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This thesis examines aleatory strategies and dynamics in an experimental strand of British fiction between 1959 and 1979. Drawing upon musicological theories of the 'aleatory' and unpacking the literary significance, it offers a working definition of the aleatory novel as a foregrounding of chance and complex narrative chaotics that are offered to the reader with, at least, the suggestion of requiring activation or animation. Aleatory strategies are shown to reflect a set of diverse and overlapping conceptual understandings and socio-cultural dynamics relating to a paradigm of chance in crisis. Possessing the potential to extend the complexities and contradictions inherent in the incorporation of chance within the novel and its formal qualities, aleatory novels amplify the manner by which both writers and readers conjoin perspectives in their relations with a fictional text and its representation of an emergent chaotic reality. This thesis examines the aleatory in various selected authors whose concerns are among those that retrospectively help define the experimental novelist's view in Britain during the period. B.S. Johnson explores issues of identity and working class consciousness within innovative modes of aleatory form, aware of personal and political struggle. Rayner Heppenstall, Ann Quin, Wilson Harris, and Doris Lessing engage with aleatorical stylistics to articulate ontological instability, personal and collective trauma, and the fragmentation of grand narratives. Brigid Brophy and Eva Figes foreground issues of gender through aleatoric and ludic perspectives and various intensely personal struggles within patriarchal structures. Finally, John Fowles and Iris Murdoch indicate a popularization of complex conceptual engagements with chance within more conventional modes of writing, thus taking textual and conceptual experimentation to a wider readership. Aligned with positions of apparent marginalization, aleatory dynamics encourage readerly engagements with chance and chaos as fertile grounds for collaborative agitation against the imposition of totalizing narratives and order.

This thesis presents a processual ontology of noise by virtue of which morphogenesis (in its most general understanding as the processes by which order/form is created) must be instantiated. Noise is here outlined as the far from equilibrium environment out of which metastable temporary 'solutions' can emerge as the system transitions through the pre-individual state space. While frequently addressed by humanities and arts studies on the basis of its supposed disruptive character (often in terms of aesthetics), this thesis aims to thoroughly examine noise's conceptual potencies. To explore and amplify the epistemic consequences not merely of the ineliminability of noise but of its originative power as well as within the course of the elimination of givenness by epistemology. This philosophical work is informed by many different fields of contemporary science (namely: statistical physics, information theory, probability theory, 4E cognition, synthetic biology, nonlinear dynamics, complexity science and computer science) in order to assess and highlight the problems of the metascientific and ideological foundations of diverse projects of prediction and control of uncertainty. From algorithmic surveillance back to cybernetics and how these rendered noise "informationally heretical". This conveys an analysis of how contemporary prediction technologies are dramatically transforming our relationship with the future and with uncertainty in a great number of our social structures. It is a philosophico-critical anthropology of data ontology and a critique of reductive pan-info-computationalism. Additionally, two practical examples of noise characterised as an enabling constraint for the functioning of complex adaptive systems are presented. These are at once biophysical and cognitive, : 1) interaction-dominance constituted by 'pink noise' and 2) noise as a source of variability that cells may exploit in (synthetic) biology. Finally, noise is posited as an intractable active ontological randomness that limits the scope of determinism and that goes beyond unpredictability in any epistemological sense due to the insuperability of the situation in which epistemology finds itself following the critique of the given.

Pseudo-random sequences are a crucial component of cryptography, particularly in stream cipher design. In this thesis we will investigate several measures of randomness for certain classes of finitely generated sequences. We will present a heuristic algorithm for calculating the k-error linear complexity of a general sequence, of either finite or infinite length, and results on the closeness of the approximation generated. We will present an linear time algorithm for determining the linear complexity of a sequence whose characteristic polynomial is a power of an irreducible element, again presenting variations for both finite and infinite sequences. This algorithm allows the linear complexity of such sequences to be determined faster than was previously possible. Finally we investigate the stability of m-sequences, in terms of both k-error linear complexity and k-error period. We show that such sequences are inherently stable, but show that some are more stable than others.

