Multiplicity phenomena

Experiments with the system H2-02 were performed also by Horak et al. (21-23) who observed pronounced ignition-extinction phenomena. They were able to construct a reliable mathematical model based on the heat and mass balances describing the gas-to-solid heat and mass transfer. Their general conclusion is that the multiplicity phenomena may be explained in terms of thermokinetic theory. However, on the other hand, because of the high thermal capacity of the pellet, the oscillations cannot be described by this mechanism (72). Obviously we should examine a more detailed kinetic mechanism to be able to analyze successfully this phenomenon (25). 

After rewriting the Frank-Kamenetskii (32), Cardoso and Luss (33), and Aris (2) results the conditions governing the multiplicity phenomena are ... 

Sharma et al (28) point out that the simple mass and chemical series resistance model previously used by Schmitz and Amundsen (29) is completely inadequate for describing such a system, since it is precisely the complex nature of the interactions of diffusion and reaction which give rise to the complex reactor multiplicity phenomena. Sharma et al s analysis is somewhat incomplete since they do not evaluate the film/bulk interactions, nor do they make an appraisal of the validity of the Teramoto linearisation approximation. Again, this particular form of approximation could be highly inappropriate if the concentration of reagent B falls to zero in the mass transfer film. This probably occurs at their highest temperature steady states at a /M(1) value of around 100. 

Multiple phenomena contribute to irreversible losses in an actual fuel cell ... 

The actual fuel cell potential is decreased from its full potential, the Nemst potential, because of irreversible losses. Multiple phenomena contribute to irreversible losses in an actual fuel cell. Eor the hydrogen oxidation reaction, the func-tionahty of fuel cell voltage, E, is typically given by [42-44]... 

Significant gains in nnderstanding and predictive ability are envisioned to result from the development of multiscale simulation methods for the investigation of complicated systems that encompass behavior over wide ranges of time and length scales. Snch systems usually require a multidisciplinary approach. Often, multiscale simulations involve multiple phenomena that occur simultaneously with complex, subtle interactions that can confound intuition. While much... 

The multiplicity phenomenon in chemically reactive systems was first observed in 1918 by Liljenroth [1] for ammonia oxidation and it later appeared in the Russian literature of the 1940s [2]. However, it was not until the 1950s that major investigations of this phenomenon began. This development was inspired by the Minnesota school of Amundson and Aris and their students [3-5]. The Prague school also had a notable contribution in expanding the field [13-16]. 

When the kinetics of the reaction are non-monotonic and at the same time the system is non-isothermal, the situation may become complex especially for exothermic reactions. For non-monotonic kinetics multiplicity of the steady states may arise for isothermal as well as for mildly endothermic reactions =0, P <0. For exothermic reactions both concentration multiplicity (resulting from the nonmonotonic kinetics) as well as thermal multiplicity (resulting from the exothermicity of the reaction) are combined to give a slightly more complicated multiplicity phenomenon than discussed previously,... 

The phenomenon of parametric sensitivity is not directly related to the multiplicity phenomenon, for parametric sensitivity is found using plug flow pseudo-homogeneous models which, by definition, do not show multiplicity of the steady states. A good review of the phenomenon is given by Rajadhyaksha and Palekar (1984). More recent research on this problem include the extensive work of Westerterp and co-workers (e.g. Westerterp and Ptasinky, 1984a,b Westerterp el al., 1984 Westerterp and Overtoom, 1985). 

Stability, on the other hand, is strongly connected with the multiplicity phenomenon as discussed in chapter 4 for simple lumped parameter systems. In fixed bed catalytic reactors, the situation is much more complicated and may give rise to extremely complex behaviour. A relatively simple and practically oriented discussion of the problem is given by McGreavy (1984). 

It has been said that optimization of a transmission system is realizable only when a reasonably accurate channel model is available for investigating the power line network performance in detail (Biglieri et al., 2003). The model proposed by Hensen was straight forward. The attenuation was increasing with frequency and do not take into consideration the multiple phenomenon (Hensen Schulz, 2000). 

It is clear from Figure 3.9 that for an exothermic reaction, there is a possibility of three steady states (stationery nonequilibrium states), whereas for an endothermic reaction, there is only one steady state. For more information regarding this very important phenomenon (multiplicity phenomenon or bifurcation behavior), see Chapter 7. 

Mechanisms of Leukocyte Adsorption. The exact mechanism of leukocyte adhesion to filter media is not yet fuUy understood. Multiple mechanisms simultaneously contribute to the adhesion of cells to biomaterials, however, physical and biological mechanisms have been distinguished. Physical mechanisms include barrier phenomenon, surface tension, and electrostatic charge biological mechanisms include cell activation and cell to cell binding. 

