A technique for flow-enhanced magnetic resonance angiography of the lower extremities

A two-dimensional, flow-enhanced gradient echo pulse sequence for nuclear magnetic resonance angiography is described. It employs interleaved, presaturated slices to acquire data efficiently on imagers which favor interleaved acquisition over sequential acquisition for multislice imaging. It is useful on any imager when the effective TR is extended to enhance the sensitivity to slow flow. The technique was applied to the region from aortic bifurcation to the iliac bifurcations of three normal volunteers. The right and left common iliac arteries and veins, the separation of the external and internal iliac arteries, and secondary branches were clearly depicted.     

Incompressible reacting flows

We establish steady-state convergence results for a system of
reaction-convection-diffusion equations that model in particular combustion phenomena in the presence of nontrivial incompressible fluid motion. Despite the presence of the convection terms, we find that the asymptotic behavior of the system is identical to the case we have previously considered in which the velocity field was set equal to zero. In particular we are again able to establish the convergence of solutions to steady-states and to explicitly calculate the steady-states from the initial and boundary data. Key to our analysis is the establishment of high-order uniform bounds on the temperature and mass fraction components, a process significantly complicated by the presence of the convection terms.

     

From PCA's to equilibrium systems and back

Stationary measures for probabilistic cellular automata (PCA's) ind dimensions give rise to space-time histories whose statistics may naturally be described by Gibbs states ind+1 dimensions for an interaction energy ? obtained from the PCA. In this note we study the converse question: Do all Gibbs states for this ? correspond to statistical space-time histories for the PCA? Our main result states that the answer is yes, at least for translation invariant or periodic Gibbs states. Thus ergodicity questions for PCA's can, at least partially, be formulated as questions of uniqueness of Gibbs states.     

Counting connected graphs asymptotically

We find the asymptotic number of connected graphs with k vertices and k−1+l edges when k,l approach infinity, re-proving a result of Bender, Canfield and McKay. We use the probabilistic method, analyzing breadth-first search on the random graph G(k,p) for an appropriate edge probability p. Central is the analysis of a random walk with fixed beginning and end which is tilted to the left.