Subgeometric rates of convergence for a class of continuous-time Markov process

Let (Phi(t))(t is an element of R+) be a Harris ergodic continuous-time Markov process on a general state space, with invariant probability measure pi. We investigate the rates of convergence of the transition function P-t(x, (.)) to pi; specifically, we find conditions under which r(t) vertical bar vertical bar P-t (x, (.)) - pi vertical bar vertical bar -> 0 as t -> infinity, for suitable subgeometric rate functions r(t), where vertical bar vertical bar - vertical bar vertical bar denotes the usual total variation norm for a signed measure. We derive sufficient conditions for the convergence to hold, in terms of the existence of suitable points on which the first hitting time moments are bounded. In particular, for stochastically ordered Markov processes, explicit bounds on subgeometric rates of convergence are obtained. These results are illustrated in several examples.

A study of the evolution of the representational capabilities of process modeling grammars

A plethora of process modeling techniques has been proposed over the years. One way of evaluating and comparing the scope and completeness of techniques is by way of representational analysis. The purpose of this paper is to examine how process modeling techniques have developed over the last four decades. The basis of the comparison is the Bunge-Wand-Weber representation model, a benchmark used for the analysis of grammars that purport to model the real world and the interactions within it. This paper presents a comparison of representational analyses of several popular process modeling techniques and has two main outcomes. First, it provides insights, within the boundaries of a representational analysis, into the extent to which process modeling techniques have developed over time. Second, the findings also indicate areas in which the underlying theory seems to be over-engineered or lacking in specialization.

A framework of issues in large process modeling projects

As process management projects have increased in size due to globalised and company-wide initiatives, a corresponding growth in the size of process modeling projects can be observed. Despite advances in languages, tools and methodologies, several aspects of these projects have been largely ignored by the academic community. This paper makes a first contribution to a potential research agenda in this field by defining the characteristics of large-scale process modeling projects and proposing a framework of related issues. These issues are derived from a semi -structured interview and six focus groups conducted in Australia, Germany and the USA with enterprise and modeling software vendors and customers. The focus groups confirm the existence of unresolved problems in business process modeling projects. The outcomes provide a research agenda which directs researchers into further studies in global process management, process model decomposition and the overall governance of process modeling projects. It is expected that this research agenda will provide guidance to researchers and practitioners by focusing on areas of high theoretical and practical relevance.

Hydrometallurgical process modeling using advanced mathematical tools

Hydrometallurgical process modeling is the main objective of this Master’s thesis work. Three different leaching processes namely, high pressure pyrite oxidation, direct oxidation zinc concentrate (sphalerite) leaching and gold chloride leaching using rotating disc electrode (RDE) are modeled and simulated using gPROMS process simulation program in order to evaluate its model building capabilities. The leaching mechanism in each case is described in terms of a shrinking core model. The mathematical modeling carried out included process model development based on available literature, estimation of reaction kinetic parameters and assessment of the model reliability by checking the goodness fit and checking the cross correlation between the estimated parameters through the use of correlation matrices. The estimated parameter values in each case were compared with those obtained using the Modest simulation program. Further, based on the estimated reaction kinetic parameters, reactor simulation and modeling for direct oxidation zinc concentrate (sphalerite) leaching is carried out in Aspen Plus V8.6. The zinc leaching autoclave is based on Cominco reactor configuration and is modeled as a series of continuous stirred reactors (CSTRs). The sphalerite conversion is calculated and a sensitivity analysis is carried out so to determine the optimum reactor operation temperature and optimum oxygen mass flow rate. In this way, the implementation of reaction kinetic models into the process flowsheet simulation environment has been demonstrated.

