification to the said Thomas Clark or any other Person or Persons whosoever for any Loss Injury or Damage which he the said Thomas Clark or any other Person or Persons whosoever may thereby sustain. Secondly on this further Condition that it shall and may be lawful to and for His Majesty his Heirs and Successors and to and for his and their Officers, Soldiers and Servants at any time hereafter by order of the Commander in Chief of His Majesty’s Forces for the time being or by order of the Officer commanding his Majesty’s forces in Upper Canada for the time being or by order of the Officer of His Majesty’s Corps of Royal Engineers commanding in the said Province of Upper Canada for the time being to enter upon the said Lot Piece and parcel of Land which the said Thomas Clark is hereby permitted to occupy during pleasure or upon any part thereof and to take down and from the said Lot piece and parcel of Land or from any part thereof to remove any dwelling House Store or other Buildings on the said Lot, piece or Parcel of Land or any part thereof erected and to remove any goods or Chattels on the said Lot piece and parcel of Land or on any part thereof or on any such dwelling House Store or other building found or being and that His Majesty his Heirs and Successors or any other Person or Persons whosoever shall not be liable or responsible to the said Thomas Clark or to any other Person or Persons whosoever for any Loss, Injury or Damage which he or they shall or may in such case sustain. Thirdly on this further Condition that the said Thomas Clark shall not erect on the said Lot Piece or Parcel of Land which the said Thomas Clark is hereby permitted to occupy during pleasure or upon any part thereof at any time or times hereafter any dwelling House store or other Building whatsoever of Stone or brick or of any other materials wood only exccepted and that if any dwelling House or Store or other building of Stone or brick or of any other materials except wood shall at any time be erected on the said Lot, piece or parcel of Land or upon any part thereof, then and in such case, this present permission and every Clause and Article thereof shall from thenceforth cease and determine and be absolutely and entirely null and void. And lastly on this further Condition that the said Thomas Clark or any other Person whosoever shall not assign this permission to occupy the said Lot, Piece or Parcel of Land above described to any Person of Persons whosoever, and if any such assignment shall be made by the said Thomas Clark or by any other Person in his right, or on his behalf, that then and in such case such assignment and this permission to occupy during pleasure the said Lot piece and parcel of Land above described, and every Clause and Article thereof shall from thenceforth cease and determine and be absolutely and entirely null and void. Given under my hand at the Castle of St. Lewis in the City of Quebec in the Province of Lower Canada this Ninth day of July in the year of our Lord one thousand seven hundred and ninety eight and in the thirty eighth year of His Majesty’s Reign. [Signed here by Robert Prescott] By Order of the Commander in Chief [Signed here by James Green (Illegible signature)] I the said Thomas Clark above named do hereby accept the above written Permission to occupy during pleasure the said Lot piece and parcel of Land above described upon and subject to the several Provisioes and Conditions above written and each and every of them severally and respectively. In witness whereof I have hereunto set my hand the Sixteenth day of August in the year of our Lord one thousand seven hundred and ninety eight and in the thirty eighth year of His Majesty’s Reign. [Signed here by Thomas Clark] Signed in the presence of [Illegible signature – looks like J. M Donell Lt. Col.] [Illegible – looks like 2d. Battn R. C. Sm?] [Signed here by C. Anderson] Whereas Inconveniences did arise from the peculiar situation of the Ground contiguous to the above described Lot of Land and the occupation thereof, if estimated by the above Limits would prove highly disadvantageous to Mr. Thomas Clark be it known that in consideration thereof we do permit the above Lot to extend one half Chain more in length up stream so as to comprehend the space allowed for the Road between Lots Two + Three, and we do hereby appropriate the said additional space wholly to the use of the said Thomas Clark. In witness whereof we have hereunto subscribed this Thirteenth Day of October in the Year of our Lord one thousand Eight Hundred and one. [Signed here by J. M’Donell Lt. Col] 2d. Battn. R. C. [in?] Com of Fort George + Dependencies Robt. Pilkington Captain Royal Engineers

A System for Models of First Order Theories

If you want to know whether a property is true or not in a specific algebraic structure,you need to test that property on the given structure. This can be done by hand, which can be cumbersome and erroneous. In addition, the time consumed in testing depends on the size of the structure where the property is applied. We present an implementation of a system for finding counterexamples and testing properties of models of first-order theories. This system is supposed to provide a convenient and paperless environment for researchers and students investigating or studying such models and algebraic structures in particular. To implement a first-order theory in the system, a suitable first-order language.( and some axioms are required. The components of a language are given by a collection of variables, a set of predicate symbols, and a set of operation symbols. Variables and operation symbols are used to build terms. Terms, predicate symbols, and the usual logical connectives are used to build formulas. A first-order theory now consists of a language together with a set of closed formulas, i.e. formulas without free occurrences of variables. The set of formulas is also called the axioms of the theory. The system uses several different formats to allow the user to specify languages, to define axioms and theories and to create models. Besides the obvious operations and tests on these structures, we have introduced the notion of a functor between classes of models in order to generate more co~plex models from given ones automatically. As an example, we will use the system to create several lattices structures starting from a model of the theory of pre-orders.

