Master of Science / Department of Mechanical and Nuclear Engineering / Jeremy A. Roberts / A novel approach based on the Karhunen-Loéve Transform (KLT) is presented for treatment of the energy variable in response matrix methods, which are based on the partitioning of global domains into independent nodes linked by approximate boundary conditions. These conditions are defined using truncated expansions of nodal boundary fluxes in each phase-space variable (i.e., space, angle, and energy). There are several ways in which to represent the dependence on these variables, each of which results in a trade-off between accuracy and speed. This work provides a method to expand in energy that can reduce the number of energy degrees of freedom needed for sub-0.1% errors in nodal fission densities by up to an order of magnitude. The Karhunen-Loéve Transform is used to generate basis sets for expansion in the energy variable that maximize the amount of physics captured by low-order moments, thus permitting low-order expansions with less error than basis sets previously studied, e.g., the Discrete Legendre Polynomials (DLP) or modified DLPs. To test these basis functions, two 1-D test problems were developed: (1) a 10-pin representation of the junction between two heterogeneous fuel assemblies, and (2) a 70-pin representation of a boiling water reactor. Each of these problems utilized two cross-section libraries based on a 44-group and 238-group structure. Furthermore, a 2-D test problem based on the C5G7 benchmark is used to show applicability to higher dimensions.

Nowadays, electricity markets are becoming more deregulated, especially development of smart grid and introduction of renewable energy promote regulations of energy markets. On the other hand, the uncertainties of new energy sources and market participants’ bidding bring more challenges to power system operation and transmission system planning. These problems motivate us to study spot price (also called locational marginal pricing) of electricity markets, the strategic bidding of wind power producer as an independent power producer into power market, transmission expansion planning considering wind power investment, and analysis of the maximum loadability of a power grid. The work on probabilistic spot pricing for a utility grid includes renewable wind power generation in a deregulated environment, taking into account both the uncertainty of load forecasting and the randomness of wind speed. Based on the forecasted normal-distributed load and Weibull-distributed wind speed, probabilistic optimal power flow is formulated by including spinning reserve cost associated with wind power plants and emission cost in addition to conventional thermal power plant cost model. Simulations show that the integration of wind power can effectively decrease spot price, also increase the risk of overvoltage. Based on the concept of loacational marginal pricing which is determined by a marketclearing algorithm, further research is conducted on optimal offering strategies for wind power producers participating in a day-ahead market employing a stochastic market-clearing algoivrithm. The proposed procedure to drive strategic offers relies on a stochastic bilevel model: the upper level problem represents the profit maximization of the strategic wind power producer, while the lower level one represents the marketing clearing and the corresponding price formulation aiming to co-optimize both energy and reserve. Thirdly, to improve wind power integration, we propose a bilevel problem incorporating two-stage stochastic programming for transmission expansion planning to accommodate large-scale wind power investments in electricity markets. The model integrates cooptimizations of energy and reserve to deal with uncertainties of wind power production. In the upper level problem, the objective of independent system operator (ISO) modelling transmission investments under uncertain environments is to minimize the transmission and wind power investment cost, and the expected load shedding cost. The lower level problem is composed of a two stage stochastic programming problem for energy schedule and reserve dispatch simultaneously. Case studies are carried out for illustrating the effectiveness of the proposed model. The above market-clearing or power system operation is based on direct current optimal power flow (DC-OPF) model which is a linear problem without reactive power constraints. Power system maximum loadability is a crucial index to determine voltage stability. The fourth work in this thesis proposes a Lagrange semi-definite programming (SDP) method to solve the non-linear and non-convex optimization alternating current (AC) problem of the maximum loadability of security constrained power system. Simulation results from the IEEE three-bus system and IEEE 24-bus Reliability Test System (RTS) show that the proposed method is able to obtain the global optimal solution for the maximum loadability problem. Lastly, we summarize the conclusions from studies on the above mentioned optimization problems of electric power market under modern grid, as well as the influence of wind power integration on power system reliability, and transmission expansion planning, as well as the operations of electricity markets. Meanwhile, we also present some open questions on the related research, such as non-convex constraints in the lower-level problem of a bilevel problem, and integrating N-1 security criterion of transmission planning. / Graduate / lei.ming296@gmail.com

Doctor of Philosophy / Department of Biology / Samantha Wisely / Habitat fragmentation and destruction are the most ubiquitous and serious environmental threats confronting the long-term survival of plant and animal species worldwide. However, some native or exotic species can take advantages of these alterations and expand their range, placing endemic species at risk of extinction by changing the composition of biotic communities and altering ecosystem. Capybara (Hydrochoerus hydrochaeris) are a widely distributed rodent throughout most of South and Central America, but restricted to areas of standing water. As the Gran Chaco ecosystem of Paraguay has been converted from dry tropical forest to pastureland, I hypothesized that this habitat alteration created potential for invasion by capybara into newly fragmented areas. I used ecological niche modeling to generate hypotheses about how the distribution of capybara has been affected by land use change, and tested those hypotheses with phylogeographic analyses. To understand the mechanisms that have allowed the invasion, I investigated home range, habitat use and thermoregulation of capybara via radiotelemetry in a deforested area in which capybara had recently invaded. Genetic analyses confirm a rapid range expansion scenario with evidence of secondary contact between two distinct phylogroups which had previously been disjunct. Modeling results indicated that conversion of forest to pastureland allowed the expansion to occur. Capybara selected water significantly more than it was available to them, and avoided shrub forest. I found a significant positive correlation between body temperature and distance from water, and a significant negative correlation between distance from water and Chaco ambient temperature. Capybara proximity to water appeared to be tightly linked to body thermoregulation. These results suggest that although capybara have expanded into the Chaco forest as it is converted to pastureland, the presence of permanent water sources in those pastures are the mechanism that allow capybara to persist in this habitat. This is the first study to characterize capybara in a xeric habitat without a year round water source, and scarce natural grasslands. My results show how anthropogenic habitat modification has allowed capybara to thrive. Understanding how capybara invade and utilize the deforested Central Dry Chaco will provide valuable information for the future management of the species and the Chaco ecosystem.

Recent developments in the study of Majorana fermions through braid theory have shown that there exists a set of interchanges that allow for the realization of true quantum computation. Alongside these developments there have been studies of topological superconductivity which show the existence of states that exhibit non-Abelian exchange statistics. Motivated by these developments we study the differences between Abelian and non-Abelian topological phase in the vortex state through the Bogoliubov de-Gennes (BdG) formalism. Due to our interests in low-energy states we first implement computationally efficient algorithms for calculating the mean fields and computing eigenpairs in an arbitrary energy window. We have shown that these algorithms adequately reproduce results obtained from a variety of other techniques and show that these algorithms retain spatial inhomogeneity information. Our results show topological superconductivity and vortex states can coexist; providing a means to realize zero-energy bound states, the number of which corresponds to the topological phase. With the use of our methods we present results contrasting the differences between Abelian and non-Abelian topological phase. Our calculations show that an increase in Zeeman field affects numerous parameters within topological superconductors. It causes the order parameter to become more sensitive to temperature variations in addition to a reduced rate of recovery to the bulk value from a vortex core. The increased field suppresses spin-up local density of states (LDOS) in close proximity to the vortex core for low-energy states. Further, it narrows the spectral gap at the lattice centre. Both energy spectrum and LDOS calculations confirm that trivial topological phase have no zero-energy bound states, Abelian phases have an even number, while non-Abelian phases have an odd number.

No description available.

Over the last decades, there have been remarkable shifts in the area of Information Retrieval (IR) as huge amount of information is increasingly accumulated on the Web. The gigantic information explosion increases the need for discovering new tools that retrieve meaningful knowledge from various complex information sources. Thus, techniques primarily used to search and extract important information from numerous database sources have been a key challenge in current IR systems. Topic modeling is one of the most recent techniquesthat discover hidden thematic structures from large data collections without human supervision. Several topic models have been proposed in various fields of study and have been utilized extensively for many applications. Latent Dirichlet Allocation (LDA) is the most well-known topic model that generates topics from large corpus of resources, such as text, images, and audio.It has been widely used in many areas in information retrieval and data mining, providing efficient way of identifying latent topics among document collections. However, LDA has a drawback that topic cohesion within a concept is attenuated when estimating infrequently occurring words. Moreover, LDAseems not to consider the meaning of words, but rather to infer hidden topics based on a statisticalapproach. However, LDA can cause either reduction in the quality of topic words or increase in loose relations between topics. In order to solve the previous problems, we propose a domain specific topic model that combines domain concepts with LDA. Two domain specific algorithms are suggested for solving the difficulties associated with LDA. The main strength of our proposed model comes from the fact that it narrows semantic concepts from broad domain knowledge to a specific one which solves the unknown domain problem. Our proposed model is extensively tested on various applications, query expansion, classification, and summarization, to demonstrate the effectiveness of the model. Experimental results show that the proposed model significantly increasesthe performance of applications.

Thesis (MSc (Mathematics))--University of Stellenbosch, 2010. / ENGLISH ABSTRACT: In this thesis, higher order numerical methods for weak approximation of solutions of stochastic differential equations (SDEs) are presented. They are motivated by option pricing problems in finance where the price of a given option can be written as the expectation of a functional of a diffusion process. Numerical methods of order at most one have been the most used so far and higher order methods have been difficult to perform because of the unknown density of iterated integrals of the d-dimensional Brownian motion present in the stochastic Taylor expansion. In 2001, Kusuoka constructed a higher order approximation scheme based on Malliavin calculus. The iterated stochastic integrals are replaced by a family of finitely-valued random variables whose moments up to a certain fixed order are equivalent to moments of iterated Stratonovich integrals of Brownian motion. This method has been shown to outperform the traditional Euler-Maruyama method. In 2004, this method was refined by Lyons and Victoir into Cubature on Wiener space. Lyons and Victoir extended the classical cubature method for approximating integrals in finite dimension to approximating integrals in infinite dimensional Wiener space. Since then, many authors have intensively applied these ideas and the topic is today an active domain of research. Our work is essentially based on the recently developed higher order schemes based on ideas of the Kusuoka approximation and Lyons-Victoir “Cubature on Wiener space” and mostly applied to option pricing. These are the Ninomiya-Victoir (N-V) and Ninomiya- Ninomiya (N-N) approximation schemes. It should be stressed here that many other applications of these schemes have been developed among which is the Alfonsi scheme for the CIR process and the decomposition method presented by Kohatsu and Tanaka for jump driven SDEs. After sketching the main ideas of numerical approximation methods in Chapter 1 , we start Chapter 2 by setting up some essential terminologies and definitions. A discussion on the stochastic Taylor expansion based on iterated Stratonovich integrals is presented, we close this chapter by illustrating this expansion with the Euler-Maruyama approximation scheme. Chapter 3 contains the main ideas of Kusuoka approximation scheme, we concentrate on the implementation of the algorithm. This scheme is applied to the pricing of an Asian call option and numerical results are presented. We start Chapter 4 by taking a look at the classical cubature formulas after which we propose in a simple way the general ideas of “Cubature on Wiener space” also known as the Lyons-Victoir approximation scheme. This is an extension of the classical cubature method. The aim of this scheme is to construct cubature formulas for approximating integrals defined on Wiener space and consequently, to develop higher order numerical schemes. It is based on the stochastic Stratonovich expansion and can be viewed as an extension of the Kusuoka scheme. Applying the ideas of the Kusuoka and Lyons-Victoir approximation schemes, Ninomiya- Victoir and Ninomiya-Ninomiya developed new numerical schemes of order 2, where they transformed the problem of solving SDE into a problem of solving ordinary differential equations (ODEs). In Chapter 5 , we begin by a general presentation of the N-V algorithm. We then apply this algorithm to the pricing of an Asian call option and we also consider the optimal portfolio strategies problem introduced by Fukaya. The implementation and numerical simulation of the algorithm for these problems are performed. We find that the N-V algorithm performs significantly faster than the traditional Euler-Maruyama method. Finally, the N-N approximation method is introduced. The idea behind this scheme is to construct an ODE-valued random variable whose average approximates the solution of a given SDE. The Runge-Kutta method for ODEs is then applied to the ODE drawn from the random variable and a linear operator is constructed. We derive the general expression for the constructed operator and apply the algorithm to the pricing of an Asian call option under the Heston volatility model. / AFRIKAANSE OPSOMMING: In hierdie proefskrif, word ’n hoërorde numeriese metode vir die swak benadering van oplossings tot stogastiese differensiaalvergelykings (SDV) aangebied. Die motivering vir hierdie werk word gegee deur ’n probleem in finansies, naamlik om opsiepryse vas te stel, waar die prys van ’n gegewe opsie beskryf kan word as die verwagte waarde van ’n funksionaal van ’n diffusie proses. Numeriese metodes van orde, op die meeste een, is tot dus ver in algemene gebruik. Dit is moelik om hoërorde metodes toe te pas as gevolg van die onbekende digtheid van herhaalde integrale van d-dimensionele Brown-beweging teenwoordig in die stogastiese Taylor ontwikkeling. In 2001 het Kusuoka ’n hoërorde benaderings skema gekonstrueer wat gebaseer is op Malliavin calculus. Die herhaalde stogastiese integrale word vervang deur ’n familie van stogastiese veranderlikes met eindige waardes, wat se momente tot ’n sekere vaste orde bestaan. Dit is al gedemonstreer dat hierdie metode die tradisionele Euler-Maruyama metode oortref. In 2004 is hierdie metode verfyn deur Lyons en Victoir na volumeberekening op Wiener ruimtes. Lyons en Victoir het uitgebrei op die klassieke volumeberekening metode om integrale te benader in eindige dimensie na die benadering van integrale in oneindige dimensionele Wiener ruimte. Sedertdien het menige outeurs dié idees intensief toegepas en is die onderwerp vandag ’n aktiewe navorsings gebied. Ons werk is hoofsaaklik gebaseer op die onlangse ontwikkelling van hoërorde skemas, wat op hul beurt gebaseer is op die idees van Kusuoka benadering en Lyons-Victoir "Volumeberekening op Wiener ruimte". Die werk word veral toegepas op die prysvastelling van opsies, naamlik Ninomiya-Victoir en Ninomiya-Ninomiya benaderings skemas. Dit moet hier beklemtoon word dat baie ander toepassings van hierdie skemas al ontwikkel is, onder meer die Alfonsi skema vir die CIR proses en die ontbinding metode wat voorgestel is deur Kohatsu en Tanaka vir sprong aangedrewe SDVs. Na ’n skets van die hoof idees agter metodes van numeriese benadering in Hoofstuk 1 , begin Hoofstuk 2 met die neersetting van noodsaaklike terminologie en definisies. ’n Diskussie oor die stogastiese Taylor ontwikkeling, gebaseer op herhaalde Stratonovich integrale word uiteengeset, waarna die hoofstuk afsluit met ’n illustrasie van dié ontwikkeling met die Euler-Maruyama benaderings skema. Hoofstuk 3 bevat die hoofgedagtes agter die Kusuoka benaderings skema, waar daar ook op die implementering van die algoritme gekonsentreer word. Hierdie skema is van toepassing op die prysvastelling van ’n Asiatiese call-opsie, numeriese resultate word ook aangebied. Ons begin Hoofstuk 4 deur te kyk na klassieke volumeberekenings formules waarna ons op ’n eenvoudige wyse die algemene idees van "Volumeberekening op Wiener ruimtes", ook bekend as die Lyons-Victoir benaderings skema, as ’n uitbreiding van die klassieke volumeberekening metode gebruik. Die doel van hierdie skema is om volumeberekening formules op te stel vir benaderings integrale wat gedefinieer is op Wiener ruimtes en gevolglik, hoërorde numeriese skemas te ontwikkel. Dit is gebaseer op die stogastiese Stratonovich ontwikkeling en kan beskou word as ’n ontwikkeling van die Kusuoka skema. Deur Kusuoka en Lyon-Victoir se idees oor benaderings skemas toe te pas, het Ninomiya-Victoir en Ninomiya- Ninomiya nuwe numeriese skemas van orde 2 ontwikkel, waar hulle die probleem omgeskakel het van een waar SDVs opgelos moet word, na een waar gewone differensiaalvergelykings (GDV) opgelos moet word. Hierdie twee skemas word in Hoofstuk 5 uiteengeset. Alhoewel die benaderings soortgelyk is, is daar ’n beduidende verskil in die algoritmes self. Hierdie hoofstuk begin met ’n algemene uiteensetting van die Ninomiya-Victoir algoritme waar ’n arbitrêre vaste tyd horison, T, gebruik word. Dié word toegepas op opsieprysvastelling en optimale portefeulje strategie probleme. Verder word numeriese simulasies uitgevoer, die prestasie van die Ninomiya-Victoir algoritme was bestudeer en vergelyk met die Euler-Maruyama metode. Ons maak die opmerking dat die Ninomiya-Victoir algoritme aansienlik vinniger is. Die belangrikste resultaat van die Ninomiya-Ninomiya benaderings skema word ook voorgestel. Deur die idee van ’n Lie algebra te gebruik, het Ninomiya en Ninomiya ’n stogastiese veranderlike met GDV-waardes gekonstrueer wat se gemiddeld die oplossing van ’n gegewe SDV benader. Die Runge-Kutta metode vir GDVs word dan toegepas op die GDV wat getrek is uit die stogastiese veranderlike en ’n lineêre operator gekonstrueer. ’n Veralgemeende uitdrukking vir die gekonstrueerde operator is afgelei en die algoritme is toegepas op die prysvasstelling van ’n Asiatiese opsie onder die Heston onbestendigheids model.

Two methodologies are presented for analyzing the choice between centralized and decentralized energy infrastructures from a least-cost perspective. The first of these develops a novel minimum spanning tree network algorithm to approximate the shortest-length network that connects a given fraction of total system population. This algorithm is used to identify high priority locations for decentralized electrification in 150 countries. The second methodology utilizes a mixed-integer programming framework to determine the least-cost combination of centralized and decentralized electricity infrastructure that is capable of serving demand throughout a given system. This methodology is demonstrated through a case study of Rwanda. The centralized-decentralized electrification paradigm is also approached from an energy security perspective, incorporating stochastic events and probabilistic parameters into a simulation model that is used to compare different development paths. The impact of explicitly modeling stochastic events as opposed to utilizing a conventional formulation is also considered Finally, a subsidy-free lighting cost curve is developed and a model is presented to compare the costs and benefits of three different financial mechanisms that can be employed to make capital intensive energy systems more accessible to rural populations. The optimal contract is determined on the basis of utility-maximization for a range of costs to the providing agency and a comprehensive single and multi-factor sensitivity analysis is performed.

La Réaction Sulfatique Interne (RSI) est une pathologie endogène qui peut toucher les matériaux cimentaires ayant été exposés à des températures supérieures à environ 65°C. Elle est causée par une formation tardive de l'ettringite dans le matériau durci, induisant le développement de pressions de cristallisation et de gonflements importants. Au jeune âge, l'élévation de température peut être due soit à l'exothermie de l'hydratation du ciment, en particulier au cœur des pièces massives, soit à la préfabrication où un échauffement est appliqué au matériau au jeune âge pour accélérer la prise et permettre un décoffrage plus rapide. L'élévation de température sur un béton durci (incendie, stockage de déchets radioactifs, structures stratégiques) représente un autre cas potentiel de développement des expansions induites par la RSI. Lors du développement de cette réaction, on observe la formation de fissures et une dégradation des performances mécaniques nuisant à la capacité portante et aux fonctionnalités en service des structures touchées par cette pathologie. L'objectif de cette recherche est de préciser et quantifier la relation entre l'histoire thermique subie (au jeune âge ou sur béton mature) et la courbe caractérisant le gonflement libre en fonction du temps (potentiel et cinétique de gonflement) afin de compléter les recommandations de prévention (basées le plus souvent sur la limitation de l'élévation de température) et de réparation des structures atteintes de cette pathologie et d'améliorer la prévision de l'état d'une structure endommagée dans le cadre d'un diagnostic. Pour les outils de calcul, tel le module RGIB du code CESAR, qui permettent de recalculer les structures atteintes de cette pathologie, la présente recherche a pour but de valider, améliorer ou élaborer la loi de couplage donnant l'expansion induite par la RSI en fonction de l'histoire thermique, au jeune âge ou lors d'échauffements tardifs. Le programme expérimental s'est focalisé sur la compréhension de l'effet de l'histoire thermique (température et durée d'échauffement) au jeune âge sur le développement des expansions, en étoffant la base de données permettant de valider les modèles de prédiction proposés dans la littérature. Il a également étudié l'effet de différents traitements thermiques tardifs où peu de données sont disponibles dans la littérature. Ces effets ont été étudiés sur des corps d'épreuve en béton potentiellement sujets à la formation différée d'ettringite : des traitements thermiques à plusieurs températures (61, 66, 71, 81, 86°C) et pendant des durées de cure de 1 à 28 jours ont été appliqués. Le suivi massique et dimensionnel des corps d'épreuve a permis d'identifier l'existence d'un effet de pessimum vis-à-vis de la durée de cure. Les caractéristiques des expansions ont été quantifiées et comparées aux histoires thermiques afin d'établir le couplage entre histoire thermique et gonflement. La pertinence du concept « d'énergie utile », associé à l'intégrale de la température en fonction du temps au-dessus d'une valeur seuil correspondant à la déstabilisation de l'ettringite, a été démontrée par la mise en évidence de courbes maîtresses. Une interprétation cohérente des résultats d'expansions (cinétiques et magnitudes) et des effets de la RSI sur les propriétés mécaniques en fonction des différentes histoires thermiques a été proposée, en lien avec une loi de prédiction des expansions / Delayed Ettringite Formation (DEF) is an internal swelling reaction that can affect concretes heated at a temperature higher than about 65°C. This phenomenon