The main mean motion commensurabilities in the planar circular and elliptic problem

1993 ◽  
Vol 57 (1-2) ◽  
pp. 99-108 ◽  
Author(s):  
Mich�le Moons ◽  
Alessandro Morbidelli
Keyword(s):  
Elliptic Problem ◽  
Mean Motion

the effects of resonance with Jupiter in the system of short-period comets

1974 ◽  
Vol 22 ◽  
pp. 193-203
Author(s):  
L̆ubor Kresák
Keyword(s):  
Structural Effects ◽  
Order Resonance ◽  
Mean Motion ◽  
Short Period ◽  
The Mean ◽  
Compound Effect ◽  
Low Order

AbstractStructural effects of the resonance with the mean motion of Jupiter on the system of short-period comets are discussed. The distribution of mean motions, determined from sets of consecutive perihelion passages of all known periodic comets, reveals a number of gaps associated with low-order resonance; most pronounced are those corresponding to the simplest commensurabilities of 5/2, 2/1, 5/3, 3/2, 1/1 and 1/2. The formation of the gaps is explained by a compound effect of five possible types of behaviour of the comets set into an approximate resonance, ranging from quick passages through the gap to temporary librations avoiding closer approaches to Jupiter. In addition to the comets of almost asteroidal appearance, librating with small amplitudes around the lower resonance ratios (Marsden, 1970b), there is an interesting group of faint diffuse comets librating in characteristic periods of about 200 years, with large amplitudes of about±8% in μ and almost±180° in σ, around the 2/1 resonance gap. This transient type of motion appears to be nearly as frequent as a circulating motion with period of revolution of less than one half that of Jupiter. The temporary members of this group are characteristic not only by their appearance but also by rather peculiar discovery conditions.

On the construction of orthogonal curvilinear grids for regional oceanic modeling: algorithm and user guide

2020 ◽  
Vol 48 (4) ◽  
pp. 45-111
Author(s):  
A. F. Shepetkin
Keyword(s):  
Inverse Problem ◽  
Numerical Solution ◽  
Elliptic Problem ◽  
Software Package ◽  
Conformal Transformation ◽  
Iterative Procedure ◽  
Geometric Shape ◽  
Curvilinear Grids ◽  
Grid Points ◽  
Grid Nodes

A new algorithm for constructing orthogonal curvilinear grids on a sphere for a fairly general geometric shape of the modeling region is implemented as a “compile-once - use forever” software package. It is based on the numerical solution of the inverse problem by an iterative procedure -- finding such distribution of grid points along its perimeter, so that the conformal transformation of the perimeter into a rectangle turns this distribution into uniform one. The iterative procedure itself turns out to be multilevel - i.e. an iterative loop built around another, internal iterative procedure. Thereafter, knowing this distribution, the grid nodes inside the region are obtained solving an elliptic problem. It is shown that it was possible to obtain the exact orthogonality of the perimeter at the corners of the grid, to achieve very small, previously unattainable level of orthogonality errors, as well as make it isotropic -- local distances between grid nodes about both directions are equal to each other.

Influence of Partial Blocking of the Electrode Surface on the Transfer Coefficients

1993 ◽  
Vol 58 (3) ◽  
pp. 496-505
Author(s):  
Ondřej Wein
Keyword(s):  
Surface Activity ◽  
Elliptic Problem ◽  
Electrode Surface ◽  
Driving Force ◽  
Two Dimensional ◽  
Transfer Coefficients ◽  
Constant Potential ◽  
Numeric Solution ◽  
Active Zones ◽  
Partial Blocking

Partial blocking of the transport surface under the stagnant (nerst) layer is simulated by periodically alternating bands of perfectly insulating zones and active zones with a constant potential of driving force. The numeric solution of the corresponding two-dimensional elliptic problem is represented by a simple empirical correlation for the transfer coefficients. The result is interpreted in terms of a simple electrochemical problem about limiting diffusion currents at electrodes with non-uniform surface activity.

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