Ensemble effect definition

The operators Fk(t) defined in Eq.(49) are taken as fluctuations based on the idea that at t=0 the initial values of the bath operators are uncertain. Ensemble averages over initial conditions allow for a definite specification of statistical properties. The statistical average of the stochastic forces Fk(t) is calculated over the solvent effective ensemble by taking the trace of the operator product pmFk (this is equivalent to sum over the diagonal matrix elements of this product), so that = Trace(pmFk) is identically zero (Fjk(t)=Fk(t) in this particular case). The non-zero correlation functions of the fluctuations are solvent statistical averages over products of operator forces,... 

The transformation used above to enumerate tautomers would lead to identical products when applied to symmetrically substituted pyrazoles. The set of structures generated in the enumeration process is converted to a sorted list of canonical SMILES [23] from which duplicates are easily eliminated. Structures registered in alternative tautomeric forms are converted to identical lists of SMILES that can each be represented by their common first member. This effectively extends the definition of canonical SMILES to cover an ensemble of tautomeric forms and makes it possible to check for duplicate structures without having to register multiple forms [16, 26]. 

We may thus remark that the conformational results for aziridine acyl derivatives retain the undoubtedly positive aspect of evidencing the ensemble of effects causing the internal mobility of these molecules nevertheless more efforts seem necessary to achieve more precise definition of the conformer... 

Areal Porosity and Tortuosity. Areal porosity or areosity, Ap, is defined as the effective areal ratio of the open pore cross-section to the bulk space. A more strict definition of areosity was introduced by Ruth and Suman (56). However, the areosity as defined by them is not a property of the porous medium only but a property of both the porous medium and the transport strength of the fluid such as the flow strength and electric current strength. The areal porosity is undoubtedly a very useful quantity for a bundled or ensemble passage model because it represents the ratio of the total passage cross-sectional area to the total cross-sectional area of the porous medium at a given planar section. 

Definition of unambiguous business rules is not always straightforward and in these situations it is useful to generate an ensemble of equivalent structures.If rules to rank the structures in the ensemble can be defined, then it becomes possible to select one of these to represent the ensemble. For example, enumeration of tautomers using Leatherface creates a sorted list of canonical SMILES, the first of which is used to represent the ensemble. This effectively extends the concept of canonicalisation to an ensemble of structures, and the term canonical tautomer may be encountered in the literature. ... 

To examine the ensemble requirements of a reaction, a suitable probe adlayer should restrict access to the surface by the reacting species in a known and controllable way. As will be shown, both the carbon and ethylidyne adlayers are inert in the sense that they are not consumed by the reaction. The two adlayers differ in their distribution on the surface, however carbon adsorbs as graphitic islands, whereas ethylidyne adsorbs as isolated molecules in a p(2x2) structure. Information about ensemble requirements can then be obtained through studies of the respective reactions as a function of probe adlayer coverage. Of course, these adlayers cannot isolate ensemble requirements perfectiy, as other effects, such as ion adsorption, may occur to some degree. Nonetheless, they represent a simplified electrocatalytic substrate with which definitive information about the surface reaction mechanism can be determined. 

The definition of the configurational ensemble and the associated probabilities allows us to obtain the effective value in the disordered solid of any quantity that can be theoretically obtained for each ordered configuration. If is the value of the given magnitude for configuration k, then the effective value in the disordered solid is ... 

In this model, it has been generally assumed that s=, although the definition of the dielectric constant for monolayers is still debatable. In this case, the mutual inductive depolarization effects that must occur when an ensemble of dipoles are closely packed, as well as the interfacial effects associated with the polarization of molecules at the sub-phase surface are neglected. An estimate Of the surface potential change caused by protein dipoles on the gold surface, is given by the sum of two contributions(P) and can be written as... 

This book on Polymer Fracture might as well have been called Kinetic Theory of Polymer Fracture . The term kinetic theory , however, needs some definition or, at least, some explanation. A kinetic theory deals with and particularly considers the effect of the existence and discrete size, of the motion and of the physical properties of molecules on the macroscopic behavior of an ensemble, gaseous or other. A kinetic theory of strength does have to consider additional aspects such as elastic and anelastic deformations, chemical and physical reactions, and the sequence and distribution of different disintegration steps. 

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