The Variations of Charpy V-Notch Impact Test Properties In Steel Plates

A survey of the variation to be expected in Charpy V-Notch tests obtained from plates was conducted by the Committee on Product Standards at the request of the Committee on General Metallurgy. The results of the survey are presented in this report. The survey data consisted of longitudinal and transverse impact test values obtained from seven specified locations on plates produced to ASTM A-572 as-rolled, A-516 normalized and A-537 quenched and tempered. Three testing temperatures were used for each grade. The data were collected from industry production during 1973 and 1974. Sufficient data were received to estimate limits of variation for impact tests taken at specified locations in plates.--Summar

Notes on Shapes of Polyhedra

These are course notes I wrote for my Fall 2013 graduate topics course on geometric structures, taught at ICERM. The notes rework many of proofs in William P. Thurston's beautiful but hard-to-understand paper, "Shapes of Polyhedra". A number of people, both in and out of the class, found these notes very useful and so I decided to put them on the arXiv.Comment: This is a 21 page expository pape

QCD Constraints on Form Factor Shapes

This talk presents an introduction to the use of dispersion relations to constrain the shapes of hadronic form factors consistent with QCD. The applications described include methods for studying |V_{cb}| and |V_{ub}|, the strange quark mass, and the pion charge radius.Comment: 8 pages, 3 eps figures, presented at ``Exclusive & Semi-exclusive Processes at High Momentum Transfer,'' Jefferson Lab, Newport News, VA, May 20-22, 199

On power corrections to event shapes

Recent work on the theme of power corrections in perturbative QCD is briefly reviewed, with an emphasis on event shapes in e+ e- annihilation. The factorization of soft gluon effects is the main tool: it leads to resummation, and thus highlights the limitations of perturbation theory, pointing to nonperturbative corrections whose size can be estimated. Power corrections can be resummed into shape functions, for which QCD--based models are available. Theoretical progress is closing in on the nonperturbative frontier.Comment: 15 pages, no figures. Invited talk at the XIV Italian Meeting on High Energy Physics, Parma, April 2002. Extended versio

On equilibrium shapes of charged flat drops

Equilibrium shapes of two-dimensional charged, perfectly conducting liquid drops are governed by a geometric variational problem that involves a perimeter term modeling line tension and a capacitary term modeling Coulombic repulsion. Here we give a complete explicit solution to this variational problem. Namely, we show that at fixed total charge a ball of a particular radius is the unique global minimizer among all sufficiently regular sets in the plane. For sets whose area is also fixed, we show that balls are the only minimizers if the charge is less than or equal to a critical charge, while for larger charge minimizers do not exist. Analogous results hold for drops whose potential, rather than charge, is fixed

Investigation on the Effect of Shapes on the Drying Kinetics and Sensory Evaluation Study of Dried Jackfruit

Jackfruits are seasonal and highly nutritional fruits indigenous to the Southwestern rainforests of India. However much of the produce are spoilt annually due to poor preservation techniques. Minimal studies have been conducted on the drying kinetics of jackfruit and the effect of shapes on the drying kinetics. In this research, drying curves of three different shaped jackfruit slices were obtained using a convective oven at 40oC, 50oC, 60oC and 70oC. Modified Midilli-Kucuk Model was found to be the best kinetic model for drying of jackfruits. At all temperatures, effective moisture diffusivity values and activation energy varied from 2.66 x 10-10 - 4.85 x 10-10 m2/s and 16.08 - 20.07 kJ/mol respectively. Drying was found to be most efficient at 50oC using the square shaped slices with a R2, RMSE and SSE value of 0.9984, 0.01127 and 0.002668 respectively. Sensory evaluation of untreated and additive-added dried jackfruit slices was conducted by 40 untrained sensory panelists. Jackfruit with ascorbic acid and sugar coating had highest aesthetics value due to better retention of colour by ascorbic acid. However sugar coated jackfruit had the most favorable taste and smell. Further optimization must be done to satisfy consumers collectively to enable a highly marketable product

On the sign-imbalance of partition shapes

Let the sign of a standard Young tableau be the sign of the permutation you get by reading it row by row from left to right, like a book. A conjecture by Richard Stanley says that the sum of the signs of all SYTs with n squares is 2^[n/2]. We present a stronger theorem with a purely combinatorial proof using the Robinson-Schensted correspondence and a new concept called chess tableaux. We also prove a sharpening of another conjecture by Stanley concerning weighted sums of squares of sign-imbalances. The proof is built on a remarkably simple relation between the sign of a permutation and the signs of its RS-corresponding tableaux.Comment: 12 pages. Better presentatio

On the Influence of Pulse Shapes on Ionization Probability

We investigate analytical expressions for the upper and lower bounds for the ionization probability through ultra-intense shortly pulsed laser radiation. We take several different pulse shapes into account, including in particular those with a smooth adiabatic turn-on and turn-off. For all situations for which our bounds are applicable we do not find any evidence for bound-state stabilization.Comment: 21 pages LateX, 10 figure

The Effect of Baryons on Halo Shapes

Observational evidence indicates a mismatch between the shapes of collisionless dark matter (DM) halos and those of observed systems. Using hydrodynamical cosmological simulations we investigate the effect of baryonic dissipation on halo shapes. We show that dissipational simulations produce significantly rounder halos than those formed in equivalent dissipationless simulations. Gas cooling causes an average increase in halo principal axis ratios of ~ 0.2-0.4 in the inner regions and a systematic shift that persists out to the virial radius, alleviating any tension between theory and observations. Although the magnitude of the effect may be overestimated due to overcooling, cluster formation simulations designed to reproduce the observed fraction of cold baryons still produce substantially rounder halos. Subhalos also exhibit a trend of increased axis ratios in dissipational simulations. Moreover, we demonstrate that subhalos are generally rounder than corresponding field halos even in dissipationless simulations. Lastly, we analyze a series of binary, equal-mass merger simulations of disk galaxies. Collisionless mergers reveal a strong correlation between DM halo shape and stellar remnant morphology. In dissipational mergers, the combination of strong gas inflows and star formation leads to an increase of the DM axis ratios in the remnant. All of these results highlight the vital role of baryonic processes in comparing theory with observations and warn against over-interpreting discrepancies with collisionless simulations on small scales.Comment: 8 pages, 3 figures. To appear in the proceedings of the XXIst IAP Colloquium "Mass Profiles and Shapes of Cosmological Structures", Paris 4-9 July 2005, France, (Eds.) G. Mamon, F. Combes, C. Deffayet, B. Fort, EAS Publications Serie