Dynamics, term

Generally speaking, neither dynamical, nor relaxation parts of (A7.20) are diagonal over index q. It is simpler to diagonalize the dynamical term, proceeding to the GF, where scalar product (j L) = (JzLq) =... 

With complex kinetics a steady-state split boundary problem of the type of Example ENZSPLIT may not converge satisfactorily. To overcome this, the problem may be reformulated in the more natural dynamic form. Expressed in dynamic terms, the model relations become. 

For a more detailed analysis of measured transport restrictions and reaction kinetics, a more complex reactor simulation tool developed at Haldor Topsoe was used. The model used for sulphuric acid catalyst assumes plug flow and integrates differential mass and heat balances through the reactor length [16], The bulk effectiveness factor for the catalyst pellets is determined by solution of differential equations for catalytic reaction coupled with mass and heat transport through the porous catalyst pellet and with a film model for external transport restrictions. The model was used both for optimization of particle size and development of intrinsic rate expressions. Even more complex models including radial profiles or dynamic terms may also be used when appropriate. 

We have used an ordinary derivative since t is the only independent variable in this lumped system. The units of this component continuity equation are moles of A per unit time. The left-hand side of the equation is the dynamic term. The first two terms on the right-hand side are the convective terms. The last term is the generation term. 

The feedforward controller contains a stcadyslate gain and dynamic terms. For this system the dynamic element is a first-order lead-lag. The unit step reaponae of this lead-lag is an initial change to a value that is (—followed by an exponential rise or decay to the final steadystate value... 

The application of force to a stationary or moving system can be described in static, kinematic, or dynamic terms that define the mechanical similarity of processing equipment and the solids or liquids within their confines. Static similarity relates the deformation under constant stress of one body... 

The application of force to a stationary or moving system can be described in static, kinematic, or dynamic terms that define the mechanical similarity of processing equipment and the solids or liquids within their confines. Static similarity relates the deformation under constant stress of one body or structure to that of another it exists when geometric similarity is maintained even as elastic or plastic deformation of stressed structural components occurs [53], In contrast, kinematic similarity encompasses the additional dimension of time, while dynamic similarity involves the forces (e.g., pressure, gravitational, centrifugal) that accelerate or retard moving masses in dynamic systems. The inclusion of tune as another dimension necessitates the consideration of corresponding times, t and t, for which the time scale ratio t, defined as t = t It, is a constant. 

In this section we develop a dynamic model from the same basis and assumptions as the steady-state model developed earlier. The model will include the necessarily unsteady-state dynamic terms, giving a set of initial value differential equations that describe the dynamic behavior of the system. Both the heat and coke capacitances are taken into consideration, while the vapor phase capacitances in both the dense and bubble phase are assumed negligible and therefore the corresponding mass-balance equations are assumed to be at pseudosteady state. This last assumption will be relaxed in the next subsection where the chemisorption capacities of gas oil and gasoline on the surface of the catalyst will be accounted for, albeit in a simple manner. In addition, the heat and mass capacities of the bubble phases are assumed to be negligible and thus the bubble phases of both the reactor and regenerator are assumed to be in a pseudosteady state. Based on these assumptions, the dynamics of the system are controlled by the thermal and coke dynamics in the dense phases of the reactor and of the regenerator. 

The above experimental developments represent powerful tools for the exploration of molecular structure and dynamics complementary to other techniques. However, as is often the case for spectroscopic techniques, only interactions with effective and reliable computational models allow interpretation in structural and dynamical terms. The tools needed by EPR spectroscopists are from the world of quantum mechanics (QM), as far as the parameters of the spin Hamiltonian are concerned, and from the world of molecular dynamics (MD) and statistical thermodynamics for the simulation of spectral line shapes. The introduction of methods rooted into the Density Functional Theory (DFT) represents a turning point for the calculations of spin-dependent properties [7],... 

