Diffusion extended source

Figure 3-6 Diffusion in an infinite medium with an extended source, (a) The extended source with width 5 = 1 mm (b) the solution.

Diffusion in an infinite medium with an extended source... 

For one-dimensional diffusion in an infinite medium with constant D, if the initial condition is an extended source, meaning C is finite in a region ( 8, 8), and 0 outside the region (Figure 3-6a) ... 

In actual practice, any tubular light source will have a finite diameter and will not behave as a true line source. Radiation from an extended light source will emanate from points displaced from the lamp s axis, causing the lamp to appear rather like a diffuse light source. In addition, imperfections in the... 

The Milagro detector s large field of view and continuous duty cycle make it an ideal instrument for the discovery of previously unknown sources. Recent publications cover topics including detection of the Crab Nebula[l], limits on TeV emission from GRB [2] and a TeV all-sky survey of the northern celestial hemisphere[3]. Recently we have presented papers on the detection of diffuse TeV emission from the Galactic plane[4], limits on TeV emission from satellite detected GRB[5], a study of nearby AGN[6] and limits on relic neutralino annihilation derived from TeV flux limits from the sun[7]. The focus of this paper is the search for extended sources of TeV gamma rays with the Milagro detector. 

The second method, which is particularly useful with extended sources such as diffusing optical fibers, is to place the diffuser into a sphere that has a highly reflective inside coating. This randomizes the light by multiple reflections and a known small fraction escapes through an output port to be detected, again usually by... 

Why use MaxEnt for COMPTEL The main reason is that for a COMPTEL-like response with its unusual point-spread-function and 3-D data space, we know of no other way to make true intensity images. Note that other methods such as maximum-likelihood are extremely important in searches for point-sources, but they do not yield intensity distributions, rather they give maps of significance or point-source flux under the assumption of a single or at most a few sources. Especially for diffuse, extended emission the MaxEnt method is valuable in providing quantitative intensity distributions. 

The data contained in the present catalog was optimized for point source detection. The electronic system response was designed to as low a frequency as possible to preserve information on widely extended sources. Diffuse emission from the galactic plane and HII region such as the Orion Nebula have been mapped at 11 and 19.8 ym but the data still has to be processed to optimize these observations. 

With respect to the practical considerations of gas flow and vacuum requirements, the PHPMS experiment might, upon cursory consideration, appear to be easily extended into the VHP region. That is, several MS-based analysis techniques routinely use ion source pressures of 1 atm. However, when an attempt to increase the pressure within a PHPMS ion source is made, the factors that do become problematic are those related to the subtle principles on which the method is based. Most importantly, the PHPMS method requires that the fundamental mode of diffusion be quickly established within the ion source after each e-beam pulse, so that all ions are transported to the walls in accordance with a simple first-order rate law while the IM reactions of interest are occurring. This ensures that a constant relationship exists between the ion density in the cell and the detected ion signal. The rates of the IM reactions can then be quantitatively determined from the observed time dependencies of the reactant ion signal because the contribution of diffusion to the time dependencies are well known and easily accounted for. 

Initially, a substance is concentrated at one point along a straight line that extends to infinity to both sides. For convenience, the position of the point is defined as x = 0. One real-world problem is the spill of toxic substance into a narrow lake. This problem is called the one-dimensional (or 1-D) point-source problem. With time, the substance would diffuse out and be diluted. The concentration variation as a function of time is shown in Figure l-7a. The mathematical description of the concentration of the substance as a function of x and t is... 

The simplifying assumptions that permit us to consider only specular reflections are no longer met when the wall surfaces contain features that are comparable in size to the wavelength of the sound. In this case, the reflected sound will be scattered in various directions, a phenomenon referred to as difjusion. The source image model cannot be easily extended to handle diffusion. Most auralization systems use another geometrical model, called ray tracing [Krokstad et al., 1968], to model diffuse reflections. A discussion of these techniques is beyond the scope of this paper. 

We extend this analysis to the multilayer situation to describe particle activation energies for ID diffusion on a 3D cubic lattice. The constant source row boundary condition is extended to a thickness of up to five layers for this analysis. The diffusion front for each layer is defined using the seawater methodology of Sapoval et al. [161]. 

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