Redfield model

The importance (or not) of the distinction between N and P as a model currency is closely related to the concept of the Redfield ratio (Redfield et al. 1963). Because many models impHcidy or expHcitly enforce fixed elemental ratios, the distinction between N and P hmitation is often of fittle importance in models. In most cases a fixed ratio (e.g., Redfield ) model will behave almost identically in terms of primary production, plankton abundance, and carbon fluxes, whether N or P is specified to be the primary fimiting nutrient (the exception is when initial or boundary conditions are drawn from observations in which deviations from the Redfield N P ratio are present). 

Christian, J. R. (2005). Biogeochetnical cycling in the oHgotrophic ocean Redfield and non-Redfield models. Limnol. Oceanogr. 50, 646-657. 

Essentially all organic matter in the ocean is ultimately derived from inorganic starting materials (nutrients) converted by photosynthetic algae into biomass. A generalized model for the production of plankton biomass from nutrients in seawater was presented by Redfield, Ketchum and Richards (1963). The schematic "RKR" equation is given below ... 

Redfield, J. A., and J. H. Murphy, 1971, Sectionalized Compressible and Momentum Integral Models for Channel Hydrodynamics, ASME Paper 71-HT-14. (6)... 

The assumption of a single electron spin and a single T2 holds usually for S = 1/2 and for S > 1 in certain limits. Let us assume that the instantaneous distortions of the solvation sphere of the ion result in a transient ZFS and that the time-dependence of the transient ZFS can be described by the pseudorotation model, with the magnitude of the transient ZFS equal to At and the correlation time t . The simple picture of electron relaxation for S = 1 is valid if the Redfield condition (Att <5c 1) applies. Under the extreme narrowing conditions ((Os v 1), the longitudinal and transverse electron spin relaxation rates are equal to each other and to the low-field limit rate Tgo, occurring in Eqs. (14) and (15). The low field-limit rate is then given by (27,86) ... 

As in Eq. (64), the electron spin spectral densities could be evaluated by expanding the electron spin tensor operators in a Liouville space basis set of the static Hamiltonian. The outer-sphere electron spin spectral densities are more complicated to evaluate than their inner-sphere counterparts, since they involve integration over the variable u, in analogy with Eqs. (68) and (69). The main simplifying assumption employed for the electron spin system is that the electron spin relaxation processes can be described by the Redfield theory in the same manner as for the inner-sphere counterpart (95). A comparison between the predictions of the analytical approach presented above, and other models of the outer-sphere relaxation, the Hwang and Freed model (HF) (138), its modification including electron spin... 

Models for the outer-sphere PRE, allowing for faster rotational motion, have been developed, in analogy with the inner sphere approaches discussed in the Section V.C. The outer-sphere counterpart of the work by Kruk et al. 123) was discussed in the same paper. In the limit of very low magnetic field, the expressions for the outer-sphere PRE for slowly rotating systems 96,144) were found to remain valid for an arbitrary rotational correlation time Tr. New, closed-form expressions were developed for outer-sphere relaxation in the high-field limit. The Redfield description of the electron spin relaxation in terms of spectral densities incorporated into that approach, was valid as long as the conditions A t j 1 and 1 were fulfilled. The validity... 

If the system under consideration possesses non-adiabatic electronic couplings within the excited-state vibronic manifold, the latter approach no longer is applicable. Recently, we have developed a simple model which allows for the explicit calculation of RF s for electronically nonadiabatic systems coupled to a heat bath [2]. The model is based on a phenomenological dissipation ansatz which describes the major bath-induced relaxation processes excited-state population decay, optical dephasing, and vibrational relaxation. The model has been applied for the calculation of the time and frequency gated spontaneous emission spectra for model nonadiabatic electron-transfer systems. The predictions of the model have been tested against more accurate calculations performed within the Redfield formalism [2]. It is natural, therefore, to extend this... 

Redfield 1970). This model is able to account for the exponential slope with internal fields which are reasonably consistent with the disorder of the amorphous semiconductors. 

Pahlow, M. (2005). Linking chlorophyll-nutrient dynamics to the Redfield N C ratio with a model of optimal phytoplankton growth. Mar. Ecol. — Progr. Ser. 287, 33—43. 

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