Network formation by contact arrested propagation

We propose here a network growth model which we term Contact Arrested Propagation (CAP). One representation of the CAP model comprises a set of two-dimensional line segments on a lattice, propagating independently at constant speed in both directions until they collide. The generic form of the model extends to arbitrary networks, and, in particular, to three-dimensional lattices, where it may be realised as a set of expanding planes, halted upon intersection. The model is implemented as a simple and completely background independent substitution system. We restrict attention to one-, two- and three-dimensional background lattices and investigate how CAP networks are influenced by lattice connectivity, spatial dimension, system size and initial conditions. Certain scaling properties exhibit little sensitivity to the particular lattice connectivity but change significantly with lattice dimension, indicating universality. Suggested applications of the model include various fracturing and fragmentation processes, and we expect that CAP may find many other uses, due to its simplicity, generality and ease of implementation

The formalism of non-commutative quantum mechanics and its extension to many-particle systems

Thesis (MSc (Physics))--University of Stellenbosch, 2010.ENGLISH ABSTRACT: Non-commutative quantum mechanics is a generalisation of quantum mechanics which incorporates the notion of a fundamental shortest length scale by introducing non-commuting position coordinates. Various theories of quantum gravity indicate the existence of such a shortest length scale in nature. It has furthermore been realised that certain condensed matter systems allow effective descriptions in terms of non-commuting coordinates. As a result, non-commutative quantum mechanics has received increasing attention recently. A consistent formulation and interpretation of non-commutative quantum mechanics, which unambiguously defines position measurement within the existing framework of quantum mechanics, was recently presented by Scholtz et al. This thesis builds on the latter formalism, extends it to many-particle systems and links it up with non-commutative quantum field theory via second quantisation. It is shown that interactions of particles, among themselves and with external potentials, are altered as a result of the fuzziness induced by non-commutativity. For potential scattering, generic increases are found for the differential and total scattering cross sections. Furthermore, the recovery of a scattering potential from scattering data is shown to involve a suppression of high energy contributions, disallowing divergent interaction forces. Likewise, the effective statistical interaction among fermions and bosons is modified, leading to an apparent violation of Pauli’s exclusion principle and foretelling implications for thermodynamics at high densities.AFRIKAANSE OPSOMMING: Nie-kommutatiewe kwantummeganika is ’n veralgemening van kwantummeganika wat die idee van ’n fundamentele kortste lengteskaal invoer d.m.v. nie-kommuterende ko¨ordinate. Verskeie teorie¨e van kwantum-grawitasie dui op die bestaan van so ’n kortste lengteskaal in die natuur. Dit is verder uitgewys dat sekere gekondenseerde materie sisteme effektiewe beskrywings in terme van nie-kommuterende koordinate toelaat. Gevolglik het die veld van nie-kommutatiewe kwantummeganika onlangs toenemende aandag geniet. ’n Konsistente formulering en interpretasie van nie-kommutatiewe kwantummeganika, wat posisiemetings eenduidig binne bestaande kwantummeganika raamwerke defineer, is onlangs voorgestel deur Scholtz et al. Hierdie tesis brei uit op hierdie formalisme, veralgemeen dit tot veeldeeltjiesisteme en koppel dit aan nie-kommutatiewe kwantumveldeteorie d.m.v. tweede kwantisering. Daar word gewys dat interaksies tussen deeltjies en met eksterne potensiale verander word as gevolg van nie-kommutatiwiteit. Vir potensiale verstrooi ¨ıng verskyn generiese toenames vir die differensi¨ele and totale verstroi¨ıngskanvlak. Verder word gewys dat die herkonstruksie van ’n verstrooi¨ıngspotensiaal vanaf verstrooi¨ıngsdata ’n onderdrukking van ho¨e-energiebydrae behels, wat divergente interaksiekragte verbied. Soortgelyk word die effektiewe statistiese interaksie tussen fermione en bosone verander, wat ly tot ’n skynbare verbreking van Pauli se uitsluitingsbeginsel en dui op verdere gevolge vir termodinamika by ho¨e digthede

