Optimum Shape of Constant Stress Toroidal Shells

2013 ◽  
Vol 135 (2) ◽  
Author(s):  
Vu Truong Vu
Keyword(s):  
Cross Section ◽  
Cross Sections ◽  
Thickness Distribution ◽  
Analytical Form ◽  
Optimum Shape ◽  
Constant Thickness ◽  
Toroidal Shell ◽  
Volume Increase ◽  
Material Saving ◽  
Better Than

The paper presents the optimization of toroidal shell cross-sections under internal pressure. The wall thickness distribution along a circular centerline is derived in an analytical form. In membrane solution, this cross-section gives a constant Mises stress all over the shell. Therefore, it leads to material saving and contained volume increase in comparison with the traditional cross-section of circular constant thickness. The optimum shapes are designed for two states of shell, one is elasticity and the other is up to destruction. The maximum material saving can reach 70% in some configurations of toroid. Results of the proposed method are as good as or better than those found in literature.

Triple differential cross sections for the ionization of helium by intermediate-energy electrons

1988 ◽  
Vol 66 (1) ◽  
pp. 82-85
Author(s):  
K. S. Baliyan ◽  
M. K. Srivastava
Keyword(s):  
Cross Section ◽  
Cross Sections ◽  
Differential Cross ◽  
Intermediate Energy ◽  
Incident Electron Energy ◽  
Cross Section Data ◽  
Satisfactory Description ◽  
Triple Differential Cross Section ◽  
Section Data ◽  
Better Than

The recent triple differential cross-section data of Jung for the ionization of helium in the coplanar asymmetric geometry at 250 eV incident electron energy is analyzed within the framework of the second Born (B2) and modified Glauber (MG) approximations. At this energy B2 and MG results, although better than those obtained by using the first Born and Glauber approximations, do not lead to a satisfactory description of the experimental data in all the kinematic situations considered here.

scholarly journals The determination of normal stresses in cross-sections of the three-flue reinforced concrete chimney

2008 ◽  
Vol 3 (2) ◽  
pp. 081-095
Author(s):  
Małgorzata Dobrowolska ◽  
Marta Słowik
Keyword(s):  
Reinforced Concrete ◽  
Cross Section ◽  
Cross Sections ◽  
Analytical Form ◽  
Normal Stresses ◽  
Full Cross Section ◽  
Steel Bars ◽  
Reinforced Concrete Chimney ◽  
Physical Laws

In the paper there is presented the algorithm of calculation of normal stresses in reinforced concrete three-flue chimney. The calculation has been made for full cross-section and for cross-section weakened by openings. The governing equations has been derived in an analytical form assuming linear physical laws for concrete and steel and, as for as considered cross-section weakened by openings, taking into account the additional reinforcing steel bars at the openings. In addition coefficients B and C have been determined, which are useful at dimensioning.

The absorption of high-energy photons in matter

1958 ◽  
Vol 244 (1237) ◽  
pp. 245-258 ◽  
Keyword(s):  
Pair Production ◽  
Cross Section ◽  
Cross Sections ◽  
Born Approximation ◽  
Liquid Scintillation ◽  
Scintillation Counter ◽  
High Energy ◽  
A Value ◽  
Peak Energy ◽  
Better Than

Total absorption cross-sections of hydrogen, carbon, copper, silver, lead and uranium have been measured for photons of mean energy 94 MeV. The method was to measure the transmission through an absorber of photons from the Oxford synchrotron, using a biased liquid scintillation counter to select photons of energy near the peak energy of the machine. The experimental data for hydrogen have been used to deduce a value for the cross-section for pair production in the field of the electron of 4.7 ± 0.4 millibarn. The relative cross-sections for the heavier elements have been determined to better than ± 0.2 %, and confirm the most recent calculations of the correction to the Born approximation in the theory of pair production.

Total and K-shell photoeffect cross sections at K-edges of Cu, Zr, Ag, Sn, Ta, Au, and Pb

1981 ◽  
Vol 59 (7) ◽  
pp. 853-858 ◽  
Author(s):  
K. S. Puttaswamy ◽  
Ramakrishna Gowda ◽  
B. Sanjeevaiah
Keyword(s):  
Cross Section ◽  
Cross Sections ◽  
Experimental Uncertainty ◽  
Total Attenuation ◽  
Empirical Relations ◽  
Better Than

