Quasi-uniform distribution

The quasi-one-dimensional model used in the previous sections for analysis of various characteristics of fiow in a heated capillary assumes a uniform distribution of the hydrodynamical and thermal parameters in the cross-section of micro-channel. In the frame of this model, the general characteristics of the fiow with a distinct interface, such as position of the meniscus, rate evaporation and mean velocities of the liquid and its vapor, etc., can be determined for given drag and intensity of heat transfer between working fluid and wall, as well as vapor and wall. In accordance with that, the governing system of equations has to include not only the mass, momentum and energy equations but also some additional correlations that determine... 

Assuming a quasi-uniform power distribution in the throughput or in the volume, a characteristic length of the dispersion space becomes irrelevant. In the relevance list, Eq. (45), the parameter d must be cancelled. The target number Os = d Jd has to be dropped and the dimensionless numbers La and Oh have to be built by 6(32 instead of d. At given and constant material conditions (()/p,A pb/p-j, tp, Ci = const) the process characteristics will be represented in the following pi space ... 

Fig. 15.13. Spontaneous formation of quasi-regular concentric waves in a heterogenous medium. Plotted are the simulation results in a 2-dimensional lattice (15.11) of 150x150 predator-prey oscillators (15.6) with periodic boundary conditions at 6 consecutive time instances (from a to f) starting from homogeneous initial conditions. Plotted is the density of the prey as grey level. Parameters K = 3, k = 3.5, x = b = 1, 5 = 1, e = 0.1, C = diag(l, 1). Growth rates o are taken from a uniform distribution in the range 5 0.4.

The model of the operation process of the complex technical system with the distinguished their operation states is proposed in (Kolowrocki Soszynska, 2008). The semi-markov process is used to construct a general probabilistic model of the considered complex industrial system operation process. To construct this model there were defined the vector of the probabilities of the system initial operation states, the matrix of the probabilities of transitions between the operation states, the matrix of the distribution functions and the matrix of the density functions of the conditional sojourn times in the particular operation states. To describe the system operation process conditional sojourn times in the particular operation states the uniform distribution, the triangular distribution, the double trapezium distribution, the quasi- trapezium distribution, the exponential distribution, the WeibuU s... 

The nucleolytic activity is somewhere between the processive and distributive modes, and the degradation of DNA occurs quasi-uniformly from both 3 and 5 termini. Nevertheless, there are some sequence-dependent stops at the GC-rich... 

The present model takes into account how capillary, friction and gravity forces affect the flow development. The parameters which influence the flow mechanism are evaluated. In the frame of the quasi-one-dimensional model the theoretical description of the phenomena is based on the assumption of uniform parameter distribution over the cross-section of the liquid and vapor flows. With this approximation, the mass, thermal and momentum equations for the average parameters are used. These equations allow one to determine the velocity, pressure and temperature distributions along the capillary axis, the shape of the interface surface for various geometrical and regime parameters, as well as the influence of physical properties of the liquid and vapor, micro-channel size, initial temperature of the cooling liquid, wall heat flux and gravity on the flow and heat transfer characteristics. 

Significant simplification of the governing equations may be achieved by using a quasi-one-dimensional model for the flow. Assume that (1) the ratio of meniscus depth to its radius is sufficiently small, (2) the velocity, temperature and pressure distributions in the cross-section are close to uniform, and (3) all parameters depend on the longitudinal coordinate. Differentiating Eqs. (8.32-8.35) and (8.37) we reduce the problem to the following dimensionless equations ... 

Textural mesoporosity is a feature that is quite frequently found in materials consisting of particles with sizes on the nanometer scale. For such materials, the voids in between the particles form a quasi-pore system. The dimensions of the voids are in the nanometer range. However, the particles themselves are typically dense bodies without an intrinsic porosity. This type of material is quite frequently found in catalysis, e.g., oxidic catalyst supports, but will not be dealt with in the present chapter. Here, we will learn that some materials possess a structural porosity with pore sizes in the mesopore range (2 to 50 nm). The pore sizes of these materials are tunable and the pore size distribution of a given material is typically uniform and very narrow. The dimensions of the pores and the easy control of their pore sizes make these materials very promising candidates for catalytic applications. The present chapter will describe these rather novel classes of mesoporous silica and carbon materials, and discuss their structural and catalytic properties. 

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