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141.
142.
Summary. We derive formulas for the long time evolution of passive interfaces in three ``canonical' incompressible, inviscid, two-dimensional
flow models. The point vortex models, introduced in Part 1 [1] are (i) a ``restricted' three-vortex problem, (ii) a vortex
and a particle in a closed circular domain, and (iii) a particle in the flowfield of a mixing layer model undergoing a vortex
pairing instability. In each configuration, it was shown in Part 1 that the passive particle exhibits a geometric or Hannay-Berry
phase over long time periods induced by the slowly varying periodic background field. In this paper we show how the formula
for the evolution of a passive interface driven by the dynamics of the vortices inherits this geometric phase effect. The
interface wraps into a spiral formation around the ``parent' vortex, with a slowly varying component induced by the farfield
vorticity. The length formula for the long time growth of the slowly rotating spiral decomposes into a ``dynamic' part and
a ``geometric' part. The dynamic part is the length in the ``unperturbed' system—i.e., in the absence of the background
field—and the geometric part is the contribution of the geometric phase θ
g
for a passive particle in the flow. We derive the following simple formula for an interface along a smooth curve joining
two arbitrary particles labelled A and B . Define as the difference in interface lengths between the ``unperturbed' system and the ``perturbed' slowly varying system at
the end of the long time period T . In each case, , where ξ is the radial coordinate parametrizing the interface at t=0 .
Received September 4, 1997; second revision received January 16, 1998; accepted January 27, 1998 相似文献
143.
M. J. Marks J. Newton S. E. Bales 《Journal of polymer science. Part A, Polymer chemistry》2000,38(13):2352-2358
The use of m‐ethynylphenol (m‐EP) and p‐t‐butylphenol (PTBP) as coterminators for bisphenol A polycarbonates (BA PCs) provided long‐chain‐branched PCs, partially crosslinked PCs, or both after the thermal reaction of the terminal m‐EP groups, depending on the molar ratio of the chain terminators. Linear m‐EP/PTBP PCs were prepared by solution phosgenation of BA and the two coterminators. Differential scanning calorimetry showed the onset of the m‐EP‐end‐group reaction at about 250 °C by the appearance of a reaction exotherm. The enthalpy (ΔH) of this reaction was roughly proportional to the amount of m‐EP in the PC and to an extent could be used to monitor the progress of the reaction and estimate its kinetics. A complete m‐EP‐end‐group reaction was evident from gel permeation chromatography analysis upon heating under N2 to 380 °C for 10 min or 360 °C for 60 min. The amount, if any, of gel formed after the m‐EP‐end‐group reaction depended on XEP; those PCs with a XEP value less than or equal to 0.33 had little or no gel. The maximum XEP that precluded the formation of gels after branching was estimated to be about 0.45–0.48. The molecular weight of m‐EP/PTBP PCs increased after branching, as evidenced by gel permeation chromatography analysis. Assuming that the terminal m‐EP groups had a statistical distribution on the polymer chain ends and that they underwent only homopolymerization, the average reacted m‐EP‐group functionality according to estimated gel‐point composition was about 2.8–3.0. © 2000 John Wiley & Sons, Inc. J Polym Sci A: Polym Chem 38: 2352–2358, 2000 相似文献
144.
We explore a new relativistic anisotropic solution of the Einstein field equations for compact stars based on embedding class one condition.For this purpose,we use the embedding class one methodology by employing the Karmarkar condition.Employing this methodology,we obtain a particular differential equation that connects both the gravitational potentials e^λ and e^ν.We solve this particular differential equation choosing a simple form of generalized gravitational potential grr to describe a complete structure of the space-time within the stellar configuration.After determining this space-time geometry for the stellar models,we discuss thermodynamical observables including radial and tangential pressures,matter density,red-shift,velocity of sound,etc.,in the stellar models.We also perform a complete graphical analysis,which shows that our models satisfy all the physical and mathematical requirements of ultra-high dense collapsed structures.Further,we discuss the moment of inertia and M-R curve for rotating and non-rotating stars. 相似文献
145.
146.
E. Knecht J. H. Waltor Jr. P. Faber H. D. Newton G. Gallo und F. W. Hinrichsen 《Fresenius' Journal of Analytical Chemistry》1908,47(6-7):426-431
Ohne Zusammenfassung 相似文献
147.
G. L. Kelley J. A. Wiley R. T. Bohm W. C. Wright H. H. Willard Florence Fenwick J. M. Kolthoff O. Tomicek H. Tusker W. Chlopin L. Kaufmann H. D. Newton J. L. Hughes K. Swoboda C. Gallego A. T. Etheridge Hammer Koch A. Fölsner K. Ries W. Singleton A. Kropf G. Misson W. Silberminz E. Roshkowa A. H. Low Julius Meyer O. Kropf S. G. Clarke G. E. F. Lundell J. I. Hoffman H. A. Bright A. Pawletta L. Pisarjewski P. Düllberg und W. M. Hartmann 《Fresenius' Journal of Analytical Chemistry》1932,88(5-6):206-237
Ohne Zusammenfassung 相似文献
148.
J. Großfeld M. Tobia L. Zanchi L. Cini E. R. Bolton K. A. Williams R. Marcille A. Boutaric M. Roy D. P. Grettie R. C. Newton H. P. Kaufmann Ruth Okey Mary E. Turner T. Tusting Cocking G. Middleton J. K. Chowdhury und S. M. Das-Gupta 《Fresenius' Journal of Analytical Chemistry》1933,91(3-4):131-138
Ohne Zusammenfassung 相似文献
149.
Mohammed Ibn-elhaj Antoine Skoulios Daniel Guillon Joanna Newton Philip Hodge Harry J. Coles 《Liquid crystals》1995,19(3):373-378
The phase behaviour and the structural characterization of a new series of linear dimeric and cyclic tetrameric molecules which contain three distinct parts, a cyanobiphenyl aromatic core (A), a paraffin chain (P) and a central siloxane group (B) with the A-P-B-P-A sequence, are described. Incompatible with one another, these parts tend to locate themselves in three separate sub-layers superposed in a partially bilayered smectic A structure. Each sub-layer adapts its internal structure in order to be appropriate for superposition, as in the case of organosiloxane molecules with the A-P-B sequence reported previously. 相似文献
150.
Beale AM van der Eerden AM Kervinen K Newton MA Weckhuysen BM 《Chemical communications (Cambridge, England)》2005,(24):3015-3017
The potential of combined operando UV-Vis/Raman/XAFS has been explored by studying the active site and deactivation mechanism of silica- and alumina-supported molybdenum oxide catalysts under propane dehydrogenation conditions. 相似文献