Decoupled direct method

Dunker, A.M., "The Decoupled Direct Method for Calculating Sensitivity Coefficients in Chemical Kinetics", J. Chem. Phys.. 81,2385-2393 (1984). 

A.M Dunker, The decoupled direct method for calculating sensitivity coefficients in chemical kinetics, J. Chem. Phys. 81 (1984) 2385-2393. 

The most efficient algorithm for the solution of the sensitivity differential equations is called the decoupled direct method (ddm), which was first applied in chemical kinetics by Dunker [67, 68]. He drew attention to the fact that equations (4.1) and (4.6) have the same Jacobian, so that a stiff ode solver will use the same step size and order of approximation in the solution of both odes. The ddm method first takes a step for the solution of equation (4.1) and then performs steps for the solution of equation (4.6) for / = 1,. . . , m. The procedure is repeated in the subsequent steps. Since the Jacobian of the equations is the same, it has to be triangularized only once for each time interval. This method is applied in the program SENKIN [69]. 

For a long time the main topic of research in the area of sensitivity analysis was to find an accurate and effective method for the calculation of local concentration sensitivities. This question now seems to be settled, and the decoupled direct method (ddm) is generally considered the best numerical method. All the main combustion simulation packages such as CHEMKIN, LSENS, RUNIDL and FACSIMILE calculate sensitivities as well as the simulation results and, therefore, many publications contain sensitivity calculations. However, usually very little information is actually deduced from the sensitivity results. It is surprising that the application of principal component analysis is not widespread, since it is a simple postprocessing method which can be used to extract a lot of information from the sensitivities about the structure of the kinetic mechanism. Also, methods for parameter estimation should always be preceded by the principal component analysis of the concentration sensitivity matrix. 

The EDA system corresponding to the model is solved by a modified version of the LSODI routine, which is based on Gear s method. The version implemented performs the solution of the EDA system concomitantly to the evaluation of the parameters sensitivities based on the decoupled direct method (4). As a matter of fact, the simulation of the system is... 

Another example of the use of AD is in the calculation of the Jacobian used by the decoupled direct method. AD can provide a more automatic approach compared to using an analytic or symbolic expression for the definition of the Jacobian based on the RHS of the kinetic system of differential equations, but one which is more accurate than defining the Jacobian numerically using finite-difference methods. This approach is implemented in the freely available KPP package for atmospheric chemical simulations (Damian et al. 2002 Sandu et al. 2003 Daescu et al. 2003 KPP). 

The pulse calibration on the decoupler channel cannot be performed using the direct method since the pulse which is to be calibrated is transmitted on a different rf channel and resonance frequency to the observed nucleus. To calibrate the rf pulse on the decoupler channel it is necessary to determine the pulse length from the effect the pulse has on the nucleus observed on the transmitter/receiver channel. This indirect calibration is achieved by using a coupled IS spin system and transferring the detectable antiphase... 

The unit CPU requirement represents a single simulation of the model. Here m is the number of investigated parameters and r is the number of repetitions. Sample size Al depends on the sampling approach and convergence properties of the model output. For local analysis, the relative CPU time will depend on whether decoupled direct or brute force methods are used... 

Many components of food are in the solid state and possess very short T2. The linewidths from solid components are generally too wide to be observed directly by solution state NMR methods. However, these components can be detected by the special techniques of solid state NMR. These techniques involve the use of cross polarization excitation (from 3H to 13C), high power 3H decoupling (to inhibit... 

In contrast to applications in structural biology where X/Y correlations are nowadays normally executed as H detected, three-dimensional experiments because of sensitivity reasons,14 many studies on inorganic or organometallic compounds are still performed as two-dimensional experiments with direct detection of one heteronucleus and under -decoupling. As compared to these two categories, one-dimensional polarisation transfer methods such as (semi) selective X/Y-INEPT or INDOR-type techniques, which had in the past been shown to be particularly useful for the characterisation of substrates with only one or two heteronuclei,11 have recently received less attention.15 NOE-based correlations, which are frequently employed for the structure elucidation of bio-molecules, remain rare, and apart from an earlier report of a 13C/6Li HOESY experiment,16 have not been further investigated. 

Similar spectra can be obtained more rapidly and with less sample if the data are acquired through the proton signals, which are much more intense. Basically, the H NMR data are acquired and the H- C coupling constant used as the delay in a pulse sequence, which enables us to obtain the carbon spectrum. This method of obtaining the data is called inverse-mode , since the carbon atoms are detected through their attached hydrogen atoms rather than by direct detection, with obvious benefits in the sensitivity and the time taken to obtain a spectrum. HMQC and HMBC are both examples of inverse-mode spectra and this method is so much quicker than CH COSY that an entire HMQC spectrum can be obtained in much less time than it takes to obtain the proton-decoupled C... 

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