Rozprawy doktorskie: „Structured lattices”

1

Felderhoff, Joël. "Difficultés de Problèmes de Réseaux Structurés pour la Cryptographie Post-Quantique". Electronic Thesis or Diss., Lyon, École normale supérieure, 2024. http://www.theses.fr/2024ENSL0059.

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La sécurité des protocoles cryptographiques repose sur la difficulté présumée de problèmes algorithmiques. Parmi ceux qui ont été identifiés jusque-là, les meilleurs problèmes pouvant servir de fondation à une cryptographie résistante aux ordinateurs quantiques sont issus des réseaux euclidiens. Les réseaux euclidiens sont une structure mathématique définie comme un ensemble de vecteurs de l’espace générés par les combinaisons entières d’un nombre fini de vecteurs réels linéairement indépendants (sa base). Un exemple typique de problème de sécurité relié est le Shortest Vector Problem (SVP). Étant donné une base d’un réseau euclidien en dimension n, trouver un vecteur court non nul. Pour des raisons d’efficacité, ces problèmes sont restreints à des réseaux issus de la théorie des nombres, dit structurés. Les hypothèses de sécurité relatives à ces réseaux particuliers étant différentes de celles des réseaux non structurés, il est nécessaire de les étudier spécifiquement, c’est l’objet de cette thèse. Nous avons étudié le cas des modules NTRU et uSVP en rang 2, prouvant que le problème SVP est équivalent sur ces deux familles de réseaux. Nous montrons également une réduction pire-cas vers cas-moyens pour les réseaux uSVP en rang 2. Ensuite nous avons démontré que résoudre SVP sur un idéal premier de petite norme n’était pas plus facile que de résoudre SVP sur n’importe quel idéal
The security of cryptographic protocols is based on the presumed difficulty of algorithmic problems. Among those identified so far, some of the best problems to serve as a foundation for quantum-proof cryptography come from lattices. Lattices are a mathematical structure defined as a set of space vectors generated by integer combinations of a finite number of linearly independent real vectors (its basis). A typical example of a related security problem is the Shortest Vector Problem (SVP). Given a base of an n-dimensional lattice, find a non-zero short vector. For efficiency reasons, these problems are restricted to lattices arising from number theory, known as structured lattices. As the security assumptions for these particular lattices are different from those for unstructured lattices, it is necessary to study them specifically, which is the aim of this thesis.We have studied the case of NTRU and uSVP modules in rank 2, proving that the SVP problem is equivalent on these two families of lattices. We also show a worst-case to average-case reduction for rank-2 uSVP lattices. Then we show that solving SVP on a prime ideal of small norm is no easier than solving SVP on any ideal

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2

ASHOK, RAMYA. "A DATABASE SYSTEM TO STORE AND RETRIEVE A CONCEPT LATTICE STRUCTURE". University of Cincinnati / OhioLINK, 2005. http://rave.ohiolink.edu/etdc/view?acc_num=ucin1130552767.

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3

Jenkins, Sarah Nield Morrish. "Mechanical properties and structural evaluation of diamond structure Ti6Al4V lattices made by Electron Beam Melting". Thesis, University of Sheffield, 2017. http://etheses.whiterose.ac.uk/20954/.

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4

Banihashemi, Amir H. "Decoding complexity and trellis structure of lattices". Thesis, National Library of Canada = Bibliothèque nationale du Canada, 1997. http://www.collectionscanada.ca/obj/s4/f2/dsk3/ftp04/nq22189.pdf.

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5

Burns, D. "Factorisability, group lattices, and Galois module structure". Thesis, University of Cambridge, 1989. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.335599.

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6

O'Connor, Joseph. "Fluid-structure interactions of wall-mounted flexible slender structures". Thesis, University of Manchester, 2018. https://www.research.manchester.ac.uk/portal/en/theses/fluidstructure-interactions-of-wallmounted-flexible-slender-structures(1dab2986-b78f-4ff9-9b2e-5d2181cfa009).html.

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The fluid-structure interactions of wall-mounted slender structures, such as cilia, filaments, flaps, and flags, play an important role in a broad range of physical processes: from the coherent waving motion of vegetation, to the passive flow control capability of hair-like surface coatings. While these systems are ubiquitous, their coupled nonlinear response exhibits a wide variety of behaviours that is yet to be fully understood, especially when multiple structures are considered. The purpose of this work is to investigate, via numerical simulation, the fluid-structure interactions of arrays of slender structures over a range of input conditions. A direct modelling approach, whereby the individual structures and their dynamics are fully resolved, is realised via a lattice Boltzmann-immersed boundary model, which is coupled to two different structural solvers: an Euler-Bernoulli beam model, and a finite element model. Results are presented for three selected test cases - which build in scale from a single flap in a periodic array, to a small finite array of flaps, and finally to a large finite array - and the key behaviour modes are characterised and quantified. Results show a broad range of behaviours, which depend on the flow conditions and structural properties. In particular, the emergence of coherent waving motions are shown to be closely related to the natural frequency of the array. Furthermore, this behaviour is associated with a lock-in between the natural frequency of the array and the predicted frequency of the fluid instabilities. The original contributions of this work are: the development and application of a numerical tool for direct modelling of large arrays of slender structures; the characterisation of the behaviour of slender structures over a range of input conditions; and the exposition of key behaviour modes of slender structures and their relation to input conditions.

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7

Goel, Archak. "Design of Functionally Graded BCC Type Lattice Structures Using B-spline Surfaces for Additive Manufacturing". University of Cincinnati / OhioLINK, 2019. http://rave.ohiolink.edu/etdc/view?acc_num=ucin1552398559313737.

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Hou, An. "Strength of composite lattice structures". Diss., Georgia Institute of Technology, 1997. http://hdl.handle.net/1853/12475.

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Obiedat, Mohammad. "Incrementally Sorted Lattice Data Structures". Thesis, The George Washington University, 2015. http://pqdtopen.proquest.com/#viewpdf?dispub=3732474.

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Data structures are vital entities that strongly impact the efficiency of several software applications. Compactness, predictable memory access patterns, and good temporal and spacial locality of the structure's operations are increasingly becoming essential factors in the selection of a data structure for a specific application. In general, the less data we store and move the better for efficiency and power consumption, especially in infrastructure software and applications for hand-held devices like smartphones. In this dissertation, we extensively study a data structure named lattice data structure (LDS) that is as compact and suitable for memory hierarchies as the array, yet with a rich structure that enables devising procedures with better time bounds.

