Scaleup of wet granulation processes: science not art

Significant advances have been made in the last decade to quantify the process of wet granulation. The attributes of product granules from the granulation process are controlled by a combination of three groups of processes occurring in the granulator: (1) wetting and nucleation, (2) growth and consolidation and (3) breakage and attrition. For the first two of these processes, the key controlling dimensionless groups are defined and regime maps are presented and validated with data from tumbling and mixer granulators. Granulation is an example of particle design. For quantitative analysis, both careful characterisation of the feed formulation and knowledge of operating parameters are required. A key thesis of this paper is that the design, scaleup and operation of granulation processes can now be considered as quantitative engineering rather than a black art. Résumé

Emulation of random output simulators

Computer models, or simulators, are widely used in a range of scientific fields to aid understanding of the processes involved and make predictions. Such simulators are often computationally demanding and are thus not amenable to statistical analysis. Emulators provide a statistical approximation, or surrogate, for the simulators accounting for the additional approximation uncertainty. This thesis develops a novel sequential screening method to reduce the set of simulator variables considered during emulation. This screening method is shown to require fewer simulator evaluations than existing approaches. Utilising the lower dimensional active variable set simplifies subsequent emulation analysis. For random output, or stochastic, simulators the output dispersion, and thus variance, is typically a function of the inputs. This work extends the emulator framework to account for such heteroscedasticity by constructing two new heteroscedastic Gaussian process representations and proposes an experimental design technique to optimally learn the model parameters. The design criterion is an extension of Fisher information to heteroscedastic variance models. Replicated observations are efficiently handled in both the design and model inference stages. Through a series of simulation experiments on both synthetic and real world simulators, the emulators inferred on optimal designs with replicated observations are shown to outperform equivalent models inferred on space-filling replicate-free designs in terms of both model parameter uncertainty and predictive variance.

A detailed design study of leaching and ancillary processes in the hydrometallurgical extraction of iron from iron bearing feedstocks

A systematic survey of the possible methods of chemical extraction of iron by chloride formation has been presented and supported by a comparable study of :feedstocks, products and markets. The generation and evaluation of alternative processes was carried out by the technique of morphological analysis vihich was exploited by way of a computer program. The final choice was related to technical feasibility and economic viability, particularly capital cost requirements and developments were made in an estimating procedure for hydrometallurgjcal processes which have general applications. The systematic exploration included the compilation of relevant data, and this indicated a need.to investigate precipitative hydrolysis or aqueous ferric chloride. Arising from this study, two novel hydrometallurgical processes for manufacturing iron powder are proposed and experimental work was undertaken in the following .areas to demonstrate feasibility and obtain basic data for design purposes: (1) Precipitative hydrolysis of aqueous ferric chloride. (2) Gaseous chloridation of metallic iron, and oxidation of resultant ferrous chloride. (3) Reduction of gaseous ferric chloride with hydrogen. (4) Aqueous acid leaching of low grade iron ore. (5) Aqueous acid leaching of metallic iron. The experimentation was supported by theoretical analyses dealing with: (1) Thermodynamics of hydrolysis. (2) Kinetics of ore leaching. (3) Kinetics of metallic iron leaching. (4) Crystallisation of ferrous chloride. (5) Oxidation of anhydrous ferrous chloride. (6) Reduction of ferric chloride. Conceptual designs are suggested fbr both the processes mentioned. These draw attention to areas where further work is necessary, which are listed. Economic analyses have been performed which isolate significant cost areas, und indicate total production costs. Comparisons are mode with previous and analogous proposals for the production of iron powder.

Variational inference for diffusion processes

Diffusion processes are a family of continuous-time continuous-state stochastic processes that are in general only partially observed. The joint estimation of the forcing parameters and the system noise (volatility) in these dynamical systems is a crucial, but non-trivial task, especially when the system is nonlinear and multimodal. We propose a variational treatment of diffusion processes, which allows us to compute type II maximum likelihood estimates of the parameters by simple gradient techniques and which is computationally less demanding than most MCMC approaches. We also show how a cheap estimate of the posterior over the parameters can be constructed based on the variational free energy.

Numerical simulation of corneal transport processes

This paper presents a numerical study on the transport of ions and ionic solution in human corneas and the corresponding influences on corneal hydration. The transport equations for each ionic species and ionic solution within the corneal stroma are derived based on the transport processes developed for electrolytic solutions, whereas the transport across epithelial and endothelial membranes is modelled by using phenomenological equations derived from the thermodynamics of irreversible processes. Numerical examples are provided for both human and rabbit corneas, from which some important features are highlighted.

