72,707 research outputs found
Topological Change in Mean Convex Mean Curvature Flow
Consider the mean curvature flow of an (n+1)-dimensional, compact, mean
convex region in Euclidean space (or, if n<7, in a Riemannian manifold). We
prove that elements of the m-th homotopy group of the complementary region can
die only if there is a shrinking S^k x R^(n-k) singularity for some k less than
or equal to m. We also prove that for each m from 1 to n, there is a nonempty
open set of compact, mean convex regions K in R^(n+1) with smooth boundary for
which the resulting mean curvature flow has a shrinking S^m x R^(n-m)
singularity.Comment: 19 pages. This version includes a new section proving that certain
kinds of mean curvature flow singularities persist under arbitrary small
perturbations of the initial surface. Newest update (Oct 2013) fixes some
bibliographic reference
Comment on ``Stripes and the t-J Model''
This is a comment being submitted to Physical Review Letters on a recent
letter by Hellberg and Manousakis on stripes in the t-J model.Comment: One reference correcte
Sharp Fronts Due to Diffusion and Viscoelastic Relaxation in Polymers
A model for sharp fronts in glassy polymers is derived and analyzed. The major effect of a diffusing penetrant on the polymer entanglement network is taken to be the inducement of a differential viscoelastic stress. This couples diffusive and mechanical processes through a viscoelastic response where the strain depends upon the amount of penetrant present. Analytically, the major effect is to produce explicit delay terms via a relaxation parameter. This accounts for the fundamental difference between a polymer in its rubbery state and the polymer in its glassy state, namely the finite relaxation time in the glassy state due to slow response to changing conditions. Both numerical and analytical perturbation studies of a boundary
value problem for a dry glass polymer exposed to a penetrant solvent are completed. Concentration profiles
in good agreement with observations are obtained
ECONOMIC IMPACT OF INTRODUCING ROTATIONS ON LONG ISLAND POTATO FARMS
Potatoes have been grown continuously on many Long Island (New York) fields. Environmental concerns have raised questions about the continued usage of this practice. A farm-level linear programming model was used to investigate the economic impacts of crop rotations which result in reduced potato acreage. Crop rotations (an Integrated Pest Management tactic) reduced total pesticide use, but also reduced returns above variable costs as successively stringent rotation requirements were forced into the solution. The crop rotations which caused the least effect on income were identified.Resource /Energy Economics and Policy,
On the discrete spectrum of quantum layers
Consider a quantum particle trapped between a curved layer of constant width
built over a complete, non-compact, smooth surface embedded in
. We assume that the surface is asymptotically flat in the sense
that the second fundamental form vanishes at infinity, and that the surface is
not totally geodesic. This geometric setting is known as a quantum layer. We
consider the quantum particle to be governed by the Dirichlet Laplacian as
Hamiltonian. Our work concerns the existence of bound states with energy
beneath the essential spectrum, which implies the existence of discrete
spectrum. We first prove that if the Gauss curvature is integrable, and the
surface is weakly -parabolic, then the discrete spectrum is non-empty.
This result implies that if the total Gauss curvature is non-positive, then the
discrete spectrum is non-empty. We next prove that if the Gauss curvature is
non-negative, then the discrete spectrum is non-empty. Finally, we prove that
if the surface is parabolic, then the discrete spectrum is non-empty if the
layer is sufficiently thin.Comment: Clarifications and corrections to previous version, conjecture from
previous version is proven here (Theorem 1.5), additional references include
Numerical renormalization group study of the correlation functions of the antiferromagnetic spin- Heisenberg chain
We use the density-matrix renormalization group technique developed by White
\cite{white} to calculate the spin correlation functions
for isotropic Heisenberg rings up to
sites. The correlation functions for large and are found to obey
the scaling relation
proposed by Kaplan et al. \cite{horsch} , which is used to determine
. The asymptotic correlation function and
the magnetic structure factor show logarithmic corrections
consistent with , where is related
to the cut-off dependent coupling constant , as
predicted by field theoretical treatments.Comment: Accepted in Phys. Rev. B. 4 pages of text in Latex + 5 figures in
uuencoded form containing the 5 postscripts (mailed separately
Shock Formation in a Multidimensional Viscoelastic Diffusive System
We examine a model for non-Fickian "sorption overshoot" behavior in diffusive polymer-penetrant systems. The equations of motion proposed by Cohen and White [SIAM J. Appl. Math., 51 (1991), pp. 472â483] are solved for two-dimensional problems using matched asymptotic expansions. The phenomenon of shock formation predicted by the model is examined and contrasted with similar behavior in classical reaction-diffusion systems. Mass uptake curves produced by the model are examined and shown to compare favorably with experimental observations
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