P Two-dimensional

FIGURE 13.7 Instrumental setup of (a) a GCxGC system (Anon., GC x GC Comprehensive Two-Dimensional Gas Chromotography Form No. 209-184 R2.58-REV-1 LECO Corporation, St Joseph, MI 49085 P3, 2008. With permission.) (b) a LC x LC system based on a second-dimension column with two storage loops (T. Hyotylainen, LC x LC switching valves configuration Chromedia Amsterdam P Two Dimensional LC (LC x LC), 2008. With permission.). 

Steinberg RA, Coffino P. Two-dimensional gel analysis of cyclic AMP effects in cultured S49 mouse lymphoma cells protein modifications, inductions and repressions. Cell 1979 18 719-733. 

Richetti, P Prost, J. Barois, P. Two-dimensional aggregation and crystallization of colloidal suspension of latex spheres. J. Phys. Lett. (Paris), 1984, 45(23), L1137-L1143. 

Picard, R, Paquet, M.-J., Dufourc, E.J., and Auger, M. 1998. Measurement of the lateral diffusion of dipal-mitoylphosphatidylcholine adsorbed on silica beads in the absence and presence of melittin A P two-dimensional exchange solid-state NMR study. Biophys. J. 74 857-868. 

Bart, H.J. Germerdonk, R., and Ning, P., Two-dimensional non-isothermal model for toluene adsorption in a fixed-bed adsorber, Chem. Eng. Process.. 35( 1). 57-64 (1996). 

Kilz P. Two-dimensional chromatography as an essential means for understanding macromolecular structure. Chromatographia 2004 59 3-14. 

Lilley, K. S., Razzaq, A. and Dupree, P., Two-dimensional gel electrophoresis recent advances in sample preparation, detection and quantitation. Cum Opin. Chem. Biol, 6, 46-50 (2002). 

Molloy, M.P., Two-dimensional electrophoresis of membrane proteins using immobilized pH gradients. Anal. Biochem., 280, 1-10 (2000). 

The nature of the short-range structural disorder and its dependence on the fictive temperature are investigated in a phosphate glass of compound 60ZnO 4OP2O5 using P two-dimensional phase adjusted... 

Rajasekaran, P. R. Wolff, J. Zhou, C. Kinsel, M. Trautmann, C. Aouadi, S. Kohli, P. Two dimensional anisotropic etching in tracked glass. J Mater Chem 2009,19, 8142-8149. 

In order for two-dimensional experiments to be conducted on a routine basis, the NMR instrumentation used must fulfill certain criteria. Whereas the requirements discussed next are essential for producing quality P two-dimensional spectra, they will also benefit the variety of one-dimensional techniques available to the spectroscopist. 

Gayda, J., Gabb, T.P., Two Dimensional Viscoelastic Stress Analysis of a Prototypical JIMO Turbine Wheel , NASA/TM-2005-213650, Washington, D.C., June, 2005... 

The data could be expressed equally well in terms of F versus P, or in the form of the conventional adsorption isotherm plot, as shown in Fig. Ill-18. The appearance of these isotherms is discussed in Section X-6A. The Gibbs equation thus provides a connection between adsorption isotherms and two-dimensional equations of state. For example, Eq. III-57 corresponds to the adsorption isotherm... 

Brasseur G and De Baets P 1986 Ions in the mesosphere and lower thermosphere a two-dimensional model J. Geophys. Res. 91 4025-46... 

Aue W P, Kharan J and Ernst R R 1976 Homonuclear broadband decoupling and two-dimensional J-resolved NMR spectroscopy J. Chem. Phys. 64 4226-7... 

Jeener J, Meier B H, Bachmann P and Ernst R R 1979 Investigation of exchange processes by two-dimensional NMR spectroscopy J. Chem. Rhys. 71 4546-53... 

Merks R P J and de Beer R 1979 Two-dimensional Fourier transform of electron spin-echo envelope modulation. An alternative for ENDOR J. Phys. Chem. 83 3319-22... 

Crommie M F, Lutz C P and Eigler D M 1993 Imaging standing waves in a two-dimensional electron gas Nature 363 524... 

Abel E W, Coston T P J, Orrell K G, Sik V and Stephenson D 1986 Two-dimensional NMR exohange speotrosoopy. Quantitative treatment of multisite exohanging systems J. Magn. Reson. 70 34-53... 

Olsen R A, Philipsen P H T, Baerends E J, Kroes G J and Louvik O M 1997 Direct subsurface adsorption of hydrogen on Pd(111) quantum mechanical calculations on a new two-dimensional potential energy surfaced. Chem. Phys. 106 9286... 

Andres R P ef a/1996 Self-assembly of a two-dimensional superlattice of molecularly linked metal clusters Science 273 1690... 

Fig. 9. Two-dimensional sketch of the 3N-dimensional configuration space of a protein. Shown are two Cartesian coordinates, xi and X2, as well as two conformational coordinates (ci and C2), which have been derived by principle component analysis of an ensemble ( cloud of dots) generated by a conventional MD simulation, which approximates the configurational space density p in this region of configurational space. The width of the two Gaussians describe the size of the fluctuations along the configurational coordinates and are given by the eigenvalues Ai.

U-V-P schemes belong to the general category of mixed finite element techniques (Zienkiewicz and Taylor, 1994). In these techniques both velocity and pressure in the governing equations of incompressible flow are regarded as primitive variables and are discretized as unknowns. The method is named after its most commonly used two-dimensional Cartesian version in which U, V and P represent velocity components and pressure, respectively. To describe this scheme we consider the governing equations of incompressible non-Newtonian flow (Equations (1.1) and (1.4), Chapter 1) expressed as... 

Bell, B.C. and Surana, K. S, 1994. p-version least squares finite element formulations for two-dimensional, incompressible, non-Newtonian isothermal and non-isothcmial fluid flow. hit. J. Numer. Methods Fluids 18, 127-162. 

Using a irocedure similar to the formulation of two-dimensional forms the working equations of the U-V - P scheme in axisymmetric coordinate systems are derived on the basis of Equations (4.10) and (4.11) as... 

Here, the momentum veetor p eontains the momenta along all eoordinates of the system, and the eoordinate veetor q likewise eontains the eoordinates along all sueh degrees of freedom. For example, in the two-dimensional partiele in a box problem eonsidered above, q = (x, y) has two eomponents as does p = (Px, Py), and the aetion integral is ... 

Figure 10.6 Two-dimensional representation of i and i (broken lines) and their resultant ifotai (solid line) for scattering by a molecule situated at the origin and illuminated by unpolarized light along the x axis. The intensity in any direction is proportional to the length of the radius vector at that angle. (Reprinted from Ref, 2, p. 168.)...

---