Optimal design for correlated processes with input-dependent noise

Optimal design for parameter estimation in Gaussian process regression models with input-dependent noise is examined. The motivation stems from the area of computer experiments, where computationally demanding simulators are approximated using Gaussian process emulators to act as statistical surrogates. In the case of stochastic simulators, which produce a random output for a given set of model inputs, repeated evaluations are useful, supporting the use of replicate observations in the experimental design. The findings are also applicable to the wider context of experimental design for Gaussian process regression and kriging. Designs are proposed with the aim of minimising the variance of the Gaussian process parameter estimates. A heteroscedastic Gaussian process model is presented which allows for an experimental design technique based on an extension of Fisher information to heteroscedastic models. It is empirically shown that the error of the approximation of the parameter variance by the inverse of the Fisher information is reduced as the number of replicated points is increased. Through a series of simulation experiments on both synthetic data and a systems biology stochastic simulator, optimal designs with replicate observations are shown to outperform space-filling designs both with and without replicate observations. Guidance is provided on best practice for optimal experimental design for stochastic response models. © 2013 Elsevier Inc. All rights reserved.

Bayesian precalibration of a large stochastic microsimulation model

Calibration of stochastic traffic microsimulation models is a challenging task. This paper proposes a fast iterative probabilistic precalibration framework and demonstrates how it can be successfully applied to a real-world traffic simulation model of a section of the M40 motorway and its surrounding area in the U.K. The efficiency of the method stems from the use of emulators of the stochastic microsimulator, which provides fast surrogates of the traffic model. The use of emulators minimizes the number of microsimulator runs required, and the emulators' probabilistic construction allows for the consideration of the extra uncertainty introduced by the approximation. It is shown that automatic precalibration of this real-world microsimulator, using turn-count observational data, is possible, considering all parameters at once, and that this precalibrated microsimulator improves on the fit to observations compared with the traditional expertly tuned microsimulation. © 2000-2011 IEEE.

On the Structure of Spatial Branching Processes

The paper is a contribution to the theory of branching processes with discrete time and a general phase space in the sense of [2]. We characterize the class of regular, i.e. in a sense sufficiently random, branching processes (Φk) k∈Z by almost sure properties of their realizations without making any assumptions about stationarity or existence of moments. This enables us to classify the clans of (Φk) into the regular part and the completely non-regular part. It turns out that the completely non-regular branching processes are built up from single-line processes, whereas the regular ones are mixtures of left-tail trivial processes with a Poisson family structure.

Discrete Models of Time-Fractional Diffusion in a Potential Well

Mathematics Subject Classification: 26A33, 45K05, 60J60, 60G50, 65N06, 80-99.

Some Properties of Mittag-Leffler Functions and Matrix-Variate Analogues: A Statistical Perspective

Mathematical Subject Classification 2010:26A33, 33E99, 15A52, 62E15.

A Stochastic Approach for Investigation Ultrafast Phenomena in Semiconductors

2002 Mathematics Subject Classification: 65C05

Stability of the Inventory-Backorder Process in the (R; S) Inventory/Production Model

2000 Mathematics Subject Classification: 60G52, 90B30.

A Computational Approach for the Statistical Estimation of Discrete Time Branching Processes with Immigration

2010 Mathematics Subject Classification: 60J80.

Intenzitásalapú modellezés és a mértékcsere (Intensity-based modeling and thje change of measure)

A dolgozatban a hitelderivatívák intenzitásalapú modellezésének néhány kérdését vizsgáljuk meg. Megmutatjuk, hogy alkalmas mértékcserével nemcsak a duplán sztochasztikus folyamatok, hanem tetszőleges intenzitással rendelkező pontfolyamat esetén is kiszámolható az összetett kár- és csődfolyamat eloszlásának Laplace-transzformáltja. _____ The paper addresses questions concerning the use of intensity based modeling in the pricing of credit derivatives. As the specification of the distribution of the lossprocess is a non-trivial exercise, the well-know technique for this task utilizes the inversion of the Laplace-transform. A popular choice for the model is the class of doubly stochastic processes given that their Laplace-transforms can be determined easily. Unfortunately these processes lack several key features supported by the empirical observations, e.g. they cannot replicate the self-exciting nature of defaults. The aim of the paper is to show that by using an appropriate change of measure the Laplace-transform can be calculated not only for a doubly stochastic process, but for an arbitrary point process with intensity as well. To support the application of the technique, we investigate the e®ect of the change of measure on the stochastic nature of the underlying process.