Off-center rattling and anisotropic expansion of type-I clathrates studied by Raman scattering.

Dynamical motions of the guest ions in type-I clathrates Sr8Ga16Si(30-x)Gex and Ba8Ga16Si(30-x)Gex have been studied by Raman scattering spectroscopy, to clarify the role of guest vibration modes in these systems with unusual thermal transport behaviors. An anomalous decrease of the guest energies with decreasing temperature is observed for both systems. The Ge-doping expands the cage surrounding the 6d site anisotropically for Sr8Ga16Si(30-x)Gex, but isotropically for Ba8Ga16Si(30-x)Gex. Especially for Sr8Ga16Si(30-x)Gex, off-center rattling arises simultaneously with the anisotropic expansion, and it is confirmed that these anomalies play a crucial role to suppress lattice thermal conductivity in these systems.

Pressure-induced superconductor-insulator transition in the spinel compound CuRh2S4.

We performed resistivity measurements in CuRh2S4 under quasihydrostatic pressure of up to 8.0 GPa, and found a pressure-induced superconductor-insulator transition. Initially, with increasing pressure, the superconducting transition temperature T(c) increases from 4.7 K at ambient pressure to 6.4 K at 4.0 GPa, but decreases at higher pressures. With further compression, superconductivity in CuRh2S4 disappears abruptly at a critical pressure P(SI) between 5.0 and 5.6 GPa, when it becomes an insulator.

A mathematical model of biological evolution.

In order to understand generally how the biological evolution rate depends on relevant parameters such as mutation rate, intensity of selection pressure and its persistence time, the following mathematical model is proposed: dNn(t)/dt = (mn(t) - mu)Nn(t) + muNn-1(t) (n = 0,1,2,3,...), where Nn(t) and mn(t) are respectively the number and Malthusian parameter of replicons with step number n in a population at time t and mean is the mutation rate, assumed to be a positive constant. The step number of each replicon is defined as either equal to or larger by one than that of its parent, the latter case occurring when and only when mutation has taken place. The average evolution rate defined by v infinity identical to lim t leads to infinity sigma infinity n = o nNn(t)/t sigma infinity n = o Nn(t) is rigorously obtained for the case (i) mn(t) = mn is independent of t (constant fitness model), where mn is essentially periodic with respect to n, and for the case (ii) mn(t) = s(-1) n+[t/tau] (periodic fitness model), together with the long time average -m infinity of the average Malthusian parameter -m identical to sigma infinity n = o mn(t)Nn(t)/sigma infinity n = o Nn(t). The biological meaning of the results is discussed, comparing them with the features of actual molecular evolution and with some results of computer simulation of the model for finite populations.