is related to a late formation of a normal hydrate (ettringite) of cement inducing crystallization pressure and significant expansions. This late formation of ettringite may affect concretes exposed to high temperatures at early age; it may be the case of precast elements, and massive concrete parts heated due to cement hydration (combination of the exothermic hydration and the low heat transfer conditions). Late in service exposure to high temperatures (fire, radioactive waste depositories and parts of structures of power plant) correspond to another situation that can induce expansion generated by DEF. In most cases, DEF leads to concrete swelling, cracking, decrease of the mechanical properties of the affected materials and thus potential problems in terms of serviceability and bearing capacity of the affected structures. The objectives of this study are to quantify and predict the relation between thermal history and swelling characteristics (magnitude and kinetics) in order to propose recommendations for prevention of DEF (A critical condition for the development of this reaction consists in the temperature increase at early age. Thus, temperature limitation is recommended as one of the most efficient ways to avoid DEF expansions), and for assessment and repair of structures affected by this pathology. For numerical tools, such as RGIB module of the CESAR-LCPC F.E. software, which allow to re-assess the structures affected by this phenomenon, this research aims to validate, or improve, or develop a coupling law giving the expansion induced by DEF depending on a thermal history at early age or on mature concrete. The investigations carried out were focused on the effect of temperature and curing duration of early age heat treatments on the risk of developing expansion. They also included effect of late heat treatments which correspond to scarce data in the literature. The experiments were performed on concrete specimens, using a sulfate, aluminate and alkali-rich cement, aiming to quantify the expansion magnitudes and kinetics due to different thermal histories and to identify the existence of an eventual pessimum effect with respect to the thermal energy, as mentioned in the literature. A number of heat treatments at 61, 66, 71, 81 and 86°C were applied for durations from 1 to 28 days. Monitoring of the specimens dimensions allowed identifying a pessimum effect with respect to the thermal curing duration. The swelling characteristics (magnitude and kinetics) have been quantified, using a mathematical relation, and compared to thermal histories applied to determine a link between thermal history and swelling. The relevance of the concept of ‘effective thermal energy' associated with the integral of the temperature as a function of time beyond a threshold value corresponding to the destabilization of ettringite was demonstrated by the identification of master curves. A consistent interpretation of the results of expansions (kinetics and magnitudes) and effects on the mechanical properties according to different thermal histories, has been proposed in connection with the law for predicting expansions

Thesis (MSc)--Stellenbosch University, 2011. / ENGLISH ABSTRACT: The primary objective of the work was to investigate the negative thermal expansion of organic materials and to determine the mechanisms governing this phenomenon by using the principles of crystal engineering. To this end, the following three compounds were studied in detail: • 4,4'-Diiodobiphenyl • 4-Iodobenzoic acid • Methyl Paraben The rationale behind this work was to determine the mechanisms responsible for the observed negative thermal expansion and to uncover the structural factors that induce negative thermal expansion. Single-crystal X-ray diffraction was employed as the primary analytical tool, owing to the unique information it can provide regarding intermolecular interactions in the solid state. A total of twenty organic compounds were analysed, of which three exhibited negative thermal expansion. Each compound employs a specific mechanism for negative thermal expansion, two of which are closely related and the third distinct. / AFRIKAANSE OPSOMMING: Die hoof doel van hierdie studie was om ondersoek in te stel in die verskynsel van ‘negative thermal expansion’ in organiese materiale en gevolglik die meganisme vas te stel deur die beginsels van kristalmanipulsie (‘crystal engineering’) te gebruik. Gevolglik was drie organise stowwe ondersoek: • 4,4'-Diiodobiphenyl /4,4'-Diiodobifeniel • 4-Iodobenzoic acid /4-Iodobensoësuur • Methyl Paraben Die redenasie hieragter is om die meganisme verantwoordelik vir die ‘negative thermal expansion’ vas te stel en die verskillende faktore wat bydra tot dit te bevestig. Enkel-kristal diffraksie word benut as die primêre analitiese tegniek as gevolg van die unieke inligting wat verkry kan word met betrekking tot die intermolekulêre interaksies. 'n Totaal van twintig stowwe is geanaliseer waarvan drie die spesifieke termisie eienskap besit. Elk van die drie stowwe het ‘n ander meganisme te vore laat kom waarvan twee baie ooreenstem en die derde verskil.