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Finite dimensional integrable Hamiltonian systems associated with DSI equation by Bargmann constraints
The Davey-Stewartson I equation is a typical integrable equation in 2+1
dimensions. Its Lax system being essentially in 1+1 dimensional form has been
found through nonlinearization from 2+1 dimensions to 1+1 dimensions. In the
present paper, this essentially 1+1 dimensional Lax system is further
nonlinearized into 1+0 dimensional Hamiltonian systems by taking the Bargmann
constraints. It is shown that the resulting 1+0 dimensional Hamiltonian systems
are completely integrable in Liouville sense by finding a full set of integrals
of motion and proving their functional independence.Comment: 10 pages, in LaTeX, to be published in J. Phys. Soc. Jpn. 70 (2001
Critical Current Density and Resistivity of MgB2 Films
The high resistivity of many bulk and film samples of MgB2 is most readily
explained by the suggestion that only a fraction of the cross-sectional area of
the samples is effectively carrying current. Hence the supercurrent (Jc) in
such samples will be limited by the same area factor, arising for example from
porosity or from insulating oxides present at the grain boundaries. We suggest
that a correlation should exist, Jc ~ 1/{Rho(300K) - Rho(50K)}, where Rho(300K)
- Rho(50K) is the change in the apparent resistivity from 300 K to 50 K. We
report measurements of Rho(T) and Jc for a number of films made by hybrid
physical-chemical vapor deposition which demonstrate this correlation, although
the "reduced effective area" argument alone is not sufficient. We suggest that
this argument can also apply to many polycrystalline bulk and wire samples of
MgB2.Comment: 11 pages, 3 figure
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