168,365 research outputs found
Nonlinear Young integrals via fractional calculus
For H\"older continuous functions and , we define
nonlinear integral via fractional calculus. This
nonlinear integral arises naturally in the Feynman-Kac formula for stochastic
heat equations with random coefficients. We also define iterated nonlinear
integrals.Comment: arXiv admin note: substantial text overlap with arXiv:1404.758
Quantized Quasi-Two Dimensional Bose-Einstein Condensates with Spatially Modulated Nonlinearity
We investigate the localized nonlinear matter waves of the quasi-two
dimensional Bose-Einstein condensates with spatially modulated nonlinearity in
harmonic potential. It is shown that the whole Bose-Einstein condensates,
similar to the linear harmonic oscillator, can have an arbitrary number of
localized nonlinear matter waves with discrete energies, which are
mathematically exact orthogonal solutions of the Gross-Pitaevskii equation.
Their novel properties are determined by the principle quantum number n and
secondary quantum number l: the parity of the matter wave functions and the
corresponding energy levels depend only on n, and the numbers of density
packets for each quantum state depend on both n and l which describe the
topological properties of the atom packets. We also give an experimental
protocol to observe these novel phenomena in future experiments.Comment: 5 pages, 5 figure
Model-Independent Reionization Observables in the CMB
We represent the reionization history of the universe as a free function in
redshift and study the potential for its extraction from CMB polarization
spectra. From a principal component analysis, we show that the ionization
history information is contained in 5 modes, resembling low-order Fourier modes
in redshift space. The amplitude of these modes represent a compact description
of the observable properties of reionization in the CMB, easily predicted given
a model for the ionization fraction. Measurement of these modes can ultimately
constrain the total optical depth, or equivalently the initial amplitude of
fluctuations to the 1% level regardless of the true model for reionization.Comment: 4 pages, 5 figures, submitted to PRD (rapid communications
Light scattering and absorption properties of dust particles retrieved from satellite measurements
We use the radiative transfer model and chemistry transport model to improve our retrievals of dust optical properties from satellite measurements. The optical depth and absorbing optical depth of mineral dust can be obtained from our improved retrieval algorithm. The solar radiative forcing of dust aerosols has also been calculated using refined optical model and radiative transfer model
CMB Lensing Reconstruction on the Full Sky
Gravitational lensing of the microwave background by the intervening dark
matter mainly arises from large-angle fluctuations in the projected
gravitational potential and hence offers a unique opportunity to study the
physics of the dark sector at large scales. Studies with surveys that cover
greater than a percent of the sky will require techniques that incorporate the
curvature of the sky. We lay the groundwork for these studies by deriving the
full sky minimum variance quadratic estimators of the lensing potential from
the CMB temperature and polarization fields. We also present a general
technique for constructing these estimators, with harmonic space convolutions
replaced by real space products, that is appropriate for both the full sky
limit and the flat sky approximation. This also extends previous treatments to
include estimators involving the temperature-polarization cross-correlation and
should be useful for next generation experiments in which most of the
additional information from polarization comes from this channel due to
sensitivity limitations.Comment: Accepted for publication in Phys. Rev. D; typos correcte
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