Non-linear kinetics

The kinetics of alkylation by triphenylmethyl compounds have been studied. Hart and Cassis353 found that the alkylation of phenol and o-cresol by triphenylmethyl chloride in o-dichlorobenzene gave non-linear kinetic plots which were, however, rendered linear by presaturation of the reaction mixture with hydrogen chloride, precise third-order kinetics, equation (182)... 

WASP/TOXIWASP/WASTOX. The Water Quality Analysis Simulation Program (WASP, 3)is a generalized finite-difference code designed to accept user-specified kinetic models as subroutines. It can be applied to one, two, and three-dimensional descriptions of water bodies, and process models can be structured to include linear and non-linear kinetics. Two versions of WASP designed specifically for synthetic organic chemicals exist at this time. TOXIWASP (54) was developed at the Athens Environmental Research Laboratory of U.S. E.P.A. WASTOX (55) was developed at HydroQual, with participation from the group responsible for WASP. Both codes include process models for hydrolysis, biolysis, oxidations, volatilization, and photolysis. Both treat sorption/desorption as local equilibria. These codes allow the user to specify either constant or time-variable transport and reaction processes. 

A brief overview on why most of the autoxidation reactions develop complicated kinetic patterns is given in Section II. A preliminary survey of the literature revealed that the majority of autoxidation studies were published on a small number of substrates such as L-ascor-bic acid, catechols, cysteine and sulfite ions. The results for each of these substrates will be discussed in a separate section. Results on other metal ion mediated autoxidation reactions are collected in Section VII. In recent years, non-linear kinetic features were discovered in some systems containing dioxygen. These reactions form the basis of a new exciting domain of autoxidation chemistry and will be covered in Section VIII. 

The oxidation of benzaldehyde with dioxygen in the presence of Co(II) and bromide ion also shows non-linear kinetic phenomena. The net reaction of the oxidation process is given as follows ... 

In later work, Roelofs and co-workers discovered further details of the reaction by investigating the sub-systems, and they suggested a 21 step chemical model (RWJ model) to explain the observed non-linear kinetic patterns (163). According to the experimental observations, the oscillation process can be divided into two distinct alternating stages, the stoichiometries of which can be approximated as follows ... 

The fourth explanation for non-linear kinetics differs from the previous three in that it concerns the composition of the solution rather than any intrinsic property of the solid reactants or products. Changing solution composition can produce apparent or true parabolic dissolution kinetics either through the influence of changing pH and COj equilibria, or through the effect of chemical affinity and the reverse reaction rate. These phenomena have been discussed in detail by Helgeson and Murphy (V7) and Helgeson and others ( 1 8). 

Non-linear kinetics have been reported for aminolysis of sulfamate esters RNHSO2ONP (Np=/7-N02C6H4) in chloroform. The first-order rate constants obs for reaction with imidazoles (primarily) under pseudo-first-order conditions display saturation curvature with increasing amine concentration, according to the expression... 

Saturable clearance mechanisms producing non-linear kinetics... 

In all this, it should be remembered that the role of regulatory authorities is to protect the public. For entirely justifiable reasons, they will apply very strict criteria to products with a low therapeutic index, non-linear kinetics or imfavour-able physical properties. Digoxin, phenytoin and primidone provide notable examples of drugs where bioinequivalence issues have led to clinical problems. 

Non-linear pharmacokinetics are much less common than linear kinetics. They occur when drug concentrations are sufficiently high to saturate the ability of the liver enzymes to metabolise the drug. This occurs with ethanol, therapeutic concentrations of phenytoin and salicylates, or when high doses of barbiturates are used for cerebral protection. The kinetics of conventional doses of thiopentone are linear. With non-linear pharmacokinetics, the amount of drug eliminated per unit time is constant rather than a constant fraction of the amount in the body, as is the case for the linear situation. Non-linear kinetics are also referred to as zero order or saturation kinetics. The rate of drug decline is governed by the Michaelis-Menton equation ... 

Well-stirred systems are particularly convenient for the theoretician but are often less easy to realize in practice. Indeed, spatial inhomogeneities, with consequent molecular diffusion or thermal conduction processes, arise in many important situations—as varied as a single biological cell and a haystack. In the next three chapters we turn to unstirred systems, again seeking to determine bifurcation phenomena driven by non-linear kinetics. 

Peak plasma concentrations are reached within 2 to 3 h after oral dosing. Diflunisal is heavily bound to plasma protein (>99 %), has a long elimination half-life (8-12 h) and non-linear kinetics. Hence, it is used with an initial loading dose (1000 mg) and a lower maintenance dose (500-1000 mg/day). Diflusinal is excreted as glucuronide in the urine. 

Therefore, analytical estimates of the solution of a set of non-linear kinetic equations based on the superposition approximation confirm reduction of the asymptotic exponent. 

Tissue uptake clearance is a useful parameter to characterize the in vivo distribution properties of a drag since it is independent of the drag concentration in plasma. However, when the tissue uptake process depends on the drag concentration in plasma and follows non-linear kinetics, the calculated CZapp i represents an average value of its time-dependent clearance for the overall experimental period (Nishikawa et al., 1992). 