To achieve performance similar to the performance of the optimal O(log(N)) time complexity of the searching operations of other structures, we provide a hybrid searching algorithm that can be implemented by searching the lattice using the basic searching algorithm when the degree of the sortedness of the lattice is less than or equal to 0.9h, and the jump searching algorithm when the degree of the sortedness of the lattice is greater than 0.9h. A sorting procedure that can be used, during the system idle time, to incrementally increase the degree of sortedness of the lattice is given. We also provide randomized and parallel searching algorithms that can be used instead of the usual jump-and-walk searching algorithms.

A lattice can be represented by a one-dimensional array, where each cell is represented by one array element. The worst case time complexity of the basic LDS operations and the average time complexity of some of the order-statistic operations are better than the corresponding time complexities of most of other data structures operations. This makes the LDS a good choice for memory-constrained systems, for systems where power consumption is a critical issue, and for real-time systems. A potential application of the LDS is to use it as an index structure for in-memory databases.

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Kouach, Mona. "Methods for modelling lattice structures". Thesis, KTH, Hållfasthetslära (Avd.), 2019. http://urn.kb.se/resolve?urn=urn:nbn:se:kth:diva-260498.

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The application of lattice structures have become increasingly popular as additive manufacturing (AM) opens up the possibility to manufacture complex configurations. However, modelling such structures can be computationally expensive. The following thesis has been conducted in order for the department of Structural Analysis, at SAAB in Järfälla, to converge with the future use of AM and lattice structures. An approach to model lattice structures using homogenization is presented where three similar methods involving representative volume element (RVE) have been developed and evaluated. The stiffness matrices, of the RVEs, for different sizes of lattice structures, comprising of BCC strut-based units, have been obtained. The stiffness matrices were compared and analysed on a larger solid structure in order to see the deformational predictability of a lattice-based structure of the same size. The results showed that all methods were good approximations with slight differences in terms of boundary conditions (BCs) at the outer edge. The comparative analyses showed that two of the three methods matches the deformational predictability. The BCs in all methods have different influences which makes it pivotal to establish the BCs of the structure before using the approach presented in this thesis.
Ökad implementering av gitterstrukturer i komponenter är ett resultat av utvecklingen inom additiv tillverkning. Metoden öppnar upp för tillverkning av komplexa strukturer med färre delmoment. Dock så uppkommer det svårigheter vid simulering av dessa komplexa strukturer då beräkningar snabbt tyngs ner med ökad komplexitet. Följande examensarbete har utförts hos avdelningen Strukturanalys, på SAAB i Järfälla, för att de ska kunna möta upp det framtida behovet av beräkningar på additivt tillverkade gitterstrukturer. I det här arbetet presenteras ett tillvägagångsätt för modellering av gitterstrukturer med hjälp av represantiva volymselement. Styvhetsmatriser har räknats fram, för en vald gitterkonfiguration, som sedan viktats mot tre snarlika representativa volymselement. En jämförelseanalys mellan de olika styvhetsmatriserna har sedan gjorts på en större och solid modell för att se hur väl metoderna förutsett deformationen av en gitterstruktur i samma storlek. Resultaten har visat att samtliga metoder är bra approximationer med tämligen små skillnader från randeffekterna. Vid jämförelseanalysen simulerades gitterstrukturen bäst med två av de tre metoder. En av slutsatserna är att det är viktigt att förstå inverkan av randvillkoren hos gitterstrukturer innan implementering görs med det tillvägagångssätt som presenterats i det här examensarbetet.

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11

Dinter, Simon. "Nucleon structure from lattice QCD". Doctoral thesis, Humboldt-Universität zu Berlin, Mathematisch-Naturwissenschaftliche Fakultät I, 2012. http://dx.doi.org/10.18452/16629.

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In dieser Arbeit berechnen wir mit Hilfe der Gitter-QCD Observablen, die in Beziehung zur Struktur des Nukleons stehen. Ein Teil dieser Arbeit beschäftigt sich mit Momenten von Parton-Verteilungsfunktionen. Solche Momente sind wichtig für das Verständnis der Nukleon-Struktur und werden durch globale Analysen von tief-inelastischen Streuexperimenten bestimmt. Eine theoretische, nicht-perturbative Rechnung der Momente in der Gitter-QCD ist möglich. Allerdings existiert, seit solche Gitter-QCD Rechnungen vorliegen, eine Diskrepanz zwischen diesen Rechnungen und den Ergebnissen globaler Analysen experimenteller Daten. Wir untersuchen, ob systematische Effekte für diese Diskrepanz verantwortlich sind, dabei studieren wir insbesondere die Effekte angeregter Zustände. Zudem führen wir eine erste Rechnung mit vier dynamischen Quark-Flavors durch. Ein weiterer Aspekt dieser Arbeit ist eine Machbarkeitsstudie zur Berechnung des skalaren Quark-Inhalts des Nukleons in der Gitter-QCD. Dieser bestimmt den Wirkungsquerschnitt der durch ein skalares Teilchen (z.B. ein Higgs-Teilchen) vermittelten Wechselwirkung eines schweren Teilchens mit einem Nukleon und kann somit einen Einfluss bei der Suche nach Dunkler Materie haben. Bisherige Gitter-Rechnungen dieser Größe besitzen große Unsicherheiten und sind daher von geringer Signifikanz für phenomenologische Anwendungen. Wir benutzen eine Varianz-Reduktions-Methode zur Auswertung von unverbundenen Diagrammen um ein präzises Ergebnis zu erhalten. Des Weiteren stellen wir eine neue stochastische Methode zur Berechnung von Nukleon-Dreipunkt-Korrelationsfunktionen vor, die für die Berechnung von Observablen der Nukleon-Struktur benötigt werden. Wir testen die Konkurrenzfähigkeit dieser neuen Methode gegenüber der Standard-Methode. In allen Rechnungen benutzen wir Wilson twisted-Mass Fermionen mit maximalem Twist, so dass die hier berechneten Observablen nur O(a^2) Diskretisierungsfehler aufweisen.
In this thesis we compute within lattice QCD observables related to the structure of the nucleon. One part of this thesis is concerned with moments of parton distribution functions (PDFs). Those moments are essential elements for the understanding of nucleon structure and can be extracted from a global analysis of deep inelastic scattering experiments. On the theoretical side they can be computed non-perturbatively by means of lattice QCD. However, since the time lattice calculations of moments of PDFs are available, there is a tension between these lattice calculations and the results from a global analysis of experimental data. We examine whether systematic effects are responsible for this tension, and study particularly intensively the effects of excited states by a dedicated high precision computation. Moreover, we carry out a first computation with four dynamical flavors. Another aspect of this thesis is a feasibility study of a lattice QCD computation of the scalar quark content of the nucleon, which is an important element in the cross-section of a heavy particle with the nucleon mediated by a scalar particle (e.g. Higgs particle) and can therefore have an impact on Dark Matter searches. Existing lattice QCD calculations of this quantity usually have a large error and thus a low significance for phenomenological applications. We use a variance-reduction technique for quark-disconnected diagrams to obtain a precise result. Furthermore, we introduce a new stochastic method for the calculation of connected 3-point correlation functions, which are needed to compute nucleon structure observables, as an alternative to the usual sequential propagator method. In an explorative study we check whether this new method is competitive to the standard one. We use Wilson twisted mass fermions at maximal twist in all our calculations, such that all observables considered here have only O(a^2) discretization effects.

