R. S. D. Thomas

A guided clothoid spline

Abstract A method is described whereby a G 2 planar curve consisting of clothoid (Cornu spiral) segments, circular arcs and straight line segments is constructed. The curve passes through given points, is expressed parametrically, and has the attractive feature that the arc length and curvature are piecewise linear functions of the parameter. The given points through which the curve passes must be restricted somewhat so that a unique clothoid exists between each pair of points.

The Comparison Of Mathematics With Narrative

Mathematical writing, chiefly of proofs, is compared with the telling of stories. Contrasts are also noted. The positive analogy is used to support the view of mathematics as being about relations rather than objects obviating a need for ontological commitment to mathematical objects. The negative analogy is used to deny some philosophers’ identification of mathematics with fiction.

Transient waves in inhomogeneous anisotropic elastic plates

SummaryThis paper considers the problem of transient wave propagation in elastic Cosserat plates that may be anisotropic, inhomogeneous, or of variable thickness. The methods of rays and of singular wave curves are combined to find and integrate the transport equations governing growth-decay behaviour of the extensional and bending wave modes to derive a common general formula involving the material parameters and wave geometry. For inhomogeneous isotropic plates of variable thickness, conditions for the uncoupling of the wave modes are obtained and some special cases are worked out in detail.

Conditions for isonemal arrays on a Cartesian grid

Abstract The concept of an isonemal binary array on a Cartesian grid is examined, and rules for constructing all such arrays are identified. Examples are included for the various possible constructions, and tables of compound twillins of periods six and eight are given.

Isonemal prefabrics with only parallel axes of symmetry

Isonemal weaving designs, introduced into mathematical literature by Grunbaum and Shephard, were classified into thirty-nine infinite sets, and a small number of exceptions by Richard Roth. This paper refines Roths taxonomy for the first ten of these families in order to solve three problems: which designs exist in various sizes, which prefabrics can be doubled and remain isonemal, and which can be halved and remain isonemal.

Isonemal prefabrics with no axes of symmetry

This paper refines Richard Roths taxonomy of isonemal weaving designs through the final types 33-39 in order to complete the solution of three problems for those designs: which designs exist in various sizes, which prefabrics can be doubled and remain isonemal, and which can be halved and remain isonemal. These types have no symmetry axes but have quarter-turn symmetries. Jean Pedersens problem of woven cubes is also discussed.

Hermite interpolation with a pair of spirals

Abstract The Hermite interpolation problem in the plane considered here is to join two points and to match given unit tangent vectors and signed curvatures at the two points with various G 2 curves consisting of a pair of spirals. The rotation of the tangent vector of the interpolating curve from one point to the other is restricted to being less than π. The necessary and sufficient conditions for the existence of each of the various curves are given.

PERFECT COLOURINGS OF ISONEMAL FABRICS BY THICK STRIPING

Perfect colouring of isonemal fabrics by thick striping of warp and weft and the closely related topic of isonemal prefabrics that fall apart are reconsidered and their relation further explored. The catalogue of isonemal prefabrics of genus V that fall apart is extended to order 20 with designs that can be used to weave cubes with colour symmetry as well as weaving symmetry.

Transient waves in inhomogeneous elastic shells of variable thickness

SummaryThis paper considers the problem of transient wave propagation in Cosserat shells of variable thickness, the inhomogeneous material of which is linearly elastic and isotropic. We do not say that the shells are isotropic because varying thickness causes behaviour characteristic of anisotropy despite the materials being isotropic. The methods of rays and of singular wave curves are combined to find and integrate the transport equations governing growth-decay behaviour of the six possible wave modes. Conditions on material parameters, thickness variation, and wave geometry are obtained for various different uncouplings of the wave modes. Some special cases of propagation conditions and of decay equations are worked out in detail.

On the derivation of the acoustic matrix for isotropic linearly elastic shells

In this paper, we obtain the modes and velocities of acceleration waves on a thin hyperelastic shell in terms of the second fundamental form, which represents the geometrical properties of the shell, and of seven elastic moduli derived from the velocities in a plate of the same material. Some examples are studied, and approximations obtained in the case of a shallow shell.SommarioIn questo lavoro si ottengono i modi e le velocità delle onde di accelerazione in una volta sottile iperelastica, con riferimento alla seconda forma fondamentale che rappresenta le proprietà geometriche della volta e a sette moduli elastici derivati dalle velocità in una piastra dello stesso materiale. Si studiano alcuni esempi e si presentano soluzioni approssimate nel caso di una volta ribassata.