In Situ Tabulation

The basic idea underpinning ISAT is the in situ tabulation of accessed regions of composition space for a particular model application. The tabulation is achieved by integrating the chemical source terms when a region is first accessed and then storing the reaction mapping and sensitivity information in a binary tree data 

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The in situ tabulation method proposed by Pope (1997) is also adaptive. The latter is used to control tabulation errors and leads to a modest increase in the amount of information that must be stored for each representative point. 

Cannon, S. M., B. S. Brewster, and L. D. Smoot (1999). PDF modeling of lean premixed combustion using in situ tabulated chemistry. Combustion and Flame 119, 233-252. 

Reduced models based on low-dimensional manifolds can usually be simulated faster than full systems of differential equations because the resulting dynamical system contains fewer variables and is usually not stiff (see Sect. 6.7). However, the search and retrieval algorithms required to access the look-up tables can consume significant amounts of computer time. As an example, the simulation of methane combustion based on the ILDM method was eight times faster than that using a detailed mechanism (Riedel et al. 1994). Special algorithms have been developed to speed up the search and retrieval process (Androulakis 2004). In situ tabulation methods have also been developed as discussed in Sect. 7.12 below. 

Pope, S. B., Computationally efficient implementation of combustion chemistry using in situ adaptive tabulation. Combust. Theory Model. 1 (1997)... 

LES/FDF-approach. An In situ Adaptive Tabulation (ISAT) technique (due to Pope) was used to greatly reduce (by a factor of 5) the CPU time needed to solve the set of stiff differential equations describing the fast LDPE kinetics. Fig. 17 shows some of the results of interest the occurrence of hot spots in the tubular LDPE reactor provided with some feed pipe through which the initiator (peroxide) is supplied. The 2004-simulations were carried out on 34 CPU s (3 GHz) with 34 GB shared memory, but still required 34 h per macroflow time scale they served as a demo of the method. The 2006-simulations then demonstrated the impact of installing mixing promoters and of varying the inlet temperature of the initiator added. 

In situ adaptive tabulation FHigher-order PDF models... 

In situ adaptive tabulation (IS AT) was proposed by Pope (1997), and it overcomes many of the difficulties associated with pre-computed lookup tables. First, the in situ nature of the method reduces the tabulation to only those points that occur during a particular simulation (i.e., the accessed region). Secondly, an adaptive algorithm is employed to control interpolation errors while minimizing the number of points that must be tabulated. 

Shah, J. J. and R. O. Fox (1999). CFD simulation of chemical reactors Application of in situ adaptive tabulation to methane thermochlorination chemistry. Industrial Engineering Chemistry Research 38, 4200 4-212. 

Tang, Q. and S. B. Pope (2002). Implementation of combustion chemistry by in situ adaptive tabulation of rate-controlled constrained equilibrium manifolds. In Proceedings of the Combustion Institute, vol. 29, pp. 1411-1417. Pittsburgh, PA The Combustion Institute. 

Unfortunately, seawater is slightly compressible, so in situ density increases with increasing pressure. The rate at which pressure increases with increasing depth below the sea surface is nearly equal to 1 dbar per m. At 45° latitude, the actual rate is l.Oldbar/m from 0 to 2500m. Below 2500m, it increases to 1.02dbar/m. This rate increase is due to an increasing resistance to further compression. Because Earth is not a perfect sphere, the rate at which pressure increases with depth also varies with latitude. Thus, the depth at which 4500 dbar of pressure is attained is 4428 m at the equator and 23 m shallower at the poles (4405 m). Tabulated values of pressure as a... 

Dupre61 in 1901 reported experiments which indicated that the picrates of calcium, lead, and zinc, formed in situ from melted picric acid are capable of initiating the explosion of that material. Kast62 found that the dehydrated picrates are more sensitive than those which contain water of crystallization. The data tabulated... 

By far the most common application of the addition reaction is the synthesis of ketones, by hydrolysis of the intermediate imine in situ. Some examples are listed in Table 5.3, and a procedure is given for an intramolecular version. Numerous examples have been tabulated [A]. 

As nanotubes have much higher modulus compared to pol5miers, their addition normally leads to a hnear increase in composite modulus. In [53,55] the modulus increase found in different studies by adding CNTs is tabulated for functionalized and nonfunctionalized nanotubes in different matrix materials and processing methods of the composites. The big varieties shown here illustrate the manifold influencing factors, like type of nanotubes, their diameter, quality and functionality, or choice of the solvent in solution based or in situ synthesized composites. In that comparison, the effects found for melt mixed compnas-... 

Basically, f is detemiined by the number and the distribution of the electrons belonging to a single atom [2]. Values for f are tabulated e.g. in Ref. [3], The diffracted intensity then is given by 1 IFhidl thus not only the positions of the diffraction peaks are representative for the crystal structure, but also their intensities. This is in principle the basis for extremely detailed in-situ investigations of electrode materials in electrochemical environments. 

In almost all the measurements the standard reference material 4-methoxybenzyli-dene-4 -n-butyl-aniline (MBBA) or a mixture, Merck Phase V, have been used, sometimes doped with an ionic substance. MBBA is the only room-temperature nematic with dielectric anisotropy < 0 where all the material parameters have been measured. For tabulated values see e.g. Ref. [12]. Unfortunately, it is a Schiffbase and rather imstable when exposed to moisture. Therefore, it is difficult to control the long-time conductivity in situ. Thus the recent successful introduction of the very stable material 4-ethyl-2-fluoro-4 -[2-(rrani-4-n-pentylcyclohexyl)-ethyl]-biphenyl (152) doped with iodine is very promising [50, 51]. This material exhibits at low external frequencies strongly oblique travelling rolls which bifurcate supercritically, leading to a particularly interesting scenario. ... 

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