The theorem X established by Miles in the preceding paper is here given a simpler and more general proof. Some further theoretical results concerning the stability of heterogeneous shear flows are also presented, in particular a demonstration that the complex wave velocity of any unstable mode must lie in a certain semicircle .
The singular manifold method and partial fraction decomposition allow one to find some special solutions of nonintegrable partial differential equations Ž. PDE in the form of solitary waves, traveling wave fronts, and periodic pulse trains. The truncated Painleve expansion is used to reduce a nonlinear´PDE to a multilinear form. Some special solutions of… (More)
Linear polyethylenes in the amorphous region have been simulated as restricted random walks on a diamond lattice between two absorbing planes. The links among loops were studied by treating loops as Ž oriented curves. The local conformations of polyethylene chains i.e., trans and. gauche energy differences were considered in the simulation, thereby… (More)
Polyethylene chains in the amorphous region between two crystalline lamellae M unit apart are modeled as random walks with one-step memory on a cubic lattice between two absorbing boundaries. These walks avoid the two preceding steps, though they are not true self-avoiding walks. Systems of difference equations are introduced to calculate the statistics of… (More)