Time-continuous systems, multidimensional

The acquisition of a single-wavelength fluorescence spectrum of a complex multicomponent mixture is more tedious for many analytical applications that involve the measurement of some essential intermediate components or transient species. The determinations of such systems become more critical if the spectral information for those species is important to the understanding and elucidation of the properties of the final product. Similarly, this is true for chemical measurements of components whose fluorescence intensity decreases continuously with time. A rapid multidimensional data-processing technique becomes exceedingly important in the analysis of these species in a chemical reaction. 

Propagation of the fast subsystem - chemical Langevin equations The fast subset dynamics are assumed to follow a continuous Markov process description and therefore a multidimensional Fokker-Planck equation describes their time evolution. The multidimensional Fokker-Plank equation more accurately describes the evolution of the probability distribution of only the fast reactions. The solution is a distribution depicting the state occupancies. If the interest is in obtaining one of the possible trajectories of the solution, the proper course of action is to solve a system of chemical Langevin equations (CLEs). 

There are two general types of multidimensional chromatography separation schemes those in which the effluent from one column flows directly on to a second column at some time during the experiment, and those in which some type of trap exists between the two columns to decouple them (off-line mode). The purpose of a trap is often to allow collection of a fixed eluate volume to reconcentrate the analyte zone prior to the second separation step, or to allow a changeover from one solvent system to another. The use of offline multidimensional techniques (conventional sample cleanup) with incompatible mobile phases, is common in the literature, and replacing these procedures with automated on-line multidimensional separations will require continuous development efforts. 

---