Total attenuation cross sections, total and K-shell photoeffect cross sections, K-jump ratios, and total to K-shell photoeffect cross section ratios at the K-edges of the elements copper, zirconium, silver, tin, tantalum, gold, and lead are extracted from our earlier studies on total attenuation cross sections on these elements. These are compared with the latest and extensively tabulated theoretical photoeffect cross sections of Scofield and agreement within experimental uncertainty is observed. Further, empirical relations for K-edge cross sections and ratios are obtained, and the values of constants in these relations are tabulated. These empirical relations are found to reproduce the values to an accuracy better than one percent.

scholarly journals The Pulsed Electron Beam Time-of-flight Method for Measuring Absolute Total Cross Sections: Atomic Helium

1982 ◽  
Vol 35 (5) ◽  
pp. 559 ◽  
Author(s):  
Robert K Jones ◽  
RA Bonham
Keyword(s):  
Cross Section ◽  
Cross Sections ◽  
Total Electron ◽  
Pulsed Electron Beam ◽  
Section Shape ◽  
The Cross ◽  
Scattering Cross Sections ◽  
Time Of Flight Method ◽  
New Procedures ◽  
Better Than

Improvements in a previously reported experimental method have made it possible to obtain absolute total electron-scattering cross sections with a predicted accuracy of better than � 2 % (10') for certain electron kinetic energies. As a first example of the application of the new procedures the cross section for helium is reported from O' 8 to 50� 0 eV. Error estimates for all known sources of uncertainty are discussed in detail. The results confirm the earlier work of Kennerly and Bonham and the agreement is, on the average, better than 1 % with no changes in the cross-section shape.

Balanced cross sections

1969 ◽  
Vol 6 (4) ◽  
pp. 743-757 ◽  
Author(s):  
C. D. A. Dahlstrom
Keyword(s):  
Surface Area ◽  
Cross Section ◽  
Cross Sections ◽  
Geological Environment ◽  
Simple Test ◽  
Cross Sectional ◽  
Mountain Belt ◽  
Sectional Plane ◽  
Bed Thickness ◽  
Better Than

Post-depositional concentric deformation produces no significant change in rock volume. Since bed thickness remains constant in concentric deformation, the surface area of a bed and its length in a cross-sectional plane must also remain constant. Under these conditions, a simple test of the geometric validity of a cross section is to measure bed lengths at several horizons between reference lines located on the axial planes of major synclines or other areas of no interbed slip. These bed lengths must be consistent unless a discontinuity, like a décollement, intervenes. Consistency of bed length also requires consistency of shortening, whether by folding and (or) faulting, within one cross section and between adjacent cross sections.The number of possible cross-sectional explanations of a set of data is reduced by the fact that, in a specific geological environment, there is only a limited suite of structures which can exist. This imposes a set of local "ground rules" on interpretation. When these local restrictions are coupled with the geometric restrictions which follow from the law of conservation of volume, it is often possible to produce structural cross sections that have a better-than-normal chance of being right.The concept of consistency of shortening can be extrapolated to a mountain belt as a whole, thereby indicating the necessity for some kind of transfer mechanism wherein waning faults or folds are compensated by waxing en echelon features. These concepts are illustrated diagrammatically and by examples from the Alberta Foothills.

Systematic study of deformation effects on fusion cross-sections using various proximity potentials

Open Physics ◽  
2014 ◽  
Vol 12 (6) ◽  
Author(s):  
Tapan Rajbongshi ◽  
Kushal Kalita
Keyword(s):  
Experimental Data ◽  
Cross Section ◽  
Cross Sections ◽  
Fusion Cross Section ◽  
Proximity Potential ◽  
Deformation Parameters ◽  
Barrier Penetration ◽  
Experimental Fusion ◽  
Static Quadrupole ◽  
Better Than

AbstractThe influence of static quadrupole and hexadecapole (positive & negative) deformation of targets are studied using eleven different versions of nuclear potentials. The height and position of the interaction barrier for the reactions induced by spherical projectile (16O) on the deformed targets such as 166Er, 154Sm and 176Yb have been estimated. It is found that the nucleus-nucleus potential strongly depends on the value of the deformation parameters and orientation of the target. The experimental fusion cross-section of the reactions 16O + 176Yb, 16O +166Er and 16O +154Sm are investigated by applyingWong’s formula using various parameterizations of the proximity potential as well as an assessment of the results of a multi-dimensional barrier penetration model (BPM). The fusion cross-sections by Prox 77, Prox 88, Prox 00, Prox 00DP, Denisov DP, Bass 80, CW 76 and AW 95 potentials are found to be better than the rest in comparison to experimental data.