L-Fuzzy Relations in Coq

Heyting categories, a variant of Dedekind categories, and Arrow categories provide a convenient framework for expressing and reasoning about fuzzy relations and programs based on those methods. In this thesis we present an implementation of Heyting and arrow categories suitable for reasoning and program execution using Coq, an interactive theorem prover based on Higher-Order Logic (HOL) with dependent types. This implementation can be used to specify and develop correct software based on L-fuzzy relations such as fuzzy controllers. We give an overview of lattices, L-fuzzy relations, category theory and dependent type theory before describing our implementation. In addition, we provide examples of program executions based on our framework.

Untangling the Organizational Ambiguities in Supply Chain Risk Recognition, Assessment, and Response: The Role of Network Embeddedness

In this thesis, I focus on supply chain risk related ambiguity, which represents the ambiguities firms exhibit in recognizing, assessing, and responding to supply chain disruptions. I, primarily, argue that ambiguities associated with recognizing and responding to supply chain risk are information gathering and processing problems. Guided by the theoretical perspective of bounded rationality, I propose a typology of supply chain risk related ambiguity with four distinct dimensions. I, also, argue that the major contributor to risk related ambiguity is often the environment, specifically the web of suppliers. Hence, I focus on the characteristics of these supplier networks to examine the sources of ambiguity. I define three distinct elements of network embeddedness – relational, structural, and positional embeddedness – and argue that the ambiguity faced by a firm in appropriately identifying the nature or impacts of major disruptions is a function of these network properties. Based on a survey of large North American manufacturing firms, I found that the extent of the relational ties a firm has and its position in the network are significantly related to supply chain risk related ambiguity. However, this study did not provide any significant support for the hypothesized relationship between structural embeddedness and ambiguity. My research contributes towards the study of supply chain disruptions by using the idea of bounded rationality to understand supply chain risk related ambiguity and by providing evidence that the structure of supply chain networks influences the organizational understanding of and responses to supply chain disruptions.

L-Fuzzy Structured Query Language

Lattice valued fuzziness is more general than crispness or fuzziness based on the unit interval. In this work, we present a query language for a lattice based fuzzy database. We define a Lattice Fuzzy Structured Query Language (LFSQL) taking its membership values from an arbitrary lattice L. LFSQL can handle, manage and represent crisp values, linear ordered membership degrees and also allows membership degrees from lattices with non-comparable values. This gives richer membership degrees, and hence makes LFSQL more flexible than FSQL or SQL. In order to handle vagueness or imprecise information, every entry into an L-fuzzy database is an L-fuzzy set instead of crisp values. All of this makes LFSQL an ideal query language to handle imprecise data where some factors are non-comparable. After defining the syntax of the language formally, we provide its semantics using L-fuzzy sets and relations. The semantics can be used in future work to investigate concepts such as functional dependencies. Last but not least, we present a parser for LFSQL implemented in Haskell.

The Effects of Magnetic Dilution and Applied Pressure on Several Frustrated Spinels

The effects of magnetic dilution and applied pressure on frustrated spinels GeNi2O4, GeCo2O4, and NiAl2O4 are reported. Dilution was achieved by substitution of Mg2+ in place of magnetically active Co2+ and Ni2+ ions. Large values of the percolation thresholds were found in GeNi(2-x)MgxO4. Specifically, pc1 = 0.74 and pc2 = 0.65 in the sub-networks associated with the triangular and kagome planes, respectively. This anomalous behaviour may be explained by the kagome and triangular planes behaving as coupled networks, also know as a network of networks. In simulations of coupled lattices that form a network of networks, similar anomalous percolation threshold values have been found. In addition, at dilution levels above x=0.30, there is a T^2 dependency in the magnetic heat capacity which may indicate two dimensional spin glass behaviour. Applied pressures in the range of 0 GPa to 1.2 GPa yield a slight decrease in ordering temperature for both the kagome and triangular planes. In GeCo(2-x)MgxO4, the long range magnetic order is more robust with a percolation threshold of pc=0.448. Similar to diluted nickel germanate, at low temperatures, a T^2 magnetic heat capacity contribution is present which indicates a shift from a 3D ordered state to a 2D spin glass state in the presence of increased dilution. Dynamic magnetic susceptibility data indicate a change from canonical spin glass to a cluster glass behaviour. In addition, there is a non-linear increase in ordering temperature with applied pressure in the range P = 0 to 1.0 GPa. A spin glass ground state was observed in Ni(1-x)MgxAl2O4 for (x=0 to 0.375). Analysis of dynamic magnetic susceptibility data yield a characteristic time of tau* = 1.0x10^(-13) s, which is indicative of canonical spin glass behaviour. This is further corroborated by the linear behaviour of the magnetic specific heat contribution. However, the increasing frequency dependence of the freezing temperature suggests a trend towards spin cluster glass formation.