Secular growth

The term secular growth in this context is a reference to the long-term growth of perturbations in celestial mechanics. For example, the precession of the Earth s polar axis occurs on a long period relative to its orbital motion and much longer period than its rotation, and so may be classed as a secular motion. In the context of molecular simulations, we use this to refer to accumulation of drift that takes the system steadily away from the energy surface. 

The dynamical events that lead to the secular growth of the collision integrals are usually referred to in the literature as the ring events, in accordance with a description that can be given for them in terms of ring graphs. Statements (a)-(c) are based on phase space estimates of the type discussed here. Only in the case that the molecules are hard spheres or... 

As a result of the secular growth of the /-body collision integrals with time, we are compelled to conclude that, although the cluster expansion method can be used successfully to derive the Boltzmann equation from the liouville equation and to obtain corrections to the Boltzmann equation, there are serious difficulties in trying to represent these corrections as a power series in the density. An example of the difficulties that appear if one attempts to apply the generalized Boltzmann equation as it stands now to a problem of some interest is provided by the calculation of the density expansion of the coefficient of shear viscosity. By constructing normal solutions to the generalized Boltzmann equation, one finds that the viscosity 17 has the expansion of the form mentioned in Eq. (224),... 

The half-life of U is four orders of magnitude greater than any of the intermediate daughters. Therefore, any closed system, regardless of the initial state, will approach a state of secular equilibrium such that the activities of all the intermediate daughters are the same and are equal to the activity (Bateman, 1910). External processes that fractionate nuclides within the decay chain disrupt the state of secular equilibrium. The subsequent growth or decay of the intermediate nuclides back towards equilibrium with can be used to date the fractionation event (see Ivanovich et al., 1992). Uranium-thorium dating of speleothems is possible because of the extreme... 

The procedure globally follows the one proposed by Eichrom inc. for the determination of Sr in water. The elution of strontium is performed by passing 6.0 mL 0.05 M HNO3 through the column. Ideally, the eluate is conserved to reach the secular equilibrium between Sr and If not, a correction factor is applied for the growth of Then 5 mL of eluate are mixed with 15 mL Optiphase Hisafe 3 in a PE vial. This one is set for counting. 

While the growth of secular monarchies was, at least in some... 

In a closed system, given enough time, all nuclides in a decay series reach secular equilibrium. This means that growth is balanced by decay, and that all intermediate nuclides have the same activity. In a natural open system, however, reaction and transport... 

Compare the asymptotic solution obtained in part (a) with the exact solution for e = 0.1. Disoiss the diverging behavior of the asymptotic solution near x = 0. Does the asymptotic solution behave better near X = 0 as more terms are retained Observing the asymptotic solution, it shows that the second term is more singular (secular) than the first term, and the third term is more singular than the second term. Thus, it is seen that just like the cubic equations dealt with in Problems 6.5 and 6.6, where the cubic term is multiplied by a small parameter, this differential equation also suffers the same growth in singular behavior. 

Growth and decay of Ra after isolation of radium from 4n series at secular equilibrium. The top curve gives the decay of Ra after the first isolation relative to the secular rate. The growth curve shows the time dependence of Ra that comes from Ra (via Ac and Th). The middle decay curve shows Ra that decays (with the clock restarted) after thorium is removed when growth and decay are equal (about 22 days from t = 0). The bottom decay curve shows decay following a third purification (about 10 days after the second]... 

Secular radionuclide generator kinetics for the system Ge/ Ga. A, independent activity of the parent nuclide B, growth of cumulative parent and daughter activity in a pure parent fraction C, growth of daughter activity in a pure parent fraction D, independent decay of the separated pure daughter fraction at maximum of generated activity... 

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