Solution of porous medium type systems by linear approximation schemes

Summary The convergence of semi-discrete and discrete linear approximation schemes is analysed for nonlinear degenerate parabolic systems of porous medium type. The enthalpy formulation and variational technique are used. The semi-discretization used reduces the original parabolic P.D.E. to linear elliptic P.D.E. The algebraic correction arising from nonlinearities is treated by Newton-like iterations in finite steps. Some numerical experiments are discussed and compared with the analytical solutions.Supported by the Alexander von Humboldt-Foundation in 1989, and by SFB 123, University Heidelberg     

Laser Microbeams and Optical Tweezers in Ageing Research

We show how a technique developed within the framework of physics and physical chemistry—in a true interdisciplinary approach—can answer questions in life sciences that are not solvable by using other techniques. Herein, we focus on blood‐pressure regulation and DNA repair in ageing studies. Laser microbeams and optical tweezers are now established tools in many fields of science, particularly in the life sciences. A short glimpse is given on the wide field of non‐age‐research applications in life sciences. Then, optical tweezers are used to show that exerting a vertical pressure on cells representing the inner lining of blood vessels results in bursts of NO liberation concomitant with large changes in cell morphology. Repeated treatment of such human umbilical vein endothelial cells (HUVEC) results in stiffening, a hallmark of manifest high blood pressure, a disease primarily of the elderly. As a second application in ageing research, a laser microbeam is used to induce, with high spatial and temporal resolution, DNA damages in the nuclei of U2OS human osteosarcoma cells. A pairwise study of the recruitment kinetics of different DNA repair proteins reveals that DNA repair starts with non‐homologous end joining (NHEJ), a repair pathway, and may only after several minutes switch to the error‐free homologous recombination repair (HRR) pathway. Since DNA damages—when incorrectly repaired—accumulate with time, laser microbeams are becoming well‐used tools in ageing research.     

Self-similar properties of collisions between light nuclei

A new way of representing data on the fragmentation of nuclei is suggested. The self-similar behavior of these processes, that is dictated by their kinematics, is demonstrated. The convenience of working in accelerated nuclei is emphasized, particularly for the determination of the binding energy of a wide class of nuclear fragments.     

Quasi-contraction on a cone metric space

In this work we define and study quasi-contraction on a cone metric space. For such a mapping we prove a fixed point theorem. Among other things, we generalize a recent result of H. L. Guang and Z. Xian, and the main result of ?iri? is also recovered.     

The effect of polyethylene addition on the morphology of polystyrene/polyamide blends

The effect of a small admixture of high‐density polyethylene (HDPE) with a high or low viscosity to polystyrene/polyamide (PS/PA) blends of various compositions was studied. PS/PA blends with composition near 50/50 form sheet‐like or fiber‐like morphology at mixing that passes to the cocontinuous structure during compression molding. Ternary PS/PA/HDPE blends with PS/PA ratio about 50/50 show similar behavior. Generally, neither continuity nor shape of PS and PA phases was changed qualitatively by the addition of a small amount of HDPE. In agreement with existing rules for ternary blends, HDPE particles prefer a contact with PS phase to PA phase. On the other hand, none of these rules explains why a number of small HDPE subinclusions were dispersed into PS particles instead of HDPE‐PS core‐shell structure with a lower Gibbs free energy. Quantitative evaluation of the size of PA particles in blends with PS matrix showed that the previously proposed rule stating, that the addition of a small amount of a third immiscible component leads to a strong decrease in the size of dispersed particles, was not valid for the blends studied in this work. © 2009 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 47: 2158–2170, 2009     

Certain Liouville series

Abstract The main results of this paper give two criteria for certain infinite series of rational numbers to be Liouville. Some examples are also included. Keywords: Liouville numbers, Infinite series Mathematics Subject Classification (2000): 11J82     

Reinstallation of the COMPASS-D tokamak in IPP ASCR

The COMPASS-D tokamak, originally operated by UKAEA at Culham, UK, will be reinstalled at the Institute of Plasma Physics (IPP) AS CR. The COMPASS device was designed as a flexible tokamak in the 1980s mainly to explore the MHD physics. Its operation (with D-shaped vessel) began at the Culham Laboratory of the Association EURATOM/ UKAEA in 1992.The COMPASS-D tokamak will have the following unique features after putting in operation on IPP Prague. It will be the smallest tokamak with a clear H-mode and ITER-relevant geometry. ITER-relevant plasma conditions will be achieved by installation of two neutral beam injection systems (2 × 300 kW), enabling co-and counter-injections. Redeployment of the existing LH system (400 kW) is also envisaged. A comprehensive set of diagnostics focused mainly on the edge plasma will be installed.The scientific programme proposed for the COMPASS-D tokamak installed in IPP Prague will benefit from these unique features of COMPASS-D and consist of two main scientific projects, both highly relevant to ITER-Edge plasma physics (H-mode studies) and Wave-plasma interaction studies.The COMPASS-D tokamak will offer an important research potential as a small, flexible and low-cost facility with ITER-relevant geometry.