Source, continuous distribution

A similar acoustic technique was applied by Pickles and Bittleston (1983) to investigate blast produced by an elongated, or cigar-shaped, cloud. The cloud was modeled as an ellipsoid with an aspect ratio of 10. The explosion was simulated by a continuous distribution of volume sources along the main axis with a strength proportional to the local cross-sectional area of the ellipsoid. The blast produced by such a vapor cloud explosion was shown to be highly directional along the main axis. 

Frank-Kamenetskii first considered the nonsteady heat conduction equation. However, since the gaseous mixture, liquid, or solid energetic fuel can undergo exothermic transformations, a chemical reaction rate term is included. This term specifies a continuously distributed source of heat throughout the containing vessel boundaries. The heat conduction equation for the vessel is then... 

Gaseous emission of Infrared radiation differs in character from solid emission in that the tenner consists of discrete spectrum lines or bands, with significant discontinuities, while the latter shows a continuous distribution of energy throughout the spectrum. The predominant source or molecular radiation in the infrared is the result of vibration of the molecules in characteristic modes. Energy transitions between various stales of molecular rotation also produce infrared radiation. Complex molecular gases radiate intricate spectra, which may be analyzed to give information of the nature of the molecules or of the composition of the gas. 

Diffusion Pattern from a Continuous Point Source—The distribution of particles from a point source in a moving fluid can be determined provided we assume that the concentration gradients in the direction of fluid motion are small compared to those at right angles to it. If C, is defined as the concentration of particles over a unit area of a plane horizontal surface downstream and to one side of the mean path of the diffusing stream from a point source, then the equation of diffusion at any point x downstream and at a distance y from the mean path is... 

In general, there is no principal difference in the diffraction phenomena using the synchrotron and conventional x-ray sources, except for the presence of several highly intense peaks with fixed wavelengths in the conventionally obtained x-ray spectrum and their absence, i.e. the continuous distribution of photon energies when using synchrotron sources. Here and throughout the book, the x-rays from conventional sources are of concern unless noted otherwise. 

In the following section we will deal with an example of homogeneous heat sources. The internal heat development is continuously distributed over the whole body. In the section after that we will discuss local heat sources where the heat development is concentrated at a point or a line in the heat conducting body. 

Beer s law strictly applies only when measurements are made with monochromatic radiation. In practice, polychromatic sources that have a continuous distribution of wavelengths are used in conjunction with a grating or with a filter to isolate a nearly symmetric band of wavelengths around the wavelength to be employed (see Section 25A-3). 

Using a continuum rather than cellular model implies that the growing foam is regarded as a fluid with a continuously distributed source of flow. Hence, the flow rate is also a function of position the (hydrodynamic) pressure gradient is resulted from inertia, gravity and stress mechanisms operating in the fluid. 

Several field tests of the IL method have demonstrated that it is a practically useful tool for inferring the canopy source-sink distributions of scalars such as water vapor, heat, CO2, and ammonia. However, there is a continuing need for improvement in the knowledge of the turbulence field in the canopy and its use in determining Dj, and also in the inversion procedure to improve the robustness of the method. 

Additional information about seed dispersal is contained in the fossil record. Dispersal events can be inferred wherever there is evidence that populations were founded at large distances from the source population. It is, of course, technically difficult to detect a small population using fossil pollen or macrofossils, and even more difficult to demonstrate that the small population was isolated from the main population (Davis et al., 1991). Pollen studies in Sweden, however, record the establishment of individual colonies of beech (Fagus sylvatica) in the late Holocene (Bjorkman, 1996) and macrofossils demonstrate that populations of spruce (Picea abies) grew far in advance of the expanding species front for thousands of years (Kullman, 1996). East of James Bay, Canada, small colonies of larch (Larix laricina) have become established in patches during the past 1500 years as the population has expanded. Some of these colonies have fused into a continuous distribution. 

Applications of these tunable VUV sources continue to be mostly in the detection of atoms and small molecules by laser-induced fluorescence in molecular beam scattering studies. Of particular importance has been the improved intensities available from Mg vapor, so that it will be possible, for example, to study the internal energy distributions in CO molecules following scattering from surfaces. This capability for both very sensitive and state-selective detection of small molecules will lead to important advances in our understanding of molecular interactions at surfaces. 

Sources and Distributions of Polycyclic Aromatic Hydrocarbons and Toxicity Table 1 (Continued)... 

Synthetic copolymers are always polydisperse, i.e. they consist of a large number of similar chemical species with different molar masses and different chemical composition. Further sources of polydispersity are differences in the number of short- and long-chain branches, tactidty, sequence length, and other characterization variables. When block copolymers are considered, additional polydispersities, for example, in block length, in the number of blocks, and in the arrangement of blocks, have to be taken into account. Owing to this polydispersity, characterization of copolymers does not usually provide the number of the individual molecules or their mole fractions, mass fractions, etc. but requires the use of continuous distribution functions or their averages. 

Let us consider the interdiffusion process in a coarsened spatial scale, regarding vacancies sources/sinks as continuously distributed in an alloy. We take account of their action as a sink/source term in the equation for vacancy redistribution ... 

The history and fundamentals of continuous thermodynamics will be briefly presented here and has been discussed in detail elsewhere. Before the 1980 s many authors applied continuous distribution functions to specific cases of non-equilibrium thermodynamics, statistical thermodynamics, the VLE of petroleum fractions and the LLE of polydisperse polymer systems. Starting in 1980 a consistent version of chemical thermodynamics directly based on continuous distribution functions was developed and called continuous thermodynamics. The work of Kehlen and Ratzsch," " Gualtieri et al., Salacuse and Stell, Briano and Glandt," are to be mentioned as sources of information. In the following years several groups applied continuous thermodynamics to nearly all important types of polydisperse systems." Cotterman and Prausnitz reviewed the literature up until about 1990. In the 1980 s continuous modelling of phase equilibria was mostly focused on polymer systems, petroleum fractions and natural gases. In the last ten years, this has been expanded to also include problems with asphaltene precipitation from crude oils and wax precipitation from hydrocarbon mixtures. In section 9.4 the more recent papers are discussed. 

This general result due to a discrete distribution of sources may be generalized to a continuous distribution. Thus if total number of neutrons produced isotropically per unit time in volume dr about space point r, then we define... 

This integral satisfies Equation 2-7 for pressure, since the governing equation is linear. Physically, Equation 2-10 represents the pressure for a continuously distributed line source, where H is a crucial integration constant. 

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