Variables external

Sonochemistry is strongly affected by a variety of external variables, including acoustic frequency, acoustic intensity, bulk temperature, static pressure, ambient gas, and solvent (47). These are the important parameters which need consideration in the effective appHcation of ultrasound to chemical reactions. The origin of these influences is easily understood in terms of the hot-spot mechanism of sonochemistry. 

External Conditions The principal external variables involved in any drying study are temperature, humidity, air flow, state of subdivision of the solid, agitation of the solid, method of supporting the solid, and contact between hot surfaces and wet solid. Alf these variables will not necessarily occur in one problem. 

All these factors are the external variables. The internal mechanism of liquid flow does not affect the constant rate. 

As drying proceeds, the point is reached where the evaporating surface is unsaturated. The point of evaporation moves into tne sohd, and the dry process enters the second faJhng-rate period. The drying rate is now governed by the rate of internal moisture movement the influence of external variables diminishes. This period usually predominates in determining the overall diying time to lower moisture content. 

When experiments are carried out to select a suitable dryer and to obtain design data, the effect of changes in various extern variables is studied. These experiments should be conducted in an experimental unit that simulates the large-scale diyer from both the thermal and the material-handling aspects, and only material which is truly representative of full-scale production should be used. 

To include the volume as a dynamic variable, the equations of motion are determined in the analysis of a system in which the positions and momenta of all particles are scaled by a factor proportional to the cube root of the volume of the system. Andersen [23] originally proposed a method for constant-pressure MD that involves coupling the system to an external variable, V, the volume of the simulation box. This coupling mimics the action of a piston on a real system. The piston has a mass [which has units of (mass)(length) ]. From the Fagrangian for this extended system, the equations of motion for the particles and the volume of the cube are... 

The difference can also be seen directly from eq. (16.1). Properties which depend on derivatives of Q are independent of the actual value of Q, only its variation with an external variable (T or V) matters. Thermodynamical functions such as A, S and G, however, depend on the actual value of Q, i.e. the whole volume of phase space. 

Perturbation or chemical relaxation techniques cause an equilibrium to be upset by a sudden change in an external variable such as temperature, pressure, or electric field strength. One then measures the readjustment of the equilibrium concentrations. The time resolution may be as short as 10 10 s, although 10 6 s is the limit more commonly attainable. The method requires no mixing, which is why its time resolution is so good. On the other hand, it is applicable only to equilibria that are properly poised under the conditions used. 

Embedded in such models, in which variations were developed [12] are further detailed. The laminar burning velocity is expressed as a function of fuel type, fuel/ air ratio, level of exhaust gas recirculation, pressure, temperature, etc. Furthermore, submodels have been developed to describe the impact of engine speed, port-flow control systems, in-cylinder gross-flow motion (i.e., swirl, tumble, squish), and turbulent fluctuations u. Thus, with a wider knowledge base of the parametric impact of external variables, successful modeling of... 

However, the fundamental theory of simple foams is not as well formulated as the theory for simple emulsions. Because foams consist of gases dispersed in a semisolid film, the properties and behavior immediately become more dramatically subject to external variables, such as temperature and external air pressure. Minute changes in surface tension of the film can make or break the foam. However, a similar approach might be suggested in the foam field. In this case, the variable with which we are most concerned is whether or not a stable foam is produced and the diagrams would be drawn accordingly. 

If we consider an assembly of N molecules, each individual molecule may exist either in the HS state or in the LS state, the transformation for a fixed set of values of the external variables T, p, or x being characterized by Eq. (2). Here, N is the Avogadro number and the Gibbs free energy G per mole of the system may be expressed as ... 

As we have shown in Sections II and III, Eq. (90) may be solved to determine the state variables x given a consistent set of values of u. Since the w s are specified by mathematical relations external to Eq. (90), they are sometimes referred to as the external variables (M2). The effect of varying the external variables and at the same time satisfying Eq. (90) is given by... 

If the Newton-Raphson method is used to solve Eq. (1), the Jacobian matrix (df/3x)u is already available. The computation of the sensitivity matrix amounts to solving the same Eq. (59) with m different right-hand side vectors which form the columns — (3f/<5u)x. Notice that only the partial derivatives with respect to those external variables subject to actual changes in values need be included in the m right-hand sides. 

In addition to the structural and molecular factors listed above, the following environmental or external variables are important in determining mechanical behavior ... 

Adaptive self-control of the energy contribution in the oscillating process, exhibited in the sustaining of a value for the system s oscillation amplitude and frequency which is stable over significant variance of the amplitude of external influence, the quality factor of the oscillator (the load) and other external variables. 

