Theory of the Spatio-Temporal Dynamics of Transport Bifurcations

The development and time evolution of a transport barrier in a magnetically confined plasma with non-monotonic, nonlinear dependence of the anomalous flux on mean gradients is analyzed. Upon consideration of both the spatial inhomogeneity and the gradient nonlinearity of the transport coefficient, we find that the transition develops as a bifurcation front with radially propagating discontinuity in local gradient. The spatial location of the transport barrier as a function of input flux is calculated. The analysis indicates that for powers slightly above threshold, the barrier location $x_b(t) \sim ( D_n t (P-P_c)/P_c)^{1/2},$ where $P_c$ is the local transition power threshold and $D_n$ is the neoclassical diffusivity . This result suggests a simple explanation of the high disruptivity observed in reversed shear plasmas. The basic conclusions of this theory are insensitive to the details of the local transport model.Comment: 21 page Tex file, 10 postscript file

Crossed product of a C*-algebra by a semigroup of endomorphisms generated by partial isometries

The paper presents a construction of the crossed product of a C*-algebra by a semigroup of endomorphisms generated by partial isometries.Comment: 22 page

Supersymmetric Jarlskog Invariants: the Neutrino Sector

We generalize the notion of the Jarlskog invariant to supersymmetric models with right--handed neutrinos. This allows us to formulate basis--independent necessary and sufficient conditions for CP conservation in such models.Comment: 10 pages, no figure

Integrable hierarchy underlying topological Landau-Ginzburg models of D-type

A universal integrable hierarchy underlying topological Landau-Ginzburg models of D-tye is presented. Like the dispersionless Toda hierarchy, the new hierarchy has two distinct (``positive" and ``negative") set of flows. Special solutions corresponding to topological Landau-Ginzburg models of D-type are characterized by a Riemann-Hilbert problem, which can be converted into a generalized hodograph transformation. This construction gives an embedding of the finite dimensional small phase space of these models into the full space of flows of this hierarchy. One of flat coordinates in the small phase space turns out to be identical to the first ``negative" time variable of the hierarchy, whereas the others belong to the ``positive" flows.Comment: 14 pages, Kyoto University KUCP-0061/9

Extensions of C*-dynamical systems to systems with complete transfer operators

Starting from an arbitrary endomorphism $\alpha$ of a unital C*-algebra $A$ we construct a bigger C*-algebra $B$ and extend $\alpha$ onto $B$ in such a way that the extended endomorphism $\alpha$ has a unital kernel and a hereditary range, i.e. there exists a unique non-degenerate transfer operator for $(B,\alpha)$, called the complete transfer operator. The pair $(B,\alpha)$ is universal with respect to a suitable notion of a covariant representation and depends on a choice of an ideal in $A$. The construction enables a natural definition of the crossed product for arbitrary $\alpha$.Comment: Compressed and submitted version, 9 page

A single structured light beam as an atomic cloud splitter

We propose a scheme to split a cloud of cold non-interacting neutral atoms based on their dipole interaction with a single structured light beam which exhibits parabolic cylindrical symmetry. Using semiclassical numerical simulations, we establish a direct relationship between the general properties of the light beam and the relevant geometric and kinematic properties acquired by the atomic cloud as its passes through the beam.Comment: 10 pages, 5 figure