What is a model

There are many types of models used in chemistry, and they can be divided into different categories  

Iconic models, which are picture-like images of the original. An example of such a model is  

Molecular models (ball and stick models, space-filling models) which reproduce typical bond lengths and bond angels and hence stereochemical and congestional effects. However, certain aspects are not covered by the model they are, for instance, not soluble in cyclohexane in the same way as the original. 

Heuristic models, Rules of thumb , which are usually expressed in verbal form, e.g. 

Quantitative models is a heterogeneous group of models expressed in mathematical language. This includes what can be called hard models of general applicability, e.g. thermodynamic models, quantum mechanical models, absolute rate theory, as well as soft models or local models, usually expressed in terms of analogy and similarity, e.g. linear free energy relationships (LFERs), correlations for spectroscopic structural determination, empirical determined kinetic models, and as we shall see, models obtained by statistical treatment of experimental data from properly designed experiments. 

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Parameter estimation and identification are an essential step in the development of mathematical models that describe the behavior of physical processes (Seinfeld and Lapidus, 1974 Aris, 1994). The reader is strongly advised to consult the above references for discussions on what is a model, types of models, model formulation and evaluation. The paper by Plackett that presents the history on the discovery of the least squares method is also recommended (Plackett, 1972). 

What Is a Model Liquid Crystalline Polymer Solution Solvent Effects on the Flow Behavior of LCP Solutions... 

The hamionic oscillator of two masses is a model of a vibrating diatomic molecule. We ask the question, What would the vibrational frequency be for H2 if it were a hamionic oscillator The reduced mass of the hydrogen molecule is... 

What is a reasonable statistical model, or equation, to approximate the relationship between the independent variables and each response variable ... 

Theories abound, and it is important at all times to distinguish carefully between what has been experimentally established, what is a useful model for suggesting further experiments, and... 

What is a mathematical model The group of unknown physical quantities which interest us and the group of available data are closely interconnected. This link may be embodied in algebraic or differential equations. A proper choice of the mathematical model facilitates solving these equations and providing the subsidiary information on the coefficients of equations as well as on the initial and boundary data. 

Scanning electron microscopy and other experimental methods indicate that the void spaces in a typical catalyst particle are not uniform in size, shape, or length. Moreover, they are often highly interconnected. Because of the complexities of most common pore structures, detailed mathematical descriptions of the void structure are not available. Moreover, because of other uncertainties involved in the design of catalytic reactors, the use of elaborate quantitative models of catalyst pore structures is not warranted. What is required, however, is a model that allows one to take into account the rates of diffusion of reactant and product species through the void spaces. Many of the models in common use simulate the void regions as cylindrical pores for such models a knowledge of the distribution of pore radii and the volumes associated therewith is required. 

The important thing is that we are not dealing with a model of ary of the programs that communicate. Instead, at issue is a model of what they are talking to each other about, whether documents, financial transactions, aircraft positions, or talking pictures. 

In this activity, the volume of water is a model for concentration. How can you use your graph to compare the rate of the forward reaction with the rate of the reverse reaction What happens to these rates as the reaction proceeds ... 

Equation 4.4 is a general equation for calculating the variance of residuals. Equation 3.4 is a specific equation for calculating the variance of residuals. What is the model that gives rise to Equation 3.4 ... 

What is a hierarchical -box model How can you define it in words, and how mathematically ... 

How is the problem described and what is a conceptual model of the potential hazard ... 

The information obtained using pharmacokinetic models has a wide variety of uses such as correlating drug doses with pharmacological and toxic responses and determining an optimum dose level for an individual. However, as these models are based on a simplification of what is a very complex system it is necessary to treat the results of these analyses with some degree of caution until the model has been rigorously tested. 

Considering the highly processive mechanism of the protein degradation by the proteasome, a question naturally arises what is a mechanism behind such translocation rates Let us discuss one of the possible translocation mechanisms. In [52] we assume that the proteasome has a fluctuationally driven transport mechanism and we show that such a mechanism generally results in a nonmonotonous translocation rate. Since the proteasome has a symmetric structure, three ingredients are required for fluctuationally driven translocation the anisotropy of the proteasome-protein interaction potential, thermal noise in the interaction centers, and the energy input. Under the assumption that the protein potential is asymmetric and periodic, and that the energy input is modeled with a periodic force or colored noise, one can even obtain nonmonotonous translocation rates analytically [52]. Here we... 

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