This study takes as its focus young children's intuitive knowledge of randomness. Previous work in this field has studied the misconceptions that people, especially adults, hold in making judgements of chance (see, for example, the work of Kahneman & Tversky and Konold). In contrast, I study how primitive meaningsf or randomnessfo rm a basis for new meanings,a processw hich the misconceptionsa pproachf ails to illuminate. The guiding principle for this study is that the observation of students' evolving thought in a carefully designedc omputer-basedd omain will provide a betteru nderstanding of how the specific features of the domain shape and are shaped by activities within it. There are, then, two deeply connected strands to this thesis: the study of children's evolving meanings for randomness as expressed in a computer-based microworld, and the articulation of design principles which encapsulate pedagogic meaningsfor that microworld. More specifically, the thesis aims to shed light upon the answers to four crucial questions: Meanings for the domain: What do formalisms of stochastic behaviour look like in a domain of abstraction? What structures in the domain for stochastic abstraction optimise the articulation of intuitions and the construction of new meanings? Meanings in the domain: What articulations of informal intuitions of stochastic behaviour do we observe? How do the structures of the domain support the forging of situated meanings? The study uses an iterative design methodology, which cycles between the design of computer-based tools and the observ4tion of children, between the ages of 9 and II years, as they use these tools. The thesis identifies initial meanings for the behaviour of various stochastic phenomena and traces how new pieces of knowledge, especially relating to long term random behaviour, emerge through the forging of connections between the internal and external resources.

In this dissertation, I aim to advance our understanding of human agency and how it is computed. First, I probe the limits of what behavior we can and cannot produce agentically. Secondly, I explore microdosing with psychedelic drugs as a method of perturbing and studying changes to the sense of agency. Thirdly, I use transcranial magnetic stimulation to induce body movements and investigate how the sense of agency is affected. Finally, I summarise my findings and synthesize insights to further our understanding human agency.

Compaction is the most critical step in the construction process of asphalt pavements, which has a significant consequence on the durability of asphalt pavements. However, people’s understanding on compaction of asphalt mixture is still very limited. The objective of this thesis is therefore to explore physical mechanisms of the compaction of asphalt mixtures and to model the compaction process based on its physical mechanisms. Before exploring mechanisms of compaction, a statistical analysis of the field density data is performed to achieve a thorough understanding of the current situation of field compaction. Then, physical mechanisms are investigated in different length scales. In the length scale of the thickness of asphalt binder films (∼ 10 µm), the lubricating behavior of asphalt binder between rough aggregates is believed as the mechanism that affects the compactability of asphalt mixtures. A tribological test is developed to measure the lubricating effect of asphalt binder between rough surfaces. The results show a strong effect of asphalt binder lubrication on improving the compactability of asphalt mxitures. In the length scale of asphalt mixtures (∼ 10 cm), two mesoscopic mechanisms (aggregate rearrangement and aggregate-binder interaction) are proposed to explain the macroscopic phenomena observed in gyratory compaction process. Based on the mechanism of aggregate rearrangement, a 1D nonlocal model is then proposed to simulate the gyratory compaction process of asphalt mixtures. The results show that the model is able to simulate the compaction curve, the density profile, and the size effect observed in gyratory compaction tests. Lastly, the 1D nonlocal model is employed to study the effects of randomness in the initial density profile and compaction effort on the compaction process of asphalt mixtures. The results can explain some key features of the probability distribution of field density data. The results of this study have the potential to be used for the design of more compactable asphalt mixtures and the prediction of asphalt pavement compaction.

The article analyzes aspects of the relationship between evolution and bio-logical complexity and the attempts made by scholars and theologians to interpret it within the limits of reductionist scientism or theism. For this purpose, firstly, attention is focused on explaining the meaning of the concept of «evolution» and its historical and philosophical transformation in the context of the idea of complexity. Secondly, the notion of complexity in theology is used as evidence to support teleology. This approach is criticized by some scholars who consider evolution as a random prosses. They give it the status of a universal metaphysical assumption in evolution. The scientists and theologists both formulate metaphysical assumptions differently to interpret evolution.

