Strains, deformations and buckling in very thin torispherical pressure vessel ends

An experimental study has been made of the behaviour of "very thin" torispherical ends subjected to internal pressure. The seventeen ends tested were full-size production ends made from stainless steel, with thickness to diameter ratios (te/Di) varying from 0.002 to 0.001. At each value of te/Di the knuckle radius (ri) and crown radius (Ri) were varied to cover the range of ends frequently used. Each end was stain gauged on both inner and outer surfaces and then pressurised until buckling occurred in the knuckle region. The strain gauges were monitored throughout each test thus giving a detailed coverage of the strain distribution. High compressive hoop strains, shown to exist on both surfaces of the knuckle, are responsible for the buckling mode of failure. A shape/thickness survey was performed on each end prior to pressure testing. The effects of thickness reductions and deviations of curvature from the nominal are discussed. Residual strain measurements were made on three ends and were shown to be significantly large in the pressed and spun manufactured ends. A study of the effect of work hardening on the properties of the material from which the ends were made is also presented. It is shown that the proof stress and Vickers hardness number increases rapidly when the material is work hardened. The dependence of the elastic stress indices, limit pressures and first buckling pressures on wall thickness, knuckle radius and crown radius has been examined. The design implications of the study are discussed and a method for predicting the first buckling pressure of production ends given

Strains, deformations and buckling in very thin torispherical pressure vessel ends

An experimental study has been made of the behaviour of "very thin" torispherical ends subjected to internal pressure. The seventeen ends tested were full-size production ends made from stainless steel, with thickness to diameter ratios (te/Di) varying from 0.002 to 0.001. At each value of te/Di the knuckle radius (ri) and crown radius (Ri) were varied to cover the range of ends frequently used. Each end was stain gauged on both inner and outer surfaces and then pressurised until buckling occurred in the knuckle region. The strain gauges were monitored throughout each test thus giving a detailed coverage of the strain distribution. High compressive hoop strains, shown to exist on both surfaces of the knuckle, are responsible for the buckling mode of failure. A shape/thickness survey was performed on each end prior to pressure testing. The effects of thickness reductions and deviations of curvature from the nominal are discussed. Residual strain measurements were made on three ends and were shown to be significantly large in the pressed and spun manufactured ends. A study of the effect of work hardening on the properties of the material from which the ends were made is also presented. It is shown that the proof stress and Vickers hardness number increases rapidly when the material is work hardened. The dependence of the elastic stress indices, limit pressures and first buckling pressures on wall thickness, knuckle radius and crown radius has been examined. The design implications of the study are discussed and a method for predicting the first buckling pressure of production ends given

Pedestrian Solution of the Two-Dimensional Ising Model

The partition function of the two-dimensional Ising model with zero magnetic field on a square lattice with m x n sites wrapped on a torus is computed within the transfer matrix formalism in an explicit step-by-step approach inspired by Kaufman's work. However, working with two commuting representations of the complex rotation group SO(2n,C) helps us avoid a number of unnecessary complications. We find all eigenvalues of the transfer matrix and therefore the partition function in a straightforward way.Comment: 10 pages, 2 figures; eqs. (101) and (102) corrected, files for fig. 2 fixed, minor beautification

Coexistence of Single and Double-Quantum Vortex Lines

We discuss the configurations in which singly and doubly quantized vortex lines may coexist in a rotating superfluid. General principles of energy minimization lead to the conclusion that in equilibrium the two vortex species segregate within a cylindrical vortex cluster in two coaxial domains where the singly quantized lines are in the outer annular region. This is confirmed with simulation calculations on discrete vortex lines. Experimentally the coexistence can be studied in rotating superfluid $^3$He-A. With cw NMR techniques we find the radial distribution of the two vortex species to depend on how the cluster is prepared: (i) By cooling through $T_c$ in rotation, coexistence in the minimum energy configuration is confirmed. (ii) A glassy agglomerate is formed if one starts with an equilibrium cluster of single-quantum vortex lines and adds to it sequentially double-quantum lines, by increasing the rotation velocity in the superfluid state. This proves that the energy barriers, which separate different cluster configurations, are too high for metastabilities to anneal.Comment: 12 pages, 11 figures; Changed content, 15 pages, 14 figure

Long-lived oscillons from asymmetric bubbles

The possibility that extremely long-lived, time-dependent, and localized field configurations (``oscillons'') arise during the collapse of asymmetrical bubbles in 2+1 dimensional phi^4 models is investigated. It is found that oscillons can develop from a large spectrum of elliptically deformed bubbles. Moreover, we provide numerical evidence that such oscillons are: a) circularly symmetric; and b) linearly stable against small arbitrary radial and angular perturbations. The latter is based on a dynamical approach designed to investigate the stability of nonintegrable time-dependent configurations that is capable of probing slowly-growing instabilities not seen through the usual ``spectral'' method.Comment: RevTeX 4, 9 pages, 11 figures. Revised version with a new approach to stability. Accepted to Phys. Rev.

Evaluating Microcounseling Training

An evaluation research design was developed as an attempt to provide a more satisfactory approach to microcounseling training program evaluation. Trainee performance was measured three times during a counseling practicum, with microcounseling training occurring between the second and third observations. Trainee performance was compared to a predetermined standard for counselor behavior. Results were analyzed for both the differences between observations, and the degree of similarity to the model. Counseling behavior of trainees after microcounseling training was significantly different from their behavior prior to the training. After training they were more like the standard. The trainees performed less like the standard after some counseling experience, but before receiving microcounseling training.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/66901/2/10.1177_0193841X8300700206.pd

Volume element structure and roton-maxon-phonon excitations in superfluid helium beyond the Gross-Pitaevskii approximation

We propose a theory which deals with the structure and interactions of volume elements in liquid helium II. The approach consists of two nested models linked via parametric space. The short-wavelength part describes the interior structure of the fluid element using a non-perturbative approach based on the logarithmic wave equation; it suggests the Gaussian-like behaviour of the element's interior density and interparticle interaction potential. The long-wavelength part is the quantum many-body theory of such elements which deals with their dynamics and interactions. Our approach leads to a unified description of the phonon, maxon and roton excitations, and has noteworthy agreement with experiment: with one essential parameter to fit we reproduce at high accuracy not only the roton minimum but also the neighboring local maximum as well as the sound velocity and structure factor.Comment: 9 pages, 6 figure

Analytic Methods in Nonperturbative QCD

Recently developed analytic methods in the framework of the Field Correlator Method are reviewed in this series of four lectures and results of calculations are compared to lattice data and experiment. Recent lattice data demonstrating the Casimir scaling of static quark interaction strongly support the FCM and leave very little space for all other theoretical models, e.g. instanton gas/liquid model. Results of calculations for mesons, baryons, quark-gluon plasma and phase transition temperature demonstrate that new analytic methods are a powerful tool of nonperturbative QCD along with lattice simulations.Comment: LaTeX, 34 pages; Lectures given at the 13th Indian-Summer School "Understanding the Structure of Hadrons", August 28 - September 1, 2000, Prague, Czech Republi