2,273 research outputs found
Effect of zero-till, snow trapping, and fertilization on spring wheat and winter wheat (1983-84)
Non-Peer Reviewe
Effect of stubble height and source, rate, time, and method of application of N on yield of spring and winter wheat grown under zero-till
Non-Peer Reviewe
Interaction of snow management Ă— N & P fertilizer and their effect on spring wheat yields
Non-Peer Reviewe
Levinson's Theorem for Dirac Particles
Levinson's theorem for Dirac particles constraints the sum of the phase
shifts at threshold by the total number of bound states of the Dirac equation.
Recently, a stronger version of Levinson's theorem has been proven in which the
value of the positive- and negative-energy phase shifts are separately
constrained by the number of bound states of an appropriate set of
Schr\"odinger-like equations. In this work we elaborate on these ideas and show
that the stronger form of Levinson's theorem relates the individual phase
shifts directly to the number of bound states of the Dirac equation having an
even or odd number of nodes. We use a mean-field approximation to Walecka's
scalar-vector model to illustrate this stronger form of Levinson's theorem. We
show that the assignment of bound states to a particular phase shift should be
done, not on the basis of the sign of the bound-state energy, but rather, in
terms of the nodal structure (even/odd number of nodes) of the bound state.Comment: Latex with Revtex, 7 postscript figures (available from the author),
SCRI-06109
First normal stress difference and crystallization in a dense sheared granular fluid
The first normal stress difference () and the microstructure
in a dense sheared granular fluid of smooth inelastic hard-disks are probed
using event-driven simulations. While the anisotropy in the second moment of
fluctuation velocity, which is a Burnett-order effect, is known to be the
progenitor of normal stress differences in {\it dilute} granular fluids, we
show here that the collisional anisotropies are responsible for the normal
stress behaviour in the {\it dense} limit. As in the elastic hard-sphere
fluids, remains {\it positive} (if the stress is defined in
the {\it compressive} sense) for dilute and moderately dense flows, but becomes
{\it negative} above a critical density, depending on the restitution
coefficient. This sign-reversal of occurs due to the {\it
microstructural} reorganization of the particles, which can be correlated with
a preferred value of the {\it average} collision angle in the direction opposing the shear. We also report on the shear-induced
{\it crystal}-formation, signalling the onset of fluid-solid coexistence in
dense granular fluids. Different approaches to take into account the normal
stress differences are discussed in the framework of the relaxation-type
rheological models.Comment: 21 pages, 13 figure
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