A limiter-based well-balanced discontinuous Galerkin method for shallow-water flows with wetting and drying: Triangular grids

A novel wetting and drying treatment for second-order Runge-Kutta discontinuous Galerkin (RKDG2) methods solving the non-linear shallow water equations is proposed. It is developed for general conforming two-dimensional triangular meshes and utilizes a slope limiting strategy to accurately model inundation. The method features a non-destructive limiter, which concurrently meets the requirements for linear stability and wetting and drying. It further combines existing approaches for positivity preservation and well-balancing with an innovative velocity-based limiting of the momentum. This limiting controls spurious velocities in the vicinity of the wet/dry interface. It leads to a computationally stable and robust scheme -- even on unstructured grids -- and allows for large time steps in combination with explicit time integrators. The scheme comprises only one free parameter, to which it is not sensitive in terms of stability. A number of numerical test cases, ranging from analytical tests to near-realistic laboratory benchmarks, demonstrate the performance of the method for inundation applications. In particular, super-linear convergence, mass-conservation, well-balancedness, and stability are verified

Modellvorhaben zum Einsatz verschiedener gefährdeter Rinderrassen in extensiven Beweidungssystemen des Feuchtgrünlandes unter den Rahmenbedingungen der Agrarreform und einer innovativen, nachhaltigen Wirtschaftsweise im Biosphärenreservat Flusslandschaft Elbe

Ziel des Projektes ist die Überprüfung der Integration und Akzeptanz alter gefährdeter Rinderrassen in landwirtschaftlichen Betriebe zur Umsetzung von Naturschutzzielen

MATHEMATICAL CURIOSITIES ABOUT DIVISION OF INTEGERS

As mathematics educators, our focus of attention is mainly placed on the learning and teaching of mathematics. But, as we study phenomena of mathematical learning and teaching, we often come across intriguing mathematical phenomena that capture our interest. We find ourselves often bouncing mathematical ideas back and forth, not just looking for (new/better) ways of teaching or presenting a mathematical concept, but also of uncovering and discovering potential understandings of the concept. These mathematical issues we encounter represent for us a significant aspect of our work, and are also very stimulating. One of these issues arose for us as we were tackling issues of division of numbers and of conventions relating to the remainder; issues that are, mathematically speaking, as we hope to communicate, very interesting and thought provoking. Thus, we explore four different avenues/curiosities about division, where operations with positive and negative numbers are considered, as well as the meaning one can draw out of these operations

Triangular grids

A novel wetting and drying treatment for second‐order Runge‐Kutta discontinuous Galerkin methods solving the nonlinear shallow‐water equations is proposed. It is developed for general conforming two‐dimensional triangular meshes and utilizes a slope limiting strategy to accurately model inundation. The method features a nondestructive limiter, which concurrently meets the requirements for linear stability and wetting and drying. It further combines existing approaches for positivity preservation and well balancing with an innovative velocity‐based limiting of the momentum. This limiting controls spurious velocities in the vicinity of the wet/dry interface. It leads to a computationally stable and robust scheme, even on unstructured grids, and allows for large time steps in combination with explicit time integrators. The scheme comprises only one free parameter, to which it is not sensitive in terms of stability. A number of numerical test cases, ranging from analytical tests to near‐realistic laboratory benchmarks, demonstrate the performance of the method for inundation applications. In particular, superlinear convergence, mass conservation, well balancedness, and stability are verified

The effect of phoria and fixation disparity on the hitting placement of baseball players

Twenty players from Pacific University\u27s baseball team were tested on the Pacific Sports Vision Performance Profile (PSVPP) to determine if phoria and fixation disparity, as measured by the PSVPP, correlates to actual hitting tendencies. PSVPP results indicate that a statistically significant correlation exists between actual batting placement and phorias indicated by the PSVPP (pe0.001). Those exophoric players who bat right handed tend to hit to left field, orthophores tend to hit to centerfield, and esophores tend to hit to right field. The reverse is true for left and right field placement for left handed hitters. Furthermore, a trend was also noted in the phorias and fixation disparities of starters (\u27first string\u27 players) vs. non-starters in that the starter\u27s values were found to be closer to orthophoric. This suggests that as one moves up the ranks in baseball, those athletes who perform the best may be likely to have or develop a low or zero phoria and fixation disparity. It also points to the possibility that hitting placement may be affected by phoria compensation using prism

