33,385 research outputs found
A Robust Numerical Method for Integration of Point-Vortex Trajectories in Two Dimensions
The venerable 2D point-vortex model plays an important role as a simplified
version of many disparate physical systems, including superfluids,
Bose-Einstein condensates, certain plasma configurations, and inviscid
turbulence. This system is also a veritable mathematical playground, touching
upon many different disciplines from topology to dynamic systems theory.
Point-vortex dynamics are described by a relatively simple system of nonlinear
ODEs which can easily be integrated numerically using an appropriate adaptive
time stepping method. As the separation between a pair of vortices relative to
all other inter-vortex length scales decreases, however, the computational time
required diverges. Accuracy is usually the most discouraging casualty when
trying to account for such vortex motion, though the varying energy of this
ostensibly Hamiltonian system is a potentially more serious problem. We solve
these problems by a series of coordinate transformations: We first transform to
action-angle coordinates, which, to lowest order, treat the close pair as a
single vortex amongst all others with an internal degree of freedom. We next,
and most importantly, apply Lie transform perturbation theory to remove the
higher-order correction terms in succession. The overall transformation
drastically increases the numerical efficiency and ensures that the total
energy remains constant to high accuracy.Comment: 21 pages, 4 figure
Techniques of linear prediction, with application to oceanic and atmospheric fields in the tropical Pacific
The problem of constructing optimal linear prediction models by multivariance regression methods is reviewed. It is well known that as the number of predictors in a model is increased, the skill of the prediction grows, but the statistical significance generally decreases. For predictions using a large number of candidate predictors, strategies are therefore needed to determine optimal prediction models which properly balance the competing requirements of skill and significance. The popular methods of coefficient screening or stepwise regression represent a posteriori predictor selection methods and therefore cannot be used to recover statistically significant models by truncation if the complete model, including all predictors, is statistically insignificant. Higher significance can be achieved only by a priori reduction of the predictor set. To determine the maximum number of predictors which may be meaningfully incorporated in a model, a model hierarchy can be used in which a series of best fit prediction models is constructed for a (prior defined) nested sequence of predictor sets, the sequence being terminated when the significance level either falls below a prescribed limit or reaches a maximum value. The method requires a reliable assessment of model significance. This is characterized by a quadratic statistic which is defined independently of the model skill or artificial skill. As an example, the method is applied to the prediction of sea surface temperature anomalies at Christmas Island (representative of sea surface temperatures in the central equatorial Pacific) and variations of the central and east Pacific Hadley circulation (characterized by the second empirical orthogonal function (EOF) of the meridional component of the trade wind anomaly field) using a general multipleâtimeâlag prediction matrix. The ordering of the predictors is based on an EOF sequence, defined formally as orthogonal variables in the composite space of all (normalized) predictors, irrespective of their different physical dimensions, time lag, and geographic position. The choice of a large set of 20 predictors at 12 time lags yields significant predictability only for forecast periods of 3 to 5 months. However, a prior reduction of the predictor set to 4 predictors at 10 time lags leads to 95% significant predictions with skill values of the order of 0.4 to 0.7 up to 6 or 8 months. For infinitely long time series the construction of optimal prediction models reduces essentially to the problem of linear system identification. However, the model hierarchies normally considered for the simulation of general linear systems differ in structure from the model hierarchies which appear to be most suitable for constructing pure prediction models. Thus the truncation imposed by statistical significance requirements can result in rather different models for the two cases. The relation between optimal prediction models and linear dynamical models is illustrated by the prediction of eastâwest sea level changes in the equatorial Pacific from wind field anomalies. It is shown that the optimal empirical prediction is statistically consistent in this case with both the firstâorder relaxation and damped oscillator models recently proposed by McWilliams and Gent (but with somewhat different model parameters than suggested by the authors). Thus the data do not allow a distinction between the two physical models; the simplest acceptable model is the firstâorder damped response. Finally, the problem of estimating forecast skill is discussed. It is usually stated that the forecast skill is smaller than the true skill, which in turn is smaller than the hindcast skill, by an amount which in both cases is approximately equal to the artificial skill. However, this result applies to the mean skills averaged over the ensemble of all possible hindcast data sets, given the true model. Under the more appropriate side condition of a given hindcast data set and an unknown true model, the estimation of the forecast skill represents a problem of statistical inference and is dependent on the assumed prior probability distribution of true models. The Bayesian hypothesis of a uniform prior distribution yields an average forecast skill equal to the hindcast skill, but other (equally acceptable) assumptions yield lower forecast skills more compatible with the usual hindcastâaveraged expressio
Ruthenocuprates RuSr2(Eu,Ce)2Cu2O10: Intrinsic magnetic multilayers
We report ac susceptibility data on RuSr_2(Eu,Ce)_2Cu_2O_(10-y) (Ru-1222, Ce
content x=0.5 and 1.0), RuSr_2GdCu_2O_8 (Ru-1212) and SrRuO_3. Both Ru-1222
(x=0.5, 1.0) sample types exhibit unexpected magnetic dynamics in low magnetic
fields: logarithmic time relaxation, switching behavior, and `inverted'
hysteresis loops. Neither Ru-1212 nor SrRuO_3 exhibit such magnetic dynamics.
The results are interpreted as evidence of the complex magnetic order in
Ru-1222. We propose a specific multilayer model to explain the data, and note
that superconductivity in the ruthenocuprate is compatible with both the
presence and absence of the magnetic dynamics.Comment: 9 pages, 11 figures, Revtex; submitted to Phys.Rev.
Domestic money and US output and inflation
Recent empirical research found that the strong short-term relationship between monetary aggregates and US real output and inflation, as outlined in the classical study by M. Friedman and Schwartz, mostly disappeared since the early 1980s. In the light of the B. Friedman and Kuttner (1992) information value approach, we reevaluate the vanishing relationship between US monetary aggregates and these macroeconomic fundamentals by taking into account the international currency feature of the US dollar. In practice, by using official US data for foreign flows constructed by Porter and Judson (1996) we find that domestic money (currency component of M1 corrected for the foreign holdings of dollars) contains valuable information about future movements of US real output and inflation. Statistical evidence here provided thus suggests that the Friedman and Schwartz's stylized facts can be reestablished once the focus of analysis is back on the domestic monetary aggregates. This Version: August, 2001. Klassifikation: E3, E4, E
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