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

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)

Daytime lidar measurements of tidal winds in the mesospheric sodium layer at Urbana, Illinois

For more than 15 years lidar systems have been used to study the chemistry and dynamics of the mesospheric sodium layer. Because the layer is an excellent tracer of atmospheric wave motions, sodium lidar has proven to be particularly useful for studying the influence of gravity waves and tides on mesospheric dynamics. These waves, which originate in the troposphere and stratosphere, propagate through the mesosphere and dissipate their energy near the mesopause making important contributions to the momentum and turbulence budget in this region of the atmosphere. Recently, the sodium lidar was modified for daytime operation so that wave phenomena and chemical effects could be monitored throughout the complete diurnal cycle. The results of continuous 24 hour lidar observations of the sodium layer structure are presented alond with measurement of the semidiurnal tidal winds

Work distribution for the driven harmonic oscillator with time-dependent strength: Exact solution and slow driving

We study the work distribution of a single particle moving in a harmonic oscillator with time-dependent strength. This simple system has a non-Gaussian work distribution with exponential tails. The time evolution of the corresponding moment generating function is given by two coupled ordinary differential equations that are solved numerically. Based on this result we study the behavior of the work distribution in the limit of slow but finite driving and show that it approaches a Gaussian distribution arbitrarily well