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There is an increased focus worldwide on understanding and modeling rolling resistance because reducing the rolling resistance by just a few percent will lead to substantial energy savings. This paper reviews the state of the art of rolling resistance research, focusing on measuring techniques, surface and texture modeling, contact models, tire models, and macro-modeling of rolling resistance.

Small‐angle X‐ray scattering (SAXS) patterns are calculated from a three‐dimensional model of photosynthetic thylakoid membranes. The intricate structure of the thylakoids is represented by sampling random `electron density points' on geometric surfaces. The simulation setup works as a virtual instrument, allowing direct comparison with experimental data. The simulations qualitatively reproduce experimental data and thus clarify the structural origin of the scattering features. This is used to explain recent SAXS measurements and as a guideline for new experiments and future quantitative modeling. The setup has general applicability for model testing purposes when modeling scattering from membrane systems of complex geometries.

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Aside from the obvious statement that it should be a theory capable of unifying all our knowledge about insulin secretion, in both health and disease, not much is known about a systems biology of regulated exocytosis in pancreatic β-cells. Let us recall common knowledge: Patients with diabetes suffer from an absolute or relative lack of the hormone insulin. Insulin is produced by pancreatic β-cells and secreted by regulated exocytosis. In type 1 diabetes (juvenile diabetes) β-cells are destroyed by autoimmune mechanisms. In type 2 diabetes, and pre-diabetic states, we observe a decline in β-cell function. There has been a great deal of experimental work over the last 50 years, and a fair amount of mathematical modelling since the 1980s, but the systems biology approach is new and not fully developed. Genome-wide scans for diabetes genes have pointed to promising candidates involved in β-cell function, raising the importance of systems issues to a new level. This book gives a snapshot of the field at the threshold of a possible explosion in knowledge. We introduce recent advances in observational techniques, ranging from genetic epidemiology via proteomics to multi-parameter cell sensoring, MRI, ET and nanoparticle-based cell imaging. We summarize what these techniques have revealed regarding β-cell function: the generation of huge new data sets, dealing with ions, DNA, proteins, electrical phenomena, cell membranes, cell organelles and tissue, in extreme spatial and temporal scales from Ångström to micrometres and from picoseconds to minutes and hours. Because it is an exciting area of research, there are many new ideas about the systems biology of insulin secretion, but they often diverge to such an incredible degree that it seems impossible to decide which of the many possible directions one should pursue. The division of the text into five overlapping parts reflects the duality between the medical pull and the technological push originating from model-based measurements and mathematical modelling, estimation, control and simulation: The clinical and pharmaceutical need of a systems biology approach is to go beyond umbrella diagnosis and solely symptomatic non-individualized treatment-by distinguishing different levels and different traits of functioning within a comprehensive picture of the disease(s). The technological push towards systems biology is based on the v vi Preface design and use of the so-called mathematical microscope. By that term we denote general and/or specific mathematical methods to:

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