A new method for analysing the equilibrium and time-dependent behaviour of Markovian models

Many large-scale stochastic systems, such as telecommunications networks, can be modelled using a continuous-time Markov chain. However, it is frequently the case that a satisfactory analysis of their time-dependent, or even equilibrium, behaviour is impossible. In this paper, we propose a new method of analyzing Markovian models, whereby the existing transition structure is replaced by a more amenable one. Using rates of transition given by the equilibrium expected rates of the corresponding transitions of the original chain, we are able to approximate its behaviour. We present two formulations of the idea of expected rates. The first provides a method for analysing time-dependent behaviour, while the second provides a highly accurate means of analysing equilibrium behaviour. We shall illustrate our approach with reference to a variety of models, giving particular attention to queueing and loss networks. (C) 2003 Elsevier Ltd. All rights reserved.

Mean anisotropy of homogeneous Gaussian random fields and anisotropic norms of linear translation-invariant operators on multidimensional integer lattices

Sensitivity of output of a linear operator to its input can be quantified in various ways. In Control Theory, the input is usually interpreted as disturbance and the output is to be minimized in some sense. In stochastic worst-case design settings, the disturbance is considered random with imprecisely known probability distribution. The prior set of probability measures can be chosen so as to quantify how far the disturbance deviates from the white-noise hypothesis of Linear Quadratic Gaussian control. Such deviation can be measured by the minimal Kullback-Leibler informational divergence from the Gaussian distributions with zero mean and scalar covariance matrices. The resulting anisotropy functional is defined for finite power random vectors. Originally, anisotropy was introduced for directionally generic random vectors as the relative entropy of the normalized vector with respect to the uniform distribution on the unit sphere. The associated a-anisotropic norm of a matrix is then its maximum root mean square or average energy gain with respect to finite power or directionally generic inputs whose anisotropy is bounded above by a≥0. We give a systematic comparison of the anisotropy functionals and the associated norms. These are considered for unboundedly growing fragments of homogeneous Gaussian random fields on multidimensional integer lattice to yield mean anisotropy. Correspondingly, the anisotropic norms of finite matrices are extended to bounded linear translation invariant operators over such fields.

gl(2 vertical bar 2) current superalgebra and non-unitary conformal field theory

Motivated by application of current superalgebras in the study of disordered systems such as the random XY and Dirac models, we investigate gl(2\2) current superalgebra at general level k. We construct its free field representation and corresponding Sugawara energy-momentum tensor in the non-standard basis. Three screen currents of the first kind are also presented. (C) 2003 Elsevier B.V. All rights reserved.

Critical comparison of Julius Kruttschnitt Mineral Research Centre (JKMRC) blast fragmentation models

Blast fragmentation can have a significant impact on the profitability of a mine. An optimum run of mine (ROM) size distribution is required to maximise the performance of downstream processes. If this fragmentation size distribution can be modelled and controlled, the operation will have made a significant advancement towards improving its performance. Blast fragmentation modelling is an important step in Mine to Mill™ optimisation. It allows the estimation of blast fragmentation distributions for a number of different rock mass, blast geometry, and explosive parameters. These distributions can then be modelled in downstream mining and milling processes to determine the optimum blast design. When a blast hole is detonated rock breakage occurs in two different stress regions - compressive and tensile. In the-first region, compressive stress waves form a 'crushed zone' directly adjacent to the blast hole. The second region, termed the 'cracked zone', occurs outside the crush one. The widely used Kuz-Ram model does not recognise these two blast regions. In the Kuz-Ram model the mean fragment size from the blast is approximated and is then used to estimate the remaining size distribution. Experience has shown that this model predicts the coarse end reasonably accurately, but it can significantly underestimate the amount of fines generated. As part of the Australian Mineral Industries Research Association (AMIRA) P483A Mine to Mill™ project, the Two-Component Model (TCM) and Crush Zone Model (CZM), developed by the Julius Kruttschnitt Mineral Research Centre (JKMRC), were compared and evaluated to measured ROM fragmentation distributions. An important criteria for this comparison was the variation of model results from measured ROM in the-fine to intermediate section (1-100 mm) of the fragmentation curve. This region of the distribution is important for Mine to Mill™ optimisation. The comparison of modelled and Split ROM fragmentation distributions has been conducted in harder ores (UCS greater than 80 MPa). Further work involves modelling softer ores. The comparisons will be continued with future site surveys to increase confidence in the comparison of the CZM and TCM to Split results. Stochastic fragmentation modelling will then be conducted to take into account variation of input parameters. A window of possible fragmentation distributions can be compared to those obtained by Split . Following this work, an improved fragmentation model will be developed in response to these findings.

