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 $\rho$, $K^{*}$, $\pi$ , $\varphi$. The extracted masses of these radial excitations are consistent with the experimental data. Especially we find that the decay constant of $\pi(1300)$, which is the the first radial excitation of $\pi$, 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