Ill-posedness of degenerate dispersive equations

In this article we provide numerical and analytical evidence that some degenerate dispersive partial differential equations are ill-posed. Specifically we study the K(2,2) equation $u_t = (u^2)_{xxx} + (u^2)_{x}$ and the "degenerate Airy" equation $u_t = 2 u u_{xxx}$. For K(2,2) our results are computational in nature: we conduct a series of numerical simulations which demonstrate that data which is very small in $H^2$ can be of unit size at a fixed time which is independent of the data's size. For the degenerate Airy equation, our results are fully rigorous: we prove the existence of a compactly supported self-similar solution which, when combined with certain scaling invariances, implies ill-posedness (also in $H^2$)

On Unitarity Based Relations Between Various Lepton Family Violating Processes

Simple "unitarity inspired" relations between two- and three-body lepton flavor violating decays are noted and discussed. In the absence of cancellations, the existing strong bounds on $\mu \to 3e$ and $\mu\to e\gamma\gamma$ severly constrain two-body lepton flavor violating decays.Comment: 5 pages, 3 figure

Response of selected plant and insect species to simulated solid rocket exhaust mixtures and to exhaust components from solid rocket fuels

The effects of solid rocket fuel (SRF) exhaust on selected plant and and insect species in the Merritt Island, Florida area was investigated in order to determine if the exhaust clouds generated by shuttle launches would adversely affect the native, plants of the Merritt Island Wildlife Refuge, the citrus production, or the beekeeping industry of the island. Conditions were simulated in greenhouse exposure chambers and field chambers constructed to model the ideal continuous stirred tank reactor. A plant exposure system was developed for dispensing and monitoring the two major chemicals in SRF exhaust, HCl and Al203, and for dispensing and monitoring SRF exhaust (controlled fuel burns). Plants native to Merritt Island, Florida were grown and used as test species. Dose-response relationships were determined for short term exposure of selected plant species to HCl, Al203, and mixtures of the two to SRF exhaust

Graduate Quantum Mechanics Reform

We address four main areas in which graduate quantum mechanics education can be improved: course content, textbook, teaching methods, and assessment tools. We report on a three year longitudinal study at the Colorado School of Mines using innovations in all these areas. In particular, we have modified the content of the course to reflect progress in the field in the last 50 years, used textbooks that include such content, incorporated a variety of teaching techniques based on physics education research, and used a variety of assessment tools to study the effectiveness of these reforms. We present a new assessment tool, the Graduate Quantum Mechanics Conceptual Survey, and further testing of a previously developed assessment tool, the Quantum Mechanics Conceptual Survey. We find that graduate students respond well to research-based techniques that have been tested mainly in introductory courses, and that they learn much of the new content introduced in each version of the course. We also find that students' ability to answer conceptual questions about graduate quantum mechanics is highly correlated with their ability to solve calculational problems on the same topics. In contrast, we find that students' understanding of basic undergraduate quantum mechanics concepts at the modern physics level is not improved by instruction at the graduate level.Comment: accepted to American Journal of Physic

Finite-size scaling in thin Fe/Ir(100) layers

The critical temperature of thin Fe layers on Ir(100) is measured through M\"o{\ss}bauer spectroscopy as a function of the layer thickness. From a phenomenological finite-size scaling analysis, we find an effective shift exponent lambda = 3.15 +/- 0.15, which is twice as large as the value expected from the conventional finite-size scaling prediction lambda=1/nu, where nu is the correlation length critical exponent. Taking corrections to finite-size scaling into account, we derive the effective shift exponent lambda=(1+2\Delta_1)/nu, where Delta_1 describes the leading corrections to scaling. For the 3D Heisenberg universality class, this leads to lambda = 3.0 +/- 0.1, in agreement with the experimental data. Earlier data by Ambrose and Chien on the effective shift exponent in CoO films are also explained.Comment: Latex, 4 pages, with 2 figures, to appear in Phys. Rev. Lett

Is it still worth searching for lepton flavor violation in rare kaon decays?

Prospective searches for lepton flavor violation (LFV) in rare kaon decays at the existing and future intermediate-energy accelerators are considered. The proposed studies are complementary to LFV searches in muon-decay experiments and offer a unique opportunity to probe models with approximately conserved fermion-generation quantum number with sensitivity superior to that in other processes. Consequently, new searches for LFV in kaon decays are an important and independent part of the general program of searches for lepton flavor violation in the final states with charged leptons.Comment: 30 pages, 10 figures. An extended version of the talk given at the Chicago Flavor Seminar, February 27, 2004. In the new version some misprints were corrected and some new data for LFV-processes were added. The main content of the paper was not changed. The paper is published in Yad. Fiz. 68, 1272 (2005

First Observation of the Rare Decay Mode K-long -> e+ e-

In an experiment designed to search for and study very rare two-body decay modes of the K-long, we have observed four examples of the decay K-long -> e+ e-, where the expected background is 0.17+-0.10 events. This observation translates into a branching fraction of 8.7^{+5.7}_{-4.1} X 10^{-12}, consistent with recent theoretical predictions. This result represents by far the smallest branching fraction yet measured in particle physics.Comment: 9 pages, 3 figure

Large time wellposdness to the 3-D Capillary-Gravity Waves in the long wave regime

In the regime of weakly transverse long waves, given long-wave initial data, we prove that the nondimensionalized water wave system in an infinite strip under influence of gravity and surface tension on the upper free interface has a unique solution on [0,{T}/\eps] for some \eps independent of constant $T.$ We shall prove in the subsequent paper \cite{MZZ2} that on the same time interval, these solutions can be accurately approximated by sums of solutions of two decoupled Kadomtsev-Petviashvili (KP) equations.Comment: Split the original paper(The long wave approximation to the 3-D capillary-gravity waves) into two parts, this is the first on