The time-averaged velocity field in the North Pacific was estimated in two
sets of inverse calculations. The planetary geostrophic equations were the basis for
dynamical models of the flow in each case. The inverse estimates of the circulation
were obtained by minimizing a positive-definite cost function, which measured the
inconsistency...
The main result of this paper is a proof of the existence of a solution
generated by a method for the variational assimilation of observational data
into the two-dimensional, incompressible Euler equations. The data are
assumed to be given by linear (measurement) functionals acting on the space
of functions representing...
This paper synthesizes various works Wang tiles up to this point, including: the reduction from the Halting Problem to Wang Tiling Problem and notions around various aspects of periodicity, including minimal period, aperiodicity, and axis-aligned periodicity. Additionally it includes new work, including: a proof that a tiling can be periodic...
In the fall and winter of 1965, 1966, and 1967, 298 ratfish (180 males, 118 females) were collected off the Pacific coast of
Oregon and Washington and examined for food habits , parasites, growth relationships and a method of age determination. The following
food organisms were found to be the...
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Metric spaces (X, d) are ubiquitous objects in mathematics and computer science that are able to capture pairwise distance relationships d(x, y) between points x, y ∈ X. Because of this, it is natural to ask what useful generalizations there are of metric spaces for capturing “k-wise distance relationships” d(x1,...
A parallel algorithm is described for variational assimilation of observations into oceanic and atmospheric models. The algorithm may be coded first for execution on a serial computer and then trivially modified for execution on a parallel computer such as the Intel iPSC/860. The speedup factor for parallel execution is roughly...
The generalized inverse is constructed for a nonlinear, single-layer quasigeostrophic model, together with initial conditions and a finite number of interior data. With the exception of doubly Periodic boundary condition all constraints are weak. The inverse minimizes a penalty functional that is quadratic in the errors in prior estimates of...
When averaging the equations of motion, thermodynamics, and scalar conservation over turbulent fluctuations, we perform the process in several stages. First, an average is taken over the microscopic scales of turbulence, including the centimeter-scale band in which the dissipation of kinetic energy and temperature or density variance occurs. The eddy-correlation...