Bifurcation analysis of a model for atherosclerotic plaque evolution

We analyze two ordinary differential equation (ODE) models for atherosclerosis. The ODE models describe long time evolution of plaques in arteries. We show how the dynamics of the first atherosclerosis model (model A) can be understood using codimension-two bifurcation analysis. The Low-Density Lipoprotein (LDL) intake parameter (dd) is the first control parameter and the second control parameter is either taken to be the conversion rate of macrophages (bb) or the wall shear stress (σσ). Our analysis reveals that in both cases a Bogdanov-Takens (BT) point acts as an organizing center. The bifurcation diagrams are calculated partly analytically and to a large extent numerically using AUTO07 and MATCONT. The bifurcation curves show that the concentration of LDL in the plaque as well as the monocyte and the macrophage concentration exhibit oscillations for a certain range of values of the control parameters. Moreover, we find that there are threshold values for both the cholesterol intake rate dcritdcrit and the conversion rate of the macrophages bcritbcrit, which depend on the values of other parameters, above which the plaque volume increases with time. It is found that larger conversion rates of macrophages lower the threshold value of cholesterol intake and vice versa. We further argue that the dynamics for model A can still be discerned in the second model (model B) in which the slow evolution of the radius of the artery is coupled self-consistently to changes in the plaque volume. The very slow evolution of the radius of the artery compared to the other processes makes it possible to use a slow manifold approximation to study the dynamics in this case. We find that in this case the model predicts that the concentrations of the plaque constituents may go through a period of oscillations before the radius of the artery will start to decrease. These oscillations hence act as a precursor for the reduction of the artery radius by plaque growth

Stress distribution during neck formation : an approximate theory

In this paper we investigate the effects of deformation of a metal specimen, which is either a plate or a cylindrical rod in our case. In particular we study neck formation in tensile loading of a plastic metal. We try to generalize the work of Bridgman, who considered a purely two-dimensional geometry, to an effective theory that takes into account some essential three dimensional characteristics. That extending the description of neck formation to three dimensions is necessary was illustrated by recent experimental findings of [1]. We have studied existing models from the literature that describe necking for plates and cylinders to identify the consequences of the crucial assumption of uniform in-plane stress. We also developed a new model that we have not yet been able to analyze. Finally, using work of [4] in which a power law relation between the von Mises stress and the effective strain is used, a perturbation analysis for a simple flat geometry was performed. The perturbation analysis offers a good starting point for generalizing the work of Bridgman to three dimensions. Keywords: Neck formation, von Mises stress, tensile pulling, plane stress assumptio

The distributed ASCI supercomputer project

The Distributed ASCI Supercomputer (DAS) is a homogeneous wide-area distributed system consisting of four cluster computers at different locations. DAS has been used for research on communication software, parallel languages and programming systems, schedulers, parallel applications, and distributed applications. The paper gives a preview of the most interesting research results obtained so far in the DAS project

Dynamica van zelfassemblerende polymeren

Zelfassemblage is een methode die de natuur gebruikt om grotere structuren samen te stellen uit kleinere eenheden. Hierbij worden moleculen op een omkeerbare manier georganiseerd tot een zogeheten supramoleculaire structuur die is opgebouwd met niet-covalente bindingen. Deze bindingen kunnen relatief gemakkelijk worden gecreëerd of verbroken door een kleine verandering van de temperatuur of de zoutconcentratie van de oplossing waarin de zelfassemblage plaatsvindt. De statica van zelfassemblage is inmiddels voor een groot deel begrepen, maar van de dynamica van zelfassemblage is nog veel onbekend. Deze dynamica zal ik hier bespreken

Stress Relaxation of Star-Shaped Molecules in a Polymer Melt.

We present a theoretical study of stress relaxation of star-shaped polymers starting from a Rouse model for a polymer in a tube. Instead of focusing on the potential in which the chain moves, we mathematically study the Rouse equation with a time-dependent boundary condition. This boundary condition arises as a consequence of tube dilution, which is implemented in the model through a tube diameter that increases with time, depending on position along the tube. We derive a Fokker-Planck equation for the probability distribution of the position of the chain end and find an analytical expression for the mean first passage time. Our approach helps identifying the origin of the potentials, which are commonly used in existing models for stress relaxation in star polymers. Moreover, it clearly displays the underlying approximations and allows easy generalization to the case of a tethered chain in a flow