Dry grinding technology for automotive gears manufacturing: process modeling and optimization

The following thesis focused on the dry grinding process modelling and optimization for automotive gears production. A FEM model was implemented with the aim at predicting process temperatures and preventing grinding thermal defects on the material surface. In particular, the model was conceived to facilitate the choice of the grinding parameters during the design and the execution of the dry-hard finishing process developed and patented by the company Samputensili Machine Tools (EMAG Group) on automotive gears. The proposed model allows to analyse the influence of the technological parameters, comprising the grinding wheel specifications. Automotive gears finished by dry-hard finishing process are supposed to reach the same quality target of the gears finished through the conventional wet grinding process with the advantage of reducing production costs and environmental pollution. But, the grinding process allows very high values of specific pressure and heat absorbed by the material, therefore, removing the lubricant increases the risk of thermal defects occurrence. An incorrect design of the process parameters set could cause grinding burns, which affect the mechanical performance of the ground component inevitably. Therefore, a modelling phase of the process could allow to enhance the mechanical characteristics of the components and avoid waste during production. A hierarchical FEM model was implemented to predict dry grinding temperatures and was represented by the interconnection of a microscopic and a macroscopic approach. A microscopic single grain grinding model was linked to a macroscopic thermal model to predict the dry grinding process temperatures and so to forecast the thermal cycle effect caused by the process parameters and the grinding wheel specification choice. Good agreement between the model and the experiments was achieved making the dry-hard finishing an efficient and reliable technology to implement in the gears automotive industry.

Modelagem de usinas eólicas através de um processo de Markov e técnicas de confiabilidade para a estimativa anual da energia produzida

This study aims to use a computational model that considers the statistical characteristics of the wind and the reliability characteristics of a wind turbine, such as failure rates and repair, representing the wind farm by a Markov process to determine the estimated annual energy generated, and compare it with a real case. This model can also be used in reliability studies, and provides some performance indicators that will help in analyzing the feasibility of setting up a wind farm, once the power curve is known and the availability of wind speed measurements. To validate this model, simulations were done using the database of the wind farm of Macau PETROBRAS. The results were very close to the real, thereby confirming that the model successfully reproduced the behavior of all components involved. Finally, a comparison was made of the results presented by this model, with the result of estimated annual energy considering the modeling of the distribution wind by a statistical distribution of Weibull

Business process orientated holonic (PrOH) modeling

Purpose: The purpose of this paper is to describe how the application of systems thinking to designing, managing and improving business processes has resulted in a new and unique holonic-based process modeling methodology know as process orientated holonic modeling. Design/methodology/approach: The paper describes key systems thinking axioms that are built upon in an overview of the methodology; the techniques are described using an example taken from a large organization designing and manufacturing capital goods equipment operating within a complex and dynamic environment. These were produced in an 18 month project, using an action research approach, to improve quality and process efficiency. Findings: The findings of this research show that this new methodology can support process depiction and improvement in industrial sectors which are characterized by environments of high variety and low volume (e.g. projects; such as the design and manufacture of a radar system or a hybrid production process) which do not provide repetitive learning opportunities. In such circumstances, the methodology has not only been able to deliver holonic-based process diagrams but also been able to transfer strategic vision from top management to middle and operational levels without being reductionistic. Originality/value: This paper will be of interest to organizational analysts looking at large complex projects whom require a methodology that does not confine them to thinking reductionistically in "task-breakdown" based approaches. The novel ideas in this paper have great impact on the way analysts should perceive organizational processes. Future research is applying the methodology in similar environments in other industries. © Emerald Group Publishing Limited.

Building a holarchy using business process-oriented holonic (PrOH) modeling

The application of systems thinking to designing, managing, and improving business processes has developed a new "holonic-based" process modeling methodology. The theoretical background and the methodology are described using examples taken from a large organization designing and manufacturing capital goods equipment operating within a complex and dynamic environment. A key point of differentiation attributed to this methodology is that it allows a set of models to be produced without taking a task breakdown approach but instead uses systems thinking and a construct known as the "holon" to build process descriptions as a system of systems (i.e., a holarchy). The process-oriented holonic modeling methodology has been used for total quality management and business process engineering exercises in different industrial sectors and builds models that connect the strategic vision of a company to its operational processes. Exercises have been conducted in response to environmental pressures to make operations align with strategic thinking as well as becoming increasingly agile and efficient. This unique methodology is best applied in environments of high complexity, low volume, and high variety, where repeated learning opportunities are few and far between (e.g., large development projects). © 2007 IEEE.

