17,917 research outputs found
Conformal Theory of the Dimensions of Diffusion Limited Aggregates
We employ the recently introduced conformal iterative construction of
Diffusion Limited Aggregates (DLA) to study the multifractal properties of the
harmonic measure. The support of the harmonic measure is obtained from a
dynamical process which is complementary to the iterative cluster growth. We
use this method to establish the existence of a series of random scaling
functions that yield, via the thermodynamic formalism of multifractals, the
generalized dimensions D(q) of DLA for q >= 1. The scaling function is
determined just by the last stages of the iterative growth process which are
relevant to the complementary dynamics. Using the scaling relation D(3) =
D(0)/2 we estimate the fractal dimension of DLA to be D(0) = 1.69 +- 0.03.Comment: 5 pages, 3 figures, submitted to Phys. Rev. Let
Chao Yuen Ren (1892–1982)
Y. R. Chao is easily the most famous linguist to have come out of China. Born before the end of the last dynasty in China, he received a traditional Confucian education, but was also one of the first Chinese people to be sent to the West for training in modern Western science (under the Boxer Indemnity Fund). The remarkable breadth and scope of his studies included physics, mathematics, linguistics, musical and literary composition, and translation, and he was a pioneer in many of these fields
Chinese as a topic-comment (not topic-prominent and not SVO) language
Many linguists in China and the West have talked about Chinese as a topic-comment language, that is, a language in which the structure of the clause takes the form of a topic, about which something is to be said, and a comment, which is what is said about the topic, rather than being a language with a subject-predicate structure like that of English. Y. R. Chao (1968), for example, said that all Chinese clauses have topic-comment structure and there are no exceptions
Turbulence and Multiscaling in the Randomly Forced Navier Stokes Equation
We present an extensive pseudospectral study of the randomly forced
Navier-Stokes equation (RFNSE) stirred by a stochastic force with zero mean and
a variance , where is the wavevector and the dimension . We present the first evidence for multiscaling of velocity structure
functions in this model for . We extract the multiscaling exponent
ratios by using extended self similarity (ESS), examine their
dependence on , and show that, if , they are in agreement with those
obtained for the deterministically forced Navier-Stokes equation (NSE). We
also show that well-defined vortex filaments, which appear clearly in studies
of the NSE, are absent in the RFNSE.Comment: 4 pages (revtex), 6 figures (postscript
Different transport regimes in a spatially-extended recirculating background
Passive scalar transport in a spatially-extended background of roll
convection is considered in the time-periodic regime. The latter arises due to
the even oscillatory instability of the cell lateral boundary, here accounted
for by sinusoidal oscillations of frequency . By varying the latter
parameter, the strength of anticorrelated regions of the velocity field can be
controled and the conditions under which either an enhancement or a reduction
of transport takes place can be created. Such two ubiquitous regimes are
triggered by a small-scale(random) velocity field superimposed to the
recirculating background. The crucial point is played by the dependence of
Lagrangian trajectories on the statistical properties of the small-scale
velocity field, e.g. its correlation time or its energy.Comment: 9 pages Latex; 5 figure
A -anaolg of the sixth Painlev\'e equation
A -difference analog of the sixth Painlev\'e equation is presented. It
arises as the condition for preserving the connection matrix of linear
-difference equations, in close analogy with the monodromy preserving
deformation of linear differential equations. The continuous limit and special
solutions in terms of -hypergeometric functions are also discussed.Comment: 8 pages, LaTeX file (Two misprints corrected
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