Gottfried Wilhelm Leibniz seiner Zeit weit voraus als Philosoph, Mathematiker, Physiker, Techniker… – ein Extrakt der gleichnamigen Ausstellungen –

Schriftliche Fassung des gleichnamigen Lichtbild-Vortrages vom 07. November 2003 an der Universität Hannover auf Einladung der Präsidenten der Braunschweigischen Wissenschaftlichen Gesellschaft und der Universität Hannove

Convergence behavior of 3D finite elements for Neo-Hookean material

Purpose: The purpose of this paper is to examine quadratic convergence of finite element analysis for hyperelastic material at finite strains via Abaqus-UMAT as well as classification of the rates of convergence for iterative solutions in regular cases. Design/methodology/approach: Different formulations for stiffness - Hessian form of the free energy functionals - are systematically given for getting the rate-independent analytical tangent and the numerical tangent as well as rate-dependent tangents using the objective Jaumann rate of Kirchoff stress tensor as used in Abaqus. The convergence rates for available element types in Abaqus are computed and compared for simple but significant nonlinear elastic problems, such as using the 8-node linear brick (B-bar) element - also with hybrid pressure formulation and with incompatible modes - further the 20-node quadratic brick element with corresponding modifications as well as the 6-node linear triangular prism element and 4-node linear tetrahedral element with modifications. Findings: By using the Jaumann rate of Kirchoff stress tensor for both, rate dependent and rate independent problems, quadratic or nearly quadratic convergence is achieved for most of the used elements using Abaqus-UMAT interface. But in case of using rate independent analytical tangent for rate independent problems, even convergence at all is not assured for all elements and the considered problems. Originality/value: First time the convergence properties of 3D finite elements available in Abaqus sre systematically treated for elastic material at finite strain via Abaqus-UMAT. © Emerald Group Publishing Limited

Propagator of a Charged Particle with a Spin in Uniform Magnetic and Perpendicular Electric Fields

We construct an explicit solution of the Cauchy initial value problem for the time-dependent Schroedinger equation for a charged particle with a spin moving in a uniform magnetic field and a perpendicular electric field varying with time. The corresponding Green function (propagator) is given in terms of elementary functions and certain integrals of the fields with a characteristic function, which should be found as an analytic or numerical solution of the equation of motion for the classical oscillator with a time-dependent frequency. We discuss a particular solution of a related nonlinear Schroedinger equation and some special and limiting cases are outlined.Comment: 17 pages, no figure

Biochemical and Ultrastructural Changes in Tetrahymena pyriformis During Starvation *

Certain of the ultrastructural and biochemical changes occurring during the first 25 hr of starvation in Tetrahymena pyriformis were studied. Ultrastructurally, numerous profiles of degenerating mitochondria were seen in the early stages of starvation. The presence of oxidizable substrate such as glucose and acetate did not prevent this degeneration. Numerous large nucleoli were formed, many of which seemed to be passing into the cytoplasm as forming autophagic vacuoles. There was a transient increase in Oil Red O-positive bodies, presumably lipid (triglycerides). The extent and duration of this increase were pronounced in the presence of acetate. The lipid droplets appeared to arise within the cisternae of the endoplasmic reticulum. Lipid reserves were apparently utilized prior to carbohydrates, as the disappearance of lipid droplets preceded glycogen utilization, both in the presence of acetate and in the absence of exogenous substrate. A considerable loss of cellular protein also occurred. In cells from inorganic medium supplemented with glucose, glycogen occupied much of the cell, leaving only islands of cell organelles. Acid phosphatase was localized, ultrastructurally, mainly in autophagic vacuoles which contained mitochondria and other cell organelles, and in association with small, double-membraned structures which seemed to be sequestering small areas of cytoplasm. Such sequestered areas also appeared within larger autophagic vacuoles. Residual bodies containing concentric whorls of myelin-like membranes surrounding a more solid core accumulated during starvation. Acid phosphatase activity decreased in amount but not in specific activity. The specific activity of cathespin doubled or tripled, but there was little change in total enzyme.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/73300/1/j.1550-7408.1968.tb02113.x.pd

Eosinophilic oesophagitis: clinical presentation and pathogenesis

Eosinophilic oesophagitis (EoE) is an inflammatory disorder of the oesophagus which has become increasingly recognised over recent years, although it remains underdiagnosed in many centres. It is characterised histologically by a significant eosinophilic infiltration of the oesophageal mucosa (>15 eosinophils per high powered field), and clinically with features of oesophageal dysfunction such a dysphagia, food impaction, and proton pump inhibitor (PPI) resistant dyspepsia. Fibrosis and oesophageal remodelling may occur and lead to oesophageal strictures. An allergic predisposition is common in the EoE population, which appears to be primarily food antigen driven in children and aeroallergen driven in adults. Evidence suggests that the pathogenesis of EoE is due to a dysregulated immunological response to an environmental allergen, resulting in a T helper type 2 (Th2) inflammatory disease and remodelling of the oesophagus in genetically susceptible individuals. Allergen elimination and anti-inflammatory therapy with corticosteroids are currently the mainstay of treatment; however, an increasing number of studies are now focused on targeting different stages in the disease pathogenesis. A greater understanding of the underlying mechanisms resulting in EoE will allow us to improve the therapeutic options available