Solvable models of Bose-Einstein condensates: A new algebraic Bethe ansatz scheme

A new algebraic Bethe ansatz scheme is proposed to diagonalize classes of integrable models relevant to the description of Bose-Einstein condensation in dilute alkali gases. This is achieved by introducing the notion of Z-graded representations of the Yang-Baxter algebra. (C) 2003 American Institute of Physics.

Linking physiological and architectural models of cotton

Despite the strong influence of plant architecture on crop yield, most crop models either ignore it or deal with it in a very rudimentary way. This paper demonstrates the feasibility of linking a model that simulates the morphogenesis and resultant architecture of individual cotton plants with a crop model that simulates the effects of environmental factors on critical physiological processes and resulting yield in cotton. First the varietal parameters of the models were made concordant. Then routines were developed to allocate the flower buds produced each day by the crop model amongst the potential positions generated by the architectural model. This allocation is done according to a set of heuristic rules. The final weight of individual bolls and the shedding of buds and fruit caused by water, N, and C stresses are processed in a similar manner. Observations of the positions of harvestable fruits, both within and between plants, made under a variety of agronomic conditions that had resulted in a broad range of plant architectures were compared to those predicted by the model with the same environmental inputs. As illustrated by comparisons of plant maps, the linked models performed reasonably well, though performance of the fruiting point allocation and shedding algorithms could probably be improved by further analysis of the spatial relationships of retained fruit. (C) 2002 Elsevier Science Ltd. All rights reserved.

Integrable generalized spin ladder models based on the SU(1|3) and SU(3|1) algebras

We present two integrable spin ladder models which possess a general free parameter besides the rung coupling J. The models are exactly solvable by means of the Bethe ansatz method and we present the Bethe ansatz equations. We analyze the elementary excitations of the models which reveal the existence of a gap for both models that depends on the free parameter. (C) 2003 American Institute of Physics.

An approach to verifying and debugging simulation models governed by ordinary differential equations: Part 1. Methodology for residual generation

For dynamic simulations to be credible, verification of the computer code must be an integral part of the modelling process. This two-part paper describes a novel approach to verification through program testing and debugging. In Part 1, a methodology is presented for detecting and isolating coding errors using back-to-back testing. Residuals are generated by comparing the output of two independent implementations, in response to identical inputs. The key feature of the methodology is that a specially modified observer is created using one of the implementations, so as to impose an error-dependent structure on these residuals. Each error can be associated with a fixed and known subspace, permitting errors to be isolated to specific equations in the code. It is shown that the geometric properties extend to multiple errors in either one of the two implementations. Copyright (C) 2003 John Wiley Sons, Ltd.

An approach to verifying and debugging simulation models governed by ordinary differential equations: Part 2. Residuals analysis and a case study

In Part 1 of this paper a methodology for back-to-back testing of simulation software was described. Residuals with error-dependent geometric properties were generated. A set of potential coding errors was enumerated, along with a corresponding set of feature matrices, which describe the geometric properties imposed on the residuals by each of the errors. In this part of the paper, an algorithm is developed to isolate the coding errors present by analysing the residuals. A set of errors is isolated when the subspace spanned by their combined feature matrices corresponds to that of the residuals. Individual feature matrices are compared to the residuals and classified as 'definite', 'possible' or 'impossible'. The status of 'possible' errors is resolved using a dynamic subset testing algorithm. To demonstrate and validate the testing methodology presented in Part 1 and the isolation algorithm presented in Part 2, a case study is presented using a model for biological wastewater treatment. Both single and simultaneous errors that are deliberately introduced into the simulation code are correctly detected and isolated. Copyright (C) 2003 John Wiley Sons, Ltd.

Influence of shapes of selected vegetable materials on drying kinetics during fluidized bed drying

Three different particular geometrical shapes of parallelepiped, cylinder and sphere were taken from cut green beans (length:diameter = 1:1, 2:1 and 3:1) and potatoes (aspect ratio = 1:1, 2:1 and 3:1) and peas, respectively. Their drying behaviour in a fluidised bed was studied at three different drying temperatures of 30, 40 and 50 degreesC (RH = 15%). Drying curves were constructed using non-dimensional moisture ratio (MR) and time and their behaviour was modelled using exponential (MR = exp(-kt)) and Page (MR = exp(-kt(n))) models. The effective diffusion coefficient of moisture transfer was determined by Fickian method using uni- and three-dimensional moisture movements. The diffusion coefficient was least affected by the size when the moisture movement was considered three-dimensional, whereas the drying temperature had a significative effect on diffusivity as expected. The drying constant and diffusivity coefficients were on the descending order for potato, beans and peas. The Arrhenius activation energy for the peas was also highest, indicating a strong barrier to moisture movement in peas as compared to beans and skinless cut potato pieces. (C) 2003 Elsevier Science Ltd. All rights reserved.