Hill-type model

In a Hill-type model, muscle s force-producing properties are described by four parameters... 

The muscle model identification problem can be categorized by the following factors (1) time domain continuous-time or discrete-time models (2) input types stimulus period (SP), that is, pulse frequency modulation, pulse width (PW) modulation, or a combination of the two (3) model outputs for example, muscle torque or force and muscle length or position (4) loading conditions isometric or nonisometric loads and load transitions and (5) model type linear models, nonlinear Hill-type models, and other nonlinear models. 

Similar to Eq. (67), the first reaction (incorporating the enzyme phosphofructo-kinase) exhibits a Hill-type inhibition by its substrate ATP [126]. The overall ATP utilization v3 (ATP) is modeled by a saturable Michaelis Menten function. The system is specified by five kinetic parameters (with Gx lumped into Vm ), the Hill coefficient n, and the total concentration, 4 / = [ATP] + [ADP]. Note that the model is not intended to capture biological realism, rather it serves as a paradigmatic example to identify dynamic behavior in metabolic pathways. 

Walters, S., Skrzeczynski, B., Whiting, T., Bunting, F., Arnold, G. 2002. Discovery and geology of the Cannington Au-Pb-Zn deposit, Mount Isa Eastern Succession, Australia development and application of an exploration model for Broken Hill-type deposits. Special Publication (Society of Economic Geologists U.S.), 9, 95-118. 

Crucial to the mechanism of oscillations in the model is the negative feedback exerted by nuclear PER on the production of per mRNA. This negative feedback will be described by an equation of the Hill type in which n denotes the degree of cooperativity, and the threshold repression constant. To simplify the model, we consider that behaves directly as a repressor activation of a repressor upon binding of would not significantly alter the results (see Sinha Ramaswamy, 1988). 

The modeling and control of movements in this chapter relates to external control of muscles via so-called functional electrical stimulation. Macroscopic viscoelastic models started from the observation that the process of electrical stimulation transforms the viscoelastic material from a compliant, fluent state into the stiff, viscous state. Levin and Wyman [35] proposed a three-element model— damped and undamped elastic element in series. Hill s work [36] demonstrated that the heat transfer depends upon the type of contraction (isometric, slow contracting, etc). The model includes the force generator, damping and elastic elements. Winters [37] generalized Hill s model in a simple enhancement of the original, which... 

The operational model allows simulation of cellular response from receptor activation. In some cases, there may be cooperative effects in the stimulus-response cascades translating activation of receptor to tissue response. This can cause the resulting concentration-response curve to have a Hill coefficient different from unity. In general, there is a standard method for doing this namely, reexpressing the receptor occupancy and/or activation expression (defined by the particular molecular model of receptor function) in terms of the operational model with Hill coefficient not equal to unity. The operational model utilizes the concentration of response-producing receptor as the substrate for a Michaelis-Menten type of reaction, given as... 

Pedersen Device. An invention of the US arms designer J.D. Pedersen, this was a noteworthy ordnance secret of WWI. It consisted of a receiver unit that could be locked into the receiver of a Springfield or Enfield rifle. Installed, it converted the rifle into a semiautomatic weapon that fired. 30 cal pistol-type cartridges from a 40-round box magazine. To hide its identity, the mechanism was officially listed as the US. 30 cal automatic pistol Model 1918. The system was dropped after the war Ref J. Quick, Dictionary of Weapons and Military Terms , McGraw-Hill, NY (1973), 342... 

Expression in Eq. (19) is within 8% of all simulation data up to Re — 1000. Since this relation has been derived very recently (Beetstra et al., 2006), it has not been applied yet in the higher scale models discussed in Sections III and IV. However, the expression by Hill et al. in Eq. (47) derived from similar type of LBM simulations is consistent with our data, in particular when compared to the large deviations with the Ergun and Wen and Yu equations. So, we expect that the simulation results presented in Section IV.F using the Hill et al. correlation will not be very different from the results that would be obtained with expression in Eq. (19). A more detailed account of the derivation of expression in Eq. (19) and a comparison with other drag-force relations can be found in Ref. Beetstra et al. (2006). 

In CRE textbooks (Hill 1977 Levenspiel 1998 Fogler 1999), the types of reactors considered in this book are referred to as non-ideal. The flow models must take into account fluid-mixing effects on product yields. 

The preservation of near-surface to exposed kimberlitic bodies in the Buffalo Head Hills kimberlite field of northern Alberta (Fig. 1) provides an opportunity to contribute to the setting in which Class 2-type kimberlites are emplaced. This information will enhance our ability to model and evaluate known Class 2 kimberlite deposits, and to discover new fields of kimberlite within the WCSB. 

One can consider product optimization as a type of "hill climbing." The product models in Table 4 each represent a hill or a surface, with one hill or surface for each attribute. 

