Flux-based methods

Figure 7.6 Hybrid dyiiamic/static simulation algorithm. Using flux-based methods, the algorithm allows dynamic models to be integrated with stoichiometry-based models.

Fluorescence-based methods do not directly measure ionic current but, rather, measure either membrane-potential-dependent or ion-concentration-dependent changes of fluorescence signals (from fluorescent dyes loaded into the cytosol or cell membrane) as a result of ionic flux. Because fluorescence-based methods give robust and homogeneous cell population measurement, these assays are relatively easy to set up and achieve high throughput. 

This rock record yields results that are inconsistent with fluxes inferred from fluid data from seafloor hydrothermal springs. An in-depth analysis of data methods and uncertainties in fluxes based on rock data and fluid data suggest that these discrepancies are due to profound problems with both types of flux determination. 

In reactive flow analysis the Pick s law for binary systems (2.285) is frequently used as an extremely simple attempt to approximate the multicomponent molecular mass fluxes. This method is based on the hypothesis that the pseudo-binary mass flux approximations are fairly accurate for solute gas species in the particular cases when one of the species in the gas is in excess and acts as a solvent. However, this approach is generally not recommend-able for chemical reactor analysis because reactive mixtures are normally not sufficiently dilute. Nevertheless, many industrial reactor systems can be characterized as convection dominated reactive flows thus the Pickian diffusion model predictions might still look acceptable at first, but this interpretation is usually false because in reality the diffusive fluxes are then neglectable compared to the convective fluxes. 

High-order convection/advection schemes are widely used in meteorological applications solving h3rperbolic equations. For example, in European weather forecast models the explicit non-flux-based modified methods of characteristics have been very popular as they are very fast. Typical examples of this type of schemes are the semi-Lagrangian advection schemes of Bates and McDonald [9], McDonald [129] and McDonald [130]. These methods have an unrestricted time step advantage, but also an important disadvantage that they are not strictly conservative due to their non-flux-based formulation. 

A large number of explicit numerical advection algorithms were described and evaluated for the use in atmospheric transport and chemistry models by Rood [162], and Dabdub and Seinfeld [32]. A requirement in air pollution simulations is to calculate the transport of pollutants in a strictly conservative manner. For this purpose, the flux integral method has been a popular procedure for constructing an explicit single step forward in time conservative control volume update of the unsteady multidimensional convection-diffusion equation. The second order moments (SOM) [164, 148], Bott [14, 15], and UTOPIA (Uniformly Third-Order Polynomial Interpolation Algorithm) [112] schemes are all derived based on the flux integral concept. 

The fast and conservative versions of the flux-based modified method of characteristics may also be a useful for this purpose [157]. 

Roache PJ (1992) A Flux-Based Modified Method of Characteristics. Inter-nasjonal Journal for Numerical Methods in Fluids 15 1259-1275... 

Fig. 7. Estimates of the skin-bulk temperature based on latent heat flux switching method and prediction of a fit assuming a surface renewal model...

The authors proceed to calculate the reaction rates by the flux correlation method. They find that the molecular dynamics results are well described by the Grote-Hynes theory [221] of activated reactions in solutions, which is based on the generalized Langevin equation, but that the simpler Kramers model [222] is inadequate and overestimates the solvent effect. Quite expectedly, the observed deviations from transition state theory increase with increasing values of T. 

Flux-resolving, fluctuation-based methods In these methods the vertical turbulent eddy flux F is measured as pw c, where overbars and primes denote time means and fluctuations, respectively, and w is the vertical velocity component. They include eddy-covariance and eddy-accumulation methods for measuring fluxes from towers and aircraft. They are not normally regarded as atmospheric inverse methods, since that term usually refers to methods which relate a mean concentration field to a source density or surface flux distribution. 

Eulerian flux-resolving, fluctuation-based methods ... 

Two widely used practical inverse approaches are presented in the next two sections ( Estimating absolute velocities and nutrient fluxes across sections and Estimating carbon export fluxes with the adjoint method ). These serve as examples to describe details of the mathematical methods and to list achievable results. The first method, the section inverse approach, infers nutrient, carbon, and tracer fluxes across sets of sections, based on hydro-graphic, tracer, and nutrient data along these sections. The second example describes an application of the adjoint method for the determination of ocean currents, biological productivity, and downward particle fluxes. This method is specifically adapted for the utilization of many different tracers and can handle problems with heterogeneous and sparse data coverage. 

An attractive feature of this chopper-based method was the exclusion of ESI spray from the drift tube except for the brief period of ion injection. Aerosols were blocked from entering the drift tube most of the time, protecting the drift tube from the large burden of mass flux this made this design inherently clean, unlike other ESI IMS designs, for which a large demand exists for a drift tube to accept an aerosol-rich flow, which must be desolvated and swept from the drift tube. Injection pulse widths... 

Derjaguin (1946) used a statistical method to follow the motion of a free molecule flowing through a random pore space to obtain the following equation for the Knudsen flux based on total cross-sectional area of the medium ... 

Equations [18], [54], and [55] constitute a system of three equations with three unknowns, and this system is solved numerically on one-, two-or three-dimensional domains. For the sake of simplicity, we will discuss the one-dimensional case (the equations are easily extended to three-dimensional). Although finite element methods have been used extensively for the solution of Eqs. [18], and [55] in solid state electronics, flux-based approaches for the simulation of ion channels rely primarily on finite difference schemes. 

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