The Phase-Space Density Profiles of Cold Dark Matter Halos

We examine the coarse-grained phase-space density profiles of a set of recent, high-resolution simulations of galaxy-sized Cold Dark Matter (CDM) halos. Over two and a half decades in radius the phase-space density closely follows a power-law, $\rho/\sigma^3 \propto r^{-\alpha}$, with $\alpha = 1.875$. This behaviour matches the self-similar solution obtained by Bertschinger for secondary infall in a uniformly expanding universe. On the other hand, the density profile corresponding to Bertschinger's solution (a power-law of slope $r^{2\alpha-6}$) differs significantly from the density profiles of CDM halos. We show that isotropic mass distributions with power-law phase-space density profiles form a one-parameter family of structures controlled by $\kappa$, the ratio of the velocity dispersion to the peak circular velocity. For $\kappa=\alpha=1.875$ one recovers the power-law solution $\rho \propto r^{2\alpha-6}$. For $\kappa$ larger than some critical value, $\kappa_{cr}$, solutions become non-physical, leading to negative densities near the center. The critical solution, $\kappa =\kappa_{cr}$, has the narrowest phase-space density distribution compatible with the power-law phase-space density stratification constraint. Over three decades in radius the critical solution is indistinguishable from an NFW profile. Our results thus suggest that the NFW profile is the result of a hierarchical assembly process that preserves the phase-space stratification of Bertschinger's infall model but which ``mixes'' the system maximally, perhaps as a result of repeated merging.Comment: 16 pages, 4 figures; submitted to The Astrophysical Journa

Heat and Mass Transfer in Cold Regions Soils

The work upon which this report is based was made possible by a cooperative aid agreement between the U.S. Forest Service, Institute of Northern Forestry, Fairbanks, Alaska, and the Institute of Water Resources, University of Alaska. Contributions to this study were also made by the University of California at Davis and Ohio State University. The collection of winter data on pore pressures was made possible by a separate grant by the Office of Water Research and Technology (project A-053 ALAS)

Proportional-integral-plus control applications of state-dependent parameter models

This paper considers proportional-integral-plus (PIP) control of non-linear systems defined by state-dependent parameter models, with particular emphasis on three practical demonstrators: a microclimate test chamber, a 1/5th-scale laboratory representation of an intelligent excavator, and a full-scale (commercial) vibrolance system used for ground improvement on a construction site. In each case, the system is represented using a quasi-linear state-dependent parameter (SDP) model structure, in which the parameters are functionally dependent on other variables in the system. The approach yields novel SDP-PIP control algorithms with improved performance and robustness in comparison with conventional linear PIP control. In particular, the new approach better handles the large disturbances and other non-linearities typical in the application areas considered

Friendship and Education

It is has been said, by Whitehead, I believe, that all of philosophy is a footnote to Plato; likewise, it can also be said that all of education is a footnote to his teacher, Socrates

A Kinetic Study of the Hydrochlorination of Natural Rubber and Synthetic Polyisoprene Latices

The kinetics of the hydrochlorination of natural and synthetic polyisoprene are studied in order to amplify the very limited information previously recorded in the literature regarding the nature of the reaction. The polymers are reacted in a latex process, and the accumulation of precision measurements permits a much clearer understanding of the mechanism, rate control, and loci of the reaction. The reaction progress is followed kinetically by the use of a convenient density-gradient technique for measuring accurately the increase in density of the polymer during its hydrochlorination. Extent of reaction (% hydrochlorination) is evaluated from the density change by means of a calibration provided by semi-micro potentiometric titration chlorine analyses. A chain mechanism is postulated for the hydrochlorination of Hevea rubber latex on the basis of Bunn and Garner's accepted X-ray structure of rubber hydrochloride crystals (1). This mechanism proposes the coiling of a rubber chain segment into a trans-decalin-shaped transition state which is necessary and sufficient to explain the alternation along the rubbbr hydrochloride polymer chain of D- and L-asymmetric carbon atoms each separated from the next by three CH2groups. It is proved that the hydrochlorination of polyisoprene latices occurs at two different reaction loci. The main reaction takes place within the bulk of the polymer particles. Initially superimposed on this however, there is a reaction at the interphase between the particle surface and the aqueous acid. The two reaction loci react at different rates and by different mechanisms. Despite the fact that natural and synthetic polyisoprenes have different detailed chemical structures, practically identical zero-order rate constants applyto both substrates for the main (unretarded) hydrochlorination. . It follows that the substrates themselves do not participate in the rate control, since the rate of chain reactions which might give zero-order constants are very sensitive to detailed polymer structure. Energetic and concentration factors support the deduction that the rate is controlled by a purely inorganic step involving the formation of an ion pair (H+,Cl-) from solvated precursors in the rubber medium (H2Cl+ + Cl-). The surface reaction affects only the isoprene units lying within 15+/-2.5A of the particle surface, i. e. about 2.5% of the rubber in Hevea latex and up to over 20% in synthetic polyisoprene latex of sufficiently small particle size. The increased extent of surface hydrochlorination in the synthetic substrate permits kinetic measurements on it. The surface effect can be isolated at low pressures of hydrogen chloride at which the bulk rate becomes negligible. The high order surface reaction rate is controlled by the diffusion into the polymer of a reactive hydrogen chloride species of very limited stability in rubber. The retarded zero-order bulk reaction, evident only in Hevea latex hydro chlorination, is proved to be due to the presence of a basic retarder in trace amounts within the rubber particles. Although 100% hydrochlorination of synthetic polyisoprene latex is possible, the reaction with Hevea rubber latex comes to a standstill well before stoichiometric completion - a fact probably primarily due to the onset of crystallinity in natural rubber hydrochloride. The influence, on both the surface and the bulk hydrochlorination rates, of prior sulphur vulcanization of synthetic polyisoprene latex is examined. The resulting rate curves suggest that vulcanization itself has a surface locus also. The reaction kinetics are shown to be reproducible and free from uncontrolled effects despite the complexity of the latex medium ( especially Hevea latex)

