Kinetic model elastic

Similar to generalized mass-action models, lin-log kinetics provide a concise description of biochemical networks and are amenable to an analytic solution, albeit without sacrificing the interpretability of parameters. Note that lin-log kinetics are already written in term of a reference state v° and S°. To obtain an approximate kinetic model, it is thus sometimes suggested to choose the reference elasticities according to simple heuristic principles [85, 89]. For example, Visser et al. [85] report acceptable result also for the power-law formalism when setting the elasticities (kinetic orders) equal to the stoichiometric coefficients and fitting the values for allosteric effectors to experimental data. 

The rest of this chapter is organized as follows. First, in Section 6.1, we consider the collision term for monodisperse hard-sphere collisions both for elastic and for inelastic particles. We introduce the kinetic closures due to Boltzmann (1872) and Enksog (1921) for the pair correlation function, and then derive the exact source terms for the velocity moments of arbitrary order and then for integer moments. Second, in Section 6.2, we consider the exact source terms for polydisperse hard-sphere collisions, deriving exact expressions for arbitrary and integer-order moments. Next, in Section 6.3, we consider simplified kinetic models for monodisperse and polydisperse systems that are derived from the exact collision source terms, and discuss their properties vis-d-vis the hard-sphere collision models. In Section 6.4, we discuss properties of the moment-transport equations derived from Eq. (6.1) with the hard-sphere collision models. Finally, in Section 6.5 we briefly describe how quadrature-based moment methods are applied to close the collision source terms for the velocity moments. 

For elastic collisions, several different kinetic models have been proposed in order to close the Boltzmann hard-sphere collision term (Eq. 6.9). For inelastic collisions (e < 1), one must correctly account for the dependence of the dissipation of granular energy on the value of e. One method for accomplishing this task is to start from the exact (unclosed) collision integral in Eq. (6.68). From the definition of if given in Eq. (6.60), it can be... 

Two-dimensional cell modeled as a liquid and a compound drop [N Dri etal, 2003] Cell deforms with nucleus inside Bonds are elastic springs Macro/micro model for cell deformation Kinetics model based on Dembo [ 1988]. Nano scale model for hgand-receptor Uniform flow at the inlet as in parallel-flow chamber assay Results compare well with numerical and experimental results found in the literature for simple liquid drop Cell viscosity and surface tension affect Leukocyte rolling velocity Nucleus increases the bond hfetime and decreases leukocyte rolling velocity Cell with larger diameter rolls faster Uniform flow at the inlet as in parallel flow chamber assay... 

Kinetic models Direct calculation of file elasticity coefficients from a kinetic model Robust, but relies on the availabihty of a reliable kinetic model for the individual enzymes in the pathway... 

When the product ion moved with a higher kinetic energy than predicted by the stripping model, the collision apparently was more elastic— i.e., less kinetic energy of the incident ion was used for internal excitation of the products. In an ideal elastic collision with H transfer the products carry no internal energy at all. If the secondary ion moves forward and the H atom moves backwards, conservation of momentum requires that the primary ion has a velocity ... 

In the kinetic theory, the gas molecules are represented by hard spheres colliding elastically with each other and with the container walls. Details of this theory are given, for example, in ref. [1], An important parameter that can be calculated by this model is A, the mean free path of a molecule between collisions. The mean free path A of molecules is ... 

---