Numerical simulation of natural convective heat transfer and fluid flow around a heated cylinder inside an enclosure

 A collocated, non-orthogonal grid based finite volume technique has been applied for investigating the two dimensional natural convective flow and heat transfer around a heated cylinder kept in a square enclosure. The effects of different enclosure wall thermal boundary conditions, fluid Prandtl number and the ratio between enclosure and cylinder dimensions (aspect ratio) upon the flow and thermal features, have been systematically studied. It is observed that the patterns of recirculatory flow and thermal stratification in the fluid are significantly modified, if any of these parameters is varied. The overall heat transfer rates are also affected due to the changes in the flow and temperature patterns. The study presents useful observations regarding the variation of local Nusselt number along each wall, for the different cases considered. Received on 2 August 2000 / Published online: 29 November 2001     

Quantization dimension and temperature function for recurrent self-similar measures

We determine the quantization dimension function for the image measure supported on a recurrent self-similar set of an ergodic Markov measure, and its relationship with the temperature function of the thermodynamic formalism arising in multifractal analysis is established.     

A Mathematical Theory of Fame

We study empirically how the fame of WWI fighter-pilot aces, measured in numbers of web pages mentioning them, is related to their achievement, measured in numbers of opponent aircraft destroyed. We find that on the average fame grows exponentially with achievement; the correlation coefficient between achievement and the logarithm of fame is 0.72. The number of people with a particular level of achievement decreases exponentially with the level, leading to a power-law distribution of fame. We propose a stochastic model that can explain the exponential growth of fame with achievement. Next, we hypothesize that the same functional relation between achievement and fame that we found for the aces holds for other professions. This allows us to estimate achievement for professions where an unquestionable and universally accepted measure of achievement does not exist. We apply the method to Nobel Prize winners in Physics. For example, we obtain that Paul Dirac, who is a hundred times less famous than Einstein contributed to physics only two times less. We compare our results with Landau’s ranking.     

AdS/CFT superconductors with Power Maxwell electrodynamics: Reminiscent of the Meissner effect

Based on an analytic scheme and neglecting the back reaction effect several crucial properties of holographic s-wave superconductors have been investigated in the presence of an external magnetic field in the background of a D  -dimensional Schwarzschild AdS space–time. Inspired by low energy limit of heterotic string theory, in the present Letter we replace the conventional Maxwell action by a Power Maxwell action. Immersing the holographic superconductors in an external static magnetic field the spatially dependent condensate solutions have been obtained analytically. Interestingly enough it is observed that condensation can form only below a certain critical field strength (_Bc$B_c$). Finally, and most importantly it is observed that the value of this critical field strength increases as the mass of the scalar particles gets higher, which indicates the onset of a harder condensation.     

Structure of de-oxy corticosterone (4-pregnen-21-ol-3,20-dione)

Synthetic steroid de-oxy corticosterone (4-pregnen-21-ol-3,20-dione) crystallizes in the monoclinic space group P2₁, with a = 11.706(2); b = 11.171(3), c = 13.966(3) Å, and = 100.94(2)°, Z = 4. Ring A tends to acquire the conformation of a half-boat, rings B and C are in the chair configuration, and ring D is a 13, 14-half-chair. The ring junctions B/C and C/D are both trans, whereas the ring junction A/B is quasi-trans. The molecule as a whole is slightly convex toward the -side, with an angle of 16.01(0.36)° between the C10--C19 and C13--C18 vectors. Molecular packing and stacking interactions play the major role in structural association. Cohesion of the crystal is due to van der Waals interactions.     

A new first principles approach to calculate phonon spectra of disordered alloys

The lattice dynamics in substitutional disordered alloys with constituents having large size differences is driven by strong disorder in masses, inter-atomic force constants and local environments. In this paper, a new first principles approach based on special quasirandom structures and an itinerant coherent potential approximation to compute the phonon spectra of such alloys is proposed and applied to Ni?.?Pt?.? alloy. The agreement between our results and experiments is found to be much better than for previous models of disorder due to an accurate treatment of the interplay of inter-atomic forces among various pairs of chemical species. This new formalism serves as a potential solution to the longstanding problem of a proper microscopic understanding of lattice dynamical behavior of disordered alloys.     

Ab?initio study of the phonon spectrum, entropy and lattice heat capacity of disordered Re-W alloys

The Re(1-x)W(x) alloy is formed by continuous neutron bombardment of W, the core material making up the shield in fusion devices. Here, we present an ab?initio study of the lattice dynamical properties of this commercially important alloy. The dynamical (force constant) matrix was obtained through a first-principles, density functional perturbation theory. Various vibrational properties, such as fuzzy phonon dispersion relations, density of states (DOS), scattering life-times, vibrational entropy and specific heat are studied. The effects of short-range ordering is shown to be important in the 50-50 alloy.     

Radiation induced nano-scale free volume modifications in amorphous polymeric material: a study using positron annihilation lifetime spectroscopy

Radiation exposure modifies the nano scale free volume of the polymers which has direct correlation to certain properties of polymeric materials. CR-39 (DOP) polycarbonate polymeric films were exposed to gamma radiation at different doses for the study of nano scale free volume as well as structural and optical properties. An overall increase in the number of free volume holes at all doses was observed. UV–visible studies showed an improvement in the optical properties due to decrease in direct band gap energy. X-ray diffraction spectra of the polymer samples showed the increased amorphous nature of the polymer.     

Re-inventing Willis

Scientists often re-invent things that were long known. Here we review these activities as related to the mechanism of producing power law distributions, originally proposed in 1922 by Yule to explain experimental data on the sizes of biological genera, collected by Willis. We also review the history of re-invention of closely related branching processes, random graphs and coagulation models.