Taylor phase

Taylor phases are based on binary AlsMn, the structure of which was firstly solved by Taylor [22]. The phase has ternary extensions into several systems (e.g., Pd, Ni, Fe) [61], all of which are referred to as Taylor- or T-phases. Binary Al3Mn is a high-temperature phase, transforming to a triclinic variant below about 900 °C [62]. Addition of the third element Pd, Fe, or Ni stabilizes the T-phase, and hence the existence ranges of the ternary extensions extend to much lower temperatures. 

According to the Porod law [28], the intensity in the tail of a scattering curve from an isotropic two-phase structure havmg sharp phase boundaries can be given by eqnation (B 1.9.81). In fact, this equation can also be derived from the deneral xpression of scattering (61.9.56). The derivation is as follows. If we assume qr= u and use the Taylor expansion at large q, we can rewrite (61.9.56) as... 

Kane D J, Taylor A J, Trebino R and DeLong K W 1994 Single-shot measurement of the intensity and phase of a femtosecond UV laser pulse with frequency-resolved optical gating Opt. Lett. 19 1061-3... 

Table 7.1 presents us with something of a dilemma. We would obviously desire to explore i much of the phase space as possible but this may be compromised by the need for a sma time step. One possible approach is to use a multiple time step method. The underlyir rationale is that certain interactions evolve more rapidly with rime than other interaction The twin-range method (Section 6.7.1) is a crude type of multiple time step approach, i that interactions involving atoms between the lower and upper cutoff distance remai constant and change only when the neighbour list is updated. However, this approac can lead to an accumulation of numerical errors in calculated properties. A more soph sticated approach is to approximate the forces due to these atoms using a Taylor seri< expansion [Streett et al. 1978] ... 

Typical methods are those of F. C. Zevnik and R. L. Buchanan [Chem. Eng. Progi , 59, 70-77 (Feb. 1963)] and J. H. Taylor Eng. 6-Proc. Econ., 2, 259-267, 1977). The former is mainly a graphical method of estimating the cost per functional unit (Cp) based on the capacity, the maximum pressure, the maximum temperature, and the materials of construction. The Taylor method requires the determination of the costliness index, which is dependent on the complexity of the process. A simpler method was suggested by S. R. Timms (M.Phil. thesis, Aston University, England, 1980) to give the battery hmits cost for gas phase processes only in U.S. dollars with a Marshall and Swift index of 1000. The simple equation is... 

The coupling of supercritical fluid extraction (SEE) with gas chromatography (SEE-GC) provides an excellent example of the application of multidimensional chromatography principles to a sample preparation method. In SEE, the analytical matrix is packed into an extraction vessel and a supercritical fluid, usually carbon dioxide, is passed through it. The analyte matrix may be viewed as the stationary phase, while the supercritical fluid can be viewed as the mobile phase. In order to obtain an effective extraction, the solubility of the analyte in the supercritical fluid mobile phase must be considered, along with its affinity to the matrix stationary phase. The effluent from the extraction is then collected and transferred to a gas chromatograph. In his comprehensive text, Taylor provides an excellent description of the principles and applications of SEE (44), while Pawliszyn presents a description of the supercritical fluid as the mobile phase in his development of a kinetic model for the extraction process (45). 

Concerning a liquid droplet deformation and drop breakup in a two-phase model flow, in particular the Newtonian drop development in Newtonian median, results of most investigations [16,21,22] may be generalized in a plot of the Weber number W,. against the vi.scos-ity ratio 8 (Fig. 9). For a simple shear flow (rotational shear flow), a U-shaped curve with a minimum corresponding to 6 = 1 is found, and for an uniaxial exten-tional flow (irrotational shear flow), a slightly decreased curve below the U-shaped curve appears. In the following text, the U-shaped curve will be called the Taylor-limit [16]. 

According to the criteria, the dispersed phase embedded in the matrix of sample 1 must have been deformed to a maximum aspect ratio and just began or have begun to break up. By observing the relative position of the experimental data to the critical curve, the deformational behavior of the other samples can be easily evaluated. Concerning the fibrillation behavior of the PC-TLCP composite studied, the Taylor-Cox criteria seems to be valid. 

Glaser and Litt (G4) have proposed, in an extension of the above study, a model for gas-liquid flow through a b d of porous particles. The bed is assumed to consist of two basic structures which influence the fluid flow patterns (1) Void channels external to the packing, with which are associated dead-ended pockets that can hold stagnant pools of liquid and (2) pore channels and pockets, i.e., continuous and dead-ended pockets in the interior of the particles. On this basis, a theoretical model of liquid-phase dispersion in mixed-phase flow is developed. The model uses three bed parameters for the description of axial dispersion (1) Dispersion due to the mixing of streams from various channels of different residence times (2) dispersion from axial diffusion in the void channels and (3) dispersion from diffusion into the pores. The model is not applicable to turbulent flow nor to such low flow rates that molecular diffusion is comparable to Taylor diffusion. The latter region is unlikely to be of practical interest. The model predicts that the reciprocal Peclet number should be directly proportional to nominal liquid velocity, a prediction that has been confirmed by a few determinations of residence-time distribution for a wax desulfurization pilot reactor of 1-in. diameter packed with 10-14 mesh particles. 

