Steady-state methods, general description

When the dose of a drug is administered as an intravenous bolus, the volume of distribution at steady-state (Vd(ss)) can be calculated. This parameter represents the volume in which a drug would appear to be distributed during steady-state if the drug existed throughout that volume at the same concentration as in the measured fluid (plasma or blood). The volume of distribution at steady-state is generally calculated by a non-compartmental method, which is based on the use of areas (Benet Galeazzi, 1979) and does not require the application of a compartmental pharmacokinetic model or mathematical description of the disposition curve ... 

In general, a thorough spectroscopic study, as routinely carried out in the group of Prof. Dr. Dirk M. Guldi by means of steady-state emission/absorption measurements and time-resolved techniques in numerous solvents, sheds light onto the photophysical processes following photoexcitation of these systems. Equally, a detailed description of the employed spectroscopic methods will be given in the next sections. 

The identification and physicochemical characterization of 2three-electron bonded species, in general, but particularly of those based on the participation of sulfur has enormously benefitted from the availability of sensitive time-resolved techniques [71] such as the radiation chemical method of pulse radiolysis or photochemical laser flash equipment. Valuable information has also been gathered from ESR measurements under steady-state flow conditions [68] as well as in low temperature solid matrices [70, 72, 73]. In addition, excellent high level calculations have provided a good theoretical description of these species. [74-81]. 

When a nonlinear system ewolwes under far-from-equilibrium conditions in the vicinity of a bifurcation point, a purely deterministic description often proved to be incomplete. The fluctuations of the dynamical variables can play an essential role and obstruct the observation of a transition expected by a deterministic analysis. In the framework of the deterministic approach, the stability of the different states according to the values of the control parameters is studied through a mathematical analysis of the velocity field. In particular, the theory of normal forms leads to the determination of the various kinds of attractors [l,2]. As far as we are concerned with the stochastic approach, the rrLa te.n. equation, has been widely used to analyze bifurcations of homogeneous or spatially ordered steady states or of limit cycles [3,4]. Our aim in the present contribution is to insist on the generality of the method to analyze various kinds of bifurcations in nonlinear nonequilibrium systems. The general procedure proposed to obtain a local description of the probability, which allows us to determine the system s attractors, turns out to display marked analogies with the theory of normal forms. 

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