Constrained Dynamics for Quantum Mechanics I. Restricting a Particle to a Surface

We analyze constrained quantum systems where the dynamics do not preserve the constraints. This is done in particular for the restriction of a quantum particle in Euclidean n-space to a curved submanifold, and we propose a method of constraining and dynamics adjustment which produces the right Hamiltonian on the submanifold when tested on known examples. This method we hope will become the germ of a full Dirac algorithm for quantum constraints. We take a first step in generalising it to the situation where the constraint is a general selfadjoint operator with some additional structures.Comment: 49 pages, TEX, input files amssym.def, amssym.te

A simple model of price formation

A simple Ising spin model which can describe the mechanism of price formation in financial markets is proposed. In contrast to other agent-based models, the influence does not flow inward from the surrounding neighbors to the center site, but spreads outward from the center to the neighbors. The model thus describes the spread of opinions among traders. It is shown via standard Monte Carlo simulations that very simple rules lead to dynamics that duplicate those of asset prices.Comment: Version 2: 4 pages, 4 figures; added more stringent statistical analysis; to appear in Int. J. Modern Physics C, Vol. 13, No. 1 (2002

Glueball Spin

The spin of a glueball is usually taken as coming from the spin (and possibly the orbital angular momentum) of its constituent gluons. In light of the difficulties in accounting for the spin of the proton from its constituent quarks, the spin of glueballs is reexamined. The starting point is the fundamental QCD field angular momentum operator written in terms of the chromoelectric and chromomagnetic fields. First, we look at the restrictions placed on the structure of glueballs from the requirement that the QCD field angular momentum operator should satisfy the standard commutation relationships. This can be compared to the electromagnetic charge/monopole system, where the quantization of the field angular momentum places restrictions (i.e. the Dirac condition) on the system. Second, we look at the expectation value of this operator under some simplifying assumptions.Comment: 11 pages, 0 figures; added references and some discussio

the Action of Water and Saline Solutions Upon Certain Slightly Soluble Phosphates. 1

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The 6-vertex model of hydrogen-bonded crystals with bond defects

It is shown that the percolation model of hydrogen-bonded crystals, which is a 6-vertex model with bond defects, is completely equivalent with an 8-vertex model in an external electric field. Using this equivalence we solve exactly a particular 6-vertex model with bond defects. The general solution for the Bethe-like lattice is also analyzed.Comment: 13 pages, 6 figures; added references for section

Scaling Analysis and Evolution Equation of the North Atlantic Oscillation Index Fluctuations

The North Atlantic Oscillation (NAO) monthly index is studied from 1825 till 2002 in order to identify the scaling ranges of its fluctuations upon different delay times and to find out whether or not it can be regarded as a Markov process. A Hurst rescaled range analysis and a detrended fluctuation analysis both indicate the existence of weakly persistent long range time correlations for the whole scaling range and time span hereby studied. Such correlations are similar to Brownian fluctuations. The Fokker-Planck equation is derived and Kramers-Moyal coefficients estimated from the data. They are interpreted in terms of a drift and a diffusion coefficient as in fluid mechanics. All partial distribution functions of the NAO monthly index fluctuations have a form close to a Gaussian, for all time lags, in agreement with the findings of the scaling analyses. This indicates the lack of predictive power of the present NAO monthly index. Yet there are some deviations for large (and thus rare) events. Whence suggestions for other measurements are made if some improved predictability of the weather/climate in the North Atlantic is of interest. The subsequent Langevin equation of the NAO signal fluctuations is explicitly written in terms of the diffusion and drift parameters, and a characteristic time scale for these is given in appendix.Comment: 6 figures, 54 refs., 16 pages; submitted to Int. J. Mod. Phys. C: Comput. Phy

Roughness and Finite Size Effect in the NYSE Stock-Price Fluctuations

We consider the roughness properties of NYSE (New York Stock Exchange) stock-price fluctuations. The statistical properties of the data are relatively homogeneous within the same day but the large jumps between different days prevent the extension of the analysis to large times. This leads to intrinsic finite size effects which alter the apparent Hurst (H) exponent. We show, by analytical methods, that finite size effects always lead to an enhancement of H. We then consider the effect of fat tails on the analysis of the roughness and show that the finite size effects are strongly enhanced by the fat tails. The non stationarity of the stock price dynamics also enhances the finite size effects which, in principle, can become important even in the asymptotic regime. We then compute the Hurst exponent for a set of stocks of the NYSE and argue that the interpretation of the value of H is highly ambiguous in view of the above results. Finally we propose an alternative determination of the roughness in terms of the fluctuations from moving averages with variable characteristic times. This permits to eliminate most of the previous problems and to characterize the roughness in useful way. In particular this approach corresponds to the automatic elimination of trends at any scale.Comment: 13 pages, 11 fugure

Distributive Justice for Volunteers: Extrinsic Outcome Distribution Matters

Volunteer organizations continue to suffer from turnover; the current volunteer rate is the lowest since 2002. Distributive justice, satisfaction, and extrinsic outcome importance were examined as influences of volunteer intention to quit. Survey results from 294 volunteers revealed that those who perceived less than fair distribution of extrinsic outcomes experienced heightened intention to quit compared to those who perceived fair distribution. Overall satisfaction partially mediated this relationship. We explored the potential moderating role of volunteers’ assessment of the importance of extrinsic outcomes on the overall mediated relationship

Mineralogical evidence for multiple dust sources in an early Triassic loessite.

Loessite present in a borehole into the Smith Bank Formation (early Triassic age, Central North Sea) differentiates five coeval source terranes for aerosol dust, three long distance sources and two local sources. All were active immediately following the end Permian mass extinction. Long distance sources are sedimentary, basic magmatic and acid–intermediate volcanic. Although predominantly silt‐sized and dominated by quartz with subordinate feldspars, muscovite and illite, evidence of basic and acid–intermediate magmatic/volcanic sources are pervasive. Baddeleyite is diagnostic of basic magmatism, an origin supported by enrichment of plagioclase relative to potassium feldspar. Deduction of acid–intermediate volcanism comes from the collective occurrence of irregular geometry quartz, volcanic shards, Ti‐mineralization, euhedral biotite, sanidine, the co‐occurrence of apatite and zircon, and the common occurrence of a tosuditic clay mineral. The tosuditic phase occurs as an unusual diagenetic dioctahedral chlorite/smectite formed at low temperature (<45°C), during very shallow burial by the decomposition of unstable rhyo‐dacitic and andesitic grains in alkaline pore water from an adjacent lake that yielded pore fluids with a high Al:Si ratio. The Siberian Traps large igneous province is the likely source terrane for the magmatic and volcanic silt. Locally sourced clay pellets and kaolinite booklets formed from aeolian erosion of an adjacent, periodically desiccated lake‐floor and a kaolinitic regolith, respectively. Inference of a prolonged harsh, arid climate leaves no evidence of any periods of sustained humidity or climatic fluctuation, such as pedogenesis. The association between the end Permian mass extinction, emplacement and aeolian erosion of the Siberian Traps large igneous province, and location of the Smith Bank Formation in a large lacustrine endorheic basin, combine to preserve a record of prolonged harsh climate in the early Triassic

Exact Results for the Roughness of a Finite Size Random Walk

We consider the role of finite size effects on the value of the effective Hurst exponent H. This problem is motivated by the properties of the high frequency daily stock-prices. For a finite size random walk we derive some exact results based on Spitzer's identity. The conclusion is that finite size effects strongly enhance the value of H and the convergency to the asymptotic value (H=1/2) is rather slow. This result has a series of conceptual and practical implication which we discuss.Comment: 5 pages, 3 figure