Description validity

The basic Landau-Ginzburg model is valid only for relatively weak surfactants and in a limited region of the phase space. In order to find a more general mesoscopic description, valid also for strong surfactants and in a more extended region of the phase space, we derive in this section a mesoscopic Landau-Ginzburg model from the lattice CHS model [16]. 

Schaap M, Timmermans RMA, Roemer M, Boersen GAC, Builtjes PJH, Sauter FJ, Velders GJM, Beck JP (2008) The LOTOS-EUROS model description, validation and latest developments. Int J Environ Pollut 32(2) 270-290... 

Peyote was first described in 1560. The first person publishing a binomial name for it was the French botanist Charles Lemaire, who in 1845 called it Echinocactus williamsii in a horticultural catalog. He didn t describe it, however. The description validating the binomial soon came from another European botanist, Prince Salm-Dyck, who didn t provide an illustration. Above is the first published image of peyote, appearing in Curtis Botanical Magazine in 1847. 

Introduction System Description Validation Determination Validation Life Cycle Acceptance Criteria Roles and Responsibilities Procedures and Training Documentation Review and Approvals... 

Product development laboratories Utilities description Validation program overview... 

A theoretical description of the addition reaction, based on Troe s formulation of unimolecular reaction rate theory, has been constructed to address the question of the consistency of our results and the earlier low temperature measurements. These calculations show a dramatic combined temperature and pressure dependence of this rate constant which must be included when this reaction is incorporated into models of combustion chemistry. These results illustrate the need to combine individual experimental data with a theoretical overview in order to obtain a description valid over the range of T and P likely encountered in combustion systems. 

Because of the unphysical nature of a pseudopotential that depends on thermodynamic state, one would like an alternative description valid over the whole liquid range. One approach is to generalize the van der Waals mean field model by incorporating a pressure term of the form F" rather than the van der Waals V term. The expression for the cohesive energy in Eq. (3.28) is then U — —constant/F " with m > 1. An additional improvement of the simple van der Waals model is made by using hard sphere theory. The corresponding equation of state is then... 

The creation of cinchophen from the German patent description validated the patent, he argued. 

As reactants transfonn to products in a chemical reaction, reactant bonds are broken and refomied for the products. Different theoretical models are used to describe this process ranging from time-dependent classical or quantum dynamics [1,2], in which the motions of individual atoms are propagated, to models based on the postidates of statistical mechanics [3], The validity of the latter models depends on whether statistical mechanical treatments represent the actual nature of the atomic motions during the chemical reaction. Such a statistical mechanical description has been widely used in imimolecular kinetics [4] and appears to be an accurate model for many reactions. It is particularly instructive to discuss statistical models for unimolecular reactions, since the model may be fomuilated at the elementary microcanonical level and then averaged to obtain the canonical model. 

We now embark on a more fonnal description of nonlinear optical phenomena. A natural starting point for this discussion is the set of Maxwell equations, which are just as valid for nonlinear optics as for linear optics. 

Nomenclature is the compilation of descriptions of things and technical terms in a special field of knowledge, the vocabulary ofa technical language. In the history of chemistry, a systematic nomenclature became significant only rather late. In the early times of alchemy, the properties of the substance or its appearance played a major role in giving a compound a name. Libavius was the first person who tried to fix some kind of nomenclature in Alckeinia in 1,597. In essence, he gave names to chemical equipment and processes (methods, names that are often still valid in our times. 

Quantum mechanics (QM) is the correct mathematical description of the behavior of electrons and thus of chemistry. In theory, QM can predict any property of an individual atom or molecule exactly. In practice, the QM equations have only been solved exactly for one electron systems. A myriad collection of methods has been developed for approximating the solution for multiple electron systems. These approximations can be very useful, but this requires an amount of sophistication on the part of the researcher to know when each approximation is valid and how accurate the results are likely to be. A significant portion of this book addresses these questions. 

Variations in measurable properties existing in the bulk material being sampled are the underlying basis for samphng theory. For samples that correctly lead to valid analysis results (of chemical composition, ash, or moisture as examples), a fundamental theoiy of sampling is applied. The fundamental theoiy as developed by Gy (see references) employs descriptive terms reflecting material properties to calculate a minimum quantity to achieve specified sampling error. Estimates of minimum quantity assumes completely mixed material. Each quantity of equal mass withdrawn provides equivalent representation of the bulk. 

Computer simulation can be used to provide a stepping stone between experiment and the simplified analytical descriptions of the physical behavior of biological systems. But before gaining the right to do this, we must first validate a simulation by direct comparison with experiment. To do this we must compare physical quantities that are measurable or derivable from measurements with the same quantities derived from simulation. If the quantities agree, we then have some justification for using the detailed information present in the simulation to interpret the experiments. 

This structural similarity is also reflected in the amino acid sequences of the domains, which show 40% identity. They are thus clearly homologous to each other. The motif structures within the domains superpose equally well but their sequence homology is less, being around 30% between motifs 1 and 2 and 20 Xi between 3 and 4. This study, however, clearly shows that the topological description in terms of four Greek key motifs is also valid at the structural and amino acid sequence levels. 

It, therefore, appears that the equilibrium approximation is a special case of the steady-state approximation, namely, the case i > 2- This may be, but it is possible for the equilibrium approximation to be valid when the steady-state approximation is not. Consider the extreme but real example of an acid-base preequilibrium, which on the time scale of the following slow step is practically instantaneous. Suppose some kind of forcing function were to be applied to c, causing it to undergo large and sudden variations then Cb would follow Ca almost immediately, according to Eq. (3-153). The equilibrium description would be veiy accurate, but the wide variations in Cb would vitiate the steady-state description. There appear to be three classes of practical behavior, as defined by these conditions ... 

The various solutions to Equation 3 correspond to different stationary states of the particle (molecule). The one with the lowest energy is called the ground stale. Equation 3 is a non-relativistic description of the system which is not valid when the velocities of particles approach the speed of light. Thus, Equation 3 does not give an accurate description of the core electrons in large nuclei. 

It is important to realize that whenever qualitative or frontier molecular orbital theory is invoked, the description is within the orbital (Hartree-Fock or Density Functional) model for the electronic wave function. In other words, rationalizing a trend in computational results by qualitative MO theory is only valid if the effect is present at the HF or DFT level. If the majority of the variation is due to electron correlation, an explanation in terms of interacting orbitals is not appropriate. 

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