Linearization, phase-space transition state

Figure 7. Linearized transition state. Left panel The reaction coordinate part of phase space. Right panel = 0 surface of section. The shaded areas are forbidden by energy conservation.

Anal5ftical solutions to the chemical master equation are only available for extremely simple systems. Furthermore, numerical solutions to the master equation are computationally intractable for aU but the simplest systems, because as the number of unique chemical species in the system grows linearly, the number of possible states in the phase space grows combinatorially. Enumerating the transitions between states then becomes difficult. 

Another different type of phase, labelled semi-compact phase was found by Knezevic and Vannimenus in their analysis of the collapse transition on the HB 3,3) fractal [37]. In this case, the connectivity of the graph is such that a linear polymer Ccinnot fill the available space with a finite density. For Icirge v ilue of the attraction strength u the polymer shrinks into a semicompact state. In this phiise, the average monomer density tends to zero for large polymers. 

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