High-order centered difference methods with sharp shock resolution

In this paper we consider high-order centered finite difference approximations of hyperbolic conservation laws. We propose different ways of adding artificial viscosity to obtain sharp shock resolution. For the Riemann problem we give simple explicit formulas for obtaining stationary one and two-point shocks. This can be done for any order of accuracy. It is shown that the addition of artificial viscosity is equivalent to ensuring the Lax k-shock condition. We also show numerical experiments that verify the theoretical results

Fourth order difference methods for hyperbolic IBVP's

Fourth order difference approximations of initial-boundary value problems for hyperbolic partial differential equations are considered. We use the method of lines approach with both explicit and compact implicit difference operators in space. The explicit operator satisfies an energy estimate leading to strict stability. For the implicit operator we develop boundary conditions and give a complete proof of strong stability using the Laplace transform technique. We also present numerical experiments for the linear advection equation and Burgers' equation with discontinuities in the solution or in its derivative. The first equation is used for modeling contact discontinuities in fluid dynamics, the second one for modeling shocks and rarefaction waves. The time discretization is done with a third order Runge-Kutta TVD method. For solutions with discontinuities in the solution itself we add a filter based on second order viscosity. In case of the non-linear Burger's equation we use a flux splitting technique that results in an energy estimate for certain different approximations, in which case also an entropy condition is fulfilled. In particular we shall demonstrate that the unsplit conservative form produces a non-physical shock instead of the physically correct rarefaction wave. In the numerical experiments we compare our fourth order methods with a standard second order one and with a third order TVD-method. The results show that the fourth order methods are the only ones that give good results for all the considered test problems

Lärande i ljuset av kunskapens användning

Bidraget vill påvisa vikten av arbetsintegrerat lärande. Detta görs genom att redovisa resultat från en kurs på masternivå som använder pedagogiken genom att blanda det industribaserade projektarbetets pedagogik med universitetets teoretiska bas så att studenterna förstår sambandet mellan teori och praktik och får öva sin analytiska och logiska problemlösningsförmåga

Non Destructive Detection of Decay in Living Trees

It is shown that four point resistivity measurements can be used to detect decay in living trees. A low frequency alternating current is injected into the trunk and the induced voltage is measured between two points along the trunk. With additional measurement of the cross section area, the effective resistivity of the trunk is estimated. A comparison within a group of trees shows that trees in decay have approximately a factor of two lower effective resistivity than sound trees. The method is tested on several different groups of spruce (Picea abies); in total more than 300 trees are examined. The tests show that the method can detect decay caused by Heterobasidion annosum with high accuracy. Finite element modeling and simulations are used to validate the method

On the superconvergence of Galerkin methods for hyperbolic IBVP

Finite element Galerkin methods for periodic first order hyperbolic equations exhibit superconvergence on uniform grids at the nodes, i.e., there is an error estimate 0(h(sup 2r)) instead of the expected approximation order 0(h(sup r)). It will be shown that no matter how the approximating subspace S(sup h) is chosen, the superconvergence property is lost if there are characteristics leaving the domain. The implications of this result when constructing compact implicit difference schemes is also discussed

The Involvement of Lysosomes in Myocardial Aging and Disease

The myocardium is mainly composed of long-lived postmitotic cells with, if there is any at all, a very low rate of replacement through the division and differentiation of stem cells. As a consequence, cardiac myocytes gradually undergo pronounced age-related alterations which, furthermore, occur at a rate that inversely correlates with the longevity of species. Basically, these alterations represent the accumulation of structures that have been damaged by oxidation and that are useless and often harmful. These structures (so-called ‘waste’ materials), include defective mitochondria, aberrant cytosolic proteins, often in aggregated form, and lipofuscin, which is an intralysosomal undegradable polymeric substance. The accumulation of ‘waste’ reflects the insufficient capacity for autophagy of the lysosomal compartment, as well as the less than perfect functioning of proteasomes, calpains and other cellular digestive systems. Senescent mitochondria are usually enlarged, show reduced potential over their inner membrane, are deficient in ATP production, and often produce increased amounts of reactive oxygen species. The turnover of damaged cellular structures is hindered by an increased lipofuscin loading of the lysosomal compartment. This particularly restricts the autophagic turnover of enlarged, defective mitochondria, by diverting the flow of lysosomal hydrolases from autophagic vacuoles to lipofuscin-loaded lysosomes where the enzymes are lost, since lipofuscin is not degradable by lysosomal hydrolases. As a consequence, aged lipofuscin-rich cardiac myocytes become overloaded with damaged mitochondria, leading to increased oxidative stress, apoptotic cell death, and the gradual development of heart failure. Defective lysosomal function also underlies myocardial degeneration in various lysosomal storage diseases, while other forms of cardiomyopathies develop due to mitochondrial DNA mutations, resulting in an accumulation of abnormal mitochondria that are not properly eliminated by autophagy. The degradation of iron-saturated ferritin in lysosomes mediates myocardial injury in hemochromatosis, an acquired or hereditary disease associated with iron overload. Lysosomes then become sensitized to oxidative stress by the overload of low mass, redox-active iron that accumulates when iron-saturated ferritin is degraded following autophagy. Lysosomal destabilization is of importance in the induction and/or execution of programmed cell death (either classical apoptotic or autophagic), which is a common manifestation of myocardial aging and a variety of cardiac pathologies

CD28 expression in sentinel node biopsies from breast cancer patients in comparison with CD3-ζ chain expression

BACKGROUND: Immunosuppression is documented in several malignant diseases, including breast cancer. Subsequently, future therapeutic concepts might include immunological approaches. However, detailed knowledge about tumor immunogenicity and host immunoreactivity, and how to assess these adequately, is still limited. We studied CD28 and CD3-ζ expression in sentinel node biopsies (SNB) from breast cancer patients to analyze tumor-related changes in T cell activity. METHOD: 25 women underwent surgery for primary breast cancer, including SNB. Frozen sections from 21 sentinel nodes could be analyzed with a double-staining technique. CD28 expression was studied in CD4+ and CD8+ T-lymphocyte subsets and compared with CD3-ζ expression in three specified nodal regions. RESULTS: The degree of CD28 expression varied between the different lymph node areas. The lowest degree of CD28 expression was observed in CD4+ T-lymphocytes in the paracortex and germinal centers. Here, a good agreement with CD3-ζ expression was found. A higher CD28 expression was noted in CD4+ T-cells in the primary follicles, where concordance with CD3-ζ expression was weaker. The CD8+ T-lymphocyte subset displayed generally a higher degree of CD28 expression than the CD4+ subset. CONCLUSION: Sentinel lymph nodes from breast cancer patients displayed local immunosuppression of varying extent. In the areas with the lowest degree of CD28 expression an accordingly low CD3-ζ expression was found. The SNB might prove an important diagnostic tool for the evaluation of interactions between tumor and the host immune system, helping to select patients who might benefit from adjuvant immunotherapy