TORTS-INVASION OF RIGHT OF PRIVACY BY POSTCARD ADVERTISING

To promote the sale of merchandise, defendant retail clothing store mailed a series of postcards to prospective customers, one of which was the plaintiff. The cards, in feminine handwriting, read, \u27\u27Please call WAbash 1943 and ask for Carolyn. Upon reading this the plaintiff\u27s wife, who had intercepted the card, concluded that her husband was having a clandestine love affair with another woman, and when the plaintiff was unable to explain Carolyn, she left him. Subsequent inquiry revealed that Carolyn was one of the defendant\u27s employees and that the card was an advertising stunt Plaintiff filed suit on the theory that mailing the card to him was an invasion of his right of privacy. Defendant\u27s demurrer to the complaint was sustained. On appeal, held, affirmed. The contents of the card could not reasonably be construed as having a salacious meaning and did not constitute an invasion of the plaintiff\u27s right of privacy. Perry v. Moskins Stores, (Ky. 1952) 249 S.W. (2d) 812

REAL PROPERTY-NOTICE-RECITALS IN UNRECORDED DEEDS IN CHAIN OF TITLE

The plaintiff, Eiring, owner of all rights in a tract of land, attempted to convey certain mineral rights to Earnest by deed. The alleged rights passed from Earnest by subsequent mesne conveyances to McMillan, and, on the death of McMillan, to the defendant as trustee. Eiring brought an action against the defendant in statutory trespass to try title to the land. In the deed from Eiring to Earnest blank spaces were left in the granting clause. Held, the blank spaces rendered the deed void, and the deficiency was not cured by reference to another indefinite deed. After holding this, the court went on to dispose of the other points in the defendant\u27s case, as a matter of academic interest, and in a dictum said that a grantee of land is chargeable with notice of the facts appearing in all the deeds in his chain of title, whether recorded or not. Republic National Bank of Dallas v. Eiring, (Tex. Civ. App. 1951) 240 S.W. (2d) 414

A Comparison of Aggregation Methods for Probabilistic Forecasts of COVID-19 Mortality in the United States

The COVID-19 pandemic has placed forecasting models at the forefront of health policy making. Predictions of mortality and hospitalization help governments meet planning and resource allocation challenges. In this paper, we consider the weekly forecasting of the cumulative mortality due to COVID-19 at the national and state level in the U.S. Optimal decision-making requires a forecast of a probability distribution, rather than just a single point forecast. Interval forecasts are also important, as they can support decision making and provide situational awareness. We consider the case where probabilistic forecasts have been provided by multiple forecasting teams, and we aggregate the forecasts to extract the wisdom of the crowd. With only limited information available regarding the historical accuracy of the forecasting teams, we consider aggregation (i.e. combining) methods that do not rely on a record of past accuracy. In this empirical paper, we evaluate the accuracy of aggregation methods that have been previously proposed for interval forecasts and predictions of probability distributions. These include the use of the simple average, the median, and trimming methods, which enable robust estimation and allow the aggregate forecast to reduce the impact of a tendency for the forecasting teams to be under- or overconfident. We use data that has been made publicly available from the COVID-19 Forecast Hub. While the simple average performed well for the high mortality series, we obtained greater accuracy using the median and certain trimming methods for the low and medium mortality series. It will be interesting to see if this remains the case as the pandemic evolves.Comment: 32 pages, 11 figures, 5 table

CONSTITUTIONAL LAW-FOURTEENTH AMENDMENT EQUAL PROTECTION SEGREGATION IN RECREATIONAL FACILITIES FURNISHED BY A MUNICIPALITY

The plaintiff, a Negro, was denied admission to a municipal golf course under an ordinance setting aside certain public parks for the exclusive use of Negroes, and providing that all other public parks were for the exclusive use of white people. Only the public parks provided for the whites had golf courses, though in all other respects the park facilities offered were substantially equal. The plaintiff brought an action in a federal district court for a declaratory judgment as to his civil rights and for an injunction protecting such rights. The injunction was denied on the grounds that the facilities offered to Negroes were substantially equal to those reserved to the whites. On appeal, held, reversed. Statutory denial of the right to use the municipal golf course, solely because of race, is a denial of equal protection of the laws when equal facilities are not provided for members of the excluded race. Beal v. Holcombe, (5th Cir. 1951) 193 F. (2d) 384

Mortgages - Redemption - Right of Mortgagee to Require Partial Redemption

The mortgagor of the premises in question died leaving as his heirs-at-law the plaintiff and eight other children. Shortly thereafter, the mortgagee commenced proceedings to foreclose the mortgage under a power of sale. Pending these proceedings the plaintiff entered the military service of the United States and thus became entitled under the Soldiers and Sailors Civil Relief Act of 1940 to protection against the exercise of the power of sale. The mortgagee purchased at the foreclosure sale and thereafter made extensive improvements on the land. Plaintiff brought a bill to redeem the premises, tendering the entire amount of the mortgage debt. Mortgagee\u27s demurrer to the bill was sustained. On appeal, held, affirmed. The rule that a part owner of the equity of redemption must redeem the entire premises is for the benefit of the mortgagee, and the mortgagee may at his election insist upon a partial redemption. Cooper v. Peak, 258 Ala. 167, 61 S. (2d) 62 (1952)