Malaria is transmitted by the bite of an infected female Anopheles mosquito, one of the few species of the insect capable of carrying the human malaria parasite. The responsible protozoa ate from the genus P/asmodium of which only four of some 100 species can cause the disease in humans. The remaining species affect rodents, reptiles, monkeys, birds, and Hvestock. The species that infect humans are P/asmodium falciparum Plasmodium vivax Plasmodium malariae and Plasmodium ovale. Note that concomitant multiple malaria infections are commonly seen in endemic areas, a phenomenon that further compHcates choice of treatment. 

This speed becomes critical when the frequency of excitation is equal to one of the natural frequencies of the system. In forced vibration, the system is a function of the frequencies. These frequencies can also be multiples of rotor speed excited by frequencies other than the speed frequency such as blade passing frequencies, gear mesh frequencies, and other component frequencies. Figure 5-20 shows that for forced vibration, the critical frequency remains constant at any shaft speed. The critical speeds occur at one-half, one, and two times the rotor speed. The effect of damping in forced vibration reduces the amplitude, but it does not affect the frequency at which this phenomenon occurs. 

What has become an even greater concern in recent years is the phenomenon known as multiple chemical sensitivity disorder triggered by exposures to many chemicals in the environment. Synthetic chemicals are all around us. They are in the products we use, in the clothes we wear, in the food we eat, in the air we breathe at work. Because chemicals are everywhere in the environment, it is not possible to escape exposure. For this reason many people have become sensitized to the chemicals around them. In fact, it is estimated that 15% of the population has become sensitized to common household and commercial products. For some people the sensitization is not too serious a problem. They may have what appears to be a minor allergy to one or more chemicals. Other people are much more seriously affected. They may feel tired all the time, and suffer from mental confusion, breathing problems, sore muscles, and a weakened immune system. Such people suffer from a condition known as Multiple Chemical Sensitivity (MCS). 

S. Mourachov. Cellular automata simulation of the phenomenon of multiple crystallization. Comput Mater Sci 7 384, 1997. 

In general, enzymes are proteins and cany charges the perfect assumption for enzyme reactions would be multiple active sites for binding substrates with a strong affinity to hold on to substrate. In an enzyme mechanism, the second substrate molecule can bind to the enzyme as well, which is based on the free sites available in the dimensional structure of the enzyme. Sometimes large amounts of substrate cause the enzyme-catalysed reaction to diminish such a phenomenon is known as inhibition. It is good to concentrate on reaction mechanisms and define how the enzyme reaction may proceed in the presence of two different substrates. The reaction mechanisms with rate constants are defined as ... 

In all probability, further attempts at elucidating the physical background of the phenomenon of multiple desorption spectra will appear in the near future. 

Compared to the sum of covalent radii, metal-silicon single bonds are significantly shortened. This phenomenon is explained by a partial multiple bonding between the metal and silicon [62]. A comparison of several metal complexes throughout the periodic table shows that the largest effects occur with the heaviest metals. However, conclusions drawn concerning the thermodynamic stability of the respective M —Si bonds should be considered with some reservation [146], since in most cases the compared metals show neither the same coordination geometries nor the same oxidation states. 

Methods of disturbing the Boltzmann distribution of nuclear spin states were known long before the phenomenon of CIDNP was recognized. All of these involve multiple resonance techniques (e.g. INDOR, the Nuclear Overhauser Effect) and all depend on spin-lattice relaxation processes for the development of polarization. The effect is referred to as dynamic nuclear polarization (DNP) (for a review, see Hausser and Stehlik, 1968). The observed changes in the intensity of lines in the n.m.r. spectrum are small, however, reflecting the small changes induced in the Boltzmann distribution. 

A spin-gas microscopic theory has been pursued by Berker et al. [32] to explain the multiplicity of smectic ordering and the re-entrance phenomenon in strongly polar mesogens. They have used a model Hamiltonian of the form... 

Among the theories of limited applicability, those of heterogeneous catalysis processes have been most developed (4, 5, 48). They are based on the assumption of many active sites with different activity, the distribution of which may be either random (23) or thermodynamic (27, 28, 48). Multiple adsorption (46, 47) and tunnel effects (4, 46) also are considered. It seems, however, that there is in principle no specific feature of isokinetic behavior in heterogeneous catalysis. It is true only that the phenomenon has been discovered in this category and that it can be followed easily because of large possible changes of temperature. 

Because of nonlinear Interactions between buoyancy, viscous and Inertia terms multiple stable flow fields may exist for the same parameter values as also predicted by Kusumoto et al (M.). The bifurcations underlying this phenomenon may be computed by the techniques described In the numerical analysis section. The solution structure Is Illustrated In Figure 7 In terms of the Nusselt number (Nu, a measure of the growth rate) for varying Inlet flow rate and susceptor temperature. Here the Nusselt number Is defined as ... 

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