An affine approach to Peterson comparison

The Peterson comparison formula proved by Woodward relates the three-pointedGromov-Witten invariants for the quantum cohomology of partial flag varietiesto those for the complete flag. Another such comparison can be obtained bycomposing a combinatorial version of the Peterson isomorphism with a result ofLapointe and Morse relating quantum Littlewood-Richardson coefficients for theGrassmannian to k-Schur analogs in the homology of the affine Grassmannianobtained by adding rim hooks. We show that these comparisons on quantumcohomology are equivalent, up to Postnikov's strange duality isomorphism.<br

Spectroscopy of drums and quantum billiards: perturbative and non-perturbative results

We develop powerful numerical and analytical techniques for the solution of the Helmholtz equation on general domains. We prove two theorems: the first theorem provides an exact formula for the ground state of an arbirtrary membrane, while the second theorem generalizes this result to any excited state of the membrane. We also develop a systematic perturbative scheme which can be used to study the small deformations of a membrane of circular or square shapes. We discuss several applications, obtaining numerical and analytical results.Comment: 29 pages, 12 figures, 7 tabl

Energy in one dimensional linear waves in a string

We consider the energy density and energy transfer in small amplitude, one-dimensional waves on a string, and find that the common expressions used in textbooks for the introductory physics with calculus course give wrong results for some cases, including standing waves. We discuss the origin of the problem, and how it can be corrected in a way appropriate for the introductory calculus based physics course.Comment: 5 page

Magnetovac Cylinder to Magnetovac Torus

A method for mapping known cylindrical magnetovac solutions to solutions in torus coordinates is developed. Identification of the cylinder ends changes topology from R1 x S1 to S1 x S1. An analytic Einstein-Maxwell solution for a toroidal magnetic field in tori is presented. The toroidal interior is matched to an asymptotically flat vacuum exterior, connected by an Israel boundary layer.Comment: to appear in Class. Quant. Gra

An interacting quark-diquark model of baryons

A simple quark-diquark model of baryons with direct and exchange interactions is constructed. Spectrum and form factors are calculated and compared with experimental data. Advantages and disadvantages of the model are discussed.Comment: 13 pages, 3 eps-figures, accepted by Phys.Rev. C Rapid Communication

High rate continuous synthesis of nanocrystalline materials in a colliding vapor stream of microdroplets

Progress in nanotechnology is driving the need of large scale synthesis of functional nanomaterials. The lack of a workforce trained on process control and scale-up of nanomaterials manufacturing, the gap between laboratories and economically practical nanofabrication and the funding strain on the survivability of startup companies all contribute to the difficulties in scaling up nanotechnologies and their commercialization [1,2]. We report here a high rate continuous synthesis of functional inorganic nanomaterials using colliding vapor stream of reagents microdroplets

High rate continuous synthesis of nanocrystalline materials in a colliding vapor stream of microdroplets

Progress in nanotechnology is driving the need of large scale synthesis of functional nanomaterials. The lack of a workforce trained on process control and scale-up of nanomaterials manufacturing, the gap between laboratories and economically practical nanofabrication and the funding strain on the survivability of startup companies all contribute to the difficulties in scaling up nanotechnologies and their commercialization [1,2]. We report here a high rate continuous synthesis of functional inorganic nanomaterials using colliding vapor stream of reagents microdroplets

Collisionless Magnetic Reconnection via Alfven Eigenmodes

We propose an analytic approach to the problem of collisionless magnetic reconnection formulated as a process of Alfven eigenmodes' generation and dissipation. Alfven eigenmodes are confined by the current sheet in the same way that quantum mechanical waves are confined by the tanh^2 potential. The dynamical time scale of reconnection is the system scale divided by the eigenvalue propagation velocity of the n=1 mode. The prediction of the n=1 mode shows good agreement with the in situ measurement of the reconnection-associated Hall fields

Topological Constraints on the Charge Distributions for the Thomson Problem

The method of Morse theory is used to analyze the distributions of unit charges interacting through a repulsive force and constrained to move on the surface of a sphere -- the Thomson problem. We find that, due to topological reasons, the system may organize itself in the form of pentagonal structures. This gives a qualitative account for the interesting ``pentagonal buttons'' discovered in recent numerical work.Comment: 10 pages; dedicated to Rafael Sorkin on his 60th birthda

Two-dimensional shear modulus of a Langmuir foam

We deform a two-dimensional (2D) foam, created in a Langmuir monolayer, by applying a mechanical perturbation, and simultaneously image it by Brewster angle microscopy. We determine the foam stress tensor (through a determination of the 2D gas-liquid line tension, 2.35 $\pm$ 0.4 pJ$\cdot$m$^{-1}$) and the statistical strain tensor, by analyzing the images of the deformed structure. We deduce the 2D shear modulus of the foam, $\mu= 38 \pm 3 \mathrm{nN}\cdot \mathrm{m}^{-1}$. The foam effective rigidity is predicted to be $35 \pm 3 \mathrm {nN}\cdot \mathrm {m}^{- 1}$, which agrees with the value $37.5 \pm 0.8 \mathrm {nN}\cdot \mathrm {m}^{-1}$ obtained in an independent mechanical measurement.Comment: submitted May 12, 2003 ; resubmitted Sept 9, 200