DSpace Community:https://hdl.handle.net/2440/2992024-05-19T14:58:06Z2024-05-19T14:58:06ZA mathematical model for nutrient–limited uniaxial growth of a compressible tissueLi, K.Gallo, A.J.Binder, B.J.Green, J.E.F.https://hdl.handle.net/2440/1403692024-03-12T12:33:37Z2023-01-01T00:00:00ZTitle: A mathematical model for nutrient–limited uniaxial growth of a compressible tissue
Author: Li, K.; Gallo, A.J.; Binder, B.J.; Green, J.E.F.
Abstract: We consider the uniaxial growth of a tissue or colony of cells, where a nutrient (or some other chemical) required for cell proliferation is supplied at one end, and is consumed by the cells. An example would be the growth of a cylindrical yeast colony in the experiments described by Vulin et al. (2014). We develop a reaction– diffusion model of this scenario which couples nutrient concentration and cell density on a growing domain. A novel element of our model is that the tissue is assumed to be compressible. We define replicative regions, where cells have sufficient nutrient to proliferate, and quiescent regions, where the nutrient level is insufficient for this to occur. We also define pathlines, which allow us to track individual cell paths within the tissue. We begin our investigation of the model by considering an incompressible tissue where cell density is constant before exploring the solution space of the full compressible model. In a large part of the parameter space, the incompressible and compressible models give qualitatively similar results for both the nutrient concentration and cell pathlines, with the key distinction being the variation in density in the compressible case. In particular, the replicative region is located at the base of the tissue, where nutrient is supplied, and nutrient concentration decreases monotonically with distance from the nutrient source. However, for a highly-compressible tissue with small nutrient consumption rate, we observe a counter-intuitive scenario where the nutrient concentration is not necessarily monotonically decreasing, and there can be two replicative regions. For parameter values given in the paper by Vulin et al. (2014), the incompressible model slightly overestimates the colony length compared to experimental observations; this suggests the colony may be somewhat compressible. Both incompressible and compressible models predict that, for these parameter values, cell proliferation is ultimately confined to a small region close to the colony base.2023-01-01T00:00:00ZAn Equation Free algorithm accurately simulates macroscale shocks arising from heterogeneous microscale systemsMaclean, J.Bunder, J.E.Kevrekidis, I.G.Roberts, A.J.https://hdl.handle.net/2440/1400092023-11-29T23:13:51Z2021-01-01T00:00:00ZTitle: An Equation Free algorithm accurately simulates macroscale shocks arising from heterogeneous microscale systems
Author: Maclean, J.; Bunder, J.E.; Kevrekidis, I.G.; Roberts, A.J.
Abstract: Scientists and engineers often create accurate, trustworthy, computational simulation schemes—but all too often these are too computationally expensive to execute over the time or spatial domain of interest. The equation-free approach is to marry such trusted simulations to a framework for numerical macroscale reduction—the patch dynamics scheme. This article extends the patch scheme to scenarios in which the trusted simulation resolves abrupt state changes on the microscale that appear as shocks on the macroscale. Accurate simulation for problems in these scenarios requires capturing the shock within a novel patch, and also modifying the patch coupling rules in the vicinity in order to maintain accuracy. With these two extensions to the patch scheme, straightforward arguments derive consistency conditions that match the usual order of accuracy for patch schemes. The new scheme is successfully tested to simulate a heterogeneous microscale partial differential equation.This technique willempower scientists and engineers to accurately and efficiently simulate, over large spatial domains, multiscale multiphysics systems that have rapid transition layers on the microscale.2021-01-01T00:00:00ZA tale of two vortices: How numerical ergodic theory and transfer operators reveal fundamental changes to coherent structures in non-autonomous dynamical systemsBlachut, C.González-Tokman, C.https://hdl.handle.net/2440/1399692023-11-28T00:09:41Z2020-01-01T00:00:00ZTitle: A tale of two vortices: How numerical ergodic theory and transfer operators reveal fundamental changes to coherent structures in non-autonomous dynamical systems
Author: Blachut, C.; González-Tokman, C.
Abstract: Coherent structures are spatially varying regions which disperse minimally over time and organise motion in non-autonomous systems. This work develops and implements algorithms providing multilayered descriptions of time-dependent systems which are not only useful for locating coherent structures, but also for detecting time windows within which these structures undergo fundamental structural changes, such as merging and splitting events. These algorithms rely on singular value decompositions associated to Ulam type discretisations of transfer operators induced by dynamical systems, and build on recent developments in multiplicative ergodic theory. Furthermore, they allow us to investigate various connections between the evolution of relevant singular value decompositions and dynamical features of the system. The approach is tested on models of periodically and quasi-periodically driven systems, as well as on a geophysical dataset corresponding to the splitting of the Southern Polar Vortex.2020-01-01T00:00:00ZGeometry and holonomy of indecomposable conesAlekseevsky, D.Cortés, V.Leistner, T.https://hdl.handle.net/2440/1398442024-03-24T00:53:40Z2023-01-01T00:00:00ZTitle: Geometry and holonomy of indecomposable cones
Author: Alekseevsky, D.; Cortés, V.; Leistner, T.
Abstract: We study the geometry and holonomy of semi-Riemannian, time-like metric cones that are indecomposable, i.e., which do not admit a local decomposition into a semi-Riemannian product. This includes irreducible cones, for which the holonomy can be classified, as well as non-irreducible cones. The latter admit a parallel distribution of null k-planes, and we study the cases k = 1 in detail. We give structure theorems about the base manifold and in the case when the base manifold is Lorentzian, we derive a description of the cone holonomy. This result is obtained by a computation of certain cocycles of indecomposable subalgebras in so(1,n - 1).2023-01-01T00:00:00Z