Computer program documentation for a subcritical wing design code using higher order far-field drag minimization

A subsonic, linearized aerodynamic theory, wing design program for one or two planforms was developed which uses a vortex lattice near field model and a higher order panel method in the far field. The theoretical development of the wake model and its implementation in the vortex lattice design code are summarized and sample results are given. Detailed program usage instructions, sample input and output data, and a program listing are presented in the Appendixes. The far field wake model assumes a wake vortex sheet whose strength varies piecewise linearly in the spanwise direction. From this model analytical expressions for lift coefficient, induced drag coefficient, pitching moment coefficient, and bending moment coefficient were developed. From these relationships a direct optimization scheme is used to determine the optimum wake vorticity distribution for minimum induced drag, subject to constraints on lift, and pitching or bending moment. Integration spanwise yields the bound circulation, which is interpolated in the near field vortex lattice to obtain the design camber surface(s)

Computing A Glimpse of Randomness

A Chaitin Omega number is the halting probability of a universal Chaitin (self-delimiting Turing) machine. Every Omega number is both computably enumerable (the limit of a computable, increasing, converging sequence of rationals) and random (its binary expansion is an algorithmic random sequence). In particular, every Omega number is strongly non-computable. The aim of this paper is to describe a procedure, which combines Java programming and mathematical proofs, for computing the exact values of the first 64 bits of a Chaitin Omega: 0000001000000100000110001000011010001111110010111011101000010000. Full description of programs and proofs will be given elsewhere.Comment: 16 pages; Experimental Mathematics (accepted

The Lyman Break Galaxies: their Progenitors and Descendants

We study the evolution of Lyman Break Galaxies (LBGs) from z=5 to z=0 by tracing the merger trees of galaxies in a large-scale hydrodynamic simulation based on a Lambda cold dark matter model. In particular, we emphasize on the range of properties of the sample selected by the rest-frame V band luminosity, in accordance with recent near-IR observations. The predicted rest-frame V band luminosity function agrees well with the observed one when dust extinction is taken into account. The stellar content and the star formation histories of LBGs are also studied. We find that the LBGs intrinsically brighter than Mv=-21.0 at z=3 have stellar masses of at least 10^9\Msun, with a median of 10^{10}h^{-1}\Msun. The brightest LBGs (Mv<-23) at z=3 merge into clusters/groups of galaxies at z=0, as suggested from clustering studies of LBGs. Roughly one half of the galaxies with -23<Mv<-22 at z=3 fall into groups/clusters, and the other half become typical L* galaxies at z=0 with stellar mass of ~10^{11}\Msun. Descendants of LBGs at the present epoch have formed roughly 30% of their stellar mass by z=3, and the half of their current stellar population is 10 Gyr old, favoring the scenario that LBGs are the precursors of the present day spheroids. We find that the most luminous LBGs have experienced a starburst within 500 Myr prior to z=3, but also have formed stars continuously over a period of 1 Gyr prior to z=3 when all the star formation in progenitors is coadded. We also study the evolution of the mean stellar metallicity distribution of galaxies, and find that the entire distribution shifts to lower metallicity at higher redshift. The observed sub-solar metallicity of LBGs at z=3 is naturally predicted in our simulation.Comment: 29 pages, including 11 figures, ApJ in press. One reference adde

Modeling the magnetic field in the protostellar source NGC 1333 IRAS 4A

Magnetic fields are believed to play a crucial role in the process of star formation. We compare high-angular resolution observations of the submillimeter polarized emission of NGC 1333 IRAS 4A, tracing the magnetic field around a low-mass protostar, with models of the collapse of magnetized molecular cloud cores. Assuming a uniform dust alignment efficiency, we computed the Stokes parameters and synthetic polarization maps from the model density and magnetic field distribution by integrations along the line-of-sight and convolution with the interferometric response. The synthetic maps are in good agreement with the data. The best-fitting models were obtained for a protostellar mass of 0.8 solar masses, of age 9e4 yr, formed in a cloud with an initial mass-to-flux ratio ~2 times the critical value. The magnetic field morphology in NGC 1333 IRAS 4A is consistent with the standard theoretical scenario for the formation of solar-type stars, where well-ordered, large-scale, rather than turbulent, magnetic fields control the evolution and collapse of the molecular cloud cores from which stars form.Comment: 4 pages, 5 figures. Accepted by Astronomy and Astrophysic

Toward the AdS/CFT gravity dual for High Energy Collisions: I.Falling into the AdS

In the context of the AdS/CFT correspondence we discuss the gravity dual of a high energy collision in a strongly coupled ${\cal N}=4$ SYM gauge theory. We suggest a setting in which two colliding objects are made of non-dynamical heavy quarks and antiquarks, which allows to treat the process in classical string approximation. Collision ``debris'' consist of closed as well as open strings. If the latter have ends on two outgoing charges, and thus are being ``stretched'' along the collision axes. We discuss motion in AdS of some simple objects first -- massless and massive particles -- and then focus on open strings. We study the latter in a considerable detail, concluding that they rapidly become ``rectangular'' in proper time -spatial rapidity $\tau-y$ coordinates with well separated fragmentation part and a near-free-falling rapidity-independent central part. Assuming that in the collisions of ``walls'' of charges multiple stretching strings are created, we also consider the motion of a 3d stretching membrane. We then argue that a complete solution can be approximated by two different vacuum solutions of Einstein eqns, with matter membrane separating them. We identify one of this solution with Janik-Peschanski stretching black hole solution, and show that all objects approach its (retreating) horizon in an universal manner.Comment: v2 was redone, with new material and different introduction. It now includes introduction to the second paper of the series as well, in which we calculate "holograms" of falling objects, namely their stress tensor on the boundar

Expanding the thermodynamical potential and the analysis of the possible phase diagram of deconfinement in FL model

The deconfinement phase transition is studied in the FL model at finite temperature and chemical potential. At MFT approximation, the phase transition can only be the first order in the whole $\mu-T$ phase plane. By a Landau expansion we further study the phase transition order and the possible phase diagram of deconfinement. We discuss the possibilities of second order phase transitions in FL model. By our analysis the cubic term in the Landau expansion could be cancelled by the high order fluctuations. By an ansatz of the Landau parameters, we obtain the possible phase diagram with both first and second order phase transition including the tricritical point which is similar to that of the chiral phase transition.Comment: 7 pages, 8 figures, submitted to Chinese Physics

On the critical condition in gravitational shock wave collision and heavy ion collisions

In this paper, we derived a critical condition for matter equilibration in heavy ion collisions using a holographic approach. A gravitational shock waves with infinite transverse extension is used to model infinite nucleus. We constructed the trapped surface in the collision of two asymmetric planar shock waves with sources at different depth in the bulk AdS and formulated a critical condition for matter equilibration in collision of "nucleus" in the dual gauge theory. We found the critical condition is insensitive to the depth of the source closer to the AdS boundary. To understand the origin of the critical condition, we computed the Next to Leading Order stress tensor in the boundary field theory due to the interaction of the nucleus and found the critical condition corresponds to the breaking down of the perturbative expansion. We indeed expect non-perturbative effects be needed to describe black hole formation.Comment: 26 pages, 3 figure