38,818 research outputs found
Large deviation for diffusions and Hamilton--Jacobi equation in Hilbert spaces
Large deviation for Markov processes can be studied by Hamilton--Jacobi
equation techniques. The method of proof involves three steps: First, we apply
a nonlinear transform to generators of the Markov processes, and verify that
limit of the transformed generators exists. Such limit induces a
Hamilton--Jacobi equation. Second, we show that a strong form of uniqueness
(the comparison principle) holds for the limit equation. Finally, we verify an
exponential compact containment estimate. The large deviation principle then
follows from the above three verifications. This paper illustrates such a
method applied to a class of Hilbert-space-valued small diffusion processes.
The examples include stochastically perturbed Allen--Cahn, Cahn--Hilliard PDEs
and a one-dimensional quasilinear PDE with a viscosity term. We prove the
comparison principle using a variant of the Tataru method. We also discuss
different notions of viscosity solution in infinite dimensions in such context.Comment: Published at http://dx.doi.org/10.1214/009117905000000567 in the
Annals of Probability (http://www.imstat.org/aop/) by the Institute of
Mathematical Statistics (http://www.imstat.org
Earth's surface fluid variations and deformations from GPS and GRACE in global warming
Global warming is affecting our Earth's environment. For example, sea level
is rising with thermal expansion of water and fresh water input from the
melting of continental ice sheets due to human-induced global warming. However,
observing and modeling Earth's surface change has larger uncertainties in the
changing rate and the scale and distribution of impacts due to the lack of
direct measurements. Nowadays, the Earth observation from space provides a
unique opportunity to monitor surface mass transfer and deformations related to
climate change, particularly the global positioning system (GPS) and the
Gravity Recovery and Climate Experiment (GRACE) with capability of estimating
global land and ocean water mass. In this paper, the Earth's surface fluid
variations and deformations are derived and analyzed from global GPS and GRACE
measurements. The fluids loading deformation and its interaction with Earth
system, e.g., Earth Rotation, are further presented and discussed.Comment: Proceeding of Geoinformatics, IEEE Geoscience and Remote Sensing
Society (GRSS), June 24-26, 2011, Shanghai, Chin
Radial excitations of mesons and nucleons from QCD sum rules
Within the framework QCD sum rules, we use the least square fitting method to
investigate the first radial excitations of the nucleon and light mesons such
as , , , . The extracted masses of these radial
excitations are consistent with the experimental data. Especially we find that
the decay constant of , which is the the first radial excitation of
, is tiny and strongly suppressed as a consequence of chiral symmetry.Comment: 19 page
Form Factor and Boundary Contribution of Amplitude
The boundary contribution of an amplitude in the BCFW recursion relation can
be considered as a form factor involving boundary operator and unshifted
particles. At the tree-level, we show that by suitable construction of
Lagrangian, one can relate the leading order term of boundary operators to some
composite operators of N=4 super-Yang-Mills theory, then the computation of
form factors is translated to the computation of amplitudes. We compute the
form factors of these composite operators through the computation of
corresponding double trace amplitudes.Comment: 38 pages, 6 figure
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