2,531 research outputs found

### Effects of the oceans on polar motion: Extended investigations

A method was found for expressing the tide current velocities in terms of the tide height (with all variables expanded in spherical harmonics). All time equations were then combined into a single, nondifferential matrix equation involving only the unknown tide height. The pole tide was constrained so that no tidewater flows across continental boundaries. The constraint was derived for the case of turbulent oceans; with the tide velocities expressed in terms of the tide height. The two matrix equations were combined. Simple matrix inversion then yielded the constrained solution. Programs to construct and invert the matrix equations were written. Preliminary results were obtained and are discussed

### Ocean tide models for satellite geodesy and Earth rotation

A theory is presented which predicts tides in turbulent, self-gravitating, and loading oceans possessing linearized bottom friction, realistic bathymetry, and continents (at coastal boundaries no-flow conditions are imposed). The theory is phrased in terms of spherical harmonics, which allows the tide equations to be reduced to linear matrix equations. This approach also allows an ocean-wide mass conservation constraint to be applied. Solutions were obtained for 32 long and short period luni-solar tidal constituents (and the pole tide), including the tidal velocities in addition to the tide height. Calibrating the intensity of bottom friction produces reasonable phase lags for all constituents; however, tidal amplitudes compare well with those from observation and other theories only for long-period constituents. In the most recent stage of grant research, traditional theory (Liouville equations) for determining the effects of angular momentum exchange on Earth's rotation were extended to encompass high-frequency excitations (such as short-period tides)

### Numerical analysis of the master equation

Applied to the master equation, the usual numerical integration methods, such
as Runge-Kutta, become inefficient when the rates associated with various
transitions differ by several orders of magnitude. We introduce an integration
scheme that remains stable with much larger time increments than can be used in
standard methods. When only the stationary distribution is required, a direct
iteration method is even more rapid; this method may be extended to construct
the quasi-stationary distribution of a process with an absorbing state.
Applications to birth-and-death processes reveal gains in efficiency of two or
more orders of magnitude.Comment: 7 pages 3 figure

### Effects of the oceans on polar motion: Continued investigations

Data on the pole tide, the oceanic response to the Chandler wobble were presented. Observed North Sea pole tide enhancement (i.e., larger amplitudes than a static tide would possess) resulted from bottom friction, with the drag coefficient, in combination with the depth of the North Sea decreasing southward. Computer programs were written for the boundary conditions. Dissipation of the energy by North Sea pole tide currents was also computed; preliminary results indicate that such dissipation may explain a significant fraction of Chandler wobble energy loss

### Effects of the oceans on polar motion: Extended investigations

Matrix formulation of the tide equations (pole tide in nonglobal oceans); matrix formulation of the associated boundary conditions (constraints on the tide velocity at coastlines); and FORTRAN encoding of the tide equations excluding boundary conditions were completed. The need for supercomputer facilities was evident. Large versions of the programs were successfully run on the CYBER, submitting the jobs from SUNY through the BITNET network. The code was also restructured to include boundary constraints

### Functional-integral based perturbation theory for the Malthus-Verhulst process

We apply a functional-integral formalism for Markovian birth and death
processes to determine asymptotic corrections to mean-field theory in the
Malthus-Verhulst process (MVP). Expanding about the stationary mean-field
solution, we identify an expansion parameter that is small in the limit of
large mean population, and derive a diagrammatic expansion in powers of this
parameter. The series is evaluated to fifth order using computational
enumeration of diagrams. Although the MVP has no stationary state, we obtain
good agreement with the associated {\it quasi-stationary} values for the
moments of the population size, provided the mean population size is not small.
We compare our results with those of van Kampen's $\Omega$-expansion, and apply
our method to the MVP with input, for which a stationary state does exist.Comment: 24 pages, 15 figure

### Asymptotic behavior of the order parameter in a stochastic sandpile

We derive the first four terms in a series for the order paramater (the
stationary activity density rho) in the supercritical regime of a
one-dimensional stochastic sandpile; in the two-dimensional case the first
three terms are reported. We reorganize the pertubation theory for the model,
recently derived using a path-integral formalism [R. Dickman e R. Vidigal, J.
Phys. A 35, 7269 (2002)], to obtain an expansion for stationary properties.
Since the process has a strictly conserved particle density p, the Fourier mode
N^{-1} psi_{k=0} -> p, when the number of sites N -> infinity, and so is not a
random variable. Isolating this mode, we obtain a new effective action leading
to an expansion for rho in the parameter kappa = 1/(1+4p). This requires
enumeration and numerical evaluation of more than 200 000 diagrams, for which
task we develop a computational algorithm. Predictions derived from this series
are in good accord with simulation results. We also discuss the nature of
correlation functions and one-site reduced densities in the small-kappa
(large-p) limit.Comment: 18 pages, 5 figure

### Path-integral representation for a stochastic sandpile

We introduce an operator description for a stochastic sandpile model with a
conserved particle density, and develop a path-integral representation for its
evolution. The resulting (exact) expression for the effective action highlights
certain interesting features of the model, for example, that it is nominally
massless, and that the dynamics is via cooperative diffusion. Using the
path-integral formalism, we construct a diagrammatic perturbation theory,
yielding a series expansion for the activity density in powers of the time.Comment: 22 pages, 6 figure

### Absorbing-state phase transitions: exact solutions of small systems

I derive precise results for absorbing-state phase transitions using exact
(numerically determined) quasistationary probability distributions for small
systems. Analysis of the contact process on rings of 23 or fewer sites yields
critical properties (control parameter, order-parameter ratios, and critical
exponents z and beta/nu_perp) with an accuracy of better than 0.1%; for the
exponent nu_perp the accuracy is about 0.5%. Good results are also obtained for
the pair contact process

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