3,135 research outputs found
Galoisian obstructions to non-Hamiltonian integrability
We show that the main theorem of Morales--Ramis--Simo about Galoisian
obstructions to meromorphic integrability of Hamiltonian systems can be
naturally extended to the non-Hamiltonian case. Namely, if a dynamical system
is meromorphically integrable in the non-Hamiltonian sense, then the
differential Galois groups of the variational equations (of any order) along
its solutions must be virtually AbelianComment: 5 page
Flow Induced in Fluid-Particle Suspension by an Infinite Rotating Disk
An exact similarity solution is given for the flow of a fluid-particle suspension over an infinitely
large disk rotating at a constant velocity. Numerical solutions of the resulting ordinary differential
equations provide velocity distributions for both fluid and solid phases and density distributions
for the solid. The boundary-layer thicknesses of the particle cloud and the fluid are found to be approximately
equal. In addition to its intrinsic value as a solution to a physical problem, the results provide a convenient basis for judging the accuracy of approximate techniques
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