A universal concern in lattice structures, whether they be naturally occurring or engineered, is exactly how energy can and does move within them. A significant phenomenon that has been shown theoretically, numerically, and experimentally to affect the behavior of energy in lattice structures is that of discrete breathers, also known as energy localizations or intrinsic localized modes. Discrete breathers affect the energy distribution in a lattice or array by concentrating it in localized and oscillatory fashion. While these have been known to occur in linear lattices with defects, they also occur in perfect (translationally invariant) nonlinear lattices of sufficient anharmonicity. This thesis seeks to further the study of the latter case, specifically by investigating how white and Lévy stable noise can be used to manipulate and create discrete breathers in a macro-scale nonlinear electric lattice. Using a dynamical model from literature and the Euler-Maruyama method of numerical integration, the effects of both additive white noise and Lévy stable noise on breathers in this array are investigated. These breathers are first initialized in the array using small randomized initial voltage conditions and a driving frequency below the system's natural frequency. It is found that additive white noise can in fact affect the number of breathers present by causing some of them to combine. Additionally, noise can be used to shorten the transient time before breather appearance. Importantly, to garner these effects, the noise must be applied during this transient phase. Applying it after will have little effect as already-formed breathers are too robust. The results are mostly the same for Lévy stable noise, although the large flights from the mean characteristic of this noise type require that the noise intensity used be reduced significantly. Next the ability of white noise to generate discrete breathers is investigated. The initial conditions are set to zero, meaning that no breathers will form in the system without some kind of intervention. Applying noise for either the entire simulation duration or only the first half both resulted in the consistent and reliable creation of discrete breathers. Additionally, it is found that a temporary burst of noise across the array can be used to create breathers on command at any time. The breathers created will exhibit some noisy behavior, but this can be minimized by applying the necessary noise to only one cell. Thus, additive noise can serve as a useful means of breather creation, a key result of this thesis. These results testify to the significance of the interactions between the discrete breathers in this nonlinear electric line and noise. Noise can influence the number of breathers present, and even create breathers on command. The latter result is of particular significance and represents a promising area for future work.

The technology and cyberspace sector is losing billions each year to hardware security threats. The incidents of usage of counterfeiting chips are doubling each year. The Electronic Resellers Association International (ERAI) reported that in the year 2011 more than 1300 counterfeits were reported. The incidents were double of what were reported in 2008. The report from Federal Contracts acknowledges the threats emanating from counterfeit chips and says it threatens the successful operations of US Weapon Systems. Meanwhile, electronic counterfeiting of chips continues to be a very profitable business on the dark web by crooked operatives. Physical Unclonable Functions (PUFs) are emerging as hardware security primitives to deal with security issues such as cloning, hacking, copying, and detection of Trojans. PUFs are one-way physical structures embedded in chips to generate a unique signature for each chip. The well-known silicon-based PUFs are Arbiter PUF (APUF) and Ring Oscillator PUF (ROPUF). The PUF uses timing delays caused by manufacturing process variations to generate challenge-response pairs (CRPs) unique to each chip. APUFs and ROPUFs are observed to be vulnerable to modeling attacks.In this research, a novel hybrid PUF is proposed which is a combination of both types of delay based PUFs, to generate strong cryptographic keys. The proposed design uses the CRPs of APUF and ROs of ROPUF to generate an n-bit response corresponding to an n-bit challenge, whereas primitive PUFs generate a 1-bit response for an n-bit challenge. The CRPs produced using the proposed PUF are unique and random and can be considered as cryptographic keys. The experimental results show that the uniqueness of APUF and ROPUF CRPs increase by 23% and 19%, respectively; when applied through the proposed scheme. The average passing rate for randomness is observed to be 97%.The CRPs generated from the delay based PUFs are tested against machine learning attacks. The machine learning attacks are carried out considering different scenarios where the adversary has access to 50%, 70%, 80%, and 90% of the CRPs. The models are trained for four different best-optimizing algorithms: Adagrad, Adadelta, SGD, and NAdam. The results show that even after training for the same number of epochs, the average accuracy for the proposed PUF model is 7% compared to 56% and 72% of APUF and ROPUF, respectively. The lower prediction accuracy of the proposed PUF shows that CRPs generated from the proposed scheme are far more immune to machine learning attacks when compared to other delay based PUFs.

This dissertation challenges the critical accounts that have confined the aesthetic fertility of randomness to early twentieth-century literature, and notably to Mallarmé and the Surrealists. I supplement this truncated genealogy and argue that the narratives from the 1960s onward allow for a significantly novel articulation of chance and writing. A paradox encapsulates the creative contradiction at work: randomness can productively be framed and analyzed in constrained prose. I therefore track its emplotment in the novels by proponents of 'Pataphysics and the Oulipo. Writers such as Jarry and Perec borrow the materialist concept of the clinamen in order to rekindle the association between letters and atoms, and disrupt the traditional understanding of creation as inspiration. My critical contribution is to turn the materialist clinamen into a literary paradigm, and to flag it as the symptom of a broader, decisive transformation in contemporary fiction beyond oulipian procedures and modernist strategies. The clinamen holds in tension poetics as a set of rules and aesthetics as the ultimate singularity of an authorial intent. My dissertation situates this pivotal tension between chance and necessity within a broader genealogy: I deploy my hypothesis from Balzac, Proust, and Breton to Beckett, Queneau, and Modiano. My critical observations not only touch on aesthetics, but also epistemological questions. I disentangle the paradoxes involved in the conceptualization of randomness to propose a delineation of its conflictual articulation with determinism and intentionality. My rereading strategically uses a parameter of randomness that has been underexplored in science, philosophy, and literature: space. The spatialization of randomness is a crucial component of its genealogy, and it brings to light the complex moves involved in its integration in literature. My take on the legacy of randomness focuses on a specific device: the clinamen, a term from ancient physics that indicates the aleatory moment and place where atoms swerve from their fated fall. I trace the exemplary surfacing of the clinamen in philosophy, starting with Democritus, Epicurus, and Lucretius; I map its disruptive actualization in theory from Bergson to Meillassoux, through Althusser, Lacan, Derrida, Deleuze, Serres, and Nancy.