Concurrent flow of liquid and gas can be simulated by the homogeneous model of Section 6.8.1 and Eqs. 6.109 or 6.112, but several adequate correlations of separated flows in terms of Lockhart-Martinelli parameters of pipeline flow type are available. A number of them is cited by Shah (Gas-Liquid-Solid Reactor Design, McGraw-Hill, New York, 1979, p. 184). The correlation of Sato (1973) is shown on Figure 6.9 and is represented by either... 

An entirely distinct series of model complexes has been carried out in order to show that metal porphyrins will actually bind to the type of substrate with which P-450 interacts. Hill, Macfarlane, Mann, and Williams (51) have studied molecular complex formation between such molecules as quinones and sterols and several metal porphyrins. The complexes between some of the porphyrins and sterols are remarkable strong. At the same time they have devised NMR methods for the elucidation of the structures of these complexes. 

McEachern JC, Shaw CA (1996) An alternative to the LTP orthodoxy a plasticity-pathology continuum model. Brain Res Brain Res Rev 22(1) 51—92 Mackie K, Lai Y, Westenbroek R, Mitchell R (1995) Cannabinoids activate an inwardly rectifying potassium conductance and inhibit Q-type calcium currents in AtT20 cells transfected with rat brain cannabinoid receptor. J Neurosci 15(10) 6552—61 Mackie K, Devane WA, Hille B (1993) Anandamide, an endogenous cannabinoid, inhibits calcium currents as a partial agonist in N18 neuroblastoma cells. Mol Pharmacol 44(3) 498-503 Mackie K, Hille B (1992) Cannabinoids inhibit N-type calcium channels in neuroblastoma-glioma cells. Proc Natl Acad Sci USA 89(9) 3825-9... 

It is helpful to contrast the view we adopt in this book with the perspective of Hill (1986). In that case, the normative example is some separable system such as the polyatomic ideal gas. Evaluation of a partition function for a small system is then the essential task of application of the model theory. Series expansions, such as a virial expansion, are exploited to evaluate corrections when necessary. Examples of that type fill out the concepts. In the present book, we establish and then exploit the potential distribution theorem. Evaluation of the same partition functions will still be required. But we won t stop with an assumption of separability. On the basis of the potential distribution theorem, we then formulate additional simplified low-dimensional partition function models to describe many-body effects. Quasi-chemical treatments are prototypes for those subsequent approximate models. Though the design of the subsequent calculation is often heuristic, the more basic development here focuses on theories for discovery of those model partition functions. These deeper theoretical tools are known in more esoteric settings, but haven t been used to fill out the picture we present here. 

On the basis of the known structure for c-type lysozyme and the nature of the groups involved in its catalytic activity, and early models of a-lactalbumin structure, there were good structural reasons that militated against a-lactalbumin having lytic activity. This point of view was well developed in the useful reviews by Hill and Brew (1975) and by Brew and Hill (1975). Recent X-ray structural determinations for a-... 

Important trends in N2 isotherm when the PS beads are used as a physical template are shown in Table 1 and Fig. 2. In Table 1, PI is the alumina prepared without any templates, P2 is prepared without ]4iysical template (PS bead), P3 is prepared without chemical template (stearic acid), and P4 is prepared with all templates. For above 10 nm of pore size and spherical pore system, the Barrett-Joyner-Halenda (BJH) method underestimates the characteristics for spherical pores, while the Broekhoff-de Boer-Frenkel-Halsey-Hill (BdB-FHH) model is more accurate than the BJH model at the range 10-100 nm [13]. Therefore, the pore size distribution between 1 and 10 nm and between 10 and 100 nm obtained from the BJH model and BdB-FHH model on the desorption branch of nitrogen isotherm, respectively. N2 isotherm of P2 has typical type IV and hysteresis loop, while that of P3 shows reduced hysteresis loop at P/Po ca. 0.5 and sharp lifting-up hysteresis loop at P/Po > 0.8. This sharp inflection implies a change in the texture, namely, textural macro-porosity [4,14]. It should be noted that P3 shows only macropore due to the PS bead-free from alumina framework. 

Figure 5-2 The plot of the misfit functional value as a function of model parameters tn. The vector of the steepest ascent, l(m ), shows the direction of "climbing on the hill" along the misfit functional surface. The intersection between the vertical plane P drawn through the direction of the steepest descent at point m and the misfit functional surface is shown by a solid parabola-type curve. The steepest descent step begins at a point 0(m ) and ends at a point 0(m +i) at the minimum of this curve. The second parabola-type curve (on the left) is drawn for one of the subsequent iteration points. Repeating the steepest descent iteration, we move along the set of mutually orthogonal segments, as shown by the solid arrows in the space M of the model parameters.

An example of a model nonlinear in parameters is Eq. (7-166). Here it is not possible through any number of transformations to obtain a linear form in all the parameters k0, E, K o, Eaa, Km, Ea. Note that for some Langmuir-Hinshelwood rate expressions it is possible to linearize the model in parameters at isothermal conditions and obtain the kinetic constants for each temperature, followed by Arrhenius-type plots to obtain activation energies (see, e.g., Churchill, The Interpretation and Use of Piate Data The Rate Concept, McGraw-Hill, 1974). 

---