Product solution, multidimensional systems

Product solutions for temperatures In multidimensional systems (a) semi-infinite plate (b) infinite rectangular bar (c) semi-infinite rectangular bar (cf) rectangular parallelepiped (e) semi-infinite cylinder (0 short cylinder. 

We start this chapter with the analysis of lumped systems in which the temperature of a body varies with time but remains uniform throughout at any time. Then we consider the variation of temperature with time as well as position for one-dimensional heat conduction problems such as those associated with a large plane wall, a long cylinder, a sphere, and a semi infinite medium using transient temperature charts and analytical solutions. Finally, we consider transient heat conduction in multidimensional systems by utilizing the product solution. 

In order to pursue heteronuclear multidimensional NMR experiments, a bacterial system for expression of apoLp-III has been developed which allows facile production of 150 - 200 mg/L l N-iabeled apoLp-III or 100 - 125 mg/L 15N/l3c-double labeled apoLp-III. Figure 2, panel A shows the IH- n HSQC spectrum of a 1.0 mM solution of lipid-free, uniformly N-labeled apoLp-III. Panel A also indicates that, although the chemical shift dispersion in the H-dimension is rather small (6.5 ppm to 9.5 ppm), it is generally upfield shifted, consistent with the fact that the protein secondary structure is predominantly a-helix (13). The chemical shifts in the N-dimension are well-dispersed which results in good separation of the overall crosspeaks. However, certain regions in the spectrum are still crowded as shown in Figure 2. 

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