13 research outputs found
Thermal photons in QGP and non-ideal effects
We investigate the thermal photon production-rates using one dimensional
boost-invariant second order relativistic hydrodynamics to find proper time
evolution of the energy density and the temperature. The effect of
bulk-viscosity and non-ideal equation of state are taken into account in a
manner consistent with recent lattice QCD estimates. It is shown that the
\textit{non-ideal} gas equation of state i.e behaviour
of the expanding plasma, which is important near the phase-transition point,
can significantly slow down the hydrodynamic expansion and thereby increase the
photon production-rates. Inclusion of the bulk viscosity may also have similar
effect on the hydrodynamic evolution. However the effect of bulk viscosity is
shown to be significantly lower than the \textit{non-ideal} gas equation of
state. We also analyze the interesting phenomenon of bulk viscosity induced
cavitation making the hydrodynamical description invalid. We include the
viscous corrections to the distribution functions while calculating the photon
spectra. It is shown that ignoring the cavitation phenomenon can lead to
erroneous estimation of the photon flux.Comment: 11 pages, 13 figures; accepted for publication in JHE
Prevalence of KRAS mutations in metastatic colorectal cancer: A retrospective observational study from India
Primer of adaptive finite element methods
Adaptive finite element methods (AFEM) are a fundamental numerical instrument in science and engineering to approximate partial differential equations. In the 1980s and 1990s a great deal of effort was devoted to the design of a posteriori error estimators, following the pioneering work of Babuska. These are computable quantities, depending on the discrete solution(s) and data, that can be used to assess the approximation quality and improve it adaptively. Despite their practical success, adaptive processes have been shown to converge, and to exhibit optimal cardinality, only recently for dimension d > 1 and for linear elliptic PDE. These series of lectures presents an up-to-date discussion of AFEM encompassing the derivation of upper and lower a posteriori error bounds for residual-type estimators, including a critical look at the role of oscillation, the design of AFEM and its basic properties, as well as a complete discussion of convergence, contraction property and quasi-optimal cardinality of AFEM