In this dissertation we investigate two questions in the subject of algorithmic randomness. The first question we address is "Given a real, is there a probability measure for which the real is not an atom, but relative to which the real is algorithmically random?" This question was originally studied by Reimann and Slaman with respect to Martin-Lof randomness, and this research continues their investigation by considering the question with respect to stronger notions of randomness and by providing metamathematical analysis of Reimann and Slaman's methods.The second question we investigate is "What are the first-order consequences of the existence of 2-random reals?" Conidis and Slaman showed that the consequences lie somewhere between IΣ1 and BΣ2, but left open the question of further classification. We show that the existence of 2-random reals does not imply BΣ2, and thus the consequences lie strictly between IΣ1 and BΣ2. Furthermore, by utilizing the methods in this proof we are able to construct a κ-like model in which BΣ2 fails and thereby answer an open question posed by Kaye in 1995.

Approachi Significans is a demonstration of the interference patterns created by scientific and artistic logics. It promotes immersion in the everyday world through experimentation and a search for novel experience, as such efforts prime the mind for novel thought. It is loosely based in a search for constellations of experiences that prompt Eureka moments and an effort to illustrate the organic nature of the scientific process. The title is derived from the phrase `approaching significance,' which is used to indicate that experimental data is moving towards the confirmation of a hypothesis.

Classical perspectives on judgment and rationality view heuristics as erroneous, leading to suboptimal judgments. Conversely, ecological perspectives view heuristics as smart mechanisms that result in good judgments in the face of uncertainty. Our research focused on the hot hand heuristic and examined it using non-linear analysis methods. This research attempted to answer two questions. The first question concerned the applicability of frequency analysis methods for detecting constraints (such as the hot hand) or structure in a time series of binary data, which we attempted to investigate through Monte Carlo simulations. We found that this method was sensitive enough to detect structure. The second question was concerned with whether humans are able to discriminate random series from constrained (structured) series. We conducted an experiment which investigated whether time series validated by the frequency analysis as constrained were detectable by humans. Our results showed that humans have an ability to recognize a constrained series more often than chance. A link between the strength of constraints in the spectral analysis with performance in discrimination of the task was demonstrated, suggesting that the higher the strength of constraint (according to the spectral plots) the easier it is to discriminate. The spectral plots might hold validity to index the psychophysics of pattern detection in humans. Our results gives credence to the ecological justification for the use of heuristics (such as the belief in the hot hand), especially in a skilled situation, such as sports performance.

The prefix-free Kolmogorov complexity, K(σ), of a finite binary string σ is the length of the shortest self-delimiting program that outputs σ and is a measure of the information content of σ. There are two very natural ways to extend this notion to infinite binary strings (identified as the binary expansions of real numbers in the interval [0,1]): one can examine the initial segment complexity of a real, i.e. K(A|n)$ as a function of n, or one can examine the compressive power of A as an oracle, i.e. KA(σ) as a function of σ. Each of these approaches has a notion of minimality for reals. A real is K-trivial if the complexities of its initial segments are up to a constant just the complexities of their lengths. A real is low for K if it provides no more than an additive constant advantage to compressing any string. This dissertation examines weakenings of these notions that arise from replacing the constant bounds with slow-growing functions. The main results are that these weaker lowness notions behave very differently from the standard ones in terms of the sets of reals defined by these notions. We also include applications of these new notions to effective dimension and mutual information.

