53,698 research outputs found
The Monopole Equations in Topological Yang-Mills
We twist the monopole equations of Seiberg and Witten and show how these
equations are realized in topological Yang-Mills theory. A Floer derivative and
a Morse functional are found and are used to construct a unitary transformation
between the usual Floer cohomologies and those of the monopole equations.
Furthermore, these equations are seen to reside in the vanishing self-dual
curvature condition of an -bundle. Alternatively, they may be seen
arising directly from a vanishing self-dual curvature condition on an
-bundle in which the fermions are realized as spanning the tangent space
for a specific background.Comment: 7 pgs., LaTeX (fullpage
Building on the cultural and linguistic capital of English learner (EL) students
Approaches and strategies that value and build upon the cultural and linguistic capital of English learner students are described. Through implementing such strategies, teachers can impress upon students and families that multiculturalism and multilingualism are highly beneficial to the classroom, school, and community
The Physics Inside Topological Quantum Field Theories
We show that the equations of motion defined over a specific field space are
realizable as operator conditions in the physical sector of a generalized Floer
theory defined over that field space. The ghosts associated with such a
construction are found not to be dynamical. This construction is applied to
gravity on a four dimensional manifold, ; whereupon, we obtain Einstein's
equations via surgery, along , in a five-dimensional topological quantum
field theory.Comment: LaTeX, 7 page
Laboratory studies of the roughness and suspended load of alluvial streams
This report describes research work done under Contract No. DA-25-075-eng-3866 with the U. S. Army, Corps of Engineers, Missouri River Division, Omaha, during the period 1954-1957, on problems of suspended load transport in alluvial streams.
A total of 94 experimental runs were made in two laboratory flumes charged with fine sand of several size distributions. Special attention was given to the variation of the friction factor caused by the changing bed configuration and the damping effect of suspended sediment. The relationship between the sediment transportation rate and the hydraulic variables was also investigated. Most of the runs (General Studies, Chap. V) were made with the bed of the flume completely covered with loose sand but some special runs (Special Studies, Chap. VII) were made with the sand bed chemically solidified in place to prevent sediment transport while preserving the bed configuration previously generated by a natural flow of the same velocity with loose sand. The principal laboratory results are as follows:
1. The friction factor f for a stream with a movable sand bed may vary several fold, being highest at low or medium flow velocities and lowest at high velocity.
2. The principal cause of the variation in f is the appearance of dunes at low or medium velocities and disappearance at high velocities.
3. A secondary cause for the reduction in f for high sediment transport rates is the damping effect of the suspended sediment on the turbulence, and the concomitant reduction in the turbulent diffusion coefficients. The maximum observed reduction due directly to the sediment load was only about 28 percent.
4. The discharge and sediment transportation rate are not unique functions of depth and slope because of the variable roughness. Slope (or shear) must probably be considered a dependent variable for alluvial streams because several equilibrium flows can yield the same slope and shear stress.
The laboratory data are compared with similar data for natural streams, and the most promising existing analyses for roughness and sediment load are discussed in the light of the present findings. In addition, a critical review of early and recent literature on the resistance of sediment-laden streams is presented in Chapter II
Low-temperture electrostatic silicon-to-silicon seals using sputtered borosilicate glass
Silicon members are hermetically sealed to each other. Process produces no measurable deformation of silicon surfaces and is compatible with package designs of tight tolerance. Seals have been made with glass coatings in 10-mm to 20-mm thickness range without any prior annealing of coated silicon substrates
DOMAIN WALLS IN THE QUANTUM TRANSVERSE ISING MODEL
We discuss several problems concerning domain walls in the spin Ising
model at zero temperature in a magnetic field, , applied in the
direction. Some results are also given for the planar (-) model in a
transverse field. We treat the quantum problem in one dimension by perturbation
theory at small and numerically over a large range of . We obtain the
spin density profile by fixing the spins at opposite ends of the chain to have
opposite signs of . One dimension is special in that there the quantum
width of the wall is proportional to the size of the system. We also study
the quantitative features of the `particle' band which extends up to energies
of order above the ground state. Except for the planar limit, this particle
band is well separated from excitations having energy involving creation
of more walls. At large this particle band develops energy gaps and the
lowest sub-band has tunnel splittings of order . This scale of
energy gives rise to anomalous scaling with respect to a) finite size, b)
temperature, or c) random potentials. The intrinsic width of the domain wall
and the pinning energy are also defined and calculated in certain limiting
cases. The general conclusion is that quantum effects prevent the wall from
being sharp and in higher dimension would prevent sudden excursions in the
configuration of the wall.Comment: 40 pages and 13 figures, Phys. Rev. B, to be publishe
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