Inferred-state history

Given a measurement record of distance versus time, it will be possible to differentiate this record to obtain V = dx/dt, the time history of the second state, v. We shall give the name inferred-state history to the behaviour of a state variable deduced from a measurement record either directly or by differentiation. 

Using the procedure outlined above, we may generate a total of Ki > k inferred state histories , Z from the k original instrument outputs, z. We now sort the differential equations (DEs) defining the nominal model (equation (24.3)) into sets on the basis of the state variables they contain ... 

But, as was noted earlier, off-line differentiation can be an accurate process, and so the fact that we have the inferred-state histories, Z, means that we may deduce their derivatives, dzi/dr. We may use this fact to restate our problem as the need to satisfy the equation ... 

The equilibrium model allows certain inferences to be drawn concerning the geochemical environment which might have existed when sediments were formed, from knowledge of the thermodynamic properties of these sediments today. Thus, one can speculate about the evolution of the lithosphere, hydrosphere, and atmosphere, by assuming that equilibrium states were approached at various stages in geological history. 

There now exists some evidence for a tendency for fault sealing capacity to relate to the azimuth of fault strike in part of the North Sea. It has previously been suggested that this relates to the azimuth of the maximum and minimum horizontal stresses. However, this relationship can be inferred to relate to some yet unspecified combination of the present day stress state and the overall geological history, including previous stress states. We suspect that minor shear displacements can potentially greatly increase the stress-sensitivity of seals composed of mudrock. 

Inferring the structure of the transition state on the basis of what is known about the species that lead to it or may be formed by way of it is a practice with a long history in organic chemistry. A justification of this practice was advanced in 1955 by George S. Hammond, who reasoned that if two states, such as a transition state and an intermediate derived from it, are similar in energy, then they are similar in structure. This rationale is known as Hammond s postulate. In the formation of a carbocation from an alkyloxoninm ion, the transition state is closer in energy to the carbocation than it is to the alkyloxoninm ion, and so its structure more closely resembles the carbocation and it responds in a similar way to the stabilizing effects of alkyl snbstituents. 

Reservoir coimectivity is important to sweep efficiency in all phases of production. How efficiently a formation s pore spaces are coimected is determined through tracer analysis, where chemical or radioactive tracers are introduced at injection and monitored at production wells. The idea is simple the more tracers obtained at a producer, the better the connectivity between the injectors and it. In reservoir simulation, the oilfield s permeability and porosity distributions are determined, often by trial and error, and more than likely nonuniquely, by history matching with production and well test data. In singlephase flow reservoirs, steady-state production profiles are completely determined by the pressure equation and Darcy s law, neither of which depends on porosity. In well testing, pressure buildup and drawdown depend on porosity and compressibility, factors that do not directly enter in steady-state production. Empirical tracer tests provide further information porosity, inferred from tracer travel times, enters in steady flows where compressibility is unimportant. These three flow tests therefore provide good independent check points that are essential to good reservoir description. 

Thermotropic liquid crystals hold a dominant position in the field of the LCD however, researchers have also to pay attention to another type of liquid crystals, lyotropic liquid crystals, fi om the aspect of the life science field. Essential properties of cell membranes originate from their liquid crystalline behavior. The point of view of biophysics exists in the liquid crystal discovery time inferred from the monograph of Otto Lehmaim titled The liquid crystal and life flieory . In the experimental research of material science, the development of science cannot be expected without collaboration with a physicist, a physical chemist, and a synthetic chemist, as showing the history of research not only as that of liquid crystals but also of macromolecules and colloid science, among others. Because a considerable portion of a living organism (cell membrane, skin structure, etc.) is composed of liquid crystalline states, participation of researchers from many different fields is necessary for the bio-matter liquid crystal. I would hope to see the development of medical science, pharmacy, and foods by the full utilization of the potential of liquid crystal materials. 

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