Electromagnetic finite elements based on a four-potential variational principle

Electromagnetic finite elements based on a variational principle that uses the electromagnetic four-potential as a primary variable are derived. This choice is used to construct elements suitable for downstream coupling with mechanical and thermal finite elements for the analysis of electromagnetic/mechanical systems that involve superconductors. The main advantages of the four-potential as a basis for finite element formulation are that the number of degrees of freedom per node remains modest as the problem dimensionally increases, that jump discontinuities on interfaces are naturally accommodated, and that statics as well as dynamics may be treated without any a priori approximations. The new elements are tested on an axisymmetric problem under steady state forcing conditions. The results are in excellent agreement with analytical solutions

Analysis of superconducting electromagnetic finite elements based on a magnetic vector potential variational principle

Electromagnetic finite elements are extended based on a variational principle that uses the electromagnetic four potential as primary variable. The variational principle is extended to include the ability to predict a nonlinear current distribution within a conductor. The extension of this theory is first done on a normal conductor and tested on two different problems. In both problems, the geometry remains the same, but the material properties are different. The geometry is that of a 1-D infinite wire. The first problem is merely a linear control case used to validate the new theory. The second problem is made up of linear conductors with varying conductivities. Both problems perform well and predict current densities that are accurate to within a few ten thousandths of a percent of the exact values. The fourth potential is then removed, leaving only the magnetic vector potential, and the variational principle is further extended to predict magnetic potentials, magnetic fields, the number of charge carriers, and the current densities within a superconductor. The new element produces good results for the mean magnetic field, the vector potential, and the number of superconducting charge carriers despite a relatively high system condition number. The element did not perform well in predicting the current density. Numerical problems inherent to this formulation are explored and possible remedies to produce better current predicting finite elements are presented

Finite element analysis of time-independent superconductivity

The development of electromagnetic (EM) finite elements based upon a generalized four-potential variational principle is presented. The use of the four-potential variational principle allows for downstream coupling of EM fields with the thermal, mechanical, and quantum effects exhibited by superconducting materials. The use of variational methods to model an EM system allows for a greater range of applications than just the superconducting problem. The four-potential variational principle can be used to solve a broader range of EM problems than any of the currently available formulations. It also reduces the number of independent variables from six to four while easily dealing with conductor/insulator interfaces. This methodology was applied to a range of EM field problems. Results from all these problems predict EM quantities exceptionally well and are consistent with the expected physical behavior

Coupled structural, thermal, phase-change and electromagnetic analysis for superconductors, volume 1

This research program has dealt with the theoretical development and computer implementation of reliable and efficient methods for the analysis of coupled mechanical problems that involve the interaction of mechanical, thermal, phase-change and electromagnetic subproblems. The focus application has been the modeling of superconductivity and associated quantum-state phase-change phenomena. In support of this objective the work has addressed the following issues: (1) development of variational principles for finite elements; (2) finite element modeling of the electromagnetic problem; (3) coupling of thermal and mechanical effects; and (4) computer implementation and solution of the superconductivity transition problem. The research was carried out over the period September 1988 through March 1993. The main accomplishments have been: (1) the development of the theory of parametrized and gauged variational principles; (2) the application of those principled to the construction of electromagnetic, thermal and mechanical finite elements; and (3) the coupling of electromagnetic finite elements with thermal and superconducting effects; and (4) the first detailed finite element simulations of bulk superconductors, in particular the Meissner effect and the nature of the normal conducting boundary layer. The grant has fully supported the thesis work of one doctoral student (James Schuler, who started on January 1989 and completed on January 1993), and partly supported another thesis (Carmelo Militello, who started graduate work on January 1988 completing on August 1991). Twenty-three publications have acknowledged full or part support from this grant, with 16 having appeared in archival journals and 3 in edited books or proceedings

Coupled structural, thermal, phase-change and electromagnetic analysis for superconductors, volume 2

Two families of parametrized mixed variational principles for linear electromagnetodynamics are constructed. The first family is applicable when the current density distribution is known a priori. Its six independent fields are magnetic intensity and flux density, magnetic potential, electric intensity and flux density and electric potential. Through appropriate specialization of parameters the first principle reduces to more conventional principles proposed in the literature. The second family is appropriate when the current density distribution and a conjugate Lagrange multiplier field are adjoined, giving a total of eight independently varied fields. In this case it is shown that a conventional variational principle exists only in the time-independent (static) case. Several static functionals with reduced number of varied fields are presented. The application of one of these principles to construct finite elements with current prediction capabilities is illustrated with a numerical example

Characterization, renovation, and utilization of water from slurry transport systems

The transportation of a number of commodities as water slurries in pipelines offers a number of advantages which will make this method of transport more popular in coming years. Among the formeost of these advantages are high reliability, low operating costs, minimum environmental disruption, and ability to operate with nonpetroleum energy resources. Although coal is the most frequently mentioned material that is a candidate for slurry transport, other commodities including minerals, wood chips, and even solid refuse may be moved in this manner. Water used as a slurry transport medium must be properly characterized, renovated, and used in order to make slurry transport environmentally and economically acceptable.Project # B-145-MO Agreement # 14-34-0001-121