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12

Kahn, Giacomo. "A structural study of lattices, d-lattices and some applications in data analysis". Thesis, Université Clermont Auvergne‎ (2017-2020), 2018. http://www.theses.fr/2018CLFAC066/document.

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Nous nous intéressons à un cadre théorique de l'analyse de données : l'analyse formelle de concepts. Le formalisme de l'analyse formelle de concepts permet d'exprimer les notions centrales de la fouille de données telles que les implications ou les ensembles fermés, avec au centre la notion de treillis qui décrit la structure et les relations que ces objets ont entre eux. Pour les données multidimensionnelles, une proposition de formalisme existe en tant que généralisation de l'analyse formelle de concepts : l'analyse polyadique de concepts. Dans cette thèse, nous étudions certains problèmes de combinatoire et d'algorithmique dans le cas de l'analyse polyadique de concepts. Nous approchons aussi un cadre plus appliqué à l'analyse de données en proposant des approches de navigation conceptuelle et de classification
We are interested in formal concept analysis, a theoretical framework for data analysis.This formalism allows to express some central notions of data mining such as implications or closed itemsets, and is centered around lattices, as the description of the relational structure that those objects can have.For multidimensional data, a formalism exists as a generalisation of formal concept analysis : polyadic concept analysis.In this document, we study some combinatorial and algorithmic problems that arose in polyadic concept analysis.We also introduce more applied data analysis techniques of conceptual navigation and classification

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13

Pugh, David John Rhydwyn. "Topological structures in lattice gauge theory". Thesis, University of Oxford, 1990. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.279896.

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Papachristou, Petros G. "Probabilistic relaxation for square lattice structures". Thesis, University of Surrey, 1994. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.241395.

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AGUILERA, JEAN RODRIGO FERREIRA. "LIGHT LATTICE STRUCTURES UNDER WIND ACTION". PONTIFÍCIA UNIVERSIDADE CATÓLICA DO RIO DE JANEIRO, 2007. http://www.maxwell.vrac.puc-rio.br/Busca_etds.php?strSecao=resultado&nrSeq=10538@1.

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CONSELHO NACIONAL DE DESENVOLVIMENTO CIENTÍFICO E TECNOLÓGICO
No projeto de estruturas treliçadas esbeltas, um ponto relativamente em aberto é quanto à resposta dinâmica dessas torres sob ação do vento. Já foram observadas várias ocorrências de queda de torres por tais efeitos no Brasil e ultimamente, essas incidências vêm aumentando, trazendo diversos transtornos e prejuízos significativos à sociedade e às empresas concessionárias. Nesse contexto, brotam dois aspectos centrais: a modelagem da estrutura e a discretização da ação do vento. A montagem desses dois cenários é feita com base em um modelo numérico, no SAP2000, de uma torre de 73,75 m de altura da linha de transmissão LT - 103, na Amazônia, e uma torre de TV com 192 m de altura, localizada em Brasília-DF, ambas no Brasil. Para avaliação da excitação do vento, é utilizada a norma brasileira NBR 6123. Em estudo preliminar, propõe-se uma forma de representação simplificada das forças do vento sobre a torre, de modo a serem utilizadas resultantes por módulos, convenientemente distribuídas por seus nós principais, visando-se quer a resposta estática, quer a dinâmica. A torre de TV é ensaiada sob a ação de pulsos isolados do vento de projeto e por sucessões diversas desses pulsos com o intuito de simular rajadas de vento. Investiga-se também, para a ação de ventos normalizados extremos, a resposta linear e não-linear P-Delta do sistema. Em consequência, identificam-se pontos de insuficiência estrutural e, para as ações extremas, ensaiam-se recursos mecânicos para controle dos deslocamentos e esforços máximos produzidos pela ação estática e dinâmica do vento.
The dynamic response of slender latticed tower structures under wind excitation is still an open point in the design of such systems. In Brazil, an expressive number of accidents have been registered, in the last few decades, and a large number of material and financial losses have been equally reported, for both people and industrial plant owners. In the structural analysis scenario, two central points dominate the structural engineer concerns: the modeling of the structure and of the wind action. Two tower models are used, a 73,75m high transmission line trussed structure, LT 103, settled in the Brazilian Amazon Basin and a 193m tall trussed TV tower, built in Brasilia-DF. The wind action on the tower members is computed according to the brazilian recommendation, NBR- 6123. In a preliminary study, a simplified procedure is proposed to evaluate the wind forces on the LT-103 tower sections and to conveniently distribute them on the main tower model nodes (joints). The TV Tower is evaluated under the static and dynamic action of the wind forces, either by isolated pulses or by a train of them to model a wind gust. The tower response is computed under a linear and non-linear P-Delta behavior; some faulting spots are identified in the response reports and a combined vibration control solution is proposed incorporating steel tendons conjugated with multiple tuned mass absorbers. A comparison is also made with the NBR 15307 recommendation and a couple of comments are addressed to those who may intend to apply this regulation to investigate the behavior of slender trussed tower structures.

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Leung, Anthony Chi Hin. "Actuation properties of kagome lattice structures". Thesis, University of Cambridge, 2007. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.613328.

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Huff, Cheryl Rae. "Countable Additivity, Exhaustivity, and the Structure of Certain Banach Lattices". Thesis, University of North Texas, 1999. https://digital.library.unt.edu/ark:/67531/metadc278330/.

