Maximizers for the Strichartz Inequalities for the Wave Equation

We prove the existence of maximizers for Strichartz inequalities for the wave equation in dimensions $d\geq 3$. Our approach follows the scheme given by Shao, which obtains the existence of maximizers in the context of the Schr\"odinger equation. The main tool that we use is the linear profile decomposition for the wave equation which we prove in $\mathbb{R}^d$, $d\geq 3$, extending the profile decomposition result of Bahouri and Gerard, previously obtained in $\mathbb{R}^3$.Comment: 28 pages, revised version, minor change

Improved Sobolev embeddings, profile decomposition, and concentration-compactness for fractional Sobolev spaces

We obtain an improved Sobolev inequality in H^s spaces involving Morrey norms. This refinement yields a direct proof of the existence of optimizers and the compactness up to symmetry of optimizing sequences for the usual Sobolev embedding. More generally, it allows to derive an alternative, more transparent proof of the profile decomposition in H^s obtained in [P. Gerard, ESAIM 1998] using the abstract approach of dislocation spaces developed in [K. Tintarev & K. H. Fieseler, Imperial College Press 2007]. We also analyze directly the local defect of compactness of the Sobolev embedding in terms of measures in the spirit of [P. L. Lions, Rev. Mat. Iberoamericana 1985]. As a model application, we study the asymptotic limit of a family of subcritical problems, obtaining concentration results for the corresponding optimizers which are well known when s is an integer ([O. Rey, Manuscripta math. 1989; Z.-C. Han, Ann. Inst. H. Poincare Anal. Non Lineaire 1991], [K. S. Chou & D. Geng, Differential Integral Equations 2000]).Comment: 33 page

Pseudo-bosons and Riesz bi-coherent states

After a brief review on \D-pseudo-bosons we introduce what we call {\em Riesz bi-coherent states}, which are pairs of states sharing with ordinary coherent states most of their features. In particular, they produce a resolution of the identity and they are eigenstates of two different annihilation operators which obey pseudo-bosonic commutation rules.Comment: This paper is dedicated to the memories of Gerard Emch and of Twareque Ali. Appeared in the Proceedings of XXXIV Workshop on Geometric Methods in Physics, Bialowieza, Polan

Universality of the triplet contact process with diffusion

The one-dimensional triplet contact process with diffusion (TCPD) model has been studied using fast multispin GPU Monte Carlo simulations. In particular, the particle density \rho and the density of pairs of neighboring particles \rho_p have been monitored as a function of time. Mean field predictions for the time evolution of these observables in the critical point are \rho\sim t^{-\delta} and \rho_p\sim t^{-\delta_p} with \delta=1/3 and \delta_p=2/3. We observe that in the vicinity of the critical point of the model, the ratio \rho_p/\rho tends to a constant, which shows that the one-dimensional TCPD model is not described by mean field behavior. Furthermore, our long simulations allow us to conclude that the mean field prediction of the exponent $\delta$ is almost certainly not correct either. Since the crossover to the critical regime is extremely slow for the TCPD model, we are unable to pinpoint a precise value for \delta, though we find as an upper bound \delta < 0.32.Comment: 7 pages, 3 figure

Communication costs in a multi-tiered MPSoC

The amount of digital processing required for phased array beamformers is very large. It requires many parallel processors, which can be organized in a multi-tiered structure. Communication costs differ for each of the stages in such an architecture. For example, communication costs from the antenna front-end to the first processing stages is costly because of the amount of connections and data rate. Furthermore there is a trade-off between sequential processing exploiting locality of reference versus exploiting parallelism but adding communication costs. Thus, the optimal architecture depends on the importance that is given to the different measures.\ud \ud A model is presented to determine the partitioning of a (beamforming) system based on communication costs. It is shown that different solutions can be explored based on the cost model and the incorporated quantitative and qualitative measures. Determining the importance of each measure is subjective to the situation and application. In this work a simple beamforming application is used optimised for energy efficiency

Discovery of a Shell of Neutral Atomic Hydrogen Surrounding the Carbon Star IRC+10216

We have used the Robert C. Byrd Green Bank Telescope to perform the most sensitive search to date for neutral atomic hydrogen (HI) in the circumstellar envelope (CSE) of the carbon star IRC+10216. Our observations have uncovered a low surface brightness HI shell of diameter ~1300" (~0.8 pc), centered on IRC+10216. The HI shell has an angular extent comparable to the far ultraviolet-emitting astrosphere of IRC+10216 previously detected with the GALEX satellite, and its kinematics are consistent with circumstellar matter that has been decelerated by the local interstellar medium. The shell appears to completely surround the star, but the highest HI column densities are measured along the leading edge of the shell, near the location of a previously identified bow shock. We estimate a total mass of atomic hydrogen associated with IRC+10216 CSE of M_HI~3x10e-3 M_sun. This is only a small fraction of the expected total mass of the CSE (<1%) and is consistent with the bulk of the stellar wind originating in molecular rather than atomic form, as expected for a cool star with an effective temperature T_eff<~2200 K. HI mapping of a 2 deg x 2 deg region surrounding IRC+10216 has also allowed us to characterize the line-of-sight interstellar emission in the region and has uncovered a link between diffuse FUV emission southwest of IRC+10216 and the Local Leo Cold Cloud.Comment: Accepted to MNRAS. 16 pages. A version with full resolution figures may be found at http://www.haystack.mit.edu/hay/staff/lmatthew/Matthews_etal_IRC+10216.pd