Kinetic equations and anisotropic hydrodynamics for quark and gluon fluids

The mixture of quark and gluon fluids is studied in a one-dimensional boost-invariant setup using the set of relativistic kinetic equations treated in the relaxation time approximation. Effects of a finite quark mass, non-zero baryon number density, and quantum statistics are discussed. Comparisons between the exact kinetic-theory results and anisotropic hydrodynamics predictions are performed and a very good agreement between the two are found

Exact solution of the (0+1)-dimensional Boltzmann equation for massive Bose-Einstein and Fermi-Dirac gases

We present the exact solution of the (0+1)-dimensional Boltzmann equation for massive Bose-Einstein and Fermi-Dirac gases. For the initial conditions used typically in ultra-relativistic heavy-ion collisions, we find that the effects of quantum statistics are very small for thermodynamics-like functions such as the effective temperature, energy density or transverse and longitudinal pressures. Similarly, the inclusion of quantum statistics affects very little the shear viscosity. On the other hand, the quantum statistics becomes important for description of the phenomena connected with the bulk viscosity.Comment: version published in JPG, slightly modified numerical results for the bulk pressure, physics conclusions unchange

Eigensystem analysis of classical relaxation techniques with applications to multigrid analysis

Classical relaxation techniques are related to numerical methods for solution of ordinary differential equations. Eigensystems for Point-Jacobi, Gauss-Seidel, and SOR methods are presented. Solution techniques such as eigenvector annihilation, eigensystem mixing, and multigrid methods are examined with regard to the eigenstructure

A computer program for estimating the aerodynamic characteristics of NACA 16-series airfoils

A computer program written in a table ""look-up'' format, is presented which provides a comprehensive data base on NACA 16-series airfoils. The geometry covered is limited to cambers for a design-lift coefficient from 0.0 to 0.7 and thickness ratios from 4 to 21%. The data include Mach numbers from 0.3 to 1.6, angles of attack from -4 to 8 degrees, and lift coefficients from 0.0 to 0.8. Extrapolation is used to obtain data from Mach numbers, angles of attack, and lift coefficients beyond those for which data are available. A routine to adjust the lift and drag coefficients beyond stall is included. The uses and limitations of the program are also discussed

Datacja reliefów Szapura I. Zarys problematyki

It is assumed that eight Sasanid reliefs were carved during the reign of Shapur I in 242 – 272. There is no doubt that seven of them: NRb I, NRb IV, NRm VI, VŠ I, VŠ II, VŠ III as well as that one from Rag-i Bibi depict the ruler. Identifi cation of the king in relief from Darabgerd is subject of further disputes. What enforces dating reliefs at Naqsh-i Rajab to 242 – 244 is lack of portrayals of enemies defeated by Shapur. Starting point for more precise dating of socalled triumph reliefs is identifi cation of persons appearing in them. There is no doubt about the relief at Naqsh-i Rustam. On the basis of ŠKZ text one ought to assume that it shows Philip the Arab and Valerian thus it should be dated to 260 – 272. The problem is over dating of reliefs at Bishapur. Damages of VŠ I relief allow only identifi cation of Philip the Arab and Gordian III that is why dating can be precised to solely 244-272. Lively discussion elicit another two reliefs of Shapur I at Bishapur . One of the most interesting hypotheses seems to be thesis advanced by B. Overlaet that Uranius Antoninus is the fi gure standing next to the king. Recognision of black stone of Emesa in VŠ III relief maintains the thesis. As far as stone identifi cation seems to be sure one should deliberate if Shapur I would place in the relief a person recognized by him as not equal to himself. It is unlikely from propaganda viewpoint. In that case we can refer to the king relation to Septimius Odenathus with whom he even did not start dialog. If we interpret the arrangement of relief we have to point that its composition refers to sculptures from Apadana in Persepolis. In the context of military activities and devastations of Syria by Persian forces one should not be astonished at symbolic representation of bringing gifts Syrians. For late dating of triumph reliefs indicates their asymmetrical composition which is untypical in case of Persian sculptures. One should recognize that they could be carved by Roman craftmen deported by Shapur I during wars with western neighbour. Anyway it does not help in more precise dating because fi rst deportation took place already in 253. Taking Valerian as prisoner seems to be the most important success of Shapur I. The emperor undoubtly was residing at Bishapur so in a natural way he was put in both VŠ II and VŠ III reliefs what allows their dating to 260-272. The above mentioned speculations do not make easier dating of the most controversial relief from Darabgerd what will be undoubtly subject of future disputes