Deformations and dilations of chaotic billiards, dissipation rate, and quasi-orthogonality of the boundary wavefunctions

We consider chaotic billiards in d dimensions, and study the matrix elements M_{nm} corresponding to general deformations of the boundary. We analyze the dependence of |M_{nm}|^2 on \omega = (E_n-E_m)/\hbar using semiclassical considerations. This relates to an estimate of the energy dissipation rate when the deformation is periodic at frequency \omega. We show that for dilations and translations of the boundary, |M_{nm}|^2 vanishes like \omega^4 as \omega -> 0, for rotations like \omega^2, whereas for generic deformations it goes to a constant. Such special cases lead to quasi-orthogonality of the eigenstates on the boundary.Comment: 4 pages, 3 figure

Transformation toughened ceramics for the heavy duty diesel engine technology program

The objective of this program is to develop an advanced high temperature oxide structural ceramic for application to the heavy duty diesel engine. The approach is to employ transformation toughening by additions of ZrO.5HfO.5O2 solid solution to the oxide ceramics, mullite (2Al2O3S2SiO2) and alumina (Al2O3). The study is planned for three phases, each 12 months in duration. This report covers Phase 1. During this period, processing techniques were developed to incorporate the ZrO.5HfO.5O2 solid solution in the matrices while retaining the necessary metastable tetragonal phase. Modulus of rupture and of elasticity, coefficient of thermal expansion, fracture toughness by indent technique and thermal diffusivity of representative specimens were measured. In Phase 2, the process will be improved to provide higher mechanical strength and to define the techniques for scale up to component size. In Phase 3, full scale component prototypes will be fabri-]cated

Vertical profiles of droplet effective radius in shallow convective clouds

Conventional satellite retrievals can only provide information on cloud-top droplet effective radius (<i>r</i><sub>e</sub>). Given the fact that cloud ensembles in a satellite snapshot have different cloud-top heights, Rosenfeld and Lensky (1998) used the cloud-top height and the corresponding cloud-top <i>r</i><sub>e</sub> from the cloud ensembles in the snapshot to construct a profile of <i>r</i><sub>e</sub> representative of that in the individual clouds. This study investigates the robustness of this approach in shallow convective clouds based on results from large-eddy simulations (LES) for clean (aerosol mixing ratio <i>N</i><sub>a</sub> = 25 mg<sup>−1</sup>), intermediate (<i>N</i><sub>a</sub> = 100 mg<sup>−1</sup>), and polluted (<i>N</i><sub>a</sub> = 2000 mg<sup>−1</sup>) conditions. The cloud-top height and the cloud-top <i>r</i><sub>e</sub> from the modeled cloud ensembles are used to form a constructed <i>r</i><sub>e</sub> profile, which is then compared to the in-cloud <i>r</i><sub>e</sub> profiles. For the polluted and intermediate cases where precipitation is negligible, the constructed <i>r</i><sub>e</sub> profiles represent the in-cloud <i>r</i><sub>e</sub> profiles fairly well with a low bias (about 10 %). The method used in Rosenfeld and Lensky (1998) is therefore validated for nonprecipitating shallow cumulus clouds. For the clean, drizzling case, the in-cloud <i>r</i><sub>e</sub> can be very large and highly variable, and quantitative profiling based on cloud-top <i>r</i><sub>e</sub> is less useful. The differences in <i>r</i><sub>e</sub> profiles between clean and polluted conditions derived in this manner are however, distinct. This study also investigates the subadiabatic characteristics of the simulated cumulus clouds to reveal the effect of mixing on <i>r</i><sub>e</sub> and its evolution. Results indicate that as polluted and moderately polluted clouds develop into their decaying stage, the subadiabatic fraction <i>f</i><sub>ad</sub> becomes smaller, representing a higher degree of mixing, and <i>r</i><sub>e</sub> becomes smaller (~10 %) and more variable. However, for the clean case, smaller <i>f</i><sub>ad</sub> corresponds to larger <i>r</i><sub>e</sub> (and larger <i>r</i><sub>e</sub> variability), reflecting the additional influence of droplet collision-coalescence and sedimentation on <i>r</i><sub>e</sub>. Finally, profiles of the vertically inhomogeneous clouds as simulated by the LES and those of the vertically homogeneous clouds are used as input to a radiative transfer model to study the effect of cloud vertical inhomogeneity on shortwave radiative forcing. For clouds that have the same liquid water path, <i>r</i><sub>e</sub> of a vertically homogeneous cloud must be about 76–90 % of the cloud-top <i>r</i><sub>e</sub> of the vertically inhomogeneous cloud in order for the two clouds to have the same shortwave radiative forcing

