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Nonlinear equation

In molecular dynamics applications there is a growing interest in mixed quantum-classical models various kinds of which have been proposed in the current literature. We will concentrate on two of these models the adiabatic or time-dependent Born-Oppenheimer (BO) model, [8, 13], and the so-called QCMD model. Both models describe most atoms of the molecular system by the means of classical mechanics but an important, small portion of the system by the means of a wavefunction. In the BO model this wavefunction is adiabatically coupled to the classical motion while the QCMD model consists of a singularly perturbed Schrddinger equation nonlinearly coupled to classical Newtonian equations, 2.2. [Pg.380]

Another example of an equation nonlinear in the parameters is the sum of exponentials form vdiich is useful with some resolution correction methods ... [Pg.207]

These hyperbolic equations are analogous to the Michaelis-Menten equation. Nonlinear regression is preferable to the method proposed in the 1960s by Kitz and Wilson, which necessitates a double-reciprocal linear transformation of the data (analogous to a Lineweaver-Burk plot) that can bias the estimates of /clnact and A). [Pg.287]

H. Chate. Spatiotemporal intermittency regimes of the one-dimensional complex ginzburg-landau equation. Nonlinearity, 7 185— 204, 1994. [Pg.258]

This is our first nonlinear differential equation. Nonlinear differential equations do not have analytical solutions in general but certain ones do. Equation 4.18 can be solved analytically because the equation is separable. Dividing both sides by c and putting the time differential on the right-hand side gives... [Pg.392]

KZ. Micha lisM nten equation-nonlinear estunation ... [Pg.100]

The result here concerning separability seems to be rather pessimistic in fact. Maybe a curve-fit variable of. s would serve just as well. How might we be able to test this Would it really be worth the effort Also, the appearance of IS in the main reaction makes the rate equation nonlinear. Does this mean that separable kinetics for deactivation will not work for nonlinear kinetics ... [Pg.219]

Simultaneously, conditions of thermal (equality of temperatures), mechanical (equality of pressures) and phase equilibrium (equality of chemical potentials of both components in both phases) must be satisfied. The constraints are defined by a set of equations nonlinear both in model parameters and in fliermodynamic quantities. When correlating vapor-liquid equilibrium data at low and moderate pressures, liquid phase is described in terms of a G -model and vapor phase is either considered as an ideal gas or its nonideality is expressed by an equation of state, e. g. the virial expansion limited to the second virial coefficient (Chap. 1.6). [Pg.23]

The main difference between linear and nonlinear FEA hes in the solution of the algebraic equations. Nonlinear analysis is usually more complex and expensive than linear analysis. Nonlinear problems generally require an iterative incremental solution strategy to ensure that equihbrium is satisfied at the end of each step. Unlike linear problems, nonlinear results are not always unique. [Pg.132]

Find the value of Ca in the following nonlinear algebraic equations Nonlinear algebraic equation (Figure C.7) ... [Pg.467]


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