European Numerical Mathematics and
Advanced Applications Conference 2019
30th sep - 4th okt 2019, Egmond aan Zee, The Netherlands
13:30   Mathematical Biology (Part 2)
25 mins
Comparison of the Influence of Conifer and Deciduous Trees on Dust Concentration Emitted From Low-lying Highway by CFD
Ludek Benes
Abstract: The influence of different types of vegetative barriers along a highway notch on dustiness was studied. The mathematical model is based on RANS equations for turbulent fluid flow in Boussinesq approximation completed by the standard k-$\epsilon$ model. Pollutants, considered as passive scalar, were modelled by additional transport equation. Three effects of the vegetation should be considered: effect on the air flow, i.e. slowdown or deflection of the flow, influence on turbulence levels inside and near the vegetation and filtering of the particles present in the flow. Deposition velocity reflects four main processes by which particles depose on the leaves: Brownian diffusion, interception, impaction and gravitational settling. The numerical method is based on finite volume formulation and uses AUSM+up scheme for convective terms. Two fractions of pollutants, PM10 and PM75, emitted from a four--lane highway were numerically simulated. 49 cases of conifer-type forest differing in density, width and height were studied. A new simplified LAD profile for this type of vegetation was developed and tested. Main processes playing role in modelled cases are described. The differences between the conifer and deciduous trees on pollutants deposition were studied.
25 mins
Numerical Analysis for a three interacting species model with chemotaxis
Rafael Ordoñez
Abstract: We study the reaction-diffusion system describing three interacting species in the food chain structure with chemotaxis (diffusion equations). We propose a semi-implicit finite volume scheme for this system, we establish existence and uniqueness of the weak solution and the existence of the discrete solutions, and it also shown that the scheme converges to the corresponding weak solution for the studied model. The convergence proof uses two ingredients of interest for various applications, namely the discrete Sobolev embedding inequalities with the general boundary conditions and a space-time L^1 compactness argument that mimics the compactness lemma due to S.N. Kruzhkov. Finally, we report some numerical tests illustrating the behavior of the solution of the nite volume scheme.
25 mins
The Optimum Control on Cervical Cancer Mathematical Model
Tri Sri Noor Asih, Dwi Rizkiana Dewi, Widodo Widodo, Fajar Adi Kusumo, Lina Aryati
Abstract: The optimum control can be applied into biology problems. In cervical cancer mathematical model, the optimum control representating treatment that applied to the cervical cancer patient. If we devided the cervical cells into sub population of normal cells, infected cells, pre-cancer cells and cancer cells, the control function can be applied into sub population of pre-cancer cells. This is according to the medical research that pre-cancer stage can be regress into infected stage by effective treatment. So we include the control function in pre-cancer stage, find the optimum control by Pontryagin’s Maximum Principle, and made simulation of it. Then we compare the solution of the system between system with optimum control and system without control.
25 mins
Isogeometric Analysis of a Reaction-Diffusion Model for Human Brain Development
Jochen Hinz, Joost van Zwieten, Fred Vermolen, Matthias Moller
Abstract: Neural development has become a topic of growing interest in the past decades. On the one hand healthy adult individuals exhibit qualitatively similar neural structures, on the other hand neural development exhibits a substantial degree of randomness, which is largely confirmed by the observation that even monozygotic twins exhibit significant anatomical differences. Among other factors, this neural ‘fingerprint’ manifests itself mainly through the patterns formed in the neural folding and buckling process occurring naturally after the twentieth week of fetal development. This suggests that environmental factors can have a profound influence on the course of neural development, which in turn suggests that the underlying biological process, mathematically, exhibits a high degree of sensitivity toward perturbations in the initial condition. On the other hand, a proficient model for human brain development should be capable of producing qualitatively similar outcomes for similar setups and explain neural pathologies like lissencephaly and polymicrogyria by quantitatively different starting conditions. The derivation of proficient models for human brain development is greatly hindered by the unethicalness of experimentation on human fetuses. We propose a numerical scheme based on Isogeometric Analysis (IgA) for the development of the geometry of a brain. The development is modelled by the use of the Gray-Scott equations for pattern formation in combination with an equation for the displacement of the brain surface. The method forms an alternative to the classical finite-element method. Our method is based on a partitioning of a sphere into six patches, which are mapped onto the six faces of a cube. Major advantages of the new formalism are the use of a smooth reconstruction of the surface based on the third-order basis functions used for the computation of the concentrations. These features give a smooth representation of the brain surface. Though the third order basis functions outperform lower order basis functions in terms of accuracy, a drawback remains its higher cost of assembly. This drawback is compensated by the need of a lower resolution in case of higher order basis functions.