New mathematical modeling approach for predicting microbial inactivation by high hydrostatic pressure

A new primary model based on a thermodynamically consistent first-order kinetic approach was constructed to describe non-log-linear inactivation kinetics of pressure-treated bacteria. The model assumes a first-order process in which the specific inactivation rate changes inversely with the square root of time. The model gave reasonable fits to experimental data over six to seven orders of magnitude. It was also tested on 138 published data sets and provided good fits in about 70% of cases in which the shape of the curve followed the typical convex upward form. In the remainder of published examples, curves contained additional shoulder regions or extended tail regions. Curves with shoulders could be accommodated by including an additional time delay parameter and curves with tails shoulders could be accommodated by omitting points in the tail beyond the point at which survival levels remained more or less constant. The model parameters varied regularly with pressure, which may reflect a genuine mechanistic basis for the model. This property also allowed the calculation of (a) parameters analogous to the decimal reduction time D and z, the temperature increase needed to change the D value by a factor of 10, in thermal processing, and hence the processing conditions needed to attain a desired level of inactivation; and (b) the apparent thermodynamic volumes of activation associated with the lethal events. The hypothesis that inactivation rates changed as a function of the square root of time would be consistent with a diffusion-limited process.

The physics of baking: rheological and polymer molecular structure-function relationships in breadmaking

Molecular size and structure of the gluten polymers that make up the major structural components of wheat are related to their rheological properties via modem polymer rheology concepts. Interactions between polymer chain entanglements and branching are seen to be the key mechanisms determining the rheology of HMW polymers. Recent work confirms the observation that dynamic shear plateau modulus is essentially independent of variations in MW amongst wheat varieties of varying baking performance and is not related to variations in baking performance, and that it is not the size of the soluble glutenin polymers, but the structural and rheological properties of the insoluble polymer fraction that are mainly responsible for variations in baking performance. The rheological properties of gas cell walls in bread doughs are considered to be important in relation to their stability and gas retention during proof and baking, in particular their extensional strain hardening properties. Large deformation rheological properties of gas cell walls were measured using biaxial extension for a number of doughs of varying breadmaking quality at constant strain rate and elevated temperatures in the range 25-60 degrees C. Strain hardening and failure strain of cell walls were both seen to decrease with temperature, with cell walls in good breadmaking doughs remaining stable and retaining their strain hardening properties to higher temperatures (60 degrees C), whilst the cell walls of poor breadmaking doughs became unstable at lower temperatures (45-50 degrees C) and had lower strain hardening. Strain hardening measured at 50 degrees C gave good correlations with baking volume, with the best correlations achieved between those rheological measurements and baking tests which used similar mixing conditions. As predicted by the Considere failure criterion, a strain hardening value of I defines a region below which gas cell walls become unstable, and discriminates well between the baking quality of a range of commercial flour blends of varying quality. This indicates that the stability of gas cell walls during baking is strongly related to their strain hardening properties, and that extensional rheological measurements can be used as predictors of baking quality. (C) 2004 Elsevier B.V. All rights reserved.

The physics of baking: rheological and polymer molecular structure-function relationships in breadmaking

Molecular size and structure of the gluten polymers that make up the major structural components of wheat are related to their rheological properties via modern polymer rheology concepts. Interactions between polymer chain entanglements and branching are seen to be the key mechanisms determining the rheology of HMW polymers. Recent work confirms the observation that dynamic shear plateau modulus is essentially independent of variations in MW amongst wheat varieties of varying baking performance and is not related to variations in baking performance, and that it is not the size of the soluble glutenin polymers, but the structural and rheological properties of the insoluble polymer fraction that are mainly responsible for variations in baking performance. The rheological properties of gas cell walls in bread doughs are considered to be important in relation to their stability and gas retention during proof and baking, in particular their extensional strain hardening properties. Large deformation rheological properties of gas cell walls were measured using biaxial extension for a number of doughs of varying breadmaking quality at constant strain rate and elevated temperatures in the range 25oC to 60oC. Strain hardening and failure strain of cell walls were both seen to decrease with temperature, with cell walls in good breadmaking doughs remaining stable and retaining their strain hardening properties to higher temperatures (60oC), whilst the cell walls of poor breadmaking doughs became unstable at lower temperatures (45oC to 50oC) and had lower strain hardening. Strain hardening measured at 50oC gave good correlations with baking volume, with the best correlations achieved between those rheological measurements and baking tests which used similar mixing conditions. As predicted by the Considere failure criterion, a strain hardening value of 1 defines a region below which gas cell walls become unstable, and discriminates well between the baking quality of a range of commercial flour blends of varying quality. This indicates that the stability of gas cell walls during baking is strongly related to their strain hardening properties, and that extensional rheological measurements can be used as predictors of baking quality.

Modelling oil absorption during post-frying cooling - II: solution of the mathematical model, model testing and simulations

The mathematical models that describe the immersion-frying period and the post-frying cooling period of an infinite slab or an infinite cylinder were solved and tested. Results were successfully compared with those found in the literature or obtained experimentally, and were discussed in terms of the hypotheses and simplifications made. The models were used as the basis of a sensitivity analysis. Simulations showed that a decrease in slab thickness and core heat capacity resulted in faster crust development. On the other hand, an increase in oil temperature and boiling heat transfer coefficient between the oil and the surface of the food accelerated crust formation. The model for oil absorption during cooling was analysed using the tested post-frying cooling equation to determine the moment in which a positive pressure driving force, allowing oil suction within the pore, originated. It was found that as crust layer thickness, pore radius and ambient temperature decreased so did the time needed to start the absorption. On the other hand, as the effective convective heat transfer coefficient between the air and the surface of the slab increased the required cooling time decreased. In addition, it was found that the time needed to allow oil absorption during cooling was extremely sensitive to pore radius, indicating the importance of an accurate pore size determination in future studies.

