Homogeneous spatial distribution

This study (34) implies that a right dispersion of rubber particles may permit optimum stress field overlap that affords lower craze-initiation stresses and therefore can rapidly dissipate the strain energy in the HIPS. A more homogeneous spatial distribution of rubber particles allow for a uniform development of crazes. Prevention of the strain localization phenomenon to avoid the detrimental situation, where crazes prefer to develop in certain areas and quickly lead to a catastrophic crack, could result in a larger total volume of crazed material. Further, Donald and Kramer (22) discovered no crazes nucleating from an isolated rubber particle with diameter smaller than 1 urn because of an insufficient size of stress-enhanced zone. Since Sample-A has a small average particle size it should contain a large number of small rubber particles. Two small rubber... 

Figure 1 Initial non-homogeneous spatial distribution of Ionisation events in spurs along the track, and evolution with time by diffusion and reaction up to homogeneous distribution at 10 s.

The ion track radius is also an important parameter in such reactions, reflecting the local spatial distribution of energy deposited by an incident ion and influencing the character of subsequent chemical reactions [8-12]. We recently reported on main-chain scission and crosslinking reactions in a variety of polymer systems and proposed chemical core sizes in ion tracks based on discussion of the non-homogeneous spatial distribution of reactions [9-15]. Intratrack crosslinking reactions are also of interest with respect to the potential for the direct formation of nano-structured materials, and materials exhibiting these reactions have been successfully visualized in recent years [11,13]. However, despite the extensive experimental and theoretical study undertaken to date, many factors in the relationship between the ion track structure and the chemical core radius remain unclear. This paper proposes a new formulation that determines the chemical core radius in an ion track based on the initial... 

In other studies, mercury concentrations were evalnated in surface sediments off the northwest coast of Baja Califomia (116.8 and 117.3 W 31.9 and 32.6°N) (Table 2), and results indicated a relatively homogenous spatial distribution of the metal. Hg enrichment occurred at four stations located in the northern and central... 

The idea of homogenous spatial distribution of the particles is based on the concept of well-stirred reactor. However, even microscopic reactions produce local nonhomogenities, which can not be always eliminated by diffusion. There are many contraversions about the stochastic formulation of reaction - diffusion systems. Three directions in the theory of random fields seem to be able to cope with such complexity the theory of random measures, the theory of stochastic partial differential equations relating to trajectories, and the theory of Hilbert space valued stochastic processes. The details are beyond of our scope. 

Great efforts are needed even in a laboratory to achieve a homogeneous spatial distribution of the concentrations, temperature and pressure of a system, even in a small volume (a few mm or cm ). Outside the confines of the laboratory, chemical processes always occur under spatially inhomogeneous conditions, where the spatial distribution of the concentrations and temperature is not uniform, and transport processes also have to be taken into account. Therefore, reaction kinetic simulations frequently include the solution of partial differential equations that describe the effect of chemical reactions, material diffusion, thermal diffusion, convection and possibly turbulence. In these partial differential equations, the term f defined on the right-hand side of Eq. (2.9) is the so-called chemical source term. In the remainder of the book, we deal mainly with the analysis of this chemical source term rather than the full system of model equations. 

Spatial information about a system can be obtained by analyzing the spatial distribution of PL intensity. Fluorescent tracers may be used to image chemical uptake in biological systems. Luminescence profiles have proven useftil in the semiconductor industry for mapping impurity distributions, dislocadons, or structural homogeneity in substrate wafers or epilayers. Similar spatial infbrmadon over small regions is obtained by cathodoluminescence imaging. 

Most room models contain only one zone air node, thus assuming perfect mixing of the zone air and a homogenous temperature distribution in the space. Spatial temperature variations, such as vertical temperature gradients, are not considered. For specific applications such as displacement ventilation or atria, models with several zone air nodes in the vertical direction have been developed. ... 

The concentrations of reactants are of little significance in the theoretical treatment of the kinetics of solid phase reactions, since this parameter does not usually vary in a manner which is readily related to changes in the quantity of undecomposed reactant remaining. The inhomogeneity inherent in solid state rate processes makes it necessary to consider always both numbers and local spatial distributions of the participants in a chemical change, rather than the total numbers present in the volume of reactant studied. This is in sharp contrast with methods used to analyse rate data for homogeneous reactions in the liquid or gas phases. 

Budgets and cycles can be considered on very different spatial scales. In this book we concentrate on global, hemispheric and regional scales. The choice of a suitable scale (i.e. the size of the reservoirs), is determined by the goals of the analysis as well as by the homogeneity of the spatial distribution. For example, in carbon cycle models it is reasonable to consider the atmosphere as one reservoir (the concentration of CO2 in the atmosphere is fairly uniform). On the other hand, oceanic carbon content and carbon exchange processes exhibit large spatial variations and it is reasonable to separate the... 

To assess homogeneity, the distribution of chemical constituents in a matrix is at the core of the investigation. This distribution can range from a random temporal and spatial occurrence at atomic or molecular levels over well defined patterns in crystalline structures to clusters of a chemical of microscopic to macroscopic scale. Although many physical and optical methods as well as analytical chemistry methods are used to visualize and quantify such spatial distributions, the determination of chemical homogeneity in a CRM must be treated as part of the uncertainty budget affecting analytical chemistry measurements. 

A different situation arises with a preliminary reduced surface. In this case the measured value of y is within lO - 10 2, and as the temperature increases, the y grows by the Arrhenius Law (Equation) with the activation energy of 5.2 kcal/mole. In addition, there is dependence of y upon the triplet oxygen pressure in the set-up, though the experiment conditions allow us to neglect a priori the impact of homogeneous processes on the spatial distribution of 02( A ) molecules. Prolonged... 

When droplets are initially not uniformly dispersed inside the flow cell, i.e. the emulsion is not homogeneous, the presence of a shear flow will induce mixing and the flow behavior of the system will be dependent on the spatial distribution of both phases. Therefore, in order to study the flow and mixing of an initially non-homogeneous emulsion it is necessary to obtain information on how both phases... 

Advection is important in fragmentation processes, and an initially homogeneous system may evolve spatial variations due to spatially dependent fragmentation rates. For example, Fig. 36 shows the spatial distribution of eroded clusters in the journal bearing flow operating under good mixing... 

More recently, Saez et al. [27] have carried out numerical simulations to characterize the ultrasonic field propagation and to obtain the spatial distribution of the mechanical effects. The model is based on the assumption of linear wave propagation in a homogeneous media and the results are based on the solution of the... 

Spatial distributions of AgPEO and AgPEC were found to be rather homogeneous throughout the lagoon and the sea samples. However, elevated concentrations were present in samples taken near an industrial area and near a shipyard. 

---