What is the Relevant Parcel? Clarifying the Parcel as a Whole Standard in Murr v. Wisconsin

Murr v. Wisconsin seeks to determine whether commonly-owned, adjacent parcels of land are considered as 1 or 2 parcels for purposes of analyzing a regulatory takings claim. Nearly 40 years ago, the Court in Penn Central rejected a property owner\u27s takings claim which segmenting the entire parcel into discrete property rights because a compensatory taking must result from governmental action which interferes with the parcel as a whole. In Murr, property owners argue that a local zoning ordinance effected a taking of one of their two adjoining parcels because the ordinance prohibited the owners from developing their lot. I argue that the property owners deserve just compensation because of both material factual errors in the state court opinions and that Penn Central\u27s rejection of segmenting parcels does not require the aggregation of adjacent parcels

Generation of non-Gaussian statistics and coherent structures in ideal magnetohydrodynamics

Spectral method simulations of ideal magnetohydrodynamics are used to investigate production of coherent small scale structures, a feature of fluid models that is usually associated with inertial range signatures of nonuniform dissipation, and the associated emergence of non-Gaussian statistics. The near-identical growth of non-Gaussianity in ideal and nonideal cases suggests that generation of coherent structures and breaking of self-similarity are essentially ideal processes. This has important implications for understanding the origin of intermittency in turbulence

An update on the double cascade scenario in two-dimensional turbulence

Statistical features of homogeneous, isotropic, two-dimensional turbulence is discussed on the basis of a set of direct numerical simulations up to the unprecedented resolution $32768^2$. By forcing the system at intermediate scales, narrow but clear inertial ranges develop both for the inverse and for direct cascades where the two Kolmogorov laws for structure functions are, for the first time, simultaneously observed. The inverse cascade spectrum is found to be consistent with Kolmogorov-Kraichnan prediction and is robust with respect the presence of an enstrophy flux. The direct cascade is found to be more sensible to finite size effects: the exponent of the spectrum has a correction with respect theoretical prediction which vanishes by increasing the resolution

Non-unique factorization of polynomials over residue class rings of the integers

We investigate non-unique factorization of polynomials in Z_{p^n}[x] into irreducibles. As a Noetherian ring whose zero-divisors are contained in the Jacobson radical, Z_{p^n}[x] is atomic. We reduce the question of factoring arbitrary non-zero polynomials into irreducibles to the problem of factoring monic polynomials into monic irreducibles. The multiplicative monoid of monic polynomials of Z_{p^n}[x] is a direct sum of monoids corresponding to irreducible polynomials in Z_p[x], and we show that each of these monoids has infinite elasticity. Moreover, for every positive integer m, there exists in each of these monoids a product of 2 irreducibles that can also be represented as a product of m irreducibles.Comment: 11 page

Anomalous scaling in two and three dimensions for a passive vector field advected by a turbulent flow

A model of the passive vector field advected by the uncorrelated in time Gaussian velocity with power-like covariance is studied by means of the renormalization group and the operator product expansion. The structure functions of the admixture demonstrate essential power-like dependence on the external scale in the inertial range (the case of an anomalous scaling). The method of finding of independent tensor invariants in the cases of two and three dimensions is proposed to eliminate linear dependencies between the operators entering into the operator product expansions of the structure functions. The constructed operator bases, which include the powers of the dissipation operator and the enstrophy operator, provide the possibility to calculate the exponents of the anomalous scaling.Comment: 9 pages, LaTeX2e(iopart.sty), submitted to J. Phys. A: Math. Ge

Performance characteristics of wind profiling radars

Doppler radars used to measure winds in the troposphere and lower stratosphere for weather analysis and forecasting are lower-sensitivity versions of mesosphere-stratosphere-troposphere radars widely used for research. The term wind profiler is used to denote these radars because measurements of vertical profiles of horizontal and vertical wind are their primary function. It is clear that wind profilers will be in widespread use within five years: procurement of a network of 30 wind profilers is underway. The Wave Propagation Laboratory (WPL) has operated a small research network of radar wind profilers in Colorado for about two and one-half years. The transmitted power and antenna aperture for these radars is given. Data archiving procedures have been in place for about one year, and this data base is used to evaluate the performance of the radars. One of the prime concerns of potential wind profilers users is how often and how long wind measurements are lacking at a given height. Since these outages constitute an important part of the performance of the wind profilers, they are calculated at three radar frequencies, 50-, 405-, and 915-MHz, (wavelengths of 6-, 0.74-, and 0.33-m) at monthly intervals to determine both the number of outages at each frequency and annual variations in outages

Mirror reflectometer based on optical cavity decay time

Described is a reflectometer capable of making reflectivity measurements of low-loss highly reflecting mirror coatings and transmission measurements of low-loss antireflection coatings. The technique directly measures the intensity decay time of an optical cavity comprised of low-loss elements. We develop the theoretical framework for the device and discuss in what conditions and to what extent the decay time represents a true measure of mirror reflectivity. Current apparatus provides a decay time resolution of 10 nsec and has demonstrated a cavity total loss resolution of 5 ppm

On the decay of Burgers turbulence

This work is devoted to the decay ofrandom solutions of the unforced Burgers equation in one dimension in the limit of vanishing viscosity. The initial velocity is homogeneous and Gaussian with a spectrum proportional to $k^n$ at small wavenumbers $k$ and falling off quickly at large wavenumbers. In physical space, at sufficiently large distances, there is an ``outer region'', where the velocity correlation function preserves exactly its initial form (a power law) when $n$ is not an even integer. When $1<n<2$ the spectrum, at long times, has three scaling regions : first, a $|k|^n$ region at very small $k$\ms1 with a time-independent constant, stemming from this outer region, in which the initial conditions are essentially frozen; second, a $k^2$ region at intermediate wavenumbers, related to a self-similarly evolving ``inner region'' in physical space and, finally, the usual $k^{-2}$ region, associated to the shocks. The switching from the $|k|^n$ to the $k^2$ region occurs around a wave number $k_s(t) \propto t^{-1/[2(2-n)]}$, while the switching from $k^2$ to $k^{-2}$ occurs around $k_L(t)\propto t^{-1/2}$ (ignoring logarithmic corrections in both instances). The key element in the derivation of the results is an extension of the Kida (1979) log-corrected $1/t$ law for the energy decay when $n=2$ to the case of arbitrary integer or non-integer $n>1$. A systematic derivation is given in which both the leading term and estimates of higher order corrections can be obtained. High-resolution numerical simulations are presented which support our findings.Comment: In LaTeX with 11 PostScript figures. 56 pages. One figure contributed by Alain Noullez (Observatoire de Nice, France

Universal decay of scalar turbulence

The asymptotic decay of passive scalar fields is solved analytically for the Kraichnan model, where the velocity has a short correlation time. At long times, two universality classes are found, both characterized by a distribution of the scalar -- generally non-Gaussian -- with global self-similar evolution in time. Analogous behavior is found numerically with a more realistic flow resulting from an inverse energy cascade.Comment: 4 pages, 3 Postscript figures, submitted to PR