30,974 research outputs found
Asymptotic properties of eigenmatrices of a large sample covariance matrix
Let where is a matrix
with i.i.d. complex standardized entries having finite fourth moments. Let
in which
and where
is the Mar\v{c}enko--Pastur law with parameter ; which
converges to a positive constant as , and and are unit vectors in ,
having indices and , ranging in a compact subset
of a finite-dimensional Euclidean space. In this paper, we prove that the
sequence converges weakly to a
-dimensional Gaussian process. This result provides further evidence in
support of the conjecture that the distribution of the eigenmatrix of is
asymptotically close to that of a Haar-distributed unitary matrix.Comment: Published in at http://dx.doi.org/10.1214/10-AAP748 the Annals of
Applied Probability (http://www.imstat.org/aap/) by the Institute of
Mathematical Statistics (http://www.imstat.org
Periodicities in sunspot activity during solar cycle 23
The data of sunspot numbers, sunspot areas and solar flare index during cycle
23 are analyzed to investigate the intermediate-term periodicities. Power
spectral analysis has been performed separately for the data of the whole disk,
northern and southern hemispheres of the Sun. Several significant midrange
periodicities (175, 133, 113, 104, 84, 63 days) are detected in sunspot
activity. Most of the periodicities in sunspot numbers generally agree with
those of sunspot areas during the solar cycle 23. The study reveals that the
periodic variations in the northern and southern hemispheres of the Sun show a
kind of asymmetrical behavior. Periodicities of 175 days and 133
days are highly significant in the sunspot data of northern hemisphere showing
consistency with the findings of Lean (1990) during solar cycles 12-21. On the
other hand, southern hemisphere shows a strong periodicity of about 85 days in
terms of sunspot activity. The analysis of solar flare index data of the same
time interval does not show any significant peak. The different periodic
behavior of sunspot and flare activity can be understood in the light of
hypothesis proposed by Ballester et al. (2002), which suggests that during
cycle 23, the periodic emergence of magnetic flux partly takes place away from
developed sunspot groups and hence may not necessarily increase the magnetic
complexity of sunspot groups that leads to the generation of flares.Comment: 4 pages, 4 figure
Impurity scattering and Friedel oscillations in mono-layer black phosphorus
We study the effect of impurity scattering effect in black phosphorurene (BP)
in this work. For single impurity, we calculate impurity induced local density
of states (LDOS) in momentum space numerically based on tight-binding
Hamiltonian. In real space, we calculate LDOS and Friedel oscillation
analytically. LDOS shows strong anisotropy in BP. Many impurities in BP are
investigated using -matrix approximation when the density is low. Midgap
states appear in band gap with peaks in DOS. The peaks of midgap states are
dependent on impurity potential. For finite positive potential, the impurity
tends to bind negative charge carriers and vise versa. The infinite impurity
potential problem is related to chiral symmetry in BP
Significantly enhanced critical current densities in MgB2 tapes made by a scaleable, nano-carbon addition route
Nanocarbon-doped Fe-sheathed MgB2 tapes with different doping levels were
prepared by the in situ powder-in-tube method. Compared to the undoped tapes,
Jc for all the C-doped samples was enhanced by more than an order of magnitude
in magnetic fields above 9 T. At 4.2 K, the transport Jc for the 5 at% doped
tapes reached 1.85x104 A/cm2 at 10 T and 2.8x103 A/cm2 at 14 T, respectively.
Moreover, the critical temperature for the doped tapes decreased slightly.
Transmission electron microscopy showed a number of intra-granular dislocations
and the dispersed nanoparticles embedded within MgB2 grains induced by the C
doping. The mechanism for the enhancement of flux pinning is also discussed.
These results indicate that powder-in-tube-processed MgB2 tape is very
promising for high-field applications.Comment: 13 pages, 5 figures. to be published soo
Adiabatic heating in impulsive solar flares
The dynamic X-ray spectra of two simple, impulsive solar flares are examined together with H alpha, microwave and meter wave radio observations. X-ray spectra of both events were characteristic of thermal bremsstrahlung from single temperature plasmas. The symmetry between rise and fall was found to hold for the temperature and emission measure. The relationship between temperature and emission measure was that of an adiabatic compression followed by adiabatic expansion; the adiabatic index of 5/3 indicated that the electron distribution remained isotropic. Observations in H alpha provided further evidence for compressive energy transfer
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