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Stable Nucleation for the Ginzburg-Landau System with an Applied Magnetic Field (1998)

Bauman, P. ; Phillips, D. ; Tang, Q.

Springer

Archive for rational mechanics and analysis 142 (1998), S. 1-43

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ISSN: 1432-0673

Source: Springer Online Journal Archives 1860-2000

Topics: Mathematics , Physics

Notes: Abstract. We consider the Ginzburg‐Landau system with an applied magnetic field and analyze the behavior of solutions when the domain is a cylinder (of radius $\overline{r}$ ) and the applied field is parallel to the axis. It is shown that there is an upper critical value $\overline{h}$ such that if the modulus of the applied field is greater than $\overline{h}$ , the normal (nonsuperconducting) state (in which the order parameter is identically zero) is stable and if the modulus of the applied field is slightly below $\oh$ , the normal state is unstable. In addition, it is shown that there is a positive lower critical value $\underline{h}\leq\overline{h}$ such that the normal state is unstable if the modulus of the applied field is less than $\underline{h}$ and stable if the modulus is slightly above $\underline{h}$ . In the case of type‐II materials for whic h the Ginzburg‐Landau constant κ is large, it is shown that there is a discrete set of radii ℬ(κ) such that if $\overline{r}\notin\cal{B}(\kappa)$ and $\kappa\overline{r}$ is sufficiently large, then for each applied field of modulus slightly less than $\overline{h}$ (or slightly more than $\underline{h}$ ) there is precisely one small superconducting solution (up to a gauge transformation) which is stable. Moreover for this solution, the complex‐valued order parameter ψ is zero only on the axis of the cylinder, and its winding number is proportional to the product of κ2 and the cross‐sectional area of the cylinder. In addition, the solution exhibits “surface superconductivity” as predicted by the physicists de Gennes and St. James.

Type of Medium: Electronic Resource

URL: http://dx.doi.org/10.1007/s002050050082

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Polybutadiene-coated zirconia packing materials in solvating gas chromatography using carbon dioxide as mobile phase (1999)

Wu, N. ; Tang, Q. ; Shen, Y. ; [et al.]

Springer

Chromatographia 49 (1999), S. 431-435

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ISSN: 1612-1112

Keywords: Gas chromatography ; Supercritical fluid chromatography ; Solvating gas chromatography ; Polybutadiene coated zirconia ; CO2 mobile phase

Source: Springer Online Journal Archives 1860-2000

Topics: Chemistry and Pharmacology

Notes: Summary In this paper, practical considerations of column efficiency, separation speed, thermal stability, and column polarity of capillary columns packed with polybutadiene-coated zirconia were investigated under solvating gas chromatography (SGC) conditions using carbon dioxide as mobile phase. When compared with results obtained from conventional porous octadecyl obtained from conventional porous octadecyl bonded silica (ODS) particles, PBD-zirconia particles produced greater change in mobile phase linear velocity with pressure than conventional ODS particles under the same conditions. The maximum plate number per second (Nt) obtained with a 30 cm PBD-zirconia column was approximately 1.5 times higher than that obtained with an ODS column at 100 °C. Therefore, the PBD-zirconia phase is more suitable for fast separations than conventional ODS particles in SGC. Maximum plate numbers per meter of 76,900 and 63,300 were obtained using a 57 cm×250 μm i.d. fused silica capillary column packed with 3 μm PBD-zirconia at 50 °C and 100 °C, respectively. The PBD-zirconia phase was stable at temperatures up to 320 °C under SGC conditions using carbon dioxide as mobile phase. Polarizable aromatic compounds and low molecular weight ketones and aldehydes were eluted with symmetrical peaks from a 10 cm column packed with 3 μm PBD-zirconia. Zirconia phases with greater inertness are required for the analysis of more polar compounds by SGC.

Type of Medium: Electronic Resource

URL: http://dx.doi.org/10.1007/BF02467619

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