Construct validation follows a three-stage process. The first stage, theory formulation, involves specifying relationships among constructs and their relation to external variables (e.g., etiological factors). Disorder x is created by process y. For example, a theory about the construct panic disorder could specify that it is caused by the catastrophic misinterpretation of benign bodily cues (Clark, 1986) or by a faulty suffocation monitor (Klein, 1993). Internal... 

A thermodynamic process is reversible if an infinitesimal change in an external variable (e.g. pressure) can change the direction in which the process occurs. 

Throughout this chapter, predictions are made concerning the effect of external variables on the network structure evolution and these predictions are compared with experimental results. The predictions are based on branching theories. The purpose of this section is to outline the basis of present network formation theories and the underlying assumptions. 

An examination of the sample distributions observed in principal components projections using isomer concentration data expressed as fractional composition, as well as the clustering of samples by similar values of their second principal component score term, revealed consistent differences existed in sample profiles. The next step in this data evaluation is to statistically analyze correlations of the PLS components from analyses with the external variables such as percent sand, clay and silt, and total organic matter in samples. These correlations may play an important role in identifying factors resulting in changes in PCB composition and enable one to more clearly understand the forces determining the distribution and fate of PCB in a complex ecosystem. 

Since SIMCA is a class modeling method, class assignment is based on fit of the unknowns to the class models. This assignment allows the classification result that the unknown is none of the described classes, and has the advantage of providing the relative geometric portion of the newly classified object. This makes it possible to assess or quantitate the test sample in terms of external variables that are available for the training sets. 

The relative orientation of the molecules with respect to the substrate surface or, in other words, the molecular planes parallel to the substrate can be controlled, to a certain extent, by varying external variables such as Dt, Tgub, the chemical and physical nature of the substrate, etc. In the following lines we find examples of the... 

The relationships between structures and properties can be classified as intrinsic and extrinsic owing to the molecular arrangement and morphology, respectively. The term intrinsic refers to the 3D packing of molecules, which depends on the geometry and chemical nature of the molecules, and thus on intermolecular interactions. Extrinsic structure-property relationships are related to the formation of interfaces, e.g., grain boundaries, and the presence of defects. In both cases the role of external variables such as T, P, B as well as of internal variables such as the type of guest molecules is essential. 

Some semiconducting organic CT complexes of mixed-stack architecture exhibit the rather unusual neutral-to-ionic (N-I) phase transition upon variation of an external variable of parameter hyperspace, such as P or r. The transition manifests itself by a change of q and a dimerization distortion with the formation of donor-acceptor dimers along the stacking axis in the I-phase. 

The experimental setup is shown in Figure 5.1. Six picosecond (ps)-long pulses at 532 nm and 80 MHz repetition rate were delivered by a frequency-doubled, passively mode-locked NdYV04 laser (Hi-Q Laser Production, Austria). The maximum available average power of the laser was reduced by an external variable attenuator to about a few hundred milliwatts. The OPO gain material is a flux-grown KT10P04 crystal,... 

Univariant equilibrium for which there is one degree of freedom, represents the equilibrium between two co-existing phases. Since there is only one degree of freedom, choosing a value for one external variable, e.g. temperature, determines the remaining variable in a dependent manner, and the locus of points represented on the phase diagram for univariant behavior must lie on a line or curve. Thus the curves on the unary phase diagram represent solid-liquid, solid-vapor, solid-solid, and liquid-vapor equilibrium. 

The applicability of Eq. (21) rests on the validity of the assumption that the averages over internal and external variables are uncorrelated and thus can be calculated separately. Furthermore, theexpression of Eq. (21) emphasizes the close similarity of the irreducible Cartesian representation to the expression of the problem in terms of polar angles and the normalized 2nd rank spherical harmonics Y (see Eq. (7)). The corresponding polar angles ( (1), (t)) and (C(t), (t)), shown in Fig. 2B, describe the orientation of the internuclear vector and the magnetic field relative to the arbitrary reference frame, respectively. The different representations are related according to the following relationships.37... 

According to the definitions given in Fig. 12.5, the input/is not influenced by what happens in the system it is a so-called external variable. This is not true for the two elimination processes, O and RtoV Thus, in order to solve Eqs. 12-42 or 12-43 we have to determine how these terms depend on the system state. The only quantities which characterize the system state are (M or C. In fact, there is only one independent state variable since M and C are proportional to each other. 

The electrode potential, E, is the external variable driving electrode reactions, as appears in eqn. (80), but only the total potential difference between the electrode and electrolyte can be controlled and measured experimentally. Local distributions of potential at the electrode interface can only be taken into account through the use of a model for the electrical interface and the location of the reaction site. A calculation... 

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