Sequences with long range exclusions

Given an alphabet $S$, we consider the size of the subsets of the full sequence space $S^{\rm {\bf Z}}$ determined by the additional restriction that $x_i\not=x_{i+f(n)},\ i\in {\rm {\bf Z}},\ n\in {\rm {\bf N}}.$ Here $f$ is a positive, strictly increasing function. We review an other, graph theoretic, formulation and then the known results covering various combinations of $f$ and the alphabet size. In the second part of the paper we turn to the fine structure of the allowed sequences in the particular case where $f$ is a suitable polynomial. The generation of sequences leads naturally to consider the problem of their maximal length, which turns out highly random asymptotically in the alphabet size.Comment: 18 pages, 3 figures. Replaces earlier version, submission 1204.3439, major updat

Generation of attenuation corrected images from lidar data

The interpretation of data generated by aerosol backscatter lidars is often facilitated by presentation of RHI and PPI images. These pictures are especially useful in studies of atmospheric boundary layer structure where convective elements, stratifications and aerosol laden plumes can be easily delineated. Procedures used at the University of Wisconsin to generate lidar images on a color enhanced raster scan display are described

Summary of results and conclusions based on analysis of volume imaging and high spectral resolution lidar data acquired during FIRE phase 1, part 1

The collection of long term global statistics on cloud cover may be most easily accomplished with satellite based observations; however, measurements derived from passive satellite retrieval methods must be calibrated and verified by in situ or ground based remote sensor observations. Verification is not straight forward, however, because the highly variable nature of cloud altitude, morphology, and optical characteristics complicates the scaling of point measurements to satellite footprint sized areas. This is particularly evident for cirrus clouds which may be organized on horizontal scales of 10's of meters to 8 km or more, and have optical depths ranging from less than .003 to greater than 3. Cirrus clouds can strongly influence earths' radiative balance, but, because they are often transmissive, cirrus clouds are difficult to detect and characterize from satellite measurements. Because of its precise ranging capabilities, spatial resolution and sensitivity, lidar observations have played an important role in the detection, depiction, and characterization of cirrus clouds. Some of the characteristics of cirrus clouds are summarized which observed the High Spectral Resolution and Volume Imaging Lidars during the phase 1 IFO and ETO periods

Summary of results and conclusions based on analysis of volume imaging and high spectral resolution lidar data acquired during FIRE phase 1, part 2

Since the fall of 1986, cirrus clouds were observed with backscatter cross sections ranging from less than 1 x 10(exp -7) to 4.2 x 10(exp -5)m/sr, optical thicknesses ranging from less than .003 to greater than 2.7, and bulk average backscatter phase functions from .02 to .065/sr. Cirrus cloud structures were recorded ranging in vertical extent from 0.1 to 8 km, having horizontal scales from 10's of meters to 266 km, and exhibiting aspect ratios of from 1:5 to 1:100. The altitude relationship between cloud top and bottom boundaries and the optical center of the cloud is influenced by the type of formation observed. Cirrus morphology and generation processes appear to be related to the wind field. The high spectral resolution lidar (HSRL) was adapted to the task of cirrus cloud optical property measurement. The HSRL data reported were collected with the CuCl2 transmitter producing 50 mW of output power, achieving eye safe, direct optical depth and backscatter cross section measurements with 10 minute averaging times

The onset of nanoscale dissipation in superfluid He-4 at zero temperature: the role of vortex shedding and cavitation

Two-dimensional flow past an infinitely long cylinder of nanoscopic radius in superfluid He-4 at zero temperature is studied by time-dependent density functional theory. The calculations reveal two distinct critical phenomena for the onset of dissipation: 1) vortex-antivortex pair shedding from the periphery of the moving cylinder and 2) appearance of cavitation in the wake, which possesses similar geometry as observed experimentally for fast moving micrometer-scale particles in superfluid He-4. Vortex pairs with the same circulation are occasionally emitted in the form of dimers, which constitute the building blocks for the Benard-von Karman vortex street structure observed in classical turbulent fluids and Bose-Einstein condensates. The cavitation induced dissipation mechanism should be common to all superfluids that are self-bound and have a finite surface tension, which include the recently discovered self-bound droplets in ultracold Bose gases.Comment: 5 pages, 6 figure

First observation of bright solitons in bulk superfluid He-4

The existence of bright solitons in bulk superfluid He-4 is demonstrated by time-resolved shadowgraph i maging experiments and density functional theory (DFT) calculations. The initial liquid compression that leads to the creation of non-linear waves is produced by rapidly expanding plasma from laser ablation. Af ter the leading dissipative period, these waves transform into bright solitons, which exhibit three chara cteristic features: dispersionless propagation, negligible interaction in two-wave collision, and direct dependence between soliton amplitude and the propagation velocity. The experimental observations are supp orted by DFT calculations, which show rapid evolution of the initially compressed liquid into bright soli tons. At high amplitudes, solitons become unstable and break down into dispersive shock waves.Comment: 5 pages, 6 figures (accepted for publication in Phys. Rev. Lett.

Upper Bound on the Products of Particle Interactions in Cellular Automata

Particle-like objects are observed to propagate and interact in many spatially extended dynamical systems. For one of the simplest classes of such systems, one-dimensional cellular automata, we establish a rigorous upper bound on the number of distinct products that these interactions can generate. The upper bound is controlled by the structural complexity of the interacting particles---a quantity which is defined here and which measures the amount of spatio-temporal information that a particle stores. Along the way we establish a number of properties of domains and particles that follow from the computational mechanics analysis of cellular automata; thereby elucidating why that approach is of general utility. The upper bound is tested against several relatively complex domain-particle cellular automata and found to be tight.Comment: 17 pages, 12 figures, 3 tables, http://www.santafe.edu/projects/CompMech/papers/ub.html V2: References and accompanying text modified, to comply with legal demands arising from on-going intellectual property litigation among third parties. V3: Accepted for publication in Physica D. References added and other small changes made per referee suggestion