Forced Dynamic Phenomena

A wide class of forced unsteady-state processes have already been realized on the commercial scale using specific dynamic phenomenon, that takes place during performance of an exothermic reaction in a fixed bed of catalyst. This phenomenon is referred to in the literature as wrong-way behavior of a fixed bed reactor [20]. Substantial differences in characteristic times of heat and mass transfer in a packed bed reactor result in a surprising rise of temperature inside the reactor after... 

Electrolytic gas evolution is a dynamic phenomenon affected by interactions among all the process variables. The interaction of the potential, electrode, and electrolyte not only determines the rate at which gas is evolved, but also affects the contact angles of the bubbles that determine, in conjunction with the electrolyte surface tension, the fundamental forces binding the bubbles to the electrode. Since the process occurs at a surface, small quantities of impurities may have a large effect. The dynamics of bubble evolution... 

Ballistic impact is a complex dynamic phenomenon. Consequently its analysis is complex and therefore beyond of the scope of this paper. However, a first-order, quasi-static prediction of impact force will be described briefly and made in this paper based on a previous work [10]. Right before and after impact, the overall energy balance may hold [10] ... 

Further support for this approach is provided by modern computer studies of molecular dynamics, which show that much smaller translations than the average inter-nuclear distance play an important role in liquid state atom movement. These observations have conhrmed Swalin s approach to liquid state diffusion as being very similar to the calculation of the Brownian motion of suspended particles in a liquid. The classical analysis for this phenomenon was based on the assumption that the resistance to movement of suspended particles in a liquid could be calculated by using the viscosity as the frictional force in the Stokes equation... 

The main goal of this report is to present a phenomenon of highly general nature manifested in various dynamical systems. We present the occurrence of peculiar quantization by the parameter of intensity of the excited oscillations and we show that given unchanging conditions it is possible to excite oscillations with a strictly defined discrete set of amplitudes the rest of the amplitudes being forbidden . The realization of oscillations with a specific amplitude from the permitted discrete set of amplitudes is determined by the initial conditions. The occurrence of this unusual property is predetermined by the new general initial conditions, i.e. the nonlinear action of the external excited force with respect to the coordinate of the system subjected to excitation. 

Mechanistic Ideas. The ordinary-extraordinary transition has also been observed in solutions of dinucleosomal DNA fragments (350 bp) by Schmitz and Lu (12.). Fast and slow relaxation times have been observed as functions of polymer concentration in solutions of single-stranded poly(adenylic acid) (13 14), but these experiments were conducted at relatively high salt and are interpreted as a transition between dilute and semidilute regimes. The ordinary-extraordinary transition has also been observed in low-salt solutions of poly(L-lysine) (15). and poly(styrene sulfonate) (16,17). In poly(L-lysine), which is the best-studied case, the transition is detected only by QLS, which measures the mutual diffusion coefficient. The tracer diffusion coefficient (12), electrical conductivity (12.) / electrophoretic mobility (18.20.21) and intrinsic viscosity (22) do not show the same profound change. It appears that the transition is a manifestation of collective particle dynamics mediated by long-range forces but the mechanistic details of the phenomenon are quite obscure. 

Thereafter, the dynamic mixing behaviors of fine cohesive particles adhered to the surface of a coarser excipient was discussed as considerable importance in the manufacture of solid pharmaceuticals (3). The term ordered mixing was given to this phenomenon by Hersey (4). An ordered mixture can be produced by a dry process, simple dry mixing of fine and coarse particles. When interparticle interactions, such as van der Waals and coulombic forces, exist between the two types of particles, the fine particle adheres to the surface of the coarse particle that is, an ordered mixture spontaneously forms. As described earlier, ordered mixing... 

This phenomenon of increased conversion, yield and productivity through deliberate unsteady-state operation of a fermentor has been known for some time. Deliberate unsteady-state operation is associated with nonautonomous or externally forced systems. The unsteady-state operation of the system (periodic operation) is an intrinsic characteristic of this system in certain regions of the parameters. Moreover, this system shows not only periodic attractors but also chaotic attractors. This static and dynamic bifurcation and chaotic behavior is due to the nonlinear coupling of the system which causes all of these phenomena. And this in turn gives us the ability to achieve higher conversion, yield and productivity rates. 

The fourth term on the right hand side of (3.4) represents the elastic forces on each Brownian particle due to its neighbours along the chain the forces ensure the integrity of the macromolecule. Note that this term in equation (3.4) can be taken to be identical to the similar term in equation for dynamic of a single macromolecule due to a remarkable phenomenon - screening of intramolecular interactions, which was already discussed in Section 1.6.2. The last term on the right hand side of (3.4) represents a stochastic thermal force. The correlation function of the stochastic forces is connected... 

An analysis of the recent observation data [30,31] shows that baroclinic Rossby waves that are generated off the eastern coasts in the northern parts of the Pacific and Atlantic oceans in a period of about a year represent their dominant non-stationary dynamical response to the annual cycle of the atmospheric forcing in the latitudinal range from 10-15° to 45-50°N. In so doing, their mean phase velocities (0.02-0.03 ms 1 at 40-45°N) are higher than the theoretical values (about 0.01 ms-1). A similar situation is observed in the Black Sea as well [27]. In [32], several reasons of this phenomenon were listed such as the interaction with more large-scale non-stationary processes, topographic and nonlinear effects, and insufficient duration and spatiotemporal resolution of the observation data. 

As in the case of soil physics, we note that in comprehending this phenomenon we must learn the behavior of small particles in flowing media. What are the forces causing their movement, and what are their magnitudes These are questions bearing upon particle-dynamics, although considerably complicated. 

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