A FEM-Multigrid Scheme for Elliptic Nash-Equilibrium Multiobjective Optimal Control Problems

A finite-element multigrid scheme for elliptic Nash-equilibrium multiobjective optimal control problems with control constraints is investigated. The multigrid computational framework implements a nonlinear multigrid strategy with collective smoothing for solving the multiobjective optimality system discretized with finite elements. Error estimates for the optimal solution and two-grid local Fourier analysis of the multigrid scheme are presented. Results of numerical experiments are presented to demonstrate the effectiveness of the proposed framework.     

Multigrid Solution of a Lavrentiev-Regularized State-Constrained Parabolic Control Problem

A mesh-independent, robust, and accurate multigrid scheme to solve a linear state-constrained parabolic optimal control problem is presented. We first consider a Lavrentiev regularization of the state-constrained optimization problem. Then, a multigrid scheme is designed for the numerical solution of the regularized optimality system. Central to this scheme is the construction of an iterative pointwise smoother which can be formulated as a local semismooth Newton iteration. Results of numerical experiments and theoretical two-grid local Fourier analysis estimates demonstrate that the proposed scheme is able to solve parabolic state-constrained optimality systems with textbook multigrid efficiency.     

A poroplastic model of structural reorganisation in porous media of biomechanical interest

We present a poroplastic model of structural reorganisation in a binary mixture comprising a solid and a fluid phase. The solid phase is the macroscopic representation of a deformable porous medium, which exemplifies the matrix of a biological system (consisting e.g. of cells, extracellular matrix, collagen fibres). The fluid occupies the interstices of the porous medium and is allowed to move throughout it. The system reorganises its internal structure in response to mechanical stimuli. Such structural reorganisation, referred to as remodelling, is described in terms of “plastic” distortions, whose evolution is assumed to obey a phenomenological flow rule driven by stress. We study the influence of remodelling on the mechanical and hydraulic behaviour of the system, showing how the plastic distortions modulate the flow pattern of the fluid, and the distributions of pressure and stress inside it. To accomplish this task, we solve a highly nonlinear set of model equations by elaborating a previously developed numerical procedure, which is implemented in a non-commercial finite element solver.     

Mean exposure fractions of human body solar UV exposure patterns for application in different ambient climates

In this research, the erythemally effective UV measured using miniaturized polysulphone dosimeters to over 1250 individual body sites and collected over a 4-year period is presented relative to the total exposed skin surface area (SSA) of a life-size manikin model. A new term is also introduced, the mean exposure fraction (MEF). The MEF is used to weight modeled or measured horizontal plane UV exposures to the total unprotected SSA of an individual and is defined as the ratio of exposure per unit area received by the unprotected skin surfaces of the body relative to the exposure received on a horizontal plane. The MEF has been calculated for a range of solar zenith angles (SZA) to provide a sunburning energy data set weighted to the actual SSA of a typically clothed individual. For this research, the MEF was determined as 0.15, 0.26 and 0.41 in the SZA ranges 0°-30°, 30°-50° and 50°-80° providing information that can be used in a variety of different ambient, latitudinal and seasonal climates where total human body UV exposure information is not available.     

On the convergence of the MG/OPT method

Global convergence of the MG/OPT method for optimization is discussed. (© 2005 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Posture as a chaotic system and an application to the Parkinson’s disease

In this work we investigate and compare a number of time series of stabilograms of healthy subjects and Parkinsonians. This is carried out by means of the chaos paradigm through the preliminary computation of the first minimum of the mutual information function and the embedding dimension (using false nearest neighbours) in order to obtain the correlation dimension as well as the largest Lyapunov exponent. We show that the postural act is indeed chaotic and especially that the latter two parameters do not allow to discriminate healthy subjects from parkinsonians. Moreover we report a discrepancy of our values with those found in previous works.     

Personal solar UV exposure measurements employing modified polysulphone with an extended dynamic range

Polysulphone dosimeters using a simple to use filter have been developed and tested to provide an extended dynamic measurement range of personal solar UV exposures over an extended period (3 to 6 days). At a Southern Hemisphere subtropical site (27.6 degrees S, 151.9 degrees E), the dynamic range of the filtered polysulphone allowed measurements of erythemal exposures to approximately 100 minimum erythemal dose (MED) for a change in optical absorbance at 330 nm (deltaA330) of 0.35. In comparison, unfiltered polysulphone dosimeters were exposed to approximately 8 MED for the same deltaA330. The error associated with the use of the filtered polysulphone dosimeters is of the order of +/-15%, compared with +/-10% of the unfiltered variety. The developed filtered polysulphone dosimeter system allowed the measurement of erythemal UV exposures over 3 to 6 days at a subtropical site without the need to replace the dosimeters because of saturation. The results show that longer-term measurement programs of personal solar UV have been made more feasible with the use of these polysulphone dosimeters with an extended dynamic range compared with unfiltered polysulphone dosimeters.     

Numerical simulation of orbitally shaken viscous fluids with free surface

Orbitally shaken bioreactors are an emerging alternative to stirred‐tank bioreactors for large‐scale mammalian cell culture, but their fluid dynamics is still not well defined. Among the theoretical and practical issues that remain to be resolved, the characterization of the liquid free surface during orbital shaking remains a major challenge because it is an essential aspect of gas transfer and mixing in these reactors. To simulate the fluid behavior and the free surface shape, we developed a numerical method based on the finite element framework. We found that the large density ratio between the liquid and the gas phases induced unphysical results for the free surface shape. We therefore devised a new pressure correction scheme to deal with large density ratios. The simulations operated with this new scheme gave values of wave amplitude similar to the ones measured experimentally. These simulations were used to calculate the shear stress and to study the mixing principle in orbitally shaken bioreactors. Copyright © 2012 John Wiley & Sons, Ltd.