External with respect

The parts of the molecules that are external with respect to the catalyst should not necessarily, in a general case, correspond to the surface of the catalyst. On the contrary, the parts of the molecules that are in contact with the catalyst and fit into its valleys of atomic size must bear a certain relation to the catalyst, namely, that of a surface isomorphism. 

So, two spheres external with respect to one another are defined by the equalities = a and i = where a > 0 and < 0. If the radii of spheres ri, V2 and the distances of their centers from the origin, di and 2 are given, then... 

Internal coupling links working between the two subvarieties within a same Formal Object. They are space-time scalars, such as a frequency or a velocity. They are internal with respect to the energy variety but external with respect to the Formal Objects. 

Sample size is limited, whether mounted internally or externally with respect to the guard detector. 

Themiodynamic measurements are possible only when both the initial state and tire final state are essentially at equilibrium, i.e. internally and with respect to the surroundings. Consequently, for a spontaneous themiodynamic change to take place, some constraint—hitemal or external—must be changed or released. 

Correlated events are related in time and this time relation can be measured either with respect to an external clock or to the events themselves. Random or uncorrelated events bear no fixed time relation to each other but, on the other... 

Figure Bl.15.6. The EPR spectrum of tire perinaphthenyl radical in mineral oil taken at room temperature. (A) First derivative of the EPR absorption x with respect to the external magnetic field, Bq. (B) Integrated EPR spectrum.

Figure 4-2 Two Masses Vibrating Harmonically with Respect to their Center of Mass. The center of mass may be stationary or moving with respect to an external coordinate system.

Many physical properties of a molecule can be calculated as expectation values of a corresponding quantum mechanical operator. The evaluation of other properties can be formulated in terms of the "response" (i.e., derivative) of the electronic energy with respect to the application of an external field perturbation. 

Fretting corrosion (36,37) can lead to high contact resistance of base metal contacts, such as tin plate in electronic connectors. Small cycHcal displacements of the connector halves occur because of external vibration or differential thermal expansion and contraction of the mating contacts. The wear debris that is formed remains in the contact zone. The accumulation of oxide debris in the contact region leads to increased contact resistance. Solutions to this problem are stmctures that do not permit movement of contact surfaces with respect to one another, the use of gold as a contact finish, and the appHcation of thick coatings of contact lubricants and greases, which reduce the rate of wear and restrict access of air to the contact surfaces. 

The physical separation of charge represented allows externally apphed electric field forces to act on the solution in the diffuse layer. There are two phenomena associated with the electric double layer that are relevant electrophoresis when a particle is moved by an electric field relative to the bulk and electroosmosis, sometimes called electroendosmosis, when bulk fluid migrates with respect to an immobilized charged surface. 

For other mechanisms, the particle-scale equation must be integrated. Equation (16-140) is used to advantage. For example, for external mass transfer acting alone, the dimensionless rate equation in Table 16-13 would be transformed into the ( — Ti, Ti) coordinate system and derivatives with respect to Ti discarded. Equation (16-138) is then used to replace cfwith /ifin the transformed equation. Furthermore, for this case there are assumed to be no gradients within the particles, so we have nf=nf. After making this substitution, the transformed equation can be rearranged to... 

Airflows are determined basically by a steady-state calculation for each time step. At each time step, first, pressures at external nodes are calculated on the basis of the wind pressure coefficients and the actual wind speed and direction. Then, for all conductances, the local pressures at each side of the link are calculated. At internal links, this pressure is dependent on the (unknown) zone pressure p and the aerostatic pressure variation due to the height of the link with respect to the zone reference height. At external links, this pressure is dependent on the external node pressure and the aerostatic pressure variation due to the height of the link with respect to the stack reference height. For the aerostatic pressure, the air density is determined considering the temperature, the humidity, and (if relevant) the contaminant concentrations in the zone or in the outside air, respectively. From this, the pressure differences across each conductance can be calculated, and from this the mass airflow tor each conductance /. 

Note at this point that the potential energy of external forces is independent of material properties. Thus, its derivatives with respect to v are zero, and only U affects the minimization. 

This is not a unique way of classifying molecular properties. For example, Dykstra et al. (1990) concentrate on the response of a system to an apphed external field the electric dipole moment can be defined as the first derivative of the energy with respect to the field, and so on. I will stick with the Boys and Cook nomenclature as a broad basis for discussion. 

The viscosity of a fluid arises from the internal friction of the fluid, and it manifests itself externally as the resistance of the fluid to flow. With respect to viscosity there are two broad classes of fluids Newtonian and non-Newtonian. Newtonian fluids have a constant viscosity regardless of strain rate. Low-molecular-weight pure liquids are examples of Newtonian fluids. Non-Newtonian fluids do not have a constant viscosity and will either thicken or thin when strain is applied. Polymers, colloidal suspensions, and emulsions are examples of non-Newtonian fluids [1]. To date, researchers have treated ionic liquids as Newtonian fluids, and no data indicating that there are non-Newtonian ionic liquids have so far been published. However, no research effort has yet been specifically directed towards investigation of potential non-Newtonian behavior in these systems. 

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