Results of endoluminal grafting in an experimental aortic aneurysm model

AbstractWe studied the impact of an endoluminally placed stented aortic graft on the geometry of a surgically created abdominal aortic dilation (AAD) in nonatherosclerotic mongrel dogs. Patulous iliac vein patch infrarenal aortoplasty produced a fusiform AAD, doubling the aorta diameter. Lumbar and mesenteric aortic tributaries were preserved and no mural thrombus formed. AADs created in 23 dogs were endoluminally excluded through transfemoral placement of a thin-wall Dacron graft 4 ± 2 months later. Balloon-expandable stents were used to anchor each end of the graft to the aorta. The graft was crimped radially in its body and longitudinally at its ends to provide longitudinal and radial expandability in these respective zones. Serial color duplex, angiography, and direct caliper measurements were made. Before graft placement, a 19% ± 11% diameter growth was observed. At graft placement, flow arrest immediately occurred in the space between the graft and the AAD intima in all cases. Although microscopic recanalization of the thrombus in this space was seen at sacrifice 6 and 12 months later, no macroscopic duplex flow was imaged. A 10% ± 11% reduction in AAD diameter was measured at 6 months (p < 0.001), with no further reduction at 12 months. Graft dimensions remained stable. No anastomotic leaks developed. AAD growth stopped during the first year after effective endoluminal exclusion in normotensive dogs despite patent side branches (<1.5 mm internal diameter) and no mural thrombus at the time of graft placement. Whether microscopic recanalization of the thrombus that forms outside the graft has an impact after 1 year remains to be seen. (J Vasc Surg 1996;23:819-31.

Strong Coupling Constant from the Photon Structure Function

We extract the value of the strong coupling constant alpha_s from a single-parameter pointlike fit to the photon structure function F_2^gamma at large x and Q^2 and from a first five-parameter full (pointlike and hadronic) fit to the complete F_2^gamma data set taken at PETRA, TRISTAN, and LEP. In next-to-leading order and the MSbar renormalization and factorization schemes, we obtain alpha_s(m_Z)=0.1183 +/- 0.0050(exp.)^+0.0029_-0.0028(theor.) [pointlike] and alpha_s(m_Z)=0.1198 +/- 0.0028(exp.)^+0.0034_-0.0046(theor.) [pointlike and hadronic]. We demonstrate that the data taken at LEP have reduced the experimental error by about a factor of two, so that a competitive determination of alpha_s from F_2^gamma is now possible.Comment: 11 pages, 2 tables, 2 figures. Version accepted for publication by Phys. Rev. Let

A New 5-Flavour LO Analysis and Parametrization of Parton Distributions in the Real Photon

New, radiatively generated, LO quark (u,d,s,c,b) and gluon densities in a real, unpolarized photon are presented. We perform a global 3-parameter fit, based on LO DGLAP evolution equations, to all available data for the structure function F2^gamma(x,Q^2). We adopt a new theoretical approach called ACOT(chi), originally introduced for the proton, to deal with the heavy-quark thresholds. This defines our basic model (CJKL model), which gives a very good description of the experimental data on F2^gamma(x,Q^2), for both Q^2 and x dependences. For comparison we perform a standard fit using the Fixed Flavour-Number Scheme (FFNS_CJKL model), updated with respect to the previous fits of this type. We show the superiority of the CJKL fit over the FFNS_CJKL one and other LO fits to the F2^gamma(x,Q^2) data. The CJKL model gives also the best description of the LEP data on the Q^2 dependence of the F2^gamma, averaged over various x-regions, and the F_2,c^gamma, which were not used directly in the fit. Finally, a simple analytic parametrization of the resulting parton densities obtained with the CJKL model is given.Comment: 43 pages, RevTeX4 using axodraw style, 3 tex and 12 postscript figures, version submitted to Phys. Rev. D, small text changes, one reference added, FORTRAN program available at http://www.fuw.edu.pl/~pjank/param.html and at http://www-zeuthen.desy.de/~alorca/id4.htm

Growth and properties of strained VOx thin films with controlled stoichiometry

We have succeeded in growing epitaxial films of rocksalt VOx on MgO(001) substrates. The oxygen content as a function of oxygen flux was determined using 18O2-RBS and the vanadium valence using XAS. The upper and lower stoichiometry limits found are similar to the ones known for bulk material (0.8<x<1.3). From the RHEED oscillation period a large number of vacancies for both vanadium and oxygen were deduced, i.e. ~16% for stoichiometric VO. These numbers are, surprisingly, very similar to those for bulk material and consequently quite strain-insensitive. XAS measurements reveal that the vacancies give rise to strong low symmetry ligand fields to be present. The electrical conductivity of the films is much lower than the conductivity of bulk samples which we attribute to a decrease in the direct overlap between t2g orbitals in the coherently strained layers. The temperature dependence of the conductivity is consistent with a variable range hopping mechanism.Comment: 12 pages, 16 figures included, revised versio