ABSTRACT
An approximate solution of a separable Smoluchowski equation in one spatial dimension is constructed here in the form of a finite eigenfunction expansion. The spectrum of the Smoluchowski operator, and the corresponding eigenfunctions, are computed using the so called shooting method of adjoints. Explicit numerical solutions are presented for static and fluctuating potentials, and it is shown that for any smooth initial probablity distribution the finite expansion holds on all time scales. The method is applicable to any linear eigenproblem on a finite one-dimensional interval; the solution of the Sturm-Liouville problem has a particularly convenient form.
ABSTRACT
Magnetic ordering and Kondo behavior coexist in three (Ce,Al)-based compounds: CeAl2, Ce3Al, and Ce3Al11. A common feature apparently independent of crystal structures also prevails in terms of the size-induced transition between these two magnetic phenomena. As the particle size is reduced to nanoscale, the specific heat anomaly associated with the magnetic ordering diminishes. Although the Kondo temperature also decreases, the entropy associated with Kondo anomaly exhibits a large increase. This results in an enhancement of the Kondo behavior and an increased coefficient gamma of the linear term in specific heat. For example, in 80 A CeAl2 the extrapolated r(0) reaches 9000 mJ mol Ce-1 K-2.
