Particle tracks, description

In this sense, differential equations appear more tractable since they do not require particle tracking. Indeed, the solution of the coupled equations of mass, momentum and energy balance including the material equation, properly described on a suitable finite element mesh, theoretically provides the material lines. Nevertheless, the correct description of the basic experiments often requires the use of strong nonlinear terms. Such improvements may be unsatisfying from the numerical point of view since they can lead to stiff systems of nonlinear equations and to many convergence related problems. 

Rammohan AR, Kemoim A, Al-Dahhan MH, Dudukovic MP A Lagrangian description of flows in stirred tanks via computer-automated radioactive particle tracking (CARPT), Chem Eng Sci 56 2629-2639, 2001a. http //dx.doi.org/10.1016/S0009-2509(00)00537-6. 

Here G ° (E) denotes the yield for minimum ionizing particles or low LET radiation (for instance, 1 MeV electrons or y-rays) Kgi (E) is the field-dependent Birks constant. This formula is equivalent to the theoretical descriptions by Jaffe or Kramers (see Section 5.5). For a given field strength. Equation 43 should describe the apparent charge carrier yield as a function of the ionization density of the different particles. In Figure 20 data obtained by Ochsenbein for different particles are compared to Equation 43. The solid line was obtained with Kbi = 0.0295 cm/MeV. A more detailed consideration requires that the angle between the particle track and the electric field is to be taken into account (Aubert et al., 1990). 

In simulating physical operations carried out in stirred vessels, generally one has the choice between a Lagrangian approach and a Eulerian description. While the former approach is based on tracking the paths of many individual fluid elements or dispersed-phase particles, the latter exploits the continuum concept. The two approaches offer different vistas on the operations and require different computational capabilities. Which of the two approaches is most... 

Systems of chemical interest typically contain particles in molar quantity. Mathematical modelling of all interactions in such a system is clearly impossible. Even in a system of non-interacting particles, such as an ideal gas, it would be equally impossible to keep track of all individual trajectories. It is consequently not a trivial matter to extend the mechanical description (either classical or non-classical) of single molecules to macrosystems. It would be required in the first place to define the initial state of each particle in terms of an equation... 

The spatial distribution of the energy loss events of a eharged partiele is usually referred to as a traek. This eoneeptual pieture of a traek is the baekbone of the theoretical description of radiation chemistry. Tracks are considered to have a transitory existence and exist so long as permitted by the dilfusion and fast reactions of radiation-produced intermediates (ions, electrons, and radicals). A large body of radiation-physical and radiation-chemical phenomena requires track models for their elucidation, including (1) LET variation of product yields (2) energy loss in primary excitations and ionizations (3) yield of escaped ions (4) radiation-induced luminescence and (5) particle identification. 

This section provides a brief description of theoretical bases of the Monte Carlo track simulation codes we have developed for electrons and ions. Our database of Monte Carlo track simulation codes include electrons (code kurbuc 10 eV to 10 MeV) [174], protons lephist —1 keV to 1 MeV) [175], alpha particles (leahist —1 keV to 8 MeV) [176], all ions... 

In contrast to the modeling methods described above, simulation methods approach the mathematical description of colloid aggregation kinetics from a fundamentally different viewpoint these methods track particle and aggregate movement over one-, two-, or three-dimensional space. This chapter will only provide a brief introduction and overview of the types of simulation methods that have been developed, as this is a broad and growing field of research worthy of numerous volumes alone. The following discussion will proceed by defining four categories of simulations as follows, and as outlined in Table 3. 

Attempts to extend RANS formulation to LES of two-phase combustion may be found in [318 354 317 255 292]. They are all based on a Euler-Lagrange (EL) description of the dispersed phase in which the flow is solved using an Eulerian method and the particles are tracked with a Lagrangian approach. An alternative is the Euler-Euler (EE) description, also called two-fluid approach, in which both the gas and the dispersed phases are... 

With fully resolved simulations, we generally refer to a detailed description of the fluid-solid interface in which all the scales of ambient turbulence, and the flow scales introduced by the particles, are completely resolved by employing DNS for the fluid phase and Lagrangian tracking for the particles. 

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