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The solution by Sessin and Ferraz-Mello (1984) of the Hori auxiliary system for the motion of two planets with periods nearly commensurate in the ratio 2:1 is considerably simplified by the introduction of canonical variables. An analogous canonical transformation simplifies the elliptic restricted problem.
It is possible to calculate expectation values and transition probabilities from the Wigner phase-space distribution function. Based on the canonical transformation properties of the Wigner function, an algorithm is developed for calculating these quantities in quantum optics for coherent and squeezed states. It is shown that the expectation value of a dynamical variable can be written in terms of its vacuum expectation value of the canonically transformed variable. Parallel-axis theorems are established for the photon number and its variant. It is also shown that the transition probability between two squeezed states can be reduced to that of the transition from one squeezed state to vacuum.
The authors prove that a linear second-order system with arbitrary damping cannot be reduced to Hessenberg-triangular form by means of orthogonal transformations, while this reduction is always possible for the modal damping commonly assumed for models of flexible structures. The type of canonical form obtainable by means of orthogonal transformations acting on a second-order system is heavily dependent on the type of damping considered. If the damping matrix is merely positive semi-definite symmetric, it is generally not possible to obtain a reduction to Hessenberg-triangular form, while this reduction is trivial for zero or Rayleigh damping. If damping is modal, however, as is commonly assumed in structural models, the reduction exists and is nontrivial. Furthermore, reduction to triangular second-order Schur form is always possible for such damping: this canonical form appears likely to have applications to second-order system theory.
We report the first quantitative measurements of spontaneous temperature fluctuations in a physical system well modeled by a canonical ensemble. Using superconducting magnetometers and a carefully controlled thermal environment, we have measured the noise spectra of paramagnetic salt thermometers that were coupled to thermal reservoirs at 2 K. The noise spectra were found to be in very good agreement with the predictions of the fluctuation-dissipation theorem. Our observations are at variance with some interpretations of fluctuations in the canonical ensemble.
Department of Mathematical Sciences, University of Alberta, Edmonton, Canada This paper describes the fundamental theory of the ensemble canonical correlation (ECC) algorithm for the seasonal climate forecasting. The algorithm is a statistical regression sch eme based on maximal correlation between the predictor and predictand. The prediction error is estimated by a spectral method using the basis of empirical orthogonal functions. The ECC algorithm treats the predictors and predictands as continuous fields and is an improvement from the traditional canonical correlation prediction. The improvements include the use of area-factor, estimation of prediction error, and the optimal ensemble of multiple forecasts. The ECC is applied to the seasonal forecasting over various parts of the world. The example presented here is for the North America precipitation. The predictor is the sea surface temperature (SST) from different ocean basins. The Climate Prediction Center's reconstructed SST (1951-1999) is used as the predictor's historical data. The optimally interpolated global monthly precipitation is used as the predictand?s historical data. Our forecast experiments show that the ECC algorithm renders very high skill and the optimal ensemble is very important to the high value.
This paper presents preliminary results of an ensemble canonical correlation (ECC) prediction scheme developed at the Climate and Radiation Branch, NASA/Goddard Space Flight Center for determining the potential predictability of regional precipitation, and for climate downscaling studies. The scheme is tested on seasonal hindcasts of anomalous precipitation over the continental United States using global sea surface temperature (SST) for 1951-2000. To maximize the forecast skill derived from SST, the world ocean is divided into non-overlapping sectors. The canonical SST modes for each sector are used as the predictor for the ensemble hindcasts. Results show that the ECC yields a substantial (10-25%) increase in prediction skills for all the regions of the US in every season compared to traditional CCA prediction schemes. For the boreal winter, the tropical Pacific contributes the largest potential predictability to precipitation in the southwestern and southeastern regions, while the North Pacific and the North Atlantic are responsible to the enhanced forecast skills in the Pacific Northwest, the northern Great Plains and Ohio Valley. Most importantly, the ECC increases skill for summertime precipitation prediction and substantially reduces the spring predictability barrier over all the regions of the US continent. Besides SST, the ECC is designed with the flexibility to include any number of predictor fields, such as soil moisture, snow cover and additional local observations. The enhanced ECC forecast skill provides a new benchmark for evaluating dynamical model forecasts.
We present new observations of the early X-ray afterglows of the first 27 gamma-ray bursts (GRBs) detected with the Swift X-ray Telescope (XRT). The early X-ray afterglows show a canonical behavior, where the light curve broadly consists of three distinct power law segments. These power law segments are separated by two corresponding break times. On top of this canonical behavior of the early X-ray light curve, many events have superimposed X-ray flares, which are most likely caused by internal shocks due to long lasting sporadx activity of the central engine, up to several hours after the GRB. We find that the initial steep decay is consistent with it being the tail of the prompt emission: from photons that are radiated at large angles relative to our line of sight. The first break in the light curve takes place when the forward shock emission becomes dominant, with the intermediate shallow flux decay likely caused by the continuous energy injection into the external shock. When this energy injection stops, a second break is then observed in the light curve. This energy injection increases the energy of the afterglow shock by at least a factor of f greater than or approx. equal to 4, and augments the already severe requirements for the efficiency of the prompt gamma-ray emission.
Coordinate conditions fix momenta conjugate in Dirac Hamiltonian for general relativity, allowing study of canonical formalism of this theory
Generalized Lur coordinates used in canonical forms for controllable systems, with applications to optimal nonlinear feedback
Transition from relativistic mechanics to relativistic quantum dynamics through homogeneous canonical formalism - Schroedinger and Klein-Gordon equations
Phase-variable canonical form for single input linear dynamical systems applied to linear control theory
Linear transformation of arbitrary, completely controllable, single-input, time-variant linear dynamical system to canonical form
Transformation to phase variable canonical form
Nonsingular linear transformation of time- invariant linear dynamic system into canonical /phase-variable/ form
Canonical decomposition of nonlinear error covariance difference equation derived for discrete estimation problems
Canon Diablo octahedrite quantitative chemical and modal mineralogical composition variations in rim and plain components
Elimination of short period terms of first order general planetary theory through Von Zeipel method and Hori canonical variables
Canonical transformation and Hamilton-Jacobi theories applied to space vehicle trajectory analysis, discussing elliptical coast arc and optimal low thrust problems