General reviews of the structure and properties of liquid crystals can be found in the following G. H. Brown, J. W. Doane, and V. D. Neff. "A Review of the Structure and Physical Properties of Liquid Crystals." CRC Press, Cleveland, Ohio, 1971 P. J. Collings and M. Hind, Introduction to Liquid Crystals. Nature s Delicate Phase of Matter," Taylor and Francis, Inc., Bristol. Pennsylvania, 1997 P. J. Collins, "Liquid Crystals. Nature s Delicate Phase of Matter," Princeton University Press. Princeton. New Jersey, 1990. A thermodynamic description of the phase properties of liquid crystals can be found in S. Kumar, editor, "Liquid Crystals in the Nineties and Beyond, World Scientific, Riven Edge, New Jersey, 1995. 

Kawahara A, Chung PM, Kawaji M (2002) Investigation of two-phase flow pattern, void fraction and pressure drop in a micro-channel. Int J Multiphase Plow 28 1411-1435 Kawaji M (1999) Fluid mechanics aspects of two-phase flow Flow in other geometries. In Kand-likar SG, Shoji M, Dhir VK (eds) Handbook of phase change boiling and condensation. Taylor and Francis, Washington, DC, pp 205-259... 

Hewlett, G. F. and Hall-Taylor, N. S., "Annular Two-Phase Flow", 23-27, Pergammon Press, Oxford GB, (1970). 

Kozlowski A, Charles SA, Harris JM (2001) Development of pegylated interferons for the treatment of chronic hepatitis C. BioDrugs 15 419 29 Krown SE, AeppU D, Balfour HH Jr (1999) Phase II, randomized, open-label, community-based trial to compare the safety and activity of combination therapy with recombinant interferon-alpha2b and zidovudine versus zidovudine alone in patients with asymptomatic to mildly symptomatic HIV infection. J Acquir Immune Defic Syndr Hum Retrovirol 20 245-254 LaFleur DW, NardeUi B, Tsareva T, Mather D, Feng P, Semenuk M, Taylor K, Buergin M, Chinchilla D, Roshke V, Chen G, Ruben SM, Pitha PM, Coleman TA, Moore PA (2001) Interferon-kappa, a novel type I interferon expressed in human keratinocytes. J Biol Chem 276 39765-39771... 

In the design of optimal catalytic gas-Hquid reactors, hydrodynamics deserves special attention. Different flow regimes have been observed in co- and countercurrent operation. Segmented flow (often referred to as Taylor flow) with the gas bubbles having a diameter close to the tube diameter appeared to be the most advantageous as far as mass transfer and residence time distribution (RTD) is concerned. Many reviews on three-phase monolithic processes have been pubhshed [37-40]. 

Voecks, G.E. (1998) Unconventional utilization of monolithic catalysts for gas-phase reactions, in Structured Catalysts and Reactors, 1st edn, Chapter 7 (eds A. Cybulski and J.A. Moulijn), Marcel Dekker, New York, p. 179 (b) Groppi, G., Beretta, A., and Tronconi, E. (2006) Structured catalysts for gas-phase syntheses of chemicals, in Structured Catalysts and Reactors, 2nd edn. Chapter 8 (eds A. Cybulski and J.A., Moulijn), CRC Taylor Francis, Boca Raton, p. 243. 

Without loss of generality y = y can be assumed. If the dipole moment can be assumed to be a linear function of coordinate within the spread of the frozen Gaussian wave packet, the matrix element (gy,q,p, Pjt(r) Y,q, p ) can be evaluated analytically. Since the integrand in Eq. (201) has distinct maxima usually, we can introduce the linearization approximation around these maxima. Namely, the Taylor expansion with respect to bqp = Qq — Qo and 8po = Po — Po is made, where qj, and pj, represent the maximum positions. The classical action >5qj, p , ( is expanded up to the second order, the final phase-space point (q, p,) to the first order, and the Herman-Kluk preexponential factor Cy pj to the zeroth order. This approximation is the same as the ceUularization procedure used in Ref. [18]. Under the above assumptions, various integrations in U/i(y, q, p ) can be carried out analytically and we have... 

Taylor, S.J. and McDowell, I.J., Determination of the curcuminoid pigments in turmeric (Curcuma domestica Val) by reversed-phase high performance liquid chromatography, Chmmatographia, 34, 73, 1992. 

The following free radical chain mechanism, first suggested by Taylor and Bates to explain the polymerization of ethylene induced by free radicals in the gas phase and independently proposed by Staud-inger for liquid phase polymerizations, offers an explanation for the above general characteristics of vinyl polymerizations. 

Rossmeisl J, Norskov JK, Taylor CD, Janik MJ, Neurock M. 2006. Calculated phase diagrams for the electrochemical oxidation and reduction of water over Pt(l 11). J Phys Chem B 110 21833-21839. 

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