7 results on '"Burrage, Pamela"'
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2. The reflectionless properties of Toeplitz waves and Hankel waves: An analysis via Bessel functions.
- Author
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Burrage, Kevin, Burrage, Pamela, and MacNamara, Shev
- Subjects
- *
BESSEL functions , *WAVE analysis , *TOEPLITZ matrices , *HANKEL functions , *MATRIX functions , *WAVE equation - Abstract
We study reflectionless properties at the boundary for the wave equation in one space dimension and time, in terms of a well-known matrix that arises from a simple discretisation of space. It is known that all matrix functions of the familiar second difference matrix representing the Laplacian in this setting are the sum of a Toeplitz matrix and a Hankel matrix. The solution to the wave equation is one such matrix function. Here, we study the behaviour of the corresponding waves that we call Toeplitz waves and Hankel waves. We show that these waves can be written as certain linear combinations of even Bessel functions of the first kind. We find exact and explicit formulae for these waves. We also show that the Toeplitz and Hankel waves are reflectionless on even, respectively odd, traversals of the domain. Our analysis naturally suggests a new method of computer simulation that allows control, so that it is possible to choose — in advance — the number of reflections. An attractive result that comes out of our analysis is the appearance of the well-known shift matrix, and also other matrices that might be thought of as Hankel versions of the shift matrix. By revealing the algebraic structure of the solution in terms of shift matrices, we make it clear how the Toeplitz and Hankel waves are indeed reflectionless at the boundary on even or odd traversals. Although the subject of the reflectionless boundary condition has a long history, we believe the point of view that we adopt here in terms of matrix functions is new. [ABSTRACT FROM AUTHOR]
- Published
- 2021
- Full Text
- View/download PDF
3. Stochastic delay differential equations for genetic regulatory networks
- Author
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Tian, Tianhai, Burrage, Kevin, Burrage, Pamela M., and Carletti, Margherita
- Subjects
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GENETIC regulation , *BIOCHEMICAL engineering , *STOCHASTIC analysis , *DIFFERENTIAL equations - Abstract
Abstract: Time delay is an important aspect in the modelling of genetic regulation due to slow biochemical reactions such as gene transcription and translation, and protein diffusion between the cytosol and nucleus. In this paper we introduce a general mathematical formalism via stochastic delay differential equations for describing time delays in genetic regulatory networks. Based on recent developments with the delay stochastic simulation algorithm, the delay chemical master equation and the delay reaction rate equation are developed for describing biological reactions with time delay, which leads to stochastic delay differential equations derived from the Langevin approach. Two simple genetic regulatory networks are used to study the impact of intrinsic noise on the system dynamics where there are delays. [Copyright &y& Elsevier]
- Published
- 2007
- Full Text
- View/download PDF
4. A multi-scaled approach for simulating chemical reaction systems
- Author
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Burrage, Kevin, Tian, Tianhai, and Burrage, Pamela
- Subjects
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CHEMICAL reactions , *PROTEINS , *MOLECULES , *BIOCHEMISTRY - Abstract
In this paper we give an overview of some very recent work, as well as presenting a new approach, on the stochastic simulation of multi-scaled systems involving chemical reactions. In many biological systems (such as genetic regulation and cellular dynamics) there is a mix between small numbers of key regulatory proteins, and medium and large numbers of molecules. In addition, it is important to be able to follow the trajectories of individual molecules by taking proper account of the randomness inherent in such a system. We describe different types of simulation techniques (including the stochastic simulation algorithm, Poisson Runge–Kutta methods and the balanced Euler method) for treating simulations in the three different reaction regimes: slow, medium and fast. We then review some recent techniques on the treatment of coupled slow and fast reactions for stochastic chemical kinetics and present a new approach which couples the three regimes mentioned above. We then apply this approach to a biologically inspired problem involving the expression and activity of LacZ and LacY proteins in E. coli, and conclude with a discussion on the significance of this work. [Copyright &y& Elsevier]
- Published
- 2004
- Full Text
- View/download PDF
5. Using population of models to investigate and quantify gas production in a spatially heterogeneous coal seam gas field.
