Initial-boundary value problems for conservation laws with source terms and the Degasperis-Procesi equation

We consider conservation laws with source terms in a bounded domain with Dirichlet boundary conditions. We first prove the existence of a strong trace at the boundary in order to provide a simple formulation of the entropy boundary condition. Equipped with this formulation, we go on to establish the well-posedness of entropy solutions to the initial-boundary value problem. The proof utilizes the kinetic formulation and the compensated compactness method. Finally, we make use of these results to demonstrate the well-posedness in a class of discontinuous solutions to the initial-boundary value problem for the Degasperis-Procesi shallow water equation, which is a third order nonlinear dispersive equation that can be rewritten in the form of a nonlinear conservation law with a nonlocal source term.Comment: 24 page

Systematic Investigation of Possibilities for New Physics Effects in b --> s Penguin Processes

Although recent experimental results in b-->s penguin process seem to be roughly consistent with the standard model predictions, there may be still large possibilities of new physics hiding in this processes. Therefore, here we investigate systematically the potential new physics effects that may appear in time-dependent CP asymmetries of B --> phi K^0, B--> eta^\prime K^0 and B--> K^0 \pi^0 decay modes, by classifying the cases for the values of the mixing-induced indirect CP asymmetries, S_{phi K^0}, S_{eta^\prime K^0}, S_{K^0 pi^0} which are compared to S_{J/psi K^0}. We also show that several B_s decay modes may help to resolve the ambiguities in such an analysis. Through combining analysis with the time-dependent CP asymmetries of B_s decay modes such as B_s --> phi eta^\prime, B_s--> eta^\prime pi^0 and B_s --> K^0 bar{K}^0, we can determine where the new CP phases precisely come from.Comment: 17 pages, version to be published in Prog.Theor.Phy

Variational semi-blind sparse deconvolution with orthogonal kernel bases and its application to MRFM

We present a variational Bayesian method of joint image reconstruction and point spread function (PSF) estimation when the PSF of the imaging device is only partially known. To solve this semi-blind deconvolution problem, prior distributions are specified for the PSF and the 3D image. Joint image reconstruction and PSF estimation is then performed within a Bayesian framework, using a variational algorithm to estimate the posterior distribution. The image prior distribution imposes an explicit atomic measure that corresponds to image sparsity. Importantly, the proposed Bayesian deconvolution algorithm does not require hand tuning. Simulation results clearly demonstrate that the semi-blind deconvolution algorithm compares favorably with previous Markov chain Monte Carlo (MCMC) version of myopic sparse reconstruction. It significantly outperforms mismatched non-blind algorithms that rely on the assumption of the perfect knowledge of the PSF. The algorithm is illustrated on real data from magnetic resonance force microscopy (MRFM)

Non-Classical Response from Quench-Cooled Solid Helium Confined in Porous Gold

We have investigated the non-classical response of solid 4He confined in porous gold set to torsional oscillation. When solid helium is grown rapidly, nearly 7% of the solid helium appears to be decoupled from the oscillation below about 200 mK. Dissipation appears at temperatures where the decoupling shows maximum variation. In contrast, the decoupling is substantially reduced in slowly grown solid helium. The dynamic response of solid helium was also studied by imposing a sudden increase in the amplitude of oscillation. Extended relaxation in the resonant period shift, suggesting the emergence of the pinning of low energy excitations, was observed below the onset temperature of the non-classical response. The motion of a dislocation or a glassy solid is restricted in the entangled narrow pores and is not likely responsible for the period shift and long relaxation