On the linearization of systems of conservation laws for fluids at a material contact discontinuity

In order to investigate the linearized stability or instability of compressible flows, as it occurs for instance in Rayleigh–Taylor or Kelvin–Helmholtz instabilities, we consider the linearization at a material discontinuity of a flow modeled by a multidimensional nonlinear hyperbolic system of conservation laws. Restricting ourselves to the plane-symmetric case, the basic solution is thus a one-dimensional contact discontinuity and the normal modes of pertubations are solutions of the resulting linearized hyperbolic system with discontinuous nonconstant coefficients and source terms. While in Eulerian coordinates, the linearized Cauchy problem has no solution in the class of functions, we prove that for a large class of systems of conservation laws written in Lagrangian coordinates and including the Euler and the ideal M.H.D. systems, there exists a unique function solution of the problem that we construct by the method of characteristics.     

Laser doppler anemometry in hydrodynamic testing

Classical methods and the laser-Doppler-anemometry (LDA) application for the test section calibration of a water-cavitation tunnel is presented. The results show that the LDA is the best method for calibration and the classical methods satisfy the needs of standard tests. The advantages of the LDA are illustrated by determination of the pressure coefficient C _p for a hydrofoil of a high-speed axial pump under the stationary and nonstationary conditions, as well. The velocity vector distribution is measured around the central hydrofoil of a straight grid for angles of attack δ = 0° and 25° and undisturbed velocity v _∞ = 5.32 m/s. The results of the LDA measurements are used as a basis for the definition of the boundary conditions for numerical flow simulation and C _p calculation by the Fluent program. A flow visualization is made by aniline dyes and air bubbles.     

Anticancer Effect of Cathelicidin LL-37, Protegrin PG-1, Nerve Growth Factor NGF,and Temozolomide: Impact on the Mitochondrial Metabolism,Clonogenic Potential,and Migration of Human U251 Glioma Cells

Glioblastoma (GBM) is one of the most aggressive and lethal malignancy of the central nervous system. Temozolomide is the standard of care for gliomas, frequently results in resistance to drug and tumor recurrence. Therefore, further research is required for the development of effective drugs in order to guarantee specific treatments to succeed. The aim of current study was to investigate the effects of nerve growth factor (NGF), human cathelicidin (LL-37), protegrin-1 (PG-1), and temozolomide on bioenergetic function of mitochondria, clonogenicity, and migration of human U251 glioma cells. Colony formation assay was used to test the ability of the glioma cells to form colonies in vitro. The U251 glioma cells migration was evaluated using wound-healing assay. To study the mitochondrial metabolism in glioma cells we measured oxygen consumption rates (OCR) and extracellular acidification rates (ECAR) using a Seahorse XF cell Mito stress test kit and Seahorse XF cell Glycolysis stress kit, respectively. We revealed that LL-37, NGF, and TMZ show strong anti-tumorigenic activity on GMB. LL-37 (4 μM), TMZ (155 μM), and NGF (7.55 × 10⁻³ μM) inhibited 43.9%–60.3%, 73.5%–81.3%, 66.2% the clonogenicity of glioma U251 cells for 1–2 days, respectively. LL-37 (4 μM), and NGF (7.55 × 10⁻³ μM) inhibited the migration of U251 glioma cells on the third and fourth days. TMZ also inhibited the migration of human glioma U251 cells over 1–3 days. In contrast, PG-1 (16 μM) stimulated the migration of U251 glioma cells on the second, fourth, and sixth days. Anti-mitogenic and anti-migration activities of NGF, LL-37, and TMZ maybe are relation to their capacity to reduce the basal OCR, ATP-synthetase, and maximal respiration of mitochondria in human glioma U251 cells. Glycolysis, glycolytic capacity and glycolytic spare in glioma U251 cells haven`t been changed under the effect of NGF, LL-37, PG-1, and TMZ in regard to control level. Thus, LL-37 and NGF inhibit migration and clonogenicity of U251 glioma cells, which may indicate that these compounds have anti-mitogenic and anti-migration effects on human glioma cells. The study of the mechanisms of these effects may contribute in the future to the use of NGF and LL-37 as therapeutic agents for gliomas.     

Pizza again? On the division of polygons into sections with a common origin

The paper explores the division of a polygon into equal-area pieces using line segments originating at a common point. The mathematical background of the proposed method is very simple and belongs to secondary school geometry. Simple examples dividing a square into two, four or eight congruent pieces provide a starting point to discovering how to divide a regular polygon into any number of equal-area pieces using line segments originating from the centre. Moreover, it turns out that there are infinite ways to do the division. Discovering the basic invariant involved allows application of the same procedure to divide any tangential polygon, as after suitable adjustment, it can be used also for rectangles and parallelograms. Further generalization offers many additional solutions of the problem, and some of them are presented for the case of an arbitrary triangle and a square. Links to dynamic demonstrations in GeoGebra serve to illustrate the main results.     

Foundation, analysis, and numerical investigation of a variational network-based model for rubber

Since the pioneering work by Treloar, many models based on polymer chain statistics have been proposed to describe rubber elasticity. Recently, Alicandro, Cicalese, and the first author rigorously derived a continuum theory of rubber elasticity from a discrete model by variational convergence. The aim of this paper is twofold. First, we further physically motivate this model and complete the analysis by numerical simulations. Second, in order to compare this model to the literature, we present in a common language two other representative types of models, specify their underlying assumptions, check their mathematical properties, and compare them to Treloar’s experiments.