Made available in DSpace on 2016-03-15T19:38:08Z (GMT). No. of bitstreams: 1 Guilherme Kronemberger.pdf: 1225637 bytes, checksum: 6f698faf7a8661b382c4977e4b07f631 (MD5) Previous issue date: 2008-01-28 / Cellular automata have been studied as computer models in many different areas. They have many properties, one of them being reversibility. Reversible cellular automata can be used, among other applications, for data compressing and encryption. Apparently, the reversible rules featured in the literature seem to have been derived through exhaustive searches in their corresponding spaces. However, it would be important the availability of an algorithm that would allow their direct and easy construction, different from what occurs in literature. This is the aim of this work. Along this line, we tried to come up with an algorithm to allow the identification of one-dimensional, reversible cellular automaton rules. This was based on reversible rules with 2 states and 2, 3, 4 and 5 cells per neighborhood, and on those with 3 states and 2 and 3 cells per neighborhood, all of them drawn out of exhaustive analysis and from the literature. By studying these rules it was possible to verify in each space that: all reversible rules are balanced; they are symmetrically distributed; a subset of them herein denoted primitive reversible rules, RPs have a simple formation law, defined by homogeneous blocks of states; and, if a rule is reversible, so are all its dynamically equivalent rules. In the attempt to obtain the targetted algorithm, an approach was explored in which the non-primitive reversible rules (the so-called derived rules, RDs) were supposed to be obtained from the primitives. Along this line, two ways to construct the RDs were tried out, one based upon using all RPs jointly as a group, and another, using them individually; however, neither of them led to a positive result. Additionally, relations between the properties of reversibility and conservativity of a rule have also been studied in the rule spaces considered. / Autômatos celulares têm sido estudados como modelos computacionais em diversas áreas, sendo que muitas são as suas propriedades, entre elas a reversibilidade. Autômatos celulares reversíveis podem ser usados, entre outras aplicações, para compactação ou encriptação de dados. Aparentemente, as regras reversíveis apresentadas na literatura parecem ter sido derivadas apenas através de buscas exaustivas em seus espaços correspondentes. No entanto, seria importante a existência de um algoritmo que permitisse construí-las fácil e diretamente, diferente do que acontece na literatura. Este é o objetivo deste trabalho. Neste sentido, buscou-se um algoritmo que permitesse identificar regras de autômatos celulares unidimensionais reversíveis. Para tanto, foram obtidas em análises exaustivas e na literatura todas as regras reversíveis de 2 estados e vizinhanças de 2, 3, 4 e 5 células, e de 3 estados e vizinhanças de 2 e 3 células. Com o estudo destas regras constatou-se em cada espaço que: todas as regras reversíveis são balanceadas; elas se distribuem simetricamente; um subconjunto delas aqui denominadas regras reversíveis primitivas, RPs possui lei de formação simples, definida por blocos homogêneos de estados; e, se uma regra é reversível, todas as suas equivalentes dinâmicas também o são. Na tentativa de se obter o algoritmo desejado explorou-se uma abordagem em que as regras reversíveis não primitivas (denominadas regras derivadas, RDs), seriam obtidas a partir das primitivas. Nesse sentido foram testados dois esquemas de construção das RDs, um baseado na utilização conjunta de todas as RPs, e outro, utilizando-as individualmente; entretanto, ambos não levaram a resultado positivo. Adicionalmente, estudou-se a relação entre as propriedades de reversibilidade e conservatividade de regras nos espaços considerados.