A measurement of the neutron-proton capture cross-section

1958 ◽  
Vol 248 (1255) ◽  
pp. 539-559 ◽  
Keyword(s):  
Cross Section ◽  
Cross Sections ◽  
Recoil Proton ◽  
Statistical Error ◽  
Nuclear Research ◽  
Photographic Emulsion ◽  
Neutron Density ◽  
Capture Cross ◽  
Flux Measurements ◽  
Better Than

Measurements have been made of the neutron density as a function of distance from a polonium-beryllium source in effectively infinite tanks of water and aqueous boric acid. The ratio of the thermal-neutron capture cross-sections of boron and hydrogen was found to be 2317 ± 27. The cross-section of hydrogen calculated from this result, using the known cross-section of Harwell standard boron, 769 ± 4 barns (at a neutron velocity of 2200 m /s.), and the known cross-section of the boron used relative to Harwell standard boron, 0.985 + 0.002, was 0.327 + 0.004 barn (at 2200 m /s.) which is consistent with other recent accurate values. In preliminary experiments, it was shown that flux measurements reproducible to better than 3 % were possible with the disks of Ilford C2 nuclear research photographic emulsion used as detectors. The main source of error in the result was the statistical error for a total count of 200000 tracks. The only corrections necessary were 1.6% for recoil proton background, and 0.7 % for the disturbance of the neutron density by the detectors.

scholarly journals Constraining Velocity-dependent Self-Interacting Dark Matter with the Milky Way’s dwarf spheroidal galaxies

2021 ◽  
Author(s):  
Camila A Correa
Keyword(s):  
Dark Matter ◽  
Cross Section ◽  
Cross Sections ◽  
Yukawa Potential ◽  
Analytical Form ◽  
Orbital Evolution ◽  
Particle Model ◽  
Velocity Correlation ◽  
Dwarf Spheroidal Galaxies ◽  
Spheroidal Galaxies

Abstract The observed anti-correlation between the central dark matter (DM) densities of the bright Milky Way (MW) dwarf spheroidal galaxies (dSphs) and their orbital pericenter distances poses a potential signature of self-interacting dark matter (SIDM). In this work we investigate this possibility by analysing the range of SIDM scattering cross section per unit mass, σ/mχ, able to explain such anti-correlation. We simulate the orbital evolution of dSphs subhaloes around the MW assuming an analytical form for the gravitational potential, adopting the proper motions from the Gaia mission and including a consistent characterization of gravitational tidal stripping. The evolution of subhalo density profiles is modelled using the gravothermal fluid formalism, where DM particle collisions induce thermal conduction that depends on σ/mχ. We find that models of dSphs, such as Carina and Fornax, reproduce the observed central DM densities with fixed σ/mχ ranging between 30 and 50 cm2g−1, whereas other dSphs prefer larger values ranging between 70 and 100 cm2g−1. These cross sections correlate with the average collision velocity of DM particles within each subhalo’s core, so that systems modelled with large cross sections have lower collision velocities. We fit the cross section-velocity correlation with a SIDM particle model, where a DM particle of mass mχ = 53.93 ± 9.81 GeV interacts under the exchange of a light mediator of mass mφ = 6.6 ± 0.43 MeV, with the self-interactions being described by a Yukawa potential. The outcome is a cross section-velocity relation that explains the diverse DM profiles of MW dSph satellites and is consistent with observational constraints on larger scales.

scholarly journals Change in the amplitude of strong discontinuity wave propagating in a rod made of Murnaghan material

2021 ◽  
Vol 2131 (2) ◽  
pp. 022117
Author(s):  
M Major ◽  
I Major ◽  
B Yazyev
Keyword(s):  
Shock Wave ◽  
Numerical Analysis ◽  
Cross Section ◽  
Cross Sections ◽  
Analytical Solutions ◽  
Analytical Form ◽  
Relative Amplitude ◽  
Strong Discontinuity ◽  
Scaling Parameter ◽  
Contour Maps

Abstract The paper presents calculations of the change in amplitude of strong discontinuity wave propagating in a thin rod made of hyperelastic Murnaghan material. Two functions were assumed for the calculations, describing the change of the cross-section of the rod with the constant scaling parameter?for both decreasing cross-sections of the analysed steel rods. A numerical analysis was performed based on analytical solutions. The analytical form of solution for both rods with decreasing cross-sections allowed for preparation of contour maps for the propagating wave of strong discontinuity. Furthermore, the changes in the relative amplitude of the propagating shock wave in a thin rod were determined for two rods analysed in the study, for which the differences in the values of the relative amplitude in the final cross-section were found.

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