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A note on generalized averaged Gaussian formulas
We have recently proposed a very simple numerical method for constructing the averaged Gaussian quadrature formulas. These formulas exist in many more cases than the real positive Gauss–Kronrod formulas. In this note we try to answer whether the averaged Gaussian formulas are an adequate alternative to the corresponding Gauss–Kronrod quadrature formulas, to estimate the remainder term of a Gaussian rule
Manifestation of nonequilibrium initial conditions in molecular rotation: the generalized J-diffusion model
In order to adequately describe molecular rotation far from equilibrium, we
have generalized the J-diffusion model by allowing the rotational relaxation
rate to be angular momentum dependent. The calculated nonequilibrium rotational
correlation functions (CFs) are shown to decay much slower than their
equilibrium counterparts, and orientational CFs of hot molecules exhibit
coherent behavior, which persists for several rotational periods. As distinct
from the results of standard theories, rotational and orientational CFs are
found to dependent strongly on the nonequilibrium preparation of the molecular
ensemble. We predict the Arrhenius energy dependence of rotational relaxation
times and violation of the Hubbard relations for orientational relaxation
times. The standard and generalized J-diffusion models are shown to be almost
indistinguishable under equilibrium conditions. Far from equilibrium, their
predictions may differ dramatically
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