3,121 research outputs found
Global bifurcation for monotone fronts of elliptic equations
In this paper, we present two results on global continuation of monotone
front-type solutions to elliptic PDEs posed on infinite cylinders. This is done
under quite general assumptions, and in particular applies even to fully
nonlinear equations as well as quasilinear problems with transmission boundary
conditions. Our approach is rooted in the analytic global bifurcation theory of
Dancer and Buffoni--Toland, but extending it to unbounded domains requires
contending with new potential limiting behavior relating to loss of
compactness. We obtain an exhaustive set of alternatives for the global
behavior of the solution curve that is sharp, with each possibility having a
direct analogue in the bifurcation theory of second-order ODEs.
As a major application of the general theory, we construct global families of
internal hydrodynamic bores. These are traveling front solutions of the full
two-phase Euler equation in two dimensions. The fluids are confined to a
channel that is bounded above and below by rigid walls, with incompressible and
irrotational flow in each layer. Small-amplitude fronts for this system have
been obtained by several authors. We give the first large-amplitude result in
the form of continuous curves of elevation and depression bores. Following the
elevation curve to its extreme, we find waves whose interfaces either overturn
(develop a vertical tangent) or become exceptionally singular in that the flow
in both layers degenerates at a single point on the boundary. For the curve of
depression waves, we prove that either the interface overturns or it comes into
contact with the upper wall.Comment: 60 pages, 6 figure
Recommended from our members
Time-resolved gas-phase kinetic, quantum chemical, and RRKM studies of reactions of silylene with alcohols
Time-resolved kinetic studies of silylene, SiH2, generated by laser flash photolysis of 1-silacyclopent-3-ene and phenylsilane, have been carried out to obtain rate constants for its bimolecular reactions with methanol, ethanol, 1-propanol, 1-butanol and 2-methyl-1-butanol. The reactions were studied in the gas phase over the pressure range 1-100 Torr in SF6 bath gas, at room temperature. In the study with methanol several buffer gases were used. All five reactions showed pressure dependences characteristic of third body assisted association reactions. The rate constant pressure dependences were modelled using RRKM theory, based on Eo values of the association complexes obtained by ab initio calculation (G3 level). Transition state models were adjusted to fit experimental fall-off curves and extrapolated to obtain k∞ values in the range 1.9 to 4.5 × 10-10 cm3 molecule-1 s-1. These numbers, corresponding to the true bimolecular rate constants, indicate efficiencies of between 16 and 67% of the collision rates for these reactions. In the reaction of SiH2 + MeOH there is a small kinetic component to the rate which is second order in MeOH (at low total pressures). This suggests an additional catalysed reaction pathway, which is supported by the ab initio calculations. These calculations have been used to define specific MeOH-for-H2O substitution effects on this catalytic pathway. Where possible our experimental and theoretical results are compared with those of previous studies
Global Bifurcation of Anti-plane Shear Fronts
We consider anti-plane shear deformations of an incompressible elastic solid
whose reference configuration is an infinite cylinder with a cross section that
is unbounded in one direction. For a class of generalized neo-Hookean strain
energy densities and live body forces, we construct unbounded curves of
front-type solutions using global bifurcation theory. Some of these curves
contain solutions with deformations of arbitrarily large magnitude.Comment: 21 pages, 2 figure
Space & Logistics in Support of the Space Industry: A Real Estate & Logistics Approach
“Space” Has Many Global Meanings
The traditional meaning in this region is about exploration – rockets, astronauts, telescopes, rovers
The four people sitting here today are about another kind of “space”
We collectively have been engaged in creating great spaces to work, play, invent, manufacture
For your kind of space business to grow – you need our kind of space and business development or you cannot attract first class manufacturers and logistics firms her
- …