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The notion of uniform countable additivity or uniform absolute continuity is present implicitly in the Lebesgue Dominated Convergence Theorem and explicitly in the Vitali-Hahn-Saks and Nikodym Theorems, respectively. V. M. Dubrovsky studied the connection between uniform countable additivity and uniform absolute continuity in a series of papers, and Bartle, Dunford, and Schwartz established a close relationship between uniform countable additivity in ca(Σ) and operator theory for the classical continuous function spaces C(K). Numerous authors have worked extensively on extending and generalizing the theorems of the preceding authors. Specifically, we mention Bilyeu and Lewis as well as Brooks and Drewnowski, whose efforts molded the direction and focus of this paper. This paper is a study of the techniques used by Bell, Bilyeu, and Lewis in their paper on uniform exhaustivity and Banach lattices to present a Banach lattice version of two important and powerful results in measure theory by Brooks and Drewnowski. In showing that the notions of exhaustivity and continuity take on familiar forms in certain Banach lattices of measures they show that these important measure theory results follow as corollaries of the generalized Banach lattice versions. This work uses their template to generalize results established by Bator, Bilyeu, and Lewis.

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Renner, Dru Bryant 1977. "Exploring proton structure using lattice QCD". Thesis, Massachusetts Institute of Technology, 2004. http://hdl.handle.net/1721.1/29448.

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Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Physics, 2004.
Includes bibliographical references (leaves 219-222).
We calculate moments of the generalized parton distributions of the nucleon using lattice QCD. The generalized parton distributions determine the angular momentum decomposition of the nucleon and the transverse distributions of partons within the nucleon. Additionally, the generalized parton distributions reduce to the elastic form factors and ordinary parton distributions in particular kinematic limits. Thus by calculating moments of the generalized parton distributions in lattice QCD we can explore many facets of the structure of the nucleon. In this effort, we have developed the building block method to determine all the lattice correlation functions which con- tribute to the off forward matrix elements of the twist two operators. These matrix elements determine the generalized form factors of the nucleon which in turn give the moments of the generalized parton distributions. Thus we use our building block method to calculate all the matrix elements of the lowest twist two operators. Fur- thermore, we use our method to construct an overdetermined set of matrix elements allowing a more accurate calculation of the generalized form factors.
by Dru Bryant Renner.
Ph.D.

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19

Taylor, Lesley. "Structural investigations of novel liquid crystals". Thesis, University of Southampton, 1991. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.358364.

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Galvin, Brian Russell. "Numerical studies of localized vibrating structures in nonlinear lattices". Thesis, Monterey, California. Naval Postgraduate School, 1991. http://hdl.handle.net/10945/28408.

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Farley, Jonathan David. "The structure of function lattices : automorphisms, congruences, and ideals". Thesis, University of Oxford, 1995. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.282346.

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Zhang, Botao. "Design of Variable-Density Structures for Additive Manufacturing Using Gyroid Lattices". University of Cincinnati / OhioLINK, 2018. http://rave.ohiolink.edu/etdc/view?acc_num=ucin1535374427634743.

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Cox, Jennifer Jane. "Structure of organic molecular thin films vapour deposited on III-V semiconductor surfaces". Thesis, Imperial College London, 1999. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.327025.

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Vannutelli, Rafaela S. "Mechanical Behavior of 3D Printed Lattice-Structured Materials". Youngstown State University / OhioLINK, 2017. http://rave.ohiolink.edu/etdc/view?acc_num=ysu1516313745997898.

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CAPOBIANCO, Silvio. "Structure and invertibility in cellular automata". Doctoral thesis, La Sapienza, 2005. http://hdl.handle.net/11573/917108.

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Ayers, James T. "Hydrodynamic Drag and Flow Visualization of IsoTruss Lattice Structures". Diss., CLICK HERE for online access, 2005. http://contentdm.lib.byu.edu/ETD/image/etd782.pdf.

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Hammetter, Christopher Ian. "Designing pyramidal lattice structures for energy absorption". Thesis, University of California, Santa Barbara, 2014. http://pqdtopen.proquest.com/#viewpdf?dispub=3602080.

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Applications for energy absorption materials range from athletic equipment, to vehicle crumple zones, to blast protection for military vehicles and personnel. Many energy absorption structures employ stochastic foams because of their plateau-like stress-strain response that allows for the absorption of large amounts of energy at relatively low stresses over large compressive strains. Periodic lattice structures, when properly designed, provide the same capabilities as stochastic systems, but with a more tailorable response that provides potential for improved specific strength and energy absorption. The present dissertation provides an in-depth study of the pyramidal lattice: one particular periodic structure that strikes a good compromise between performance and manufacturability. Through finite element and analytical modeling, this study identifies key parameters of the geometry, boundary conditions, and parent material properties that determine the compressive stress-strain response of the structure. In conjunction with experimental investigations, these models are used to understand and determine the potential for improving the response of the as-manufactured polymeric pyramidal lattice structures through additional heat treatment and filling the lattice void-space with stochastic foam. Finally, additional models are developed to understand and predict the structural rate effects that arise from inertial stabilization of strut buckling during dynamic loading. Particular emphasis is given to the effects of yield strain and density of the parent material on failure modes and dynamic response. In addition to providing a strong basis for the design of pyramidal lattice materials, this work provides useful insight into the design of energy absorption materials in general.

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Novak, Jurica. "Simulated mesoscopic structures in a ferroelastic lattice". Thesis, University of Cambridge, 2000. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.621535.

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Craig, Adam Patrick. "Novel structures for lattice-mismatched infrared photodetectors". Thesis, Lancaster University, 2016. http://eprints.lancs.ac.uk/82854/.

