Two-point correlation properties of stochastic "cloud processes''

We study how the two-point density correlation properties of a point particle distribution are modified when each particle is divided, by a stochastic process, into an equal number of identical "daughter" particles. We consider generically that there may be non-trivial correlations in the displacement fields describing the positions of the different daughters of the same "mother" particle, and then treat separately the cases in which there are, or are not, correlations also between the displacements of daughters belonging to different mothers. For both cases exact formulae are derived relating the structure factor (power spectrum) of the daughter distribution to that of the mother. These results can be considered as a generalization of the analogous equations obtained in ref. [1] (cond-mat/0409594) for the case of stochastic displacement fields applied to particle distributions. An application of the present results is that they give explicit algorithms for generating, starting from regular lattice arrays, stochastic particle distributions with an arbitrarily high degree of large-scale uniformity.Comment: 14 pages, 3 figure

Tiling Spaces are Inverse Limits

Let M be an arbitrary Riemannian homogeneous space, and let Omega be a space of tilings of M, with finite local complexity (relative to some symmetry group Gamma) and closed in the natural topology. Then Omega is the inverse limit of a sequence of compact finite-dimensional branched manifolds. The branched manifolds are (finite) unions of cells, constructed from the tiles themselves and the group Gamma. This result extends previous results of Anderson and Putnam, of Ormes, Radin and Sadun, of Bellissard, Benedetti and Gambaudo, and of G\"ahler. In particular, the construction in this paper is a natural generalization of G\"ahler's.Comment: Latex, 6 pages, including one embedded figur

The structure of the hard sphere solid

We show that near densest-packing the perturbations of the HCP structure yield higher entropy than perturbations of any other densest packing. The difference between the various structures shows up in the correlations between motions of nearest neighbors. In the HCP structure random motion of each sphere impinges slightly less on the motion of its nearest neighbors than in the other structures.Comment: For related papers see: http://www.ma.utexas.edu/users/radin/papers.htm

Nutrients elimination from meat processing wastewater using Scenedesmus sp.; optimizations; artificial neural network and kinetics models

The potential of an algae-based system as an environmentally friendly and low-cost wa�ter treatment method to eliminate contaminants from water bodies has been considered. The purpose of this research was to see how effective Scenedesmus sp is in eliminating nutrients from meat processing wastewater (MPWW) throughout the phycoremediation process. Response surface methodology (RSM) and an artificial neural network (ANN) model were applied to improve the inactivation process as a function of cell concentra�tions (3–7 log10 CFU/mL) and time (1–13 days). At 103 to 107 cell/mL of Scenedesmus sp., phycoremediation was carried out at atmospheric temperature (28 ± 2 ◦C, ±2500lux for 12:12 h of light/dark and pH 8). The findings documented 73.76% as the highest removal efficacy of total nitrogen (TN) and 77.85% of total phosphorus (TP), 75.40% of ammonia nitrogen (NH4-H), 77.88% of orthophosphate (PO3− 4 ), and 64.97% of chemical oxygen demand (COD). The ANN revealed that both factors contribute significantly to the nutrient removal process. The batch kinetic coefficients of NH4-H removal were Km = 40.10 mg/L and k = 1.43 mg mg −1Chl a d −1 . Meanwhile, for PO3− 4 , 1.07 mg mg −1Chl a d−1 , as well as 42.80 mg/L, were obtained. The NH4-N yield coefficient of NH4-N was Yn = 0.0192 mg Chl a mg −1 while PO3− 4 was equal to Yp = 0.0409 mg Chl a mg −1 . These findings indicated successful use of Scenedesmus sp. for efficient pollutant removal from meat processing wastewater plants

How model sets can be determined by their two-point and three-point correlations

We show that real model sets with real internal spaces are determined, up to translation and changes of density zero by their two- and three-point correlations. We also show that there exist pairs of real (even one dimensional) aperiodic model sets with internal spaces that are products of real spaces and finite cyclic groups whose two- and three-point correlations are identical but which are not related by either translation or inversion of their windows. All these examples are pure point diffractive. Placed in the context of ergodic uniformly discrete point processes, the result is that real point processes of model sets based on real internal windows are determined by their second and third moments.Comment: 19 page

Approach to equilibrium for a class of random quantum models of infinite range

We consider random generalizations of a quantum model of infinite range introduced by Emch and Radin. The generalization allows a neat extension from the class $l_1$ of absolutely summable lattice potentials to the optimal class $l_2$ of square summable potentials first considered by Khanin and Sinai and generalised by van Enter and van Hemmen. The approach to equilibrium in the case of a Gaussian distribution is proved to be faster than for a Bernoulli distribution for both short-range and long-range lattice potentials. While exponential decay to equilibrium is excluded in the nonrandom $l_1$ case, it is proved to occur for both short and long range potentials for Gaussian distributions, and for potentials of class $l_2$ in the Bernoulli case. Open problems are discussed.Comment: 10 pages, no figures. This last version, to appear in J. Stat. Phys., corrects some minor errors and includes additional references and comments on the relation to experiment

Renormalization of the Inverse Square Potential

The quantum-mechanical D-dimensional inverse square potential is analyzed using field-theoretic renormalization techniques. A solution is presented for both the bound-state and scattering sectors of the theory using cutoff and dimensional regularization. In the renormalized version of the theory, there is a strong-coupling regime where quantum-mechanical breaking of scale symmetry takes place through dimensional transmutation, with the creation of a single bound state and of an energy-dependent s-wave scattering matrix element.Comment: 5 page

Stimulation in vitro of galactocerebroside galactosidase by N‐decanoyl 2‐amino‐2‐methylpropanol

Amides resembling ceramide (fatty acyl sphingosine) were synthesized and tested in vitro for their effects on the rat brain β‐galactosidase which hydrolyzes galactosyl ceramide. The N‐decanoyl derivative of 2‐amino‐2‐methyl‐1‐propanol was most effective, giving a 34% stimulation at 0.15 mM concentration and a 60% stimulation at maximal levels. Addition of a hydroxyl group in the 3 position reduced the degree of stimulation, as did increasing or decreasing the length of the fatty acid portion. Omission of the branched methyl group resulted in inhibition instead of stimulation. Kinetic analysis indicates that the stimulator does not affect the binding of substrate to enzyme, but does speed the rate of hydrolytic action. Stimulation was also observed with the cerebrosidase in spleen and kidney. It is suggested that the stimulators act on an enzyme site other than the substrate‐active site.Peer Reviewedhttps://deepblue.lib.umich.edu/bitstream/2027.42/141447/1/lipd0056.pd