Anyonic Realization of the Quantum Affine Lie Algebra U_q(A_N)

We give a realization of quantum affine Lie algebra $U_q(\hat A_{N-1})$ in terms of anyons defined on a two-dimensional lattice, the deformation parameter $q$ being related to the statistical parameter $\nu$ of the anyons by $q = e^{i\pi\nu}$. In the limit of the deformation parameter going to one we recover the Feingold-Frenkel fermionic construction of undeformed affine Lie algebra.Comment: 13p LaTeX Document (should be run twice

Quantum-Mechanical Non-Perturbative Response of Driven Chaotic Mesoscopic Systems

Consider a time-dependent Hamiltonian $H(Q,P;x(t))$ with periodic driving $x(t)=A\sin(\Omega t)$. It is assumed that the classical dynamics is chaotic, and that its power-spectrum extends over some frequency range $|\omega|<\omega_{cl}$. Both classical and quantum-mechanical (QM) linear response theory (LRT) predict a relatively large response for $\Omega<\omega_{cl}$, and a relatively small response otherwise, independently of the driving amplitude $A$. We define a non-perturbative regime in the $(\Omega,A)$ space, where LRT fails, and demonstrate this failure numerically. For $A>A_{prt}$, where $A_{prt}\propto\hbar$, the system may have a relatively strong response for $\Omega>\omega_{cl}$, and the shape of the response function becomes $A$ dependent.Comment: 4 pages, 2 figures, revised version with much better introductio

The Bloch-Okounkov correlation functions, a classical half-integral case

Bloch and Okounkov's correlation function on the infinite wedge space has connections to Gromov-Witten theory, Hilbert schemes, symmetric groups, and certain character functions of \hgl_\infty-modules of level one. Recent works have calculated these character functions for higher levels for \hgl_\infty and its Lie subalgebras of classical type. Here we obtain these functions for the subalgebra of type $D$ of half-integral levels and as a byproduct, obtain $q$-dimension formulas for integral modules of type $D$ at half-integral level.Comment: v2: minor changes to the introduction; accepted for publication in Letters in Mathematical Physic

Global Diffusion in a Realistic Three-Dimensional Time-Dependent Nonturbulent Fluid Flow

We introduce and study the first model of an experimentally realizable three-dimensional time-dependent nonturbulent fluid flow to display the phenomenon of global diffusion of passive-scalar particles at arbitrarily small values of the nonintegrable perturbation. This type of chaotic advection, termed {\it resonance-induced diffusion\/}, is generic for a large class of flows.Comment: 4 pages, uuencoded compressed postscript file, to appear in Phys. Rev. Lett. Also available on the WWW from http://formentor.uib.es/~julyan/, or on paper by reques

An accelerator mode based technique for studying quantum chaos

We experimentally demonstrate a method for selecting small regions of phase space for kicked rotor quantum chaos experiments with cold atoms. Our technique uses quantum accelerator modes to selectively accelerate atomic wavepackets with localized spatial and momentum distributions. The potential used to create the accelerator mode and subsequently realize the kicked rotor system is formed by a set of off-resonant standing wave light pulses. We also propose a method for testing whether a selected region of phase space exhibits chaotic or regular behavior using a Ramsey type separated field experiment.Comment: 5 pages, 3 figures, some modest revisions to previous version (esp. to the figures) to aid clarity; accepted for publication in Physical Review A (due out on January 1st 2003

Quadratic Volume Preserving Maps

We study quadratic, volume preserving diffeomorphisms whose inverse is also quadratic. Such maps generalize the Henon area preserving map and the family of symplectic quadratic maps studied by Moser. In particular, we investigate a family of quadratic volume preserving maps in three space for which we find a normal form and study invariant sets. We also give an alternative proof of a theorem by Moser classifying quadratic symplectic maps.Comment: Ams LaTeX file with 4 figures (figure 2 is gif, the others are ps