Multiscale Modeling and Simulation of Stepped Crystal Surfaces

A primary goal of this dissertation is to understand the links between mathematical models that describe crystal surfaces at three fundamental length scales: The scale of individual atoms, the scale of collections of atoms forming crystal defects, and macroscopic scale. Characterizing connections between different classes of models is a critical task for gaining insight into the physics they describe, a long-standing objective in applied analysis, and also highly relevant in engineering applications. The key concept I use in each problem addressed in this thesis is coarse graining, which is a strategy for connecting fine representations or models with coarser representations. Often this idea is invoked to reduce a large discrete system to an appropriate continuum description, e.g. individual particles are represented by a continuous density. While there is no general theory of coarse graining, one closely related mathematical approach is asymptotic analysis, i.e. the description of limiting behavior as some parameter becomes very large or very small. In the case of crystalline solids, it is natural to consider cases where the number of particles is large or where the lattice spacing is small. Limits such as these often make explicit the nature of links between models capturing different scales, and, once established, provide a means of improving our understanding, or the models themselves. Finding appropriate variables whose limits illustrate the important connections between models is no easy task, however. This is one area where computer simulation is extremely helpful, as it allows us to see the results of complex dynamics and gather clues regarding the roles of different physical quantities. On the other hand, connections between models enable the development of novel multiscale computational schemes, so understanding can assist computation and vice versa. Some of these ideas are demonstrated in this thesis. The important outcomes of this thesis include: (1) a systematic derivation of the step-flow model of Burton, Cabrera, and Frank, with corrections, from an atomistic solid-on-solid-type models in 1+1 dimensions; (2) the inclusion of an atomistically motivated transport mechanism in an island dynamics model allowing for a more detailed account of mound evolution; and (3) the development of a hybrid discrete-continuum scheme for simulating the relaxation of a faceted crystal mound. Central to all of these modeling and simulation efforts is the presence of steps composed of individual layers of atoms on vicinal crystal surfaces. Consequently, a recurring theme in this research is the observation that mesoscale defects play a crucial role in crystal morphological evolution.

Stability and ergodicity of piecewise deterministic Markov processes

The main goal of this paper is to establish some equivalence results on stability, recurrence, and ergodicity between a piecewise deterministic Markov process ( PDMP) {X( t)} and an embedded discrete-time Markov chain {Theta(n)} generated by a Markov kernel G that can be explicitly characterized in terms of the three local characteristics of the PDMP, leading to tractable criterion results. First we establish some important results characterizing {Theta(n)} as a sampling of the PDMP {X( t)} and deriving a connection between the probability of the first return time to a set for the discrete-time Markov chains generated by G and the resolvent kernel R of the PDMP. From these results we obtain equivalence results regarding irreducibility, existence of sigma-finite invariant measures, and ( positive) recurrence and ( positive) Harris recurrence between {X( t)} and {Theta(n)}, generalizing the results of [ F. Dufour and O. L. V. Costa, SIAM J. Control Optim., 37 ( 1999), pp. 1483-1502] in several directions. Sufficient conditions in terms of a modified Foster-Lyapunov criterion are also presented to ensure positive Harris recurrence and ergodicity of the PDMP. We illustrate the use of these conditions by showing the ergodicity of a capacity expansion model.

AVERAGE CONTINUOUS CONTROL OF PIECEWISE DETERMINISTIC MARKOV PROCESSES

This paper deals with the long run average continuous control problem of piecewise deterministic Markov processes (PDMPs) taking values in a general Borel space and with compact action space depending on the state variable. The control variable acts on the jump rate and transition measure of the PDMP, and the running and boundary costs are assumed to be positive but not necessarily bounded. Our first main result is to obtain an optimality equation for the long run average cost in terms of a discrete-time optimality equation related to the embedded Markov chain given by the postjump location of the PDMP. Our second main result guarantees the existence of a feedback measurable selector for the discrete-time optimality equation by establishing a connection between this equation and an integro-differential equation. Our final main result is to obtain some sufficient conditions for the existence of a solution for a discrete-time optimality inequality and an ordinary optimal feedback control for the long run average cost using the so-called vanishing discount approach. Two examples are presented illustrating the possible applications of the results developed in the paper.