20 research outputs found
Rotational kinetics of absorbing dust grains in neutral gas
We study the rotational and translational kinetics of massive particulates
(dust grains) absorbing the ambient gas. Equations for microscopic phase
densities are deduced resulting in the Fokker-Planck equation for the dust
component. It is shown that although there is no stationary distribution, the
translational and rotational temperatures of dust tend to certain values, which
differ from the temperature of the ambient gas. The influence of the inner
structure of grains on rotational kinetics is also discussed.Comment: REVTEX4, 20 pages, 2 figure
Knowledge-based energy functions for computational studies of proteins
This chapter discusses theoretical framework and methods for developing
knowledge-based potential functions essential for protein structure prediction,
protein-protein interaction, and protein sequence design. We discuss in some
details about the Miyazawa-Jernigan contact statistical potential,
distance-dependent statistical potentials, as well as geometric statistical
potentials. We also describe a geometric model for developing both linear and
non-linear potential functions by optimization. Applications of knowledge-based
potential functions in protein-decoy discrimination, in protein-protein
interactions, and in protein design are then described. Several issues of
knowledge-based potential functions are finally discussed.Comment: 57 pages, 6 figures. To be published in a book by Springe
Approximation of Sobolev classes by polynomials and ridge functions
AbstractLet Wpr(Bd) be the usual Sobolev class of functions on the unit ball Bd in Rd, and Wp∘,r(Bd) be the subclass of all radial functions in Wpr(Bd). We show that for the classes Wp∘,r(Bd) and Wpr(Bd), the orders of best approximation by polynomials in Lq(Bd) coincide. We also obtain exact orders of best approximation in L2(Bd) of the classes Wp∘,r(Bd) by ridge functions and, as an immediate consequence, we obtain the same orders in L2(Bd) for the usual Sobolev classes Wpr(Bd)