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Using the interfacial misfit (IMF) array growth mode, GaSb p-i-n diodes were grown on Si and GaAs lattice-mismatched substrates by molecular beam epitaxy (MBE) under optimised growth conditions. For the sample grown on Si, an AlSb nucleation layer was used to reduce the occurrence of twinning defects. In addition to the samples grown on mismatched substrates, an equivalent structure was further grown on a native GaSb substrate, for comparison. X-ray diffraction (XRD) was used to demonstrate that the layers were fully relaxed, and transmission electron microscopy (TEM) imaging showed arrays of 90° misfit dislocations with measured periodicities in agreement with atomistic modelling. However, after processing, device dark current densities of 0.9 Acm^-2 and 0.18 Acm^-2 were recorded for the sample grown on Si and the sample grown on GaAs, respectively, at -1.0 V and 300 K. These were compared to the sample grown on native GaSb, which had a dark current density of 0.01 Acm^-2 under the same conditions. Furthermore, TEM analysis revealed relatively high threading dislocation densities (TDDs) of ~10^8 cm^-2. It was proposed that not all the interfacial strain could be accommodated by the IMF arrays, since the array periods (9:8 for AlSb/Si and 13:14 for GaSb/GaAs) were not in exact agreement with ratio of the lattice constants (of AlSb to Si and GaSb to GaAs), i.e. a population of 60° misfit dislocations was still formed. It was therefore decided to investigate the use of nBn detector structures as lattice mismatched photodetectors. Using a design based on an InAsSb bulk-material absorber, a comparison was again drawn between two samples, one grown on mismatched GaAs and a second grown on native GaSb. This time, device dark current densities were found to be relatively similar when comparing the two samples (1.6×10^-5 Acm^-2 vs 3×10^-6 Acm^-2 at 200 K). D^* performance figures were also found to be within one order of magnitude (1.5×10^10 cmHz^1/2 W^-1 vs 9.8×10^10 cmHz^1/2 W^-1 at 200 K). Furthermore, diffusion limited performance was exhibited at all temperatures tested, so that the effects of Shockley Read Hall (SRH) generation were established to be absent (or at least much less significant). It was also found that absorption layer doping of around ~4×10^17 cm^-3 was necessary to ensure diffusion limited performance for the sample grown on GaAs and that, with this modification, diffusion limited performance was achieved even for a sample with a highly lattice-mismatched absorption layer (with higher Sb content and longer cut-off wavelength).While nBn detector structures offer very low dark currents, it will sometimes be necessary to have a detector which is sensitive to very weak signals. In telecoms applications, avalanche photodiode (APD) structures are often used as receivers for long-haul fibre optic systems. However, relatively few avalanche photodiode designs exist for wavelengths beyond 1.55 μm. Two novel separate-absorption-and-multiplication (SAM) APD structures were therefore demonstrated based on the IMF growth mode. In particular, by transitioning the lattice from 5.65 Å to 6.09 Å, it was possible to combine GaSb absorption layers with GaAs and (for improved noise performance) Al0.8Ga0.2As multiplication layers. Multiplication profiles were established using capacitance voltage modelling (together with ionisation coefficients from the literature) and excess noise measurements were then carried out. Through the presence of 1.55 μm photocurrent, it was confirmed that absorption took place in the GaSb regions, with transport to the p-n junction (in the multiplication region) taking place by diffusion. Through measurements showing 0.2

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30

Melpal, Gopalakrishna Ranjan. "Conformal Lattice Structures in Additive Manufacturing (AM)". University of Cincinnati / OhioLINK, 2018. http://rave.ohiolink.edu/etdc/view?acc_num=ucin1535382325233769.

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31

Blair, Stuart R. "Lattice Boltzmann Methods for Fluid Structure Interaction". Thesis, Monterey, California. Naval Postgraduate School, 2012. http://hdl.handle.net/10945/17325.

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Approved for public release; distribution is unlimited
The use of lattice Boltzmann methods (LBM) for fluid flow and its coupling with finite element method (FEM) structural models for fluid-structure interaction (FSI) is investigated. A body of high performance LBM software that exploits graphic processing unit (GPU) and multiprocessor programming models is developed and validated against a set of two- and three-dimensional benchmark problems. Computational performance is shown to exceed recently reported results for single-workstation implementations over a range of problem sizes. A mixed-precision LBM collision algorithm is presented that retains the accuracy of double-precision calculations with less computational cost than a full double-precision implementation. FSI modelling methodology and example applications are presented along with a novel heterogeneous parallel implementation that exploits task-level parallelism and workload sharing between the central processing unit (CPU) and GPU that allows significant speedup over other methods. Multi-component LBM fluid models are explicated and simple immiscible multi-component fluid flows in two-dimensions are presented. These multi-component fluid LBM models are also paired with structural dynamics solvers for two-dimensional FSI simulations. To enhance modeling capability for domains with complex surfaces, a novel coupling method is introduced that allows use of both classical LBM (CLBM) and a finite element LBM (FELBM) to be combined into a hybrid LBM that exploits the flexibility of FELBM while retaining the efficiency of CLBM.

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32

Xue, Boyu. "3D Printed Lattice Structure for Driveline Applications". Thesis, KTH, Materialvetenskap, 2021. http://urn.kb.se/resolve?urn=urn:nbn:se:kth:diva-299270.