Curricular Change in Institutional Context: A Profile of the SUMMIT-P Institutions

There is a national call to improve the mathematics curricula in the first two undergraduate years to improve student success and engagement. But curricular change happens in an institutional context: Who are the students, and what do they need to succeed? What is the climate for change? Does the department regularly revise its courses and curriculum? Is it common for different departments to collaborate on curricular change? What supports or obstacles does the department, college, or university have for changing the curriculum? Who are the institutional stakeholders, and what practices build their buy-in? In the SUMMIT-P project, nine different institutions ranging from small private colleges to mid-sized state universities to large public universities and a community college worked on changing the undergraduate mathematics curricula in the first two years. This paper examines the context at each institution in the project. We hope that other institutions looking to follow in our collaboration with the partner disciplines on revising the introductory mathematics curriculum at their institution will find a familiar context in one (or more) of these institutions. We include a list of questions that programs can use to examine their own institutional context

„Ich verfolgte damals alle malerischen Mittel” - Kunsttechnologische Forschungen zum Werk des Historienmalers Hermann Prell (1854–1922)

Die praktische Arbeit des Monumentalmalers Hermann Prell (1854–1922) wurde zeitlebens von einer intensiven Auseinandersetzung mit Fragen der Maltechnik begleitet, die sich in seinen umfangreichen Aufzeichnungen niederschlug. Aufgrund seiner zahlreichen Kontakte zu Zeitgenossen, wie Hans von Marées und Arnold Böcklin, stellt sein schriftlicher Nachlass eine wichtige Quelle zur kunsttechnischen Entwicklung um 1900 dar. Im Rahmen der vorliegenden Arbeit werden seine Forschungen zur Maltechnik und die Beschreibung der von ihm angewendeten Materialien sowie Techniken das erste Mal tiefgreifend untersucht und umfassend vorgestellt. Die erhaltenen Dokumente bieten die Grundlage für eine Aufschlüsselung der verwendeten Rezepturen und handelsüblichen Künstlermaterialien sowie deren Kontextualisierung. Des Weiteren ergänzen historische Abbildungen und Vorstudien zur Erarbeitung der Komposition und Maltechnik den Blick auf den Werkprozess. Ebenso wird die kunsttechnologische Untersuchung von ausgewählten Werken mit der Auswertung der Quellen kombiniert. Während seiner monumentalen Aufträge galt sein besonderes Interesse der technischen und künstlerischen Umsetzung eines Gesamtkunstwerkes. Hermann Prell widmete sich eingehend kunsttechnologisch relevanter historischer und zeitgenössischer Quellenliteratur, zum Beispiel von Cennino Cennini und Ernst Berger. Die Freskotechnik nahm im breiten technischen Spektrum seines Œuvres einen hohen Stellenwert ein. Daneben spielte die Beschäftigung mit Tempera sowohl für das Staffeleibild als auch für die Wandmalerei eine große Rolle. Insgesamt wird erstmals ein Überblick über Hermann Prells angewendete Kunsttechniken in ihrer Vielfalt sowie deren Genese gegeben.Throughout his life Hermann Prell (1854–1922) – known for his monumental paintings – accompanied his practical work with intense explorations of questions related to painting technique. This is reflected in his extensive writings. Prell was also engaged in a lively exchange with other artists, such as Hans von Marées and Arnold Böcklin. Hermann Prell’s writings combined with his contemporaries’ present an important source on painting technique around the turn of the 19th century in Germany. This study provides the first in-depth examination and comprehensive presentation of Prell’s research into painting techniques and a description of the materials and techniques he utilised. The preserved documents provide the basis for analysing the recipes the artist used and commercially available artists’ materials as well as their contextualisation with current research. Our view of his working process is further supplemented by historical reproductions and preparatory studies that served Prell to develop his compositions and painting techniques. Furthermore, the results of recent technical examinations of selected artworks are combined with an evaluation of the written sources. For his numerous large commissions for government buildings, Prell was particularly interested in the technical and artistic realisation of a Gesamtkunstwerk. He occupied himself extensively with related historical and contemporary sources, for example, the writings of Cennino Cennini and Ernst Berger. Amongst the broad technical range of his oeuvre the fresco technique assumed particular importance. In addition, his occupation with tempera’s use for easel paintings as well as wall paintings played a major role. In conclusion, for the first time Hermann Prell’s various applied techniques and materials as well as their genesis are given a comprehensive overview