Taylor et al. [90], when studying the oxidation of CO over Ir (110), also found hysteresis on decreasing and increasing the temperature. This hysteresis is ascribed primarily to the non-linear kinetic dependences of the conversions of surface substances [90]. However, in our opinion, this hysteresis is also most likely to be "false since temperature variations of catalyst were sufficiently high ( 1.25Ks ) and the steady state could hardly be achieved. 

The model also shows the discrepancy in relaxation times for the reaction rate and the concentrations of the intermediates. With decreasing temperature, the coverage 60 falls, whereas 9C0 rises. They compensate each other and in this temperature range the rate of C02 generation remains unchanged over a considerably long period of time (10-15 min). It is suggested that the non-linear kinetic model permits us to interpret qualitatively the fact of time separation. In addition, it provides a reasonable quantitative estimate for the slow relaxation time (30 out of 50 min). To improve this estimate, the model must take into consideration "side (Temkin term) proces-... 

Thus the Barelko et al. experimental data [156, 158] can be given a qualitative interpretation in terms of the non-linear kinetic models for the ideal adsorption layer. 

Analysis of the simplest non-linear kinetic models (in particular, of kinetic models for heterogeneous catalysis). The aim is to select the simplest non-linear kinetic models to carry out the most complete investigation of their steady-state and relaxation characteristics. The obtained systems of typical relationships facilitates the interpretation of complex reactions, including simpler "typical units. 

Minimizing the problems caused by the non-linear kinetics of the drug (e.g. phenytoin). 

In Fig. 10, the transients exhibit quite different behavior from opal A to opal CT. In particular, a bi-exponential decay (Eq. 2) failed to reproduce the kinetics of opal CT. In this material, the emission is red-shifted towards 2.6 eV and the PL is strongly quenched at shorter time delays, with an unusual, non-linear kinetics in semi-log scale, indicating a complex decay channel either involving multi-exponential relaxation or exciton-exciton annihilations. Runge-Kutta integration of Eq. 5 seems to confirm the latter assumption with satisfactory reproduction of the observed decays. The lifetimes and annihilation rates are Tct = 9.3 ns, ta = 13.5 ns, 7ct o = 650 ps-1 and 7 0 = 241 ps-1, for opal CT and opal A, respectively. 

Chiral surfaces Enantiomorphous crystals Homochiral peptides Mirror symmetry breaking Non-linear kinetics Self-replication of peptides... 

The enzyme is saturated by a high free-drug concentration, and the rate of metabolism remains constant over time. This is called zero order kinetics (or sometimes referred to clinically as non-linear kinetics). A constant amount of drug is metabolized per unit time. 

Since clozapine may be the gold standard and the last resort in the treatment of refractory schizophrenia, the authors of a review aimed to discover whether a trial with clozapine is adequate (15). The results favored the approach of increasing the clozapine plasma concentration in treatment-refractory schizophrenic patients who do not respond to an initial low-to-medium dose. Some patients, especially young male smokers, will need dosages over 900 mg/day, and the addition of low-dose fluvoxamine while closely monitoring clozapine concentrations can help to reduce the large number of tablets required, since fluvoxamine increases the clozapine plasma concentration 2- to 3-fold, maximally 5-fold, and reduces N-desmethylclozapine concentrations the combination can lead to non-linear kinetics of clozapine. 

The compound-soil interaction is reflected in the following parameters kd = 1.0 cm3/g (distribution coefficient) NEQ = 1.1 (Freundlich parameter) kt = 0.01 h (forward kinetic reaction rate) k2 = 0.02 h (backward kinetic reaction rate) U = 1.2 (nonlinear kinetic parameter) k3 = 0.01 hr1 (forward kinetic reaction rate) k4 = 0.02 Ir1 (backward kinetic reaction rate) W = 1.3 (non-linear kinetic parameter) k5 = 0.01 h (forward kinetic reaction rate) k6 = 0.02 Ir1 (backward kinetic reaction rate), ks = 0.005 (irreversible reaction rate). 

Tozer, T.N. Tang-Liu, D.D.S. Linear versus non-linear kinetics. In Topics in Pharmaceutical Sciences Breimer, D.D., Speiser, P., Eds. Elsevier New York, NY, 1981 ... 

The drug shows non-linear kinetics within the therapeutic range (e.g., phenytoin). 

Paclitaxel has non-linear kinetics peak plasma concentrations and drug exposure increase disproportionately with increasing doses and the pharmacokinetics depend on the schedule of administration. Saturation is reached with high-dose short infusions (4). Paclitaxel has been reported to follow both biphasic (5) and triphasic models (6). The half-life has been estimated at 6-13 hours after intravenous administration (7). 

We have shown that mesoscopic non-equilibrium thermodynamics satisfactorily describes the dynamics of activated processes in general and that of polymer crystallization in particular. Identification of the different mesoscopic configurations of the system, when it irreversibly proceeds from the initial to the final phases, through a set of internal coordinates, and application of the scheme of non-equilibrium thermodynamics enable us to derive the non-linear kinetic laws governing the behavior of the system. 

Still, todays computer power does not allow us to hilly resolve the shock transition region. We can, however, explain the non-linear kinetic plasma dynamics that generate the electromagnetic fields needed for transmission of momentum between the colliding plasma populations. Here, we report on 3D PIC simulations of the shock formation in the counter-streaming region of two colliding plasma shells. 

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