Towards a unifying framework for pattern transformation in swarm systems

This paper identifies the major challenges in the area of pattern formation. The work is also motivated by the need for development of a single framework to surmount these challenges. A framework based on the control of macroscopic parameters is proposed. The issue of transformation of patterns is specifically considered. A definition for transformation and four special cases, namely elementary and geometrical transformations by repositioning all or some robots in the pattern are provided. Two feasible tools for pattern transformation namely, a macroscopic parameter method and a mathematical tool - Moebius transformation also known as the linear fractional transformation are introduced. The realization of the unifying framework considering planning and communication is reported.

Swarm pattern transformation methodologies

The work reported in this paper is motivated by the need for developing swarm pattern transformation methodologies. Two methods, namely a macroscopic method and a mathematical method are investigated for pattern transformation. The first method is based on macroscopic parameters while the second method is based on both microscopic and macroscopic parameters. A formal definition to pattern transformation considering four special cases of transformation is presented. Simulations on a physics simulation engine are used to confirm the feasibility of the proposed transformation methods. A brief comparison between the two methods is also presented.

Perspex machine IX: transreal analysis

We introduce transreal analysis as a generalisation of real analysis. We find that the generalisation of the real exponential and logarithmic functions is well defined for all transreal numbers. Hence, we derive well defined values of all transreal powers of all non-negative transreal numbers. In particular, we find a well defined value for zero to the power of zero. We also note that the computation of products via the transreal logarithm is identical to the transreal product, as expected. We then generalise all of the common, real, trigonometric functions to transreal functions and show that transreal (sin x)/x is well defined everywhere. This raises the possibility that transreal analysis is total, in other words, that every function and every limit is everywhere well defined. If so, transreal analysis should be an adequate mathematical basis for analysing the perspex machine - a theoretical, super-Turing machine that operates on a total geometry. We go on to dispel all of the standard counter "proofs" that purport to show that division by zero is impossible. This is done simply by carrying the proof through in transreal arithmetic or transreal analysis. We find that either the supposed counter proof has no content or else that it supports the contention that division by zero is possible. The supposed counter proofs rely on extending the standard systems in arbitrary and inconsistent ways and then showing, tautologously, that the chosen extensions are not consistent. This shows only that the chosen extensions are inconsistent and does not bear on the question of whether division by zero is logically possible. By contrast, transreal arithmetic is total and consistent so it defeats any possible "straw man" argument. Finally, we show how to arrange that a function has finite or else unmeasurable (nullity) values, but no infinite values. This arithmetical arrangement might prove useful in mathematical physics because it outlaws naked singularities in all equations.

Investigating feasible tools for swarm pattern transformation

Abstract-The work reported in this paper is motivated by the need for developing swarm pattern transformation methodologies. Two methods, namely a macroscopic method and a mathematical method are investigated for pattern transformation. The first method is based on macroscopic parameters while the second method is based on both microscopic and macroscopic parameters. A formal definition to pattern transformation considering four special cases of transformation is presented. Simulations on a physics simulation engine are used to confirm the feasibility of the proposed transformation methods. A brief comparison between the two methods is also presented.

A review and implementation of swarm pattern formation and transformation models

Purpose: The purpose of this paper is to address a classic problem – pattern formation identified by researchers in the area of swarm robotic systems – and is also motivated by the need for mathematical foundations in swarm systems. Design/methodology/approach: The work is separated out as inspirations, applications, definitions, challenges and classifications of pattern formation in swarm systems based on recent literature. Further, the work proposes a mathematical model for swarm pattern formation and transformation. Findings: A swarm pattern formation model based on mathematical foundations and macroscopic primitives is proposed. A formal definition for swarm pattern transformation and four special cases of transformation are introduced. Two general methods for transforming patterns are investigated and a comparison of the two methods is presented. The validity of the proposed models, and the feasibility of the methods investigated are confirmed on the Traer Physics and Processing environment. Originality/value: This paper helps in understanding the limitations of existing research in pattern formation and the lack of mathematical foundations for swarm systems. The mathematical model and transformation methods introduce two key concepts, namely macroscopic primitives and a mathematical model. The exercise of implementing the proposed models on physics simulator is novel.

Mathematical modelling for the digital society

We argue the case for a new branch of mathematics and its applications: Mathematics for the Digital Society. There is a challenge for mathematics, a strong “pull” from new and emerging commercial and public activities; and a need to train and inspire a generation of quantitative scientists who will seek careers within the associated sectors. Although now going through an early phase of boiling up, prior to scholarly distillation, we discuss how data rich activities and applications may benefit from a wide range of continuous and discrete models, methods, analysis and inference. In ten years time such applications will be common place and associated courses may be embedded within the undergraduate curriculum.

A mathematical model, implementation and study of a swarm system

The work reported in this paper is motivated towards the development of a mathematical model for swarm systems based on macroscopic primitives. A pattern formation and transformation model is proposed. The pattern transformation model comprises two general methods for pattern transformation, namely a macroscopic transformation method and a mathematical transformation method. The problem of transformation is formally expressed and four special cases of transformation are considered. Simulations to confirm the feasibility of the proposed models and transformation methods are presented. Comparison between the two transformation methods is also reported.