An Application of Nash-Moser Theorem to Smooth Solutions of One-Dimensional Compressible Euler Equation with Gravity

We study one-dimensional motions of polytropic gas governed by the compressible Euler equations. The problem on the half space under a constant gravity gives an equilibrium which has free boundary touching the vacuum and the linearized approximation at this equilibrium gives time periodic solutions. But it is not easy to justify the existence of long-time true solutions for which this time periodic solution is the first approximation. The situation is in contrast to the problem of free motions without gravity. The reason is that the usual iteration method for quasilinear hyperbolic problem cannot be used because of the loss of regularities which causes from the touch with the vacuum. Interestingly, the equation can be transformed to a nonlinear wave equation on a higher dimensional space, for which the space dimension, being larger than 4, is related to the adiabatic exponent of the original one-dimensional problem. We try to find a family of solutions expanded by a small parameter. Applying the Nash-Moser theory, we justify this expansion.The application of the Nash-Moser theory is necessary for the sake of conquest of the trouble with loss of regularities, and the justification of the applicability requires a very delicate analysis of the problem

Problems of QCD factorization in exclusive decays of B meson to charmonium

We study the exclusive decays of $B$ meson into P-wave charmonium states $\chi_{cJ}(J=0,1)$ in the QCD factorization approach with light-cone distribution functions describing the mesons in the processes. For $B \to \chi_{c1} K$ decay, we find that there are logarithmic divergences arising from nonfactorizable spectator interactions even at twist-2 order and the decay rate is too small to accommodate the experimental data. For $B\to \chi_{c0} K$ decay, we find that aside from the logarithmic divergences arising from spectator interactions at leading-twist order, more importantly, the factorization will break down due to the infrared divergence arising from nonfactorizable vertex corrections, which is independent of the specific form of the light-cone distribution functions. Our results may indicate that QCD factorization in the present form may not be safely applied to $B$-meson exclusive decays to charmonium states.Comment: Latex, 7 pages, 1 eps figure, final version to appear in Phys.Lett.B; a few references are added, the expression of chi_c1 decay constant is give

High Performance Biological Pairwise Sequence Alignment: FPGA versus GPU versus Cell BE versus GPP

This paper explores the pros and cons of reconfigurable computing in the form of FPGAs for high performance efficient computing. In particular, the paper presents the results of a comparative study between three different acceleration technologies, namely, Field Programmable Gate Arrays (FPGAs), Graphics Processor Units (GPUs), and IBM’s Cell Broadband Engine (Cell BE), in the design and implementation of the widely-used Smith-Waterman pairwise sequence alignment algorithm, with general purpose processors as a base reference implementation. Comparison criteria include speed, energy consumption, and purchase and development costs. The study shows that FPGAs largely outperform all other implementation platforms on performance per watt criterion and perform better than all other platforms on performance per dollar criterion, although by a much smaller margin. Cell BE and GPU come second and third, respectively, on both performance per watt and performance per dollar criteria. In general, in order to outperform other technologies on performance per dollar criterion (using currently available hardware and development tools), FPGAs need to achieve at least two orders of magnitude speed-up compared to general-purpose processors and one order of magnitude speed-up compared to domain-specific technologies such as GPUs