Transition state theory and the dynamics of hard disks

The dynamics of two and five disk systems confined in a square has been studied using molecular dynamics simulations and compared with the predictions of transition state theory. We determine the partition functions Z and Z^\ddagger of transition state theory using a procedure first used by Salsburg and Wood for the pressure. Our simulations show this procedure and transition state theory are in excellent agreement with the simulations. A generalization of the transition state theory to the case of a large number of disks N is made and shown to be in full agreement with simulations of disks moving in a narrow channel. The same procedure for hard spheres in three dimensions leads to the Vogel-Fulcher-Tammann formula for their alpha relaxation time.Comment: 1 new author, new simulations and figures, less speculation. Now 6 pages, 6 figures, 1 animation. Animation may be viewed at http://www.theory.physics.manchester.ac.uk/~godfrey/supplement/activated_dynamics2.htm

Generalised Bose-Einstein phase transition in large-mm component spin glasses

It is proposed to understand finite dimensional spin glasses using a $1/m$ expansion, where $m$ is the number of spin components. It is shown that this approach predicts a replica symmetric state in finite dimensions. The point about which the expansion is made, the infinite-$m$ limit, has been studied in the mean-field limit in detail and has a very unusual phase transition, rather similar to a Bose-Einstein phase transition but with $N^{2/5}$ macroscopically occupied low-lying states.Comment: 4 pages (plus a few lines), 3 figures. v2: minor error corrected. v3: numerics supplemented by analytical arguments, references added, figure of density of states adde

Why temperature chaos in spin glasses is hard to observe

The overlap length of a three-dimensional Ising spin glass on a cubic lattice with Gaussian interactions has been estimated numerically by transfer matrix methods and within a Migdal-Kadanoff renormalization group scheme. We find that the overlap length is large, explaining why it has been difficult to observe spin glass chaos in numerical simulations and experiment.Comment: 4 pages, 6 figure

Phosphorus Immobilization in Poultry Litter and Litter-amended soils with Aluminum, Calcium and Iron amendments

Arkansas produces approximately one billion broilers each year. Phosphorous (P) runoff from fields receiving poultry litter is believed to be one of the primary factors affecting water quality in Northwest Arkansas. Poultry litter contains approximately 20 g P kg-1, of which about 2 g P kg-1 is water soluble. Soils that have received repeated heavy applications of litter may have water soluble P contents of as high as 10 mg P Kg-1 soil. The objective of this study was to determine if soluble P levels could be reduced in poultry litter and litter-amended soils with Al,Ca, and/or Fe amendments. Poultry litter was amended with alum, sodium aluminate, quick lime, slaked lime, calcitic limestone, dolomitic limestone, gypsum, ferrous chloride, ferric chloride, ferrous sulfate and ferric sulfate, and incubated in the dark at 25°C for one week. Three soils which had been excessively fertilized with poultry litter were amended with alum, ferrous sulfate, calcitic limestone, gypsum and slaked lime and incubated for 4 weeks at 25 °C. In the litter studies, the Ca treatments were tested with and without CaF2 additions in an attempt to precipitate fluorapatite. At the end of the incubation period, the litter and soils were extracted with deionized water and soluble reactive P (SRP) was determined. SRP levels in the poultry litter were reduced from over 2,000 mg P kg-1 litter to less than 1 mg P kg-1 litter with the addition of alum, quick lime, slaked lime, ferrous chloride, ferric chloride, ferrous sulfate and ferric sulfate under favorable pH conditions. S.RP levels in the soils were reduced from approximately 5 mg P Kg-1 soil to less than 0.05 mg P Kg-1 soil with the addition of alum and ferrous sulfate under favorable pH conditions. Gypsum and sodium aluminate reduced SRP levels in litter by 50 to 60 percent while calcitic and dolomitic limestone were even less effective. In soils, the Ca amendments were less effective than the Al and Fe amendments, although slaked lime was effective at high pH. The results of these studies suggest that treating litter and excessively fertilized soils with some of these compounds, particularly alum, could significantly reduce the amount of SRP in runoff from littered pastures. Therefore, chemical additions to reduce SRP in litter and soil may be a best management practice in situations where eutrophication of adjacent water bodies due to P runoff has been identified. Preliminary calculations indicate that this .p ractice may be economically feasible. However, more research is needed to determine any beneficial and/or detrimental aspects of this practice

Interface free-energy exponent in the one-dimensional Ising spin glass with long-range interactions in both the droplet and broken replica symmetry regions

The one-dimensional Ising spin-glass model with power-law long-range interactions is a useful proxy model for studying spin glasses in higher space dimensions and for finding the dimension at which the spin-glass state changes from having broken replica symmetry to that of droplet behavior. To this end we have calculated the exponent that describes the difference in free energy between periodic and antiperiodic boundary conditions. Numerical work is done to support some of the assumptions made in the calculations and to determine the behavior of the interface free-energy exponent of the power law of the interactions. Our numerical results for the interface free-energy exponent are badly affected by finite-size problems.Comment: 10 pages, 5 figures, 3 table