This dissertation explores the multifaceted interplay between efficient computation and probability distributions. We organize the aspects of this interplay according to whether the randomness occurs primarily at the level of the problem or the level of the algorithm, and orthogonally according to whether the output is random or the input is random.Part I concerns settings where the problem's output is random. A sampling problem associates to each input x a probability distribution D(x), and the goal is to output a sample from D(x) (or at least get statistically close) when given x. Although sampling algorithms are fundamental tools in statistical physics, combinatorial optimization, and cryptography, and algorithms for a wide variety of sampling problems have been discovered, there has been comparatively little research viewing sampling through the lens of computational complexity. We contribute to the understanding of the power and limitations of efficient sampling by proving a time hierarchy theorem which shows, roughly, that “a little more time gives a lot more power to sampling algorithms.”Part II concerns settings where the algorithm's output is random. Even when the specification of a computational problem involves no randomness, one can still consider randomized algorithms that produce a correct output with high probability. A basic question is whether one can derandomize algorithms, i.e., reduce or eliminate their dependence on randomness without incurring much loss in efficiency. Although derandomizing arbitrary time-efficient algorithms can only be done assuming unproven complexity-theoretic conjectures, it is possible to unconditionally construct derandomization tools called pseudorandom generators for restricted classes of algorithms. We give an improved pseudorandom generator for a new class, which we call combinatorial checkerboards. The notion of pseudorandomness shows up in many contexts besides derandomization. The so-called Dense Model Theorem, which has its roots in the famous theorem of Green and Tao that the primes contain arbitrarily long arithmetic progressions, is a result about pseudorandomness that has turned out to be a useful tool in computational complexity and cryptography. At the heart of this theorem is a certain type of reduction, and in this dissertation we prove a strong lower bound on the advice complexity of such reductions, which is analogous to a list size lower bound for list-decoding of error-correcting codes.Part III concerns settings where the problem's input is random. We focus on the topic of randomness extraction, which is the problem of transforming a sample from a high-entropy but non-uniform probability distribution (that represents an imperfect physical source of randomness) into a uniformly distributed sample (which would then be suitable for use by a randomized algorithm). It is natural to model the input distribution as being sampled by an efficient algorithm (since randomness is generated by efficient processes in nature), and we give a construction of an extractor for the case where the input distribution's sampler is extremely efficient in parallel time. A related problem is to estimate the min-entropy (“amount of randomness”) of a given parallel-time-efficient sampler, since this dictates how many uniformly random output bits one could hope to extract from it. We characterize the complexity of this problem, showing that it is “slightly harder than NP-complete.”Part IV concerns settings where the algorithm's input is random. Average-case complexity is the study of the power of algorithms that are allowed to fail with small probability over a randomly chosen input. This topic is motivated by cryptography and by modeling heuristics. A fundamental open question is whether the average-case hardness of NP is implied by the worst-case hardness of NP. We exhibit a new barrier to showing this implication, by proving that a certain general technique (namely, “relativizing proofs by reduction”) cannot be used. We also prove results on hardness amplification, clarifying the quantitative relationship between the running time of an algorithm and the probability of failure over a random input (both of which are desirable to minimize).

In this article, I introduce a novel airborne network mobility model, called the Smooth Turn Mobility Model, that captures the correlation of acceleration for airborne vehicles across time and spatial coordinates. E?ective routing in airborne networks (ANs) relies on suitable mobility models that capture the random movement pattern of airborne vehicles. As airborne vehicles cannot make sharp turns as easily as ground vehicles do, the widely used mobility models for Mobile Ad Hoc Networks such as Random Waypoint and Random Direction models fail. Our model is realistic in capturing the tendency of airborne vehicles toward making straight trajectory and smooth turns with large radius, and whereas is simple enough for tractable connectivity analysis and routing design.

The use of randomness in computer science is ubiquitous. Randomized protocols have turned out to be much more efficient than their deterministic counterparts. In addition, many problems in distributed computing and cryptography are impossible to solve without randomness. However, these applications typically require uniform random bits, while in practice almost all natural random phenomena are biased. Moreover, even originally uniform random bits can be damaged if an adversary learns some partial information about these bits. In this thesis, we study how to run randomized protocols in distributed computing and cryptography with imperfect randomness. We use the most general model for imperfect randomness where the weak random source is only required to have a certain amount of min-entropy. One important tool here is the randomness extractor. A randomness extractor is a function that takes as input one or more weak random sources, and outputs a distribution that is close to uniform in statistical distance. Randomness extractors are interesting in their own right and are closely related to many other problems in computer science. Giving efficient constructions of randomness extractors with optimal parameters is one of the major open problems in the area of pseudorandomness. We construct network extractor protocols that extract private random bits for parties in a communication network, assuming that they each start with an independent weak random source, and some parties are corrupted by an adversary who sees all communications in the network. These protocols imply fault-tolerant distributed computing protocols and secure multi-party computation protocols where only imperfect randomness is available. The probabilistic method shows that there exists an extractor for two independent sources with logarithmic min-entropy, while known constructions are far from achieving these parameters. In this thesis we construct extractors for two independent sources with any linear min-entropy, based on a computational assumption. We also construct the best known extractors for three independent sources and affine sources. Finally we study the problem of privacy amplification. In this model, two parties share a private weak random source and they wish to agree on a private uniform random string through communications in a channel controlled by an adversary, who has unlimited computational power and can change the messages in arbitrary ways. All previous results assume that the two parties have local uniform random bits. We show that this problem can be solved even if the two parties only have local weak random sources. We also improve previous results in various aspects by constructing the first explicit non-malleable extractor and giving protocols based on this extractor.

