Ergodicity and Mixing in Quantum Dynamics

After a brief historical review of ergodicity and mixing in dynamics, particularly in quantum dynamics, we introduce definitions of quantum ergodicity and mixing using the structure of the system's energy levels and spacings. Our definitions are consistent with usual understanding of ergodicity and mixing. Two parameters concerning the degeneracy in energy levels and spacings are introduced. They are computed for right triangular billiards and the results indicate a very close relation between quantum ergodicity (mixing) and quantum chaos. At the end, we argue that, besides ergodicity and mixing, there may exist a third class of quantum dynamics which is characterized by a maximized entropy.Comment: 10 pages, 6 figures and 1 tabl

Microphysical Properties of Frozen Particles Inferred from Global Precipitation Measurement (GPM) Microwave Imager (GMI) Polarimetric Measurements

Scattering differences induced by frozen particle microphysical properties are investigated, using the vertically (V) and horizontally (H) polarized radiances from the Global Precipitation Measurement (GPM) Microwave Imager (GMI) 89 and 166GHz channels. It is the first study on global frozen particle microphysical properties that uses the dual-frequency microwave polarimetric signals. From the ice cloud scenes identified by the 183.3 3GHz channel brightness temperature (TB), we find that the scatterings of frozen particles are highly polarized with V-H polarimetric differences (PD) being positive throughout the tropics and the winter hemisphere mid-latitude jet regions, including PDs from the GMI 89 and 166GHz TBs, as well as the PD at 640GHz from the ER-2 Compact Scanning Submillimeter-wave Imaging Radiometer (CoSSIR) during the TC4 campaign. Large polarization dominantly occurs mostly near convective outflow region (i.e., anvils or stratiform precipitation), while the polarization signal is small inside deep convective cores as well as at the remote cirrus region. Neglecting the polarimetric signal would result in as large as 30 error in ice water path retrievals. There is a universal bell-curve in the PD TB relationship, where the PD amplitude peaks at 10K for all three channels in the tropics and increases slightly with latitude. Moreover, the 166GHz PD tends to increase in the case where a melting layer is beneath the frozen particles aloft in the atmosphere, while 89GHz PD is less sensitive than 166GHz to the melting layer. This property creates a unique PD feature for the identification of the melting layer and stratiform rain with passive sensors. Horizontally oriented non-spherical frozen particles are thought to produce the observed PD because of different ice scattering properties in the V and H polarizations. On the other hand, changes in the ice microphysical habitats or orientation due to turbulence mixing can also lead to a reduced PD in the deep convective cores. The current GMI polarimetric measurements themselves cannot fully disentangle the possible mechanisms

IceCube SWIRP

Clouds, ice clouds in particular, are a major source of uncertainty in climate models. Submm-wave sensors fill the sensitivity gap between MW and IR.Cloud microphysical properties (particle size and shape) account for large (200 and 40) measurement uncertainty

A novel dynamic reliability-based topology optimization (DRBTO)framework for continuum structures via interval-process collocation and the first-passage theories

In view of the general inertia and damping features as well as the inevitable uncertainty factors in engineering structures,a novel dynamic reliability-based topology optimization (DRBTO) strategy is investigated for time-variant mechanical systemswith overall consideration of material dispersion and loading deviation effects. The static interval-set model is first utilized toquantify multi-source uncertainty inputs and the transient interval-process model is then established to characterize unknown-but-bounded response results, which can be readily solved through the proposed interval-process collocation approach combinedwith a classical Newmark difference scheme. Different from the traditional deterministic design framework, the present DRBTOscheme will directly consider new reliability constraints, for which the non-probabilistic time-variant reliability (NTR) index ismathematically deduced using the first-passage principle. In addition, the issues related to uncertainty-oriented design sensitivityand filtering method are discussed. The usage and effectiveness of DRBTO are demonstrated with three numerical examples