scholarly journals On long time almost sure asymptotics of renormalized branching diffusion processes

Author(s):  
N FOURNIER
1978 ◽  
Vol 89 (2) ◽  
pp. 241-250 ◽  
Author(s):  
R. Phythian ◽  
W. D. Curtis

The problem considered is the diffusion of a passive scalar in a ‘fluid’ in random motion when the fluid velocity field is Gaussian and statistically homogeneous, isotropic and stationary. A self-consistent expansion for the effective long-time diffusivity is obtained and the approximations derived from this series by retaining up to three terms are explicitly calculated for simple idealized forms of the velocity correlation function for which numerical simulations are available for comparison for zero molecular diffusivity. The dependence of the effective diffusivity on the molecular diffusivity is determined within this idealization. The results support Saffman's contention that the molecular and turbulent diffusion processes interfere destructively, in the sense that the total effective diffusivity about a fixed point is less than that which would be obtained if the two diffusion processes acted independently.


1988 ◽  
Vol 2 (4) ◽  
pp. 9-21 ◽  
Author(s):  
Zvi Griliches

Around 1974-75, output growth and associated productivity measures dropped sharply in the United States and in most other western industrialized nations and continued at rather low rates for most of the rest of the 1970s. During the late 1960s, the growth in research and development (R&D) investment slowed down markedly (in constant dollars) and did not really recover until the late 1970s. Basic research was especially hard hit, showing a substantial absolute decline during the same period. Whether this slowdown in the investment in new technologies can account for the observed productivity slowdown is a fascinating question. I shall argue below that it cannot, at least not yet, since its effects take a long time to work themselves through the innovation and diffusion processes. The oil price hikes of the early and late 1970s and their macro-consequences are, therefore, the most likely direct causes of these pervasive declines in the growth rate of productivity.


2018 ◽  
Vol 192 ◽  
pp. 00008
Author(s):  
Stéphane Munier

We report on our recent observation that the occurrence of diffractive patterns in the scattering of electrons off nuclei obeys the same law as the fluctuations of the height of genealogical trees in branching diffusion processes.


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