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Computer Simulation of Laser Produced Plasmas
Published in M.B. Hooper, Laser-Plasma Interactions 4, 2020
The construction of a simulation model is based on the following sequence of steps:Identification of the system and the physical phenomena determining its behaviour.Expression of the physical laws governing that behaviour.Representation of the physical laws by numerical equations.Programming these equations for calculation by computer.Debugging the programmes, i.e. removing programming errors to ensure calculation is correct.Validation of the model, i.e. comparing the model against known theoretical and experimental results to check accuracy of the numerical and physical representation.Presentation of the results of the calculation in terms of output variables, and in observable form.Use of the model for physical prediction within the range of its validity.
Knowledge Representation in Agent-Based Concurrent Design and Manufacturing Systems
Published in Weiming Shen, Douglas H. Norrie, Jean-Paul A. Barthès, Multi-Agent Systems for Concurrent Intelligent Design and Manufacturing, 2019
Weiming Shen, Douglas H. Norrie, Jean-Paul A. Barthès
If we turn now to concurrent engineering applications, then clearly products and processes have to be somehow represented. However, having a single agent manage the global representation of a complex product, even it were possible, would create a bottleneck, defeating the whole purpose of using agents. Thus, