Stratified transversality by isotopy

For an abstract stratified set or a -regular stratification, hence for any -, - or -regular stratification, we prove that after stratified isotopy of , a stratified subspace of , or a stratified map , can be made transverse to a fixed stratified map .

     

Elastic contact stiffness and contact resistance for the Weierstrass profile

The Weierstrass series comprises a system of superposed self-affine sine waves that can be used to define a simple idealization of a two-dimensional fractal rough surface profile. The load-compliance relation for the contact of this profile with a rigid plane is here estimated using Westergaard's solution for the contact of a single sine wave with a plane and various approximations concerning the interaction of the different terms in the series. These approximations are compared with a numerical solution for the contact of the profile defined by the first few terms of the series. Once the load-compliance relation is established, the electrical contact resistance can be determined, using an analogy between the conduction and incremental elastic contact problems. The results show that these simple estimates give quite good predictions of the relations between load, compliance and contact resistance. They also confirm that these relations are largely determined by the coarse scale features of the surface profile, in contrast to the predictions of classical asperity model theories.     

Stratified Transversality via Time-Dependent Vector Fields

For a stratification with suitable regularity, in particularfor any Whitney stratification and, via regular embedding, forany abstract stratified set, time-dependent vector fields areused to prove an extension theorem for diffeomorphisms nearthe identity defined on strata of a given dimension. Then itis shown that after isotopy a stratified map h : Z can bemade transverse to a fixed stratified map g : y .