The field of smart materials is an increasingly growing area of research. In aerodynamics applications especially, transducers have to fulfill a series of requirements such as light weight, size, energy consumption, robustness and durability. Piezoelectric transducers, devices which transform an electrical signal into motion, fulfill many of these requirements. Specifically, piezoelectric composites are of interest due to their added toughness and ease of integration into a structure. Resulting composites have a characteristic initial curvature with accompanying residual stresses that are responsible for enhanced performance, relative to flat actuators, when the active material is energized. A number of transducer designs based on composites have been developed. Two of these piezoelectric composites called Thunder® and Lipca are analyzed. Thunder is a composite of steel, polyimide adhesive, PZT, polyimide adhesive, and aluminum; and Lipca is a composite of fiberglass epoxy, carbon/epoxy, PZT, and fiberglass epoxy.Room temperature shapes of circular and rectangular Thunder® and Lipca actuators are predicted by using the Rayleigh-Ritz model. This technique is based on the assumption that the stable geometric configuration developed in the actuator after manufacturing, is the configuration that minimizes the total potential energy. This energy is a function of the displacement field which can be approximated by two functions, a four term model, and a twenty-three term model. The coefficients in the models are determined by minimizing the total potential energy of the actuator. The actuator deformations are assumed to obey the Kirchhoff hypothesis and the actuator layers are assumed to be in the state of plane stress.The four coefficient model produces results not comparable to three-dimensional surface topology maps. The twenty-three coefficient model however, is shown to have generally good agreement with the data for all studied actuators. To quantify the difference, at the cross section of each actuator, a profile is fitted by using a quadratic equation obtaining regression coefficients above 99%. For all actuators, the error between experimental and the calculated centerline data is less than 6%. For the 6R model however, the error is approximately 25%. One of the possible reasons for the error may be the tolerance of the thickness of the PZT layer. By changing the PZT thickness ±6% of the nominal value, over predicts the experimental dome height by 20%. Another possible reason for the discrepancy is the thickness of the actuator, thicker than all actuators used in this study, which might contradict the validity of the thin actuator assumption. Furthermore, by calculating the side-length-to-thickness ratio, 115 in this case, as stated by Aimmanee & Hyer (2004), may cause instability, and could result in unexpected behavior.The neutral axis position, calculated by using a force balance at equilibrium under the assumption of pure bending, for all actuators used in this study is determined and compared to the ceramic layer position. The results indicated that for all Thunder® models the neutral axis is located below the ceramic layer indicating that the PZT wafer may be in total tension. For the Lipca C2 device however, the neutral axis is found to be above the ceramic layer, indicating that the piezoelectric layer may be in total compression.Strain fields are also predicted with contradicting results when compared to the theory that the ceramic is in tension in the Thunder actuators. The contradiction on the strain calculations can be explained by the manner the strain field is derived: by differentiating and squaring the high-order polynomials of the approximated displacement component losing accuracy when it comes to predicting normal and shear strains.The Rayleigh-Ritz technique can become a tool to perform parametric studies of the key elements for manufacturing to optimize specific features of the actuators.

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The modern interaction we have with the natural environment surrounding our cities is often limited to designated areas that usually contain manicured trails. When information is very limited or absent we often avoid exploring such areas and instead opt for others both familiar and easily accessible. Mapping as a means to engage a community is a method that encourages exploration and discovery. Often there are hidden treasures of our communities’ backyards that have nearly been lost to time and memory. This practicum is an attempt to reconnect and engage residents and visitors of Thunder Bay, Ontario, with the historically significant Kaministiquia River. It focuses on the Kaministiquia from Kakabeka Falls to Lake Superior. By providing the public with information on the river’s attractions and how to access the river, it is hoped that families and individuals will utilitize the information to get outside and explore their surrounding environment.