- Author
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Psaltis, Steven, Farrell, Troy, Burrage, Kevin, Burrage, Pamela, McCabe, Peter, Moroney, Timothy, Turner, Ian, Mazumder, Saikat, and Bednarz, Tomasz
- Subjects
- *
COALBED methane , *MULTIPHASE flow , *STATISTICAL correlation , *COMBINATORICS , *HYPERCUBES - Abstract
In this work, we discuss the use of a local model developed previously [1] that describes the multiphase flow of gaseous species and liquid water within a single coal seam to investigate the gas production from a spatially heterogeneous production field. The field is located within the Surat Basin in Queensland, and is composed of a total of 80 production wells spread over a region covering approximately 36 km 2 . However, not every well is producing gas at any one time and so in this work we take a subset of 42 wells that are the top-producing wells in terms of total gas volume. We utilise a population of models approach to understand the variability in the underlying physical processes, and as a mechanism for dealing with the spatial heterogeneity that arises due to geological variation across the field. We are able to simultaneously obtain a family of parameter sets for each of these wells, in which each set in the family yields a predicted cumulative total gas production curve that matches the measured cumulative production curve for a given well to within an allowable limit of error. By analysing the results of this population of models approach we can identify the similarities between wells based on the parameter distributions, and understand the sensitivity of key model parameters. We show by example that high correlation between wells based on their parameter values may be an indicator of their similarity. A combinatorial sum of the predicted gas production is compared against the individual gas volumes (given in terms of percentage of the total volume) measured at the compression facility as a way of further calibrating a subpopulation of models. [ABSTRACT FROM AUTHOR]
- Published
- 2017
- Full Text
- View/download PDF
6. Mathematical modelling of gas production and compositional shift of a CSG (coal seam gas) field: Local model development.
- Author
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Psaltis, Steven, Farrell, Troy, Burrage, Kevin, Burrage, Pamela, McCabe, Peter, Moroney, Timothy, Turner, Ian, and Mazumder, Saikat
- Subjects
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GAS producing machines , *COALBED methane , *GAS absorption & adsorption , *CARBON dioxide , *WATER , *MATHEMATICAL models - Abstract
In this work we discuss the development of a mathematical model to predict the shift in gas composition observed over time from a producing CSG (coal seam gas) well, and investigate the effect that physical properties of the coal seam have on gas production. A detailed (local) one-dimensional, two-scale mathematical model of a coal seam has been developed. The model describes the competitive adsorption and desorption of three gas species (CH 4 , CO 2 and N 2 ) within a microscopic, porous coal matrix structure. The (diffusive) flux of these gases between the coal matrices (microscale) and a cleat network (macroscale) is accounted for in the model. The cleat network is modelled as a one-dimensional, volume averaged, porous domain that extends radially from a central well. Diffusive and advective transport of the gases occurs within the cleat network, which also contains liquid water that can be advectively transported. The water and gas phases are assumed to be immiscible. The driving force for the advection in the gas and liquid phases is taken to be a pressure gradient with capillarity also accounted for. In addition, the relative permeabilities of the water and gas phases are considered as functions of the degree of water saturation. [ABSTRACT FROM AUTHOR]
- Published
- 2015
- Full Text
- View/download PDF
7. Homogenisation for the monodomain model in the presence of microscopic fibrotic structures.
- Author
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Lawson, Brodie A.J., dos Santos, Rodrigo Weber, Turner, Ian W., Bueno-Orovio, Alfonso, Burrage, Pamela, and Burrage, Kevin
- Subjects
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HEART fibrosis , *SPATIAL resolution , *FIBROSIS , *ELECTROPHYSIOLOGY - Abstract
Computational models in cardiac electrophysiology are notorious for long runtimes, restricting the numbers of nodes and mesh elements in the numerical discretisations used for their solution. This makes it particularly challenging to incorporate structural heterogeneities on small spatial scales, preventing a full understanding of the critical arrhythmogenic effects of conditions such as cardiac fibrosis. In this work, we explore the technique of homogenisation by volume averaging for the inclusion of non-conductive micro-structures into larger-scale cardiac meshes with minor computational overhead. Importantly, our approach is not restricted to periodic patterns, enabling homogenised models to represent, for example, the intricate patterns of collagen deposition present in different types of fibrosis. We first highlight the importance of appropriate boundary condition choice for the closure problems that define the parameters of homogenised models. Then, we demonstrate the technique's ability to correctly upscale the effects of fibrotic patterns with a spatial resolution of 10 µm into much larger numerical mesh sizes of 100- 250 µm. The homogenised models using these coarser meshes correctly predict critical pro-arrhythmic effects of fibrosis, including slowed conduction, source/sink mismatch, and stabilisation of re-entrant activation patterns. As such, this approach to homogenisation represents a significant step towards whole organ simulations that unravel the effects of microscopic cardiac tissue heterogeneities. • Upscaling for feasible simulation of microscale fibrosis in cardiac electrophysiology • Practical consideration of upscaling for dynamics of sharp-fronted travelling waves • Demonstrated recovery of pro-arrhythmic effects of fibrosis in upscaled models • Selection of boundary conditions to balance numerical and upscaling errors • Significant speed-up for monodomain model simulation in the presence of microfibrosis [ABSTRACT FROM AUTHOR]
- Published
- 2023
- Full Text
- View/download PDF
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