23,092 research outputs found
Spin transfer in ultrathin BiFeO3 film under external electric field
First-principals calculations show that up-spin and down-spin carriers are
accumulating adjacent to opposite surfaces of BiFeO3(BFO) film with applying
external bias. The spin carriers are equal in magnitude and opposite in
direction, and down-spin carriers move to the direction opposing the external
electric field while up-spin ones along the field direction. This novel spin
transfer properties make BFO film an intriguing candidate for application in
spin capacitor and BFO-based multiferroic field-effect device
A Hierarchical Allometric Scaling Analysis of Chinese Cities: 1991-2014
The law of allometric scaling based on Zipf distributions can be employed to
research hierarchies of cities in a geographical region. However, the
allometric patterns are easily influenced by random disturbance from the noises
in observational data. In theory, both the allometric growth law and Zipf's law
are related to the hierarchical scaling laws associated with fractal structure.
In this paper, the scaling laws of hierarchies with cascade structure are used
to study Chinese cities, and the method of R/S analysis is applied to analyzing
the change trend of the allometric scaling exponents. The results show that the
hierarchical scaling relations of Chinese cities became clearer and clearer
from 1991 to 2014 year; the global allometric scaling exponent values
fluctuated around 0.85, and the local scaling exponent approached to 0.85. The
Hurst exponent of the allometric parameter change is greater than 0.5,
indicating persistence and a long-term memory of urban evolution. The main
conclusions can be reached as follows: the allometric scaling law of cities
represents an evolutionary order rather than an invariable rule, which emerges
from self-organized process of urbanization, and the ideas from allometry and
fractals can be combined to optimize spatial and hierarchical structure of
urban systems in future city planning.Comment: 28 pages, 10 figures, 5 table
Limit theorems for sample eigenvalues in a generalized spiked population model
In the spiked population model introduced by Johnstone (2001),the population
covariance matrix has all its eigenvalues equal to unit except for a few fixed
eigenvalues (spikes). The question is to quantify the effect of the
perturbation caused by the spike eigenvalues. Baik and Silverstein (2006)
establishes the almost sure limits of the extreme sample eigenvalues associated
to the spike eigenvalues when the population and the sample sizes become large.
In a recent work (Bai and Yao, 2008), we have provided the limiting
distributions for these extreme sample eigenvalues. In this paper, we extend
this theory to a {\em generalized} spiked population model where the base
population covariance matrix is arbitrary, instead of the identity matrix as in
Johnstone's case. New mathematical tools are introduced for establishing the
almost sure convergence of the sample eigenvalues generated by the spikes.Comment: 24 pages; 4 figure
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