Modelling describing the system

An even coarser description is attempted in Ginzburg-Landau-type models. These continuum models describe the system configuration in temis of one or several, continuous order parameter fields. These fields are thought to describe the spatial variation of the composition. Similar to spin models, the amphiphilic properties are incorporated into the Flamiltonian by construction. The Flamiltonians are motivated by fiindamental synnnetry and stability criteria and offer a unified view on the general features of self-assembly. The universal, generic behaviour—tlie possible morphologies and effects of fluctuations, for instance—rather than the description of a specific material is the subject of these models. 

The Onsager model describes the system as a molecule with a multipole moment inside of a spherical cavity surrounded by a continuum dielectric. In some programs, only a dipole moment is used so the calculation fails for molecules with a zero dipole moment. Results with the Onsager model and HF calculations are usually qualitatively correct. The accuracy increases significantly with the use of MP2 or hybrid DFT functionals. This is not the most accurate method available, but it is stable and fast. This makes the Onsager model a viable alternative when PCM calculations fail. 

Derive a dynamic mathematical model describing the system. 

The simplest and often most suitable modeling tool is the one-box model. One-box models describe the system as a single spatially homogeneous entity. Homogeneous means that no further spatial variation is considered. However, one-box models can have one or several state variables, for instance, the mean concentration of one or several compounds i which are influenced both by external forces (or inputs) and by internal processes (removal or transformation). A particular example, the model of the well-mixed reactor with one state variable, has been discussed in Section 12.4 (see Fig. 12.7). The mathematical solution of the model has been given for the special case that the model equation is linear (Box 12.1). It will be the starting point for our discussion on box models. 

Consider the exothermic first-order reaction A —> B taking place batchwise at reactor temperature Tr and coolant temperature 7j. The mathematical model describing the system is given by the mass balance on reactant A and the energy balance in the reactor ... 

The dynamic mathematical model describing the system consists of a total mass balance, two component balances, an energy balance on the reactor liquid, and a jacket energy balance ... 

The model describes the system for the case of competitive product inhibition. This is verified from the calculated values of equilibrium constants Kp for the both cellobiose and glucose. 

Using a deterministic approach, the model describes the system with a set of ODEs assembled from reaction rate laws and divides it into three compartments nucleus, cytosol, and extracellular space. A sample equation for the rate of change in concentration of the NFkB inhibitor protein IkB follows ... 

Sometimes, it is possible to derive optimal control laws when the underlying mathematical models describing the system are simple enough. In many problems though, obtaining optimal control laws mostly requires drastic simplifications of the underlying mathematical models, thereby compromising on the accuracy of control. 

Static models describing the system constituents and then-... 

The development of the comprehensive set of safety arguments would benefit from a good set of models describing the system and supporting the risk assessment ... 

Equivalent circuit (formal or mathematical) modeling presents the system in hypothetical electrical circuits consisting of well-defined ideal and sometimes nonideal electrical elements. Measurement modeling explains the experimental impedances in terms of mathematical functions in order to obtain a good fit between the calculated and experimental impedances. In the latter case the parameters obtained do not necessarily have clear physicochemical significance. Such a model describes the system s response to various possible electrical input signals. 

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