Restoration of isotropy on fractals

We report a new type of restoration of macroscopic isotropy (homogenization) in fractals with microscopic anisotropy. The phenomenon is observed in various physical setups, including diffusions, random walks, resistor networks, and Gaussian field theories. The mechanism is unique in that it is absent in spaces with translational invariance, while universal in that it is observed in a wide class of fractals.Comment: 11 pages, REVTEX, 3 postscript figures. (Compressed and encoded figures archived by "figure" command). To appear in Physical Review Letter

Modified brinley plots: advantages and disadvantages

Accepted manuscrip

Tales From the Scales: Thomas's Promises

“I don’t suspect we lost much,” said Thomas’s Promises team captain Mario Browne of the Center for Minority Health as he anticipated this week’s midpoint weigh-in. The CMH team rose from an initial rank of 185th in the first week of the competition to 152nd after week 4. Their strategy for tipping the scales even more in their favor: Regardless of the weather, no heavy corduroys or sweaters are allowed at the weigh-in, Browne joked. Competition really isn’t high on their list of incentives, he said. “We’re not so much interested in the race; we’re more interested in the social support and the motivation to do something,” he said

Dust yields in clumpy SN shells: SN 1987A revisited

We present a study of the effects of clumping on the emergent spectral energy distribution (SED) from dusty supernova (SN) shells illuminated by a diffuse radiation source distributed throughout the medium. (...) The fully 3D radiation transport problem is solved using a Monte Carlo code, MOCASSIN, and we present a set of models aimed at investigating the sensitivity of the SEDs to various clumping parameters. We find that, contrary to the predictions of analytical prescriptions, the combination of an optical and IR observational data set is sufficient to constrain dust masses even in the case where optically thick clumps are present. Using both smoothly varying and clumped grain density distributions, we obtain new estimates for the mass of dust condensed by the Type II SN 1987A by fitting the optical and infrared spectrophotometric data of Wooden et al. (1993) at two epochs (day 615 and day 775). (...) From our numerical models we derive dust masses for SN 1987A that are comparable to previous analytic clumped graphite grain mass estimates, and at least two orders of magnitude below the 0.1-0.3 Msol that have been predicted to condense as dust grains in primordial core collapse supernova ejecta. This low condensation efficiency for SN 1987A is in contrast to the case of SN 2003gd, for which a dust condensation efficiency as large as 0.12 has recently been estimated. (Abridged)Comment: accepted for publication in MNRAS. The paper contains 15 figures and 1 tabl

How Citizenship May Be Developed Through the Course of Study in Our Secondary Schools.

The Idea of training citizens in school is not a new one. Time and again, the author has felt the urge to help his pupils in their effort to become good citizens. The outcome of his study and plan to accomplish this aim is set forth in this pamphlet. The preparation of this subject has been inspired by Professor Perry, Prairie View College, my teacher in education, summer 1932. The few suggestions found herein, in most cases, have been tried out in schools where the author has taught and attended. Mention may also be made of the several authors, whose books on education have furnished me with inspiration as well as bits of information in my endeavor to write on the subject

A Study of Retardation in Five Negro High Schools in Fort Bend County, Texas 1942-1943

Educators throughout the United States are seriously concerned with the problem of retardation, for it is fundamentally important to every community. A vast number of students are retarded year after year and it is perhaps a conservative estimate that one-third of the nation\u27s children have fallen behind a year or more. This widespread prevalence of retardation has a detrimental effect upon our schools of today. This is not only a significant problem from the standpoint of the cost to the schools and to the parents, but also from the standpoint of the humiliated and often discouraged pupil. One failure may not do serious injury to a student, but once the habit of failure is formed this habit often tends to hinder the social development of the child. Irwin and Marks1 are convinced that repeating grades is the greatest crime against the educational development of the child that the school can commit. Too much time and thought cannot be given toward analysis of the important problem and for suggestive remedial measures for the betterment of the situation. This investigation is a study of retardation in five Negro High Schools in Fort Bend County, Texas for the school year 1942-43. The problem involved in this study finds expression in a series of questions. 1. What is the status of retardation of children in the Five Negro High Schools of Fort Bend County, Texas? 2. Is the status of retardation of the children in Five Negro High Schools of Fort Bend County, Texas similar to the status of other children in the nation? 3. What are the causes of retardation? 1E. A. Irwin, and L. A. Marks, Fitting the Child to the School, New York City: The MacMillan Company, (1928), p. 317

Sub-Gaussian short time asymptotics for measure metric Dirichlet spaces

This paper presents estimates for the distribution of the exit time from balls and short time asymptotics for measure metric Dirichlet spaces. The estimates cover the classical Gaussian case, the sub-diffusive case which can be observed on particular fractals and further less regular cases as well. The proof is based on a new chaining argument and it is free of volume growth assumptions

Existence of a Meromorphic Extension of Spectral Zeta Functions on Fractals

We investigate the existence of the meromorphic extension of the spectral zeta function of the Laplacian on self-similar fractals using the classical results of Kigami and Lapidus (based on the renewal theory) and new results of Hambly and Kajino based on the heat kernel estimates and other probabilistic techniques. We also formulate conjectures which hold true in the examples that have been analyzed in the existing literature