scholarly journals Phase segregation dynamics in particle systems with long range interactions. I. Macroscopic limits

1997 ◽  
Vol 87 (1-2) ◽  
pp. 37-61 ◽  
Author(s):  
Giambattista Giacomin ◽  
Joel L. Lebowitz
Keyword(s):  
Long Range ◽  
Phase Segregation ◽  
Particle Systems ◽  
Long Range Interactions

scholarly journals Macroscopic evolution of particle systems with short- and long-range interactions

Nonlinearity ◽  
2000 ◽  
Vol 13 (6) ◽  
pp. 2143-2162 ◽  
Author(s):  
Giambattista Giacomin ◽  
Joel L Lebowitz ◽  
Rossana Marra
Keyword(s):  
Long Range ◽  
Particle Systems ◽  
Long Range Interactions

MARKOV SEMIGROUPS ON UHF ALGEBRAS

1993 ◽  
Vol 05 (03) ◽  
pp. 587-600 ◽  
Author(s):  
TAKU MATSUI
Keyword(s):  
Long Range ◽  
Interacting Particle Systems ◽  
Sufficient Conditions ◽  
Particle Systems ◽  
Unique Ergodicity ◽  
Markov Semigroups ◽  
Interacting Particle ◽  
Long Range Interactions

We consider a class of Markov semigroups on UHF algebras. We establish the existence of dynamics for long range interactions. Our idea is a non-commutative extension of the argument for classical interacting particle systems. As a by-product we obtain sufficient conditions for unique ergodicity.

Error estimates for the fast multipole method. I. The two-dimensional case

1995 ◽  
Vol 448 (1934) ◽  
pp. 389-400 ◽  
Keyword(s):  
Error Estimates ◽  
Long Range ◽  
Fast Multipole Method ◽  
Analytic Form ◽  
Particle Systems ◽  
Dimensional Case ◽  
Two Dimensional ◽  
Long Range Interactions ◽  
Multipole Method ◽  
Simple Analytic Form

The Greengard-Rokhlin algorithm is a new and interesting method for computing long-range interactions in particle systems. Although the method already has been implemented and claimed to be superior to traditional and other methods, no reliable estimates of the size of the error of the method have been given. We illustrate what the error actually is for the two-dimensional case, and derive an estimate for it. The estimate has a simple analytic form which will allow its use in tuning the algorithm for best efficiency.

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