The drug-induced regressions resemble the original psychoses so precisely, that at the beginning of the study the treatment team (including the ward director) always explained the decompensation in plausible dynamic terms. Often, the patient himself agreed with the dynamic... 

Further he shows that the dynamic-coupling term runs more or less parallel with the static coupling term. The dynamic term becomes more important if the covalency increases. Under certain conditions both terms are of comparable magnitude. We will present the final result below. 

The effective interaction diameter approximation also allows the three-body correlation and perturbed two-body dynamics terms to be written... 

In order to investigate heteroatom effects on pericyclic reactions or on the behavior of aromatic systems, it is sufficient to consider the dynamic term of eq (7). 

The Dynamic Terms in Induced Circular Dichroism. D.P. Craig, E.A. Power and T. Thirunamachandran. Proc. Roy. Soc. A348, 19-38 (1976). 

These effects stem from thermodynamic principles. If in a separation with a given purity requirement the peak resolution is not high enough due to these effects there is no way to overcome this problem by increasing column efficiency, which means optimizing the fluid-dynamic term of the resolution equation (Eq. 2.33). If a tag-along effect occurs the use of a smaller particle diameter has no effect, as long as the... 

For this reason, the energy shift (34) is often termed the static mechanism because no net energy is transferred between the pair and for its dependence on static moments and static electric dipole-dipole coupling. It arises when either or both species are polar, in contrast to the dynamic term which occurs for nonpolar A and B. Note that the static term vanishes if either A or B is centrosymmetric as both the permanent moment and hyperpolarizability are zero for such species. 

The total laser-induced intermolecular energy shift is given by the sum of the two contributions (31) and (34) and applies for radiation propagating in a fixed direction relative to the two oriented molecules. A molecular average can be carried out for all possible orientations of A and B relative to each other. In this case, the static contribution (34) vanishes while the dynamic term becomes... 

To analyze this problem, we need to go back to a statement of the problem in general fluid dynamical terms. Thus we begin by restating the governing equations and boundary conditions for an oscillating bubble in a quiescent, incompressible fluid. These are the Navier-Stokes and continuity equations the three boundary conditions... 

Term in Eqs. (13.1) and (13.2)). The difference between panels a and b is a gating motion that reduces the distance between the two wells along the HC axis (ch) away from its equilibrium value (qj). This motion increases the probability of tunneling at the (nearly) degenerate configuration q (active dynamics term in Eqs. (13.1) and (13.2)). 

For a higher degree of generality than the strictly steady state analysis of this book, the unsteady state models are developed to show very briefly, some of the transient characteristics of the system. The steady state models which are the main concern of this book are obtained by omitting the dynamic terms. The model developed in this section is a distributed model. 

Any model for the biochemical oscillator controlling the onset of mitosis should account for the fact that, in some cells or at certain stages of development, mitosis can be prevented and cells cease to divide. In dynamic terms, such a transient or permanent suppression of mitotic activity can be viewed as a switch of the mitotic control system from an oscillatory into a nonoscillatory regime corresponding to a stable steady state. Models for the mitotic oscillator allow the discussion of possible mechanisms whereby the mitotic clock might be arrested. 

An example of a rhythm for which the existence of a limit cycle can still be questioned is the process of ovulation. A theoretical model shows (Lacker, 1981 Lacker, Feuer Akin, 1989) how the follicular phase of the menstrual cycle can be viewed in dynamic terms as the selection of an oocyte leading, in about two weeks, to ovulation. The latter, discontinuous process is followed by the degeneration of the luteal body, which corresponds to the luteal phase of the cycle. After the end of that phase, a new follicular phase begins. The periodicity of 28 days of the menstrual cycle in women thus follows from the succession of the follicular and luteal phases, each of which lasts 14 days. Separating these phases is the brief discontinuity of ovulation. The absence of ovulation is necessarily linked to the arrest of the hormonal rhythms observed in the course of a normal cycle. 

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