The thesis explored whether a common concept of randomness determines behaviour on two randomness cognition tasks; perceptions of randomness and predictions of future outcomes. The impact of a causal agent, presentation format, and sequence length, on randomness cognition was also investigated. Judgements of randomness were influenced by the use of causal information about sequences. Participants in a control condition, with no information about the sequence source, were not biased in their judgements of randomness, whilst those told that sequences represented either coin tosses or shots in basketball were biased. Predictions of future outcomes were shown to be strongly influenced by sequence alternation rate. However, over-alternation still occurred, particularly for mid-alternation rate sequences. Causal belief was found to influence predictions of future outcomes. People were more likely to continue the run when the cause was animate but to end it when the cause was inanimate. The effect of presentation mode was examined by comparing responses to symbol and random walk trend sequences, with mixed results. For the simplest tasks no effect was found for presentation mode. However, the trend sequence format was susceptible to influences from other variables such as a causal example. Sequence length influenced judgements of randomness, as people were more biased in their ratings of short sequences than long sequences. Two proposed mechanisms underlying randomness cognition were explored: limitations in working memory capacity (WMC) and sequence complexity. Results found no support for WMC as a general mechanism for randomness cognition, as performances on working memory and perception of randomness tasks were not correlated. Additionally, no support was found for sequence complexity as a mechanism for explaining perceptions of randomness. The results have important implications for the randomness literature as well as questioning some previously proposed underlying mechanisms. The commonly used causal example was shown to influence judgements of randomness, thus suggesting that previously reported biases towards rating higher alternation rate sequences as most random may be due to the use of a causal example. Taken together, the results raise doubts about the validity of a common concept of randomness underpinning performance on different types of randomness cognition.

High-temperature creep behavior of ceramics is characterized by nonlinear time-dependent responses, asymmetric behavior in tension and compression, temperature dependent, and nucleation and coalescence of voids leading to creep rupture. Moreover, creep rupture experiments show considerable scatter or randomness in fatigue lives of nominally equal specimens. Failure is caused by the nucleation and growth of voids at the grain boundaries. To capture the nonlinear, asymmetric, time-dependent behavior, the standard linear viscoelastic solid model is modified. Nonlinearity and asymmetry are introduced in the volumetric components by using a nonlinear function similar to a hyperbolic sine function but modified to model asymmetry. Temperature is accounted for in the model through temperature-dependent parameters. The nonlinear viscoelastic model is implemented in an ABAQUS user material subroutine. Damage is modeled using two scalar internal variables, one for the deviatoric component and the other for the volumetric component. Each damage internal variable is assumed to be governed by a nonlinear, first order ODE that is a function of stress and two parameters. Each element is assigned damage parameters sampled from a lognormal distribution. An element is deleted when damage is equal to one. Temporal increases in strains produce a sequential loss of elements (a model for void nucleation and growth), which in turn leads to failure. Nonlinear viscoelastic model parameters are determined from uniaxial tensile and compressive creep experiments on silicon nitride. The model is then used to predict the deformation of four-point bending and ball-on-ring specimens. Simulation is used to predict statistical moments of creep rupture lives. Numerical simulation results compare well with results of experiments of four-point bending specimens. A Voronoi simulation of a tensile creep test is used to study the effects of temperature, stress and damage and to evaluate model predictions. A preliminary simulation of a two-phase material is presented.

The role of randomness as a generator of long range correlations and ordinary statistical mechanics is investigated in this Dissertation. The difficulties about the derivation of thermodynamics from mechanics are pointed out and the connection between the ordinary fluctuation-dissipation process and possible anomalous properties of statistical systems is highlighted.