Convex environmental contours

Environmental contours are widely used as a basis for e.g., ship design, especially in early design phases. The traditional approach to such contours is based on the well-known Rosenblatt transformation. Here we focus on convex contours estimated using Monte Carlo methods and establish a rigorous mathematical foundation for such contours. In the present paper we also present an improved simulation procedure based on importance sampling. In particular, we show how this procedure can be extended to cases with omission factors and where the joint distribution of the environmental variables is a discrete mixture. It is well-known that contours constructed using Monte Carlo simulation typically have certain irregularities. In particular, the sets bounded by the estimated contours appear to be convex. However, when the curves are investigated more closely, they include a large number of small loops. In the present paper we provide a precise condition for convexity, and propose a smoothing method which can be used to eliminate the loops. The methods are illustrated by a numerical example

Utilization of risk priority number to systems-theoretic process analysis: A practical solution to manage a large number of unsafe control actions and loss scenarios

System-theoretic process analysis is a hazard identification method whose main assumption is that accidents can be caused by unsafe interactions of system components, as well as component failures. System-theoretic process analysis can cover a wider range of hazards compared with traditional hazard analysis methods, such as software flaws, human errors, component failures, and complex interactions of system components. Identifying more hazards is of course an important advantage of system-theoretic process analysis, but generating too many hazards may pose a practical challenge to stakeholders to utilize the results of system-theoretic process analysis. Some hazards or scenarios may be more critical with higher consequence, while others can be less critical with lower consequence. We therefore need to evaluate the analysis results to focus on more critical and important problems first, when we do not have enough time and resources. The main objective of this study has been to suggest an additional procedure to system-theoretic process analysis to ensure a systematic evaluation, screening, and prioritization of analysis results. The risk priority number approach was adopted to evaluate the criticality of the results of analyses. After investigating the strengths and limitations of traditional risk priority number approaches, three new risk priority number criteria along with four additional procedure steps were added to the system-theoretic process analysis for evaluation, screening, and prioritization of system-theoretic process analysis results. The proposed criteria and procedure have been demonstrated with a case study of a subsea gas compression system, and for this particular analysis, it was suggested that 38 of 130 unsafe control actions and 258 of 976 loss scenarios were significantly less critical and screened out, so that the resources could be prioritized to solve the remaining findings. Meanwhile, prioritization is still a rather new topic with system-theoretic process analysis, and in the end of the article, we have identified some ideas for further research in this area

Utilization of risk priority number to systems-theoretic process analysis: A practical solution to manage a large number of unsafe control actions and loss scenarios

System-theoretic process analysis is a hazard identification method whose main assumption is that accidents can be caused by unsafe interactions of system components, as well as component failures. System-theoretic process analysis can cover a wider range of hazards compared with traditional hazard analysis methods, such as software flaws, human errors, component failures, and complex interactions of system components. Identifying more hazards is of course an important advantage of system-theoretic process analysis, but generating too many hazards may pose a practical challenge to stakeholders to utilize the results of system-theoretic process analysis. Some hazards or scenarios may be more critical with higher consequence, while others can be less critical with lower consequence. We therefore need to evaluate the analysis results to focus on more critical and important problems first, when we do not have enough time and resources. The main objective of this study has been to suggest an additional procedure to system-theoretic process analysis to ensure a systematic evaluation, screening, and prioritization of analysis results. The risk priority number approach was adopted to evaluate the criticality of the results of analyses. After investigating the strengths and limitations of traditional risk priority number approaches, three new risk priority number criteria along with four additional procedure steps were added to the system-theoretic process analysis for evaluation, screening, and prioritization of system-theoretic process analysis results. The proposed criteria and procedure have been demonstrated with a case study of a subsea gas compression system, and for this particular analysis, it was suggested that 38 of 130 unsafe control actions and 258 of 976 loss scenarios were significantly less critical and screened out, so that the resources could be prioritized to solve the remaining findings. Meanwhile, prioritization is still a rather new topic with system-theoretic process analysis, and in the end of the article, we have identified some ideas for further research in this are

Classification of fracture patterns by heterogeneity and topology

Fracture patterns arise abundantly in natural and engineered systems, and their geometries depend on material properties and on the ways in which the material is deformed or forces act on it. Two-dimensional fracture patterns can be characterized by their network topology (how fractures connect to each other) and their heterogeneity (whether fractures appear clustered or uniformly distributed in space). We propose a generic model in which the topology can be adjusted by controlling the ratio between the number of dead ends and the number of junctions in the fracture network, and heterogeneity can be adjusted by biasing fracture nucleation to occur near or away from existing fractures. Based on this model we propose a characterization scheme for natural fracture systems and provide and demonstrate an algorithm for recovering model parameters from fracture pattern images