Soit F ∈ Z[X1, . . . ,Xn] une forme décomposable, c’est-à-dire un polynôme homogène de degré d qui peut être factorisé en formes linéaires sur C. Notons NF (m) le nombre de solutions entières à l’inégalité |F(x)| ≤ m et VF (m) le volume de l’ensemble {x ∈ Rn :|F(x)| ≤ m}. En 2001, Thunder [19] a prouvé une conjecture de W.M. Schmidt, énonçant que, sous des conditions de finitude appropriées, on a NF (m) << m n/d où la constante implicite ne dépend que de n et d. En outre, il a montré une formule asymptotique NF (m) = m n/d V (F) + OF (m n/(d+n−2)) où, cependant, la constante implicite dépend de F. Dans des articles ultérieurs, la préoccupation de Thunder était d’obtenir une formule asymptotique similaire, mais avec la borne supérieure du terme d’erreur |NF (m) −m n/dV (F)| ne dépendant que de n et d. Dans [20] et [22], il a réussi à prouver que si gcd(n, d) = 1, la constante implicite dans le terme d’erreur peut en effet être fonction uniquement de n et d. L’objectif principal de cette thèse est d’étendre les résultats de Thunder au cadre p-adique. `A savoir, nous sommes intéressés par les solutions à l’inégalité |F(x)| · |F(x)|p1 . . . |F(x)|pr ≤ m en x = (x1, x2, . . . ,xn) ∈ Zn avec gcd(x1, x2, . . . ,xn, p1 · · · pr) = 1. (5.4.9) où p1, . . . , pr sont des nombres premiers distincts et |·|p désigne la valeur absolue p-adique habituelle. Le chapitre 1 est consacré au cadre p-adique de ce problème et aux preuves des lemmes auxiliaires. Le chapitre 2 est consacré à l’extension des résultats de Thunder de [19]. Dans le chapitre 3, nous montrons l’effectivité de la condition sous laquelle le nombre de solutions de (5.4.9) est fini. Le chapitre 4 et le chapitre 5 généralisent les résultats de Thunder dans [20], [21] et [22]. / Let F ∈ Z[X1, . . . ,Xn] be a decomposable form, that is, a homogeneous polynomial of degree d which can be factored into linear forms over C. Denote by NF (m) the number of integer solutions to the inequality |F(x)| ≤ m and by VF (m) the volume of the set{x ∈ Rn : |F(x)| ≤ m}. In 2001, Thunder [19] proved a conjecture of W.M. Schmidt, stating that, under suitable finiteness conditions, one has NF (m) << mn/d where the implicit constant depends only on n and d. Further, he showed an asymptotic formula NF (m) = mn/dV (F) + OF (mn/(d+n−2)) where, however, the implicit constant depends on F. In subsequent papers, Thunder’s concern was to obtain a similar asymptotic formula, but with the upper bound of the error term |NF (m)−mn/dV (F)| depending only on n and d. In [20] and [22], hemanaged to prove that if gcd(n, d) = 1, the implicit constant in the error term can indeed be made depending only on n and d.The main objective of this thesis is to extend Thunder’s results to the p-adic setting. Namely, we are interested in solutions to the inequality |F(x)| · |F(x)|p1 . . . |F(x)|pr ≤ m in x = (x1, x2, . . . ,xn) ∈ Zn with gcd(x1, x2, . . . ,xn, p1 · · · pr) = 1. (5.4.3)where p1, . . . , pr are distinct primes and | · |p denotes the usual p-adic absolute value.Chapter 1 is devoted to the p-adic set-up of this problem and to the proofs of the auxiliary lemmas. Chapter 2 is devoted to extending Thunder’s results from [19]. In chapter 3, we show the effectivity of the condition under which the number of solutions of (5.4.3) is finite. Chapter 4 and chapter 5 generalize Thunder’s results from [20], [21] and [22].

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My question here revolves around my orientation with my own work; my own frustrations and inability to so often answer the question “can a meaningful place be designed?” This journey examines the theory of semiotics. Through this, three strategies have been developed to explore the branches of semiotic research in Landscape Architecture. The first strategy allows meaning to develop through time, and it is with the repeated usage of people that meaning will accrue. The second strategy shows how meaning can be determined before the design through mapping current and desired locations of meaning in space. And, the third strategy reflects on how meaning emerges from the earth when no interference from designers or users occurs. The result of the three individual strategies is a combination of solutions, illustrating how to create places of true richness. This new space will engage visitors, pull in new visitors, and help create something memorable for those engaging in a space. / October 2008

My question here revolves around my orientation with my own work; my own frustrations and inability to so often answer the question “can a meaningful place be designed?” This journey examines the theory of semiotics. Through this, three strategies have been developed to explore the branches of semiotic research in Landscape Architecture. The first strategy allows meaning to develop through time, and it is with the repeated usage of people that meaning will accrue. The second strategy shows how meaning can be determined before the design through mapping current and desired locations of meaning in space. And, the third strategy reflects on how meaning emerges from the earth when no interference from designers or users occurs. The result of the three individual strategies is a combination of solutions, illustrating how to create places of true richness. This new space will engage visitors, pull in new visitors, and help create something memorable for those engaging in a space.

My question here revolves around my orientation with my own work; my own frustrations and inability to so often answer the question “can a meaningful place be designed?” This journey examines the theory of semiotics. Through this, three strategies have been developed to explore the branches of semiotic research in Landscape Architecture. The first strategy allows meaning to develop through time, and it is with the repeated usage of people that meaning will accrue. The second strategy shows how meaning can be determined before the design through mapping current and desired locations of meaning in space. And, the third strategy reflects on how meaning emerges from the earth when no interference from designers or users occurs. The result of the three individual strategies is a combination of solutions, illustrating how to create places of true richness. This new space will engage visitors, pull in new visitors, and help create something memorable for those engaging in a space.