Converging flow of a viscoelastic liquid

Two-dimensional creeping sink flow of a Maxwell fluid is an accurate approximation to a bounded converging flow of contraction ratio at least 5 : 1 and covergence half-angles of up to 45°. In this range, a perturbation expansion in Weissenberg number can be used over most of the flow field in the range where stable processing can be carried out.     

On patched variational principles with application to elliptic and mixed elliptic-hyperbolic problems

Summary Variational principles are important tools for the approximate solution of boundary-value problems. There are many types of variational principles, and each has its advantages and disadvantages. In this paper we show how to use a combination of variational principles, each for a given subregion of the underlying region of space, so as to best utilize the chief benefits of the individual principles. Such a patched principle is particularly useful in solving transonic flow problems, where we use different principles in the elliptic and hyperbolic regions. We present the results of some numerical experiments for the Tricomi problem. These seem to indicate that our patched principle, when used in conjunction with the finite element method, leads to accuracy which is second-order in the mesh spacing, as compared to the standard numerical methods of solving this problem, which are only first-order.     

On graphs with a constant link,II

We study the following problem: For which finite graphs L do there exist graphs G such that the link (i.e., the neighborhood subgraph) of each vertex of G is isomorphic to L? We give a complete solution for the cases (i) L is a disjoint union of arcs, (ii) L is a tree with only one vertex of degree greater than two, (iii) L is a circle of prescribed length. Some other cases are also discussed. An interesting case is whether the situation is changed if we require G also to be finite. It transpires (see for example, Corollaries VII.3 and VII.4) that this is indeed the case.Part I of this paper will appear in [3]. It provides the basic definitions used in both part I and part II. Section III provides the basic tool, an identification procedure, that is used throughout the rest of the paper. Section IV sets up the basic building technique for the construction of more complicated graphs. It is shown how to build graphs such that the link of each vertex is an arc (of non-constant length), and how to control the proportional number of vertices with links of various lengths.     

On the existence of a single temperature in continuum thermodynamics

Summary A global hypothesis involving the heat flux and the entropy flux is shown to be equivalent to the existence of temperature.

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Zusammenfassung Es wird gezeigt, dass eine globale Hypothese für die Wärmezufuhr und Entropiezufuhr mit der Existenze der Temperatur äquivalent ist.

     

Thermodynamic influences on the growth of one-dimensional shock waves in materials with memory

In this paper we study one-dimensional shock waves in materials with memory, including thermodynamic influences. In particular, we derive a differential equation relating the strain and strain gradient behind the shock, and give criteria under which the wave will grow or decay.

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Zusammenfassung In dieser Arbeit werden eindimensionale Stoßwellen mit Berücksichtigung thermodynamischer Einflüsse in Werkstoffen mit Gedächtnis untersucht. Speziell wird eine Differentialgleichung abgeleitet, die das Verhältnis zwischen Spannungs- und Verzerrungsgradienten hinter der Stoßwelle herstellt. Ferner werden Bedingungen für Anwuchs und Abfall der Welle angegeben.