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Lattice structures have received a lot of attention as cellular materials in recent years because of their outstanding properties, such as high strength-to-weight ratio, heat transfer, energy absorption, and capability of improving noise, vibration and harshness (NVH) behavior. This type of structure received a boost from additive manufacturing (AM) technology, which can fabricate geometries in practically any shape. Due to economic and environmental requirements, lightweight design is increasingly used in automobile and construction equipment applications. NVH behavior is a crucial issue for construction equipment. However, the conventional structures' NVH behavior is mainly decided by the mass, so silence often requires heavy systems, leading to more energy consumption and emission. Therefore, the environmental trends and the resulting economic competition have limited traditional (heavy) solutions to improve NVH behavior and make the lightweight design more difficult. Novel solutions are necessary to light the difficulty and challenge of combining NVH and lightweight requirements. In this research, topology optimization was implemented on a New Articulated Hauler Transmission (NAHT) component to balance lightweight and NVH behavior. The topology- optimized 3D model was filled by a non-homogenous lattice structure with optimal lattice density via size optimization. Lattice structure optimization is one type of topology optimization, and it is the term for describing these procedures. To fabricate the complicated lattice structure, additive manufacturing (or 3D printing) is required (after topology and lattice structure optimization). The new models were analyzed using the finite element method (FEM), and the results of the analysis were compared with those of the original models. After the comparison, positive results were obtained, demonstrating that topology and lattice optimization can be applied in the design of construction equipment components. According to the results, lattice structure optimization can create a reliable lightweight design with good NVH behavior. Furthermore, lattice structure's organization and layout have a significant impact on the overall performance.
Gitterstrukturer har fått mycket uppmärksamhet som cellulära material under de senaste åren på grund av deras enastående egenskaper, t.ex. hög hållfasthet i förhållande till vikt, värmeöverföring, energiabsorption och förmåga att förbättra buller-, vibrations- och bullerskador (NVH-beteende). Denna typ av struktur har fått ett uppsving av tekniken för additiv tillverkning (AM), som kan tillverka geometrier i praktiskt taget vilken form som helst. På grund av ekonomiska och miljömässiga krav används lättviktsdesign i allt större utsträckning inom bilindustrin och byggnadsutrustning. NVH-egenskaperna är en viktig fråga för anläggningsutrustning. De konventionella konstruktionernas NVH-beteende bestäms dock huvudsakligen av massan, vilket innebär att tystnad ofta kräver tunga system, vilket leder till ökad energiförbrukning och större utsläpp. Miljötrenderna och den ekonomiska konkurrens som följer av detta har därför begränsat de traditionella (tunga) lösningarna för att förbättra NVH-egenskaperna och gjort lättviktsdesignen svårare. Nya lösningar är nödvändiga för att lösa svårigheten och utmaningen med att kombinera NVH- och lättviktskrav. I den här forskningen genomfördes topologioptimering på en komponent för en ny ledad transportörtransmission (NAHT) för att balansera lättvikts- och NVH-beteende. Den topologioptimerade 3D-modellen fylldes med en icke-homogen gitterstruktur med optimal gittertäthet via storleksoptimering. Gitterstrukturoptimering är en typ av topologioptimering, och det är termen för att beskriva dessa förfaranden. För att tillverka den komplicerade gitterstrukturen krävs additiv tillverkning (eller 3D-utskrift) (efter topologi- och gitterstrukturoptimering). De nya modellerna analyserades med hjälp av finita elementmetoden (FEM), och resultaten av analysen jämfördes med resultaten av de ursprungliga modellerna. Efter jämförelsen erhölls positiva resultat, vilket visar att optimering av topologi och gitterstruktur kan tillämpas vid utformning av komponenter för byggutrustning. Enligt resultaten kan optimering av gitterstrukturen skapa en tillförlitlig lättviktsdesign med bra NVH-beteende. Dessutom har gitterstrukturens organisering och layout en betydande inverkan på den totala prestandan.

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33

Kwuida, Leonard. "Dicomplemented Lattices". Doctoral thesis, Saechsische Landesbibliothek- Staats- und Universitaetsbibliothek Dresden, 2004. http://nbn-resolving.de/urn:nbn:de:swb:14-1101148726640-29266.

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Das Ziel dieser Arbeit ist es die mathematische Theorie der Begriffsalgebren zu entwickeln. Wir betrachten dabei hauptsaechlich das Repraesentationsproblem dieser vor Kurzem eingefuehrten Strukturen. Motiviert durch die Suche nach einer geeigneten Negation sind die Begriffsalgebren entstanden. Sie sind nicht nur fuer die Philosophie oder die Wissensrepraesentation von Interesse, sondern auch fuer andere Felder, wie zum Beispiel Logik oder Linguistik. Das Problem Negationen geeignet einzufuehren, ist sicher eines der aeltesten der wissenschaftlichen oder philosophischen Gemeinschaft und erregt auch zur Zeit die Aufmerksamkeit vieler Wissenschaftler. Verschiedene Typen von Logik (die sich sehr stark durch die eigefuehrte Negation unterscheiden) unterstreichen die Wichtigkeit dieser Untersuchungen. In dieser Arbeit beschaeftigen wir uns hauptsaechlich mit der kontextuellen Logik, eine Herangehensweise der Formalen Begriffsanalyse, basierend auf der Idee, den Begriff als Einheit des Denkens aufzufassen
The aim of this investigation is to develop a mathematical theory of concept algebras. We mainly consider the representation problem for this recently introduced class of structures. Motivated by the search of a "negation" on formal concepts, "concept algebras" are of considerable interest not only in Philosophy or Knowledge Representation, but also in other fields as Logic or Linguistics. The problem of negation is surely one of the oldest problems of the scientific and philosophic community, and still attracts the attention of many researchers. Various types of Logic (defined according to the behaviour of the corresponding negation) can attest this affirmation. In this thesis we focus on "Contextual Logic", a Formal Concept Analysis approach, based on concepts as units of thought

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34

Bailey, S. J. "Cathodoluminescence of quantum well structures". Thesis, University of Bristol, 1987. http://hdl.handle.net/1983/b02b03a2-c0d8-401d-a94e-8bd26b52b953.

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35

Brown, Stephen A. "The response of polyhedra in close packed structures to temperature and pressure". Thesis, This resource online, 1993. http://scholar.lib.vt.edu/theses/available/etd-11102009-020124/.

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36

Wegener, Claudia B. "Natural dualities for varieties generated by lattice-structured algebras". Thesis, University of Oxford, 1999. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.302397.

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37

Hodgetts, P. A. "The collapse behaviour of lattice hyperbolic paraboloids". Thesis, University of Cambridge, 1990. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.315959.

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38

Tornatore, Dario. "Damping Capability of Lattice Structures: a Numerical Study". Master's thesis, Alma Mater Studiorum - Università di Bologna, 2019.

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Lattices are recognized as ultra-lightweight materials with high specific stiffness and high specific strength. The applications of this architectural material range from the aerospace and automotive industry up to the biomedical one. In the literature, most of the studies address the mechanical responses of lattice structures under static, dynamic (impact) and fatigue loading conditions while only few works deal with the damping capabilities of such structures. This study focuses on the damping capability of classical lattice configurations whose architecture is made of struts (i.e. CC, CBCC, ACC, Octet, Rhombic dodecahedron). The influence of three aspects has been investigated: the geometrical parameters defining the structure of the lattice cell, the introduction of a compressive pre-stress field within the cell and the plastic constitutive behaviour of the material used for the struts. A broad sensitivity campaign has been performed in order to evaluate the amount of dissipated energy for the different cell architectures according to the variation of the strut diameter and to the presence of local instabilities (post-buckling behaviour of the struts). The numerical results highlight how the damping capability of the considered cell, for the same loading condition, is strongly related to the topology of the cell and to its relative density. By smartly tailoring these parameters, the damping capability without pre-stress can be increased up to 23% and, if the pre-stress is introduced within the cell, the damping effects can be ulteriorly intensified .

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39

Haq, Sirajul. "Mathematical models of defects in discrete lattice structures". Thesis, University of Liverpool, 2004. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.408552.