This thesis reports on new music technology research which investigates the use of cellular automata (CA) for the digital synthesis of dynamic sounds. The research addresses the problem of the sound design limitations of synthesis techniques based on CA. These limitations fundamentally stem from the unpredictable and autonomous nature of these computational models. Therefore, the aim of this thesis is to develop a sound synthesis technique based on CA capable of allowing a sound design process. A critical analysis of previous research in this area will be presented in order to justify that this problem has not been previously solved. Also, it will be discussed why this problem is worthwhile to solve. In order to achieve such aim, a novel approach is proposed which considers the output of CA as digital signals and uses DSP procedures to analyse them. This approach opens a large variety of possibilities for better understanding the self-organization process of CA with a view to identifying not only mapping possibilities for making the synthesis of sounds possible, but also control possibilities which enable a sound design process. As a result of this approach, this thesis presents a technique called Histogram Mapping Synthesis (HMS), which is based on the statistical analysis of CA evolutions by histogram measurements. HMS will be studied with four different automatons, and a considerable number of control mechanisms will be presented. These will show that HMS enables a reasonable sound design process. With these control mechanisms it is possible to design and produce in a predictable and controllable manner a variety of timbres. Some of these timbres are imitations of sounds produced by acoustic means and others are novel. All the sounds obtained present dynamic features and many of them, including some of those that are novel, retain important characteristics of sounds produced by acoustic means.

Indiana University-Purdue University Indianapolis (IUPUI) / Topology Optimization is an optimization technique used to synthesize models without any preconceived shape. These structures are synthesized keeping in mind the minimum compliance problems. With the rapid improvement in advanced manufacturing technology and increased need for lightweight high strength designs topology optimization is being used more than ever. There exist a number of commercially available software's that can be used for optimizing a product. These software have a robust Finite Element Solver and can produce good results. However, these software offers little to no choice to the user when it comes to selecting the type of optimization method used. It is possible to use a programming language like MATLAB to develop algorithms that use a specific type of optimization method but the user himself will be responsible for writing the FEA algorithms too. This leads to a situation where the flexibility over the optimization method is achieved but the robust FEA of the commercial FEA tool is lost. There have been works done in the past that links ABAQUS with MATLAB but they are primarily used as a tool for finite element post-processing. Through this thesis, the aim is to develop an interface that can be used for solving optimization problems using different methods like hard-kill as well as the material penalization (SIMP) method. By doing so it's possible to harness the potential of a commercial FEA software and gives the user the requires flexibility to write or modify the codes to have an optimization method of his or her choice. Also, by implementing this interface, it can also be potentially used to unlock the capabilities of other Dassault Systèmes software's as the firm is implementing a tighter integration between all its products using the 3DExperience platform. This thesis as described uses this interface to implement BESO and HCA based topology optimization. Since hybrid cellular atomata is the only other method other than equivalent static load method that can be used for crashworthiness optimization this work suits well for the role when extended into a non-linear region.

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In this report, we present some of the results achieved by investigating two-dimensional monomial cellular automata modulo m, where m is a non-zero positive integer. Throughout the experiments, we work with the von Neumann neighbourhood and apply the same local rule based on modular multiplication. The purpose of the study is to examine the behaviour of these cellular automata in three different environments, (i.e. the infinite plane, the finite plane and the torus), by means of elementary number theory. We notice how the distance between each pair of cells with state 0 influences the evolution of the automaton and the convergence of its configurations. Similar impact is perceived when the cells attain the values of Euler's-<img src="http://www.diva-portal.org/cgi-bin/mimetex.cgi?%5Cphi" />function or of integers with common divisors with m, when m &gt; 2. Alongside with the states of the cells, the evolution of the automaton, as well as the convergence of its configurations, are also decided by the values attributed to m, whether it is a prime, a prime power or a multiple of primes and/or prime powers.

Thesis (MSc (Mathematical Sciences)) University of Stellenbosch, 2011. / ENGLISH ABSTRACT: Cellular Automata (CA) have become a popular vehicle to study complex dynamical behaviour of systems. CA can be used to model a wide variety of physical, biological, chemical and other systems. Such systems typically consist of subparts that change their state independently, based on the state of their immediate surroundings and some generally shared laws of change. When the CA approach was used to solve the LEGO construction problem, the best solution was found when using a variant of CA allowing for the clustering of cells. The LEGO construction problem concerns the optimal layout of a set of LEGO bricks. The advantages found for using the CA method with clustering in this case are the ease of implementation, the significantly smaller memory usage to previously implemented methods, and its trivial extension to construct multicoloured LEGO sculptures which were previously too complex to construct. In our research we propose to explore the definitions of clustering in CA and investigate the implementation and application of this method. We look at the ant sorting method described by Lumer and Faieta, and compare the implementation of this algorithm using regular CA as well as the clustering variation. The ant sorting model is a simple model, in which ants move randomly in space and pick up and deposit objects on the basis of local information. / AFRIKAANSE OPSOMMING: Sellulêre Outomate (SO) het ’n populêre metode geword om die komplekse dinamiese gedrag van sisteme bestudeer. SO kan gebruik word om ’n groot verskeidenheid fisiese, biologiese, chemiese en ander tipe sisteme te modelleer. Sulke sisteme bestaan tipies uit subafdelings wat, gebaseer op die status van hulle omgewing en ’n paar algemene gedeelde reëls van verandering, hulle status onafhanklik verander. Met die gebruik van die SO benadering om the LEGO konstruksieprobleem op te los, is die beste oplossing bereik deur gebruik te maak van ’n variant van SO, waar selle saamgroepeer kan word. Die LEGO konstruksieprobleem behels die optimale uitleg van ’n stel LEGO blokkies. In hierdie geval is die voordele van die SO met sel groepering die maklike implementasie, ’n beduidende kleiner geheuegebruik teenoor voorheen geïmplementeerde metodes, en die triviale uitbreiding daarvan om gekleurde LEGO beelde wat voorheen te kompleks was, te kan bou. In ons ondersoek verken ons die definisies van selgroepering in SO en ondersoek die implementasie en toepassing van die metode. Ons kyk na die miersorteringsmetode beskryf deur Lumer en Faieta, en vergelyk die implementasie van hierdie algoritme deur gewone SO asook die groeperingsvariasie te gebruik. Die miersorteringsmodel is ’n eenvoudige model waarin miere lukraak in ’n omgewing beweeg en voorwerpe optel of neersit volgens plaaslike inligting.

Thesis (MScEng (Process Engineering))--Stellenbosch University, 2008. / The general objective for this thesis is to assess the ability of cellular automata to model relatively complex processes or phenomena, in particular thermodynamic scenarios. The mass transfer in packing materials of distillation columns was selected as an example due to the sufficient level of complexity in the distillation process, and its importance in a wide range of applications. A literature survey on cellular automata that summarizes the information currently available in formal publications and the internet is included to provide a general overview on the basic theoretical principles and the application of cellular automata models in the process engineering industry. The literature study was also used to identify potential requirements for the new research project. The study objective includes the construction of a cellular automata model that is able to represent transition of solutes from the fluid on the micro-surfaces of packing materials to the by-passing vapour stream, as well as the steady-state equilibrium between evaporation and condensation. Iterated model parameters sufficient for the realistic modelling of mass transfer as a result of thermodynamic driving forces, are required to meet this objective. The model behaviour was compared and the parameters subsequently adjusted according to the behaviour that is theoretically expected from the system being simulated. Qualitative (although sometimes in a quantitative format) rather than quantitative observations and comparisons were made seeing that the model has not yet been calibrated. The model that has been developed to date is not able to simulate the individual effects of chemical and thermodynamic properties although a realistic simulation of the cumulative effect exerted by these factors, or change thereof, on a system has been achieved. The accuracy of the results that have been obtained by using iterated parameters cannot be guaranteed for scenarios that deviate too much from the systems that have already been modelled successfully. The trade-off between the ability of the model to incorporate the effect of polarization, its ability to represent separation, in particular the condensation of hydrophilic substances, for strong hydrophilic packing materials and its ability to incorporate a large number of species limits the range of scenarios that can be successfully modelled. The model is able to represent the effect of a declining driving force (difference between the component vapour pressure of the gas phase and that of the liquid phase) that is typical of a system which is allowed to reach equilibrium after an initial disturbance. The model is also able to represent an additional driving force for separation caused by the effect of intermolecular forces. The model also displays the potential ability to represent the effect of different surface structures of the packing material on the extent of separation achieved at steady state as well as the rate at which such steady state conditions have been achieved. The model must be correctly scaled to minimize inaccurate results. Although several adjustments are needed to eliminate some limitations, the model has proven itself worthy of further development due to its capability to represent the basic characteristics of mass transfer in packing materials.

This dissertation focuses on improving the division-by-convergence algorithm. While the division by convergence algorithm has many advantages, it has some drawbacks, such as a need for extra bits in the multiplier and a large ROM table for the initial approximation. To mitigate these problems, two new methods are proposed here. In addition, the research scope is extended to seek an efficient architecture for implementing a divider with Quantum-dot Cellular Automata (QCA), an emerging technology. For the first proposed approach, a new rounding method to reduce the required precision of the multiplier for division by convergence is presented. It allows twice the error tolerance of conventional methods and inclusive error bounds. The proposed method further reduces the required precision of the multiplier by considering the asymmetric error bounds of Goldschmidt dividers. The second proposed approach is a method to increase the speed of convergence for Goldschmidt division using simple logic circuits. The proposed method achieves nearly cubic convergence. It reduces the logic complexity and delay by using an approximate squarer with a simple logic implementation and a redundant binary Booth recoder. Finally, a new architecture for division-by-convergence in QCA is proposed. State machines for QCA often have synchronization problems due to the long wire delays. To resolve this problem, a data tag method is proposed. It also increases the throughput significantly since multiple division computations can be performed in a time skewed manner using one iterative divider. / text

Since its inception, Moore's Law has been a reliable predictor of computational power. This steady increase in computational power has been due to the ability to fit increasing numbers of transistors in a single chip. A consequence of increasing the number of transistors is also increasing the power consumption. The physical properties of CMOS technologies will make this powerwall unavoidable and will result in severe restrictions to future progress and applications. A potential solution to the problem of rising power demands is to investigate alternative low power nanotechnologies for implementing logic circuits. The intrinsic properties of these emerging nanotechnologies result in them being low power in nature when compared to current CMOS technologies. This thesis specifically highlights quantum dot celluar automata (QCA) and nanomagnetic logic (NML) as just two possible technologies. Designs in NML and QCA are explored for simple arithmetic units such as full adders and subtractors. A new multilayer 5-input majority gate design is proposed for use in NML. Designs of reversible adders are proposed which are easily testable for unidirectional stuck at faults.

Molecular-based quantum cellular automata (m-QCA), as an extension of quantum-dot QCAs, offer a novel alternative in which binary information can be encoded in the molecular charge configuration of a cell and propagated via nearest-neighbor Coulombic cell-cell interactions. Appropriate functionality of m-QCAs involves a complex relationship between quantum mechanical effects, such as electron transfer processes within the molecular building blocks, and electrostatic interactions between cells. In the first part of this document, the influence of structural distortions in single m-QCA is addressed within a minimal model using an diabatic-to-adiabatic transformation. Thus, it is shown that even small changes of the classical square geometry between driver and target cells, such as those induced by distance variations or shape distortions, can make cells respond to interactions in a far less symmetric fashion, modifying and potentially impairing the expected computational behavior of the m-QCA. The model has been further extended to consider time-dependent external electric fields in which a special emphasis is given to the profiles in which this external parameter can interact with the associated molecular complex. The results of the model have been validated by a direct comparison with first-principle calculations allowing to conclude the plausibility to induce the intra-molecular charge transfer process in a controllable manner via the interaction with the external electric field. The influence played by the electric field profile in the response of the molecular complex is also investigated. The results suggests a major role played by this variable in terms of the time length in which the intra-molecular charge transfer can be observed. In the second part, first-principle theoretical calculations of the self-assembly properties and electronic structure of Ferrocene-functionalized complexes have been carried out. Hence, five different molecular complexes which offer a potential playground to realistic implement the m-QCA paradigm have been investigated. The main emphasis is given to study the interaction between localized charge-carrier molecular states and the delocalized surface states. The results of these calculations demonstrate the possibility to obtain real systems in which intra-molecular charge localization can be combined with self-assembly scaffolding and absorbed on either Highly oriented pyrolytic graphite (HOPG) or metallic-surfaces. Finally, the validation of these findings is carried out via comparison with accesible experimental results and opening the gate to plausible strategies where the paradigm can be implemented.