Algorithm SPLIT

Clearly, in designs different from those in Figs. 16.13 and 16.14 when streams are split to satisfy the CP inequality, this might create a problem with the number of streams at the pinch such that Eqs. (16.3) and (16.4) are no longer satisfied. This would then require further stream splits to satisfy the stream number criterion. Figure 16.15 presents algorithms for the overall approach. ... 

The construction of an efficient algorithm rests on the ability to separate the Hamiltonian into parts which are themselves integrable and also efficiently computable. Suppose that the MD Hamiltonian H defined by (6) is split into two parts as... 

The procedure Split selects the internal displacement coordinates, q, and momenta, tt, (describing vibrations), the coordinates, r, and velocities, v, of the centers of molecular masses, angular velocities, a>, and directional unit vectors, e, of the molecules from the initial Cartesian coordinates, q, and from momenta, p. Thus, the staring values for algorithm loop are prepared. Step 1 Vibration... 

One of the most efficient algorithms known for evaluating the Ewald sum is the Particle-mesh Ewald (PME) method of Darden et al. [8, 9]. The use of Ewald s trick of splitting the Coulomb sum into real space and Fourier space parts yields two distinct computational problems. The relative amount of work performed in real space vs Fourier space can be adjusted within certain limits via a free parameter in the method, but one is still left with two distinct calculations. PME performs the real-space calculation in the conventional manner, evaluating the complementary error function within a cutoff... 

According to Allen and Tildesley, the standard recipe to evaluate Af/ in step one of the algorithm described in Sec. IIIB involves computing the energy of atom i with all the other atoms before and after the move (see p. 159 of Ref. 25, italics by the present author) as far as simple fluids are concerned. The evaluation of Af/ can be made more efficient in this case by realizing that for short-range interactions U can be split into three contributions... 

Solution Figure 18.17a shows the stream grid with the CP-tables for the above- and below-pinch designs. Following the algorithms in Figure 18.16, a hot stream must be split above the pinch to satisfy the CP inequality, as shown in Figure 18.17b. 

Those results seem to bear out our conjecture. The different calibration statistics all show the same effects the full-wavelength approach does seem to be sort of split the difference and accommodate some, but not all, of the non-linearities the algorithm... 

Zamora, J. M. and I. E. Grossmann. A Global MINLP Optimization Algorithm for the Synthesis of Heat Exchanger Networks with No Stream Splits. Comput Chem Eng 22 367-384(1998). 

The algorithm is easily programmed on a digital computer and is quite efficient in splitting large systems into their separate parts. 

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