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40

Paupitz, Goncalves Paulo José. "Dynamic analysis and active control of lattice structures". Thesis, University of Southampton, 2007. https://eprints.soton.ac.uk/69737/.

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This thesis presents an investigation of the factors controlling the performance of two forms of active vibration control applied to lattice structures, such as those used for space applications. The structure considered is based on a lattice structure assembled by NASA in 1984. It consists of a satellite boom with 93 aluminium members connected rigidly through 33 spherical joints. The structure has two distinct forms of motion which are categorized in terms of short and long wavelength modes. The short wavelength modes occurs when the length of the individual members is a multiple of half wavelength of bending waves. The second category, named long wavelength modes occur when the length of the whole structure is a multiple of half wavelength of waves propagating by longitudinal motion in the structure. Simple expressions are derived to identify the factors that control the frequency bands where short and long wavelength modes occur. It is possible to alter the dynamic behaviour of the system by changing some of the factors in these expressions and thus study the active and passive control of vibration in a variety of such structures. The two strategies of active control considered in the thesis are feedforward control and integral force feedback control. Feedforward control usually requires deterministic forms of disturbance sources while feedback control can be applied to random disturbances. It has been found that short wavelength modes can reduce the performance in the feedback control strategy, while the results of feedforward control are not affected so much. To support this analysis, the energy dissipation and power flow mechanisms in the structure are studied. The results in this thesis are based on numerical simulations and experimental tests which have been used to validate the mathematical model of the structure.

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41

Shalchy, Faezeh, Enrique Cuan-Urquizo, Kevin Jose, Neil Ferguson, Claus Ibsen i Atul Bhaskar. "Mechanics and manufacture of lattice structures & materials". Thesis, Київський національний університет технологій та дизайну, 2021. https://er.knutd.edu.ua/handle/123456789/19222.

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42

Folinus, Charlotte Méry. "Stiffness prediction methods for additively manufactured lattice structures". Thesis, Massachusetts Institute of Technology, 2020. https://hdl.handle.net/1721.1/127918.

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Thesis: S.B., Massachusetts Institute of Technology, Department of Mechanical Engineering, May, 2020
Cataloged from the official PDF of thesis.
Includes bibliographical references (pages 87-91).
Since the initial 300 pair release of the Futurecraft 4D in April 2017, adidas has scaled its 4D program to mass produce additively manufactured shoe midsoles. The 4D midsoles are constructed from lattice structures, and if there is variation in the manufacturing process, the structure's material and/or geometric properties may be altered. This means midsoles may have the same geometry but different material properties and thus different stiffnesses, and they may also have the same material properties but different overall stiffness due to geometric changes. The current quality control test is slow, expensive, and does not scale well. This thesis explores two potential techniques: using ultrasonic waves to determine the lattices' acoustic properties, and weighing them to determine their mass. Pulse-echo testing data for n = 8 samples shows a statistically significant (p = 0.0398 < 0.05) increase in response time due to sample stiffness. Stiffness scaled linearly with lattice mass for both physical and simulated lattices, and mass predicted lattice stiffness with a minimum accuracy of 90% across a range of simulated manufacturing conditions. An analytical framework parameterized around a bivariate normal distribution can determine accuracy of new test methods or from additional mass-stiffness data. Lastly, cost minimization is presented for a hybrid test protocol which combines mass testing with secondary testing for rejected samples. At specification limits of ±1[sigma], the hybrid test achieves 99% accuracy at 69.8% of the cost for the current test. Increasing the specification limit to ±2[sigma] reduces cost further, achieving 99% accuracy at 16.4% of the current cost.
by Charlotte Méry Folinus.
S.B.
S.B. Massachusetts Institute of Technology, Department of Mechanical Engineering

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43

Wilmoth, Nathan G. "Determining the Mechanical Properties of Lattice Block Structures". Cleveland State University / OhioLINK, 2013. http://rave.ohiolink.edu/etdc/view?acc_num=csu1366275566.

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Hussein, Ahmed Yussuf. "The development of lightweight cellular structures for metal additive manufacturing". Thesis, University of Exeter, 2013. http://hdl.handle.net/10871/15023.

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Metal Additive Manufacturing (AM) technologies in particular powder bed fusion processes such as Selective Laser Melting (SLM) and Direct Metal Laser Sintering (DMLS) are capable of producing a fully-dense metal components directly from computer-aided design (CAD) model without the need of tooling. This unique capability offered by metal AM has allowed the manufacture of inter-connected lattice structures from metallic materials for different applications including, medical implants and aerospace lightweight components. Despite the many promising design freedoms, metal AM still faces some major technical and design barriers in building complex structures with overhang geometries. Any overhang geometry which exceeds the minimum allowable build angle must be supported. The function of support structure is to prevent the newly melted layer from curling due to thermal stresses by anchoring it in place. External support structures are usually removed from the part after the build; however, internal support structures are difficult or impossible to remove. These limitations are in contrast to what is perceived by designers as metal AM being able to generate all conceivable geometries. Because support structures consume expensive raw materials, use a considerable amount of laser consolidation energy, there is considerable interest in design optimisation of support structure to minimize the build time, energy, and material consumption. Similarly there is growing demand of developing more advanced and lightweight cellular structures which are self-supporting and manufacturable in wider range of cell sizes and volume fractions using metal AM. The main focuses of this research is to tackle the process limitation in metal AM and promote design freedom through advanced self-supporting and low-density Triply Periodic Minimal Surface (TPMS) cellular structures. Low density uniform, and graded, cellular structures have been developed for metal AM processes. This work presents comprehensive experimental test conducted in SLM and DMLS processes using different TPMS cell topologies and materials. This research has contributed to new knowledge in understanding the manufacturability and mechanical behaviour of TPMS cellular structures with varying cell sizes, orientations and volume fractions. The new support structure method will address the saving of material (via low volume cellular structures and easy removal of powder) and saving of energy (via reduced build-time).

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45

McConaha, Matthew. "Graded Lattice Structure Density Optimization for Additive Manufacturing". University of Cincinnati / OhioLINK, 2018. http://rave.ohiolink.edu/etdc/view?acc_num=ucin1523634949822303.

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46

Downie, Lewis James. "Structure and properties of some triangular lattice materials". Thesis, University of St Andrews, 2014. http://hdl.handle.net/10023/4423.

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This thesis is concerned with the study of two families of materials which contain magnetically frustrated triangular lattices. Each material is concerned with a different use; the first, analogues of YMnO₃, is from a family of materials called multiferroics, the second, A₂MCu₃F₁₂ (where A = Rb¹⁺, Cs¹⁺, M = Zr⁴⁺, Sn⁴⁺, Ti⁴⁺, Hf⁴⁺), are materials which are of interest due to their potentially unusual magnetic properties deriving from a highly frustrated Cu²⁺-based kagome lattice. YFeO₃, YbFeO₃ and InFeO₃ have been synthesised as their hexagonal polymorphs. YFeO₃ and YbFeO₃ have been studied in depth by neutron powder diffraction, A.C. impedance spectroscopy, Mössbauer spectroscopy and magnetometry. It was found that YFeO₃ and YbFeO₃ are structurally similar to hexagonal YMnO₃ but there is evidence for a subtle phase separation in each case. Low temperature magnetic properties are also reported, and subtle correlations between the structural, electrical and magnetic properties of these materials have been found. InFeO₃ was found to adopt a higher symmetry and is structurally similar to the high temperature phase of YMnO₃. TbInO₃ and DyInO₃ have also been synthesised and studied at various temperatures. The phase behaviour of TbInO₃ was analysed in detail using neutron powder diffraction and internal structural changes versus temperature were mapped out – there is also evidence for a subtle isosymmetric phase transition. Neither DyInO₃ nor TbInO₃ show long-range magnetic order between 2 and 300 K, or any signs of ferroelectricity at room temperature. The new compounds Cs₂TiCu₃F₁₂ and Rb₂TiCu₃F₁₂ have both been synthesised and shown to be novel kagome lattice based materials. The former shows a transition from rhombohedral to monoclinic symmetry in the powder form and from rhombohedral to a larger rhombohedral unit cell in the single crystal – a particle size based transition pathway is suggested. For Rb₂TiCu₃F₁₂ a complex triclinic unit cell is found, which distorts with lowering temperature. Both materials show magnetic transitions with lowering temperature. The solid solution Cs₂₋ₓRbₓSnCu₃F₁₂ (x = 0, 0.5, 1.0, 1.5, 2.0) was synthesised and investigated crystallographically, demonstrating a range of behaviours. Rb₂SnCu₃F₁₂ displays a rare re-entrant structural phase transition. In contrast, Cs₀.₅Rb₁.₅SnCu₃F₁₂ shows only the first transition found in the Rb⁺ end member. CsRbSnCu₃F₁₂ adopts a lower symmetry at both room temperature and below. Cs₁.₅Rb₀.₅SnCu₃F₁₂ and Cs₂SnCu₃F₁₂ show a rhombohedral - monoclinic transition, which is similar to that found in Cs₂TiCu₃F₁₂.

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47

Damon, François. "Sonder des structures complexes avec des ondes de matière". Thesis, Toulouse 3, 2015. http://www.theses.fr/2015TOU30342/document.

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Ce manuscrit présente les travaux que j'ai effectués au Laboratoire de Physique Théorique durant ma thèse. Ils portent sur l'interaction d'ondes de matière avec des réseaux optiques modulables en temps et en espace. L'utilisation de ces réseaux a permis de contrôler de manière cohérente les propriétés dynamiques d'un gaz d 'atomes ultra-froids. Cette étude théorique a été réalisée en collaboration avec le groupe Atomes Froids du Laboratoire LCAR. Les variations spatiales de l'enveloppe d u réseau créent, localement, des gaps spatiaux créant une cavité de Bragg pour onde de matière, dont nous avons étudié en détail les propriétés et qui a fait l'objet d'une réalisation expérimentale impliquant la propagation d'un condensat de Bose-Einstein de rubidium 85 dans un guide d'onde. Nous avons également étudié la propagation d'un nuage d 'atomes dans un réseau bichromatique qui permet de réaliser un simulateur quantique du modèle de Harper. Le spectre du hamiltonien de ce système a une dimension fractale pouvant être caractérisée nu mériquement. Nous avons montré, par ailleurs, qu'il est possible d'exploiter les interactions inter-atomiques répulsives d'un condensat de Bose-Einstein afin d'amplifier les corrélations position-vitesse lors de sa pro pagation dans un guide. Notre étude montre qu'une mesure des grandeurs dynamiques locales du nuage atomique permet de sonder expérimentalement les résonances d'un potentiel optique jusqu'à l'échelle du picoKelvin. Enfin, un nuage d'atomes en interaction attractive admet une solution d'équilibre : le soliton. Nous avons démontré, numériquement, que celui-ci peut être utilisé pour sonder des états liés d'un poten tiel de taille finie, en peuplant ces états lors d'une expérience de diffusion comme, par exemple, des états de surface
This thesis presents the studies that I did at the Laboratoire de Physique Théorique. It concerns the interaction between matter waves and time and space depandant optical lattices. Using such lattices allows one to manipulate coherently the dynamical properties of ultra cold atoms. This theoretical study has been done in collaboration with the Cold Atoms group at the LCAR laboratory. The spatial variations of the lattice envelope locally create spatial gaps which create a Bragg cavity for matter waves. We have st udied in detail their properties and the cavity has been realized experimentally by using a Ru bid ium 85 Bose-Einstein condensate in a wave guide. We have also studied the propagation of an atomic cloud in a bichromatic optical lattice which allows us to make a quantum simulator of the Harper madel. The spectrum of the system Hamiltonian· posseses a fractal dimension which can be numerically characterized. We have also shawn that it is possible to use the repulsive interatomic interaction of a Bose-Einstein condensate in arder to amplify the momentum-position correlation during propagation in a guide. Our st udy shows that a mesure of local dynamical quantities of the atomic cloud enables one to experimentally probe resonances of an optical potential down to the picoKelvin scale. At last, an atomic cloud with attractive interactions admit a stable solution, the soliton. We have numerically demonstrated that this soliton can be used to probe bound states of a potential by populating those states through a scattering experiment, for example surface states

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48

Ramsden, M. "Dynamic effects in the progressive failure of lattice structures". Thesis, University of Reading, 1987. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.376665.

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49

Reid, Robert. "Propagation and period-doubling of coherent structures in coupled lattice maps". Thesis, University of Warwick, 2000. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.369417.

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50

Selmi, Daniele N. "DNA lattices and protein arrays novel approaches to biological structure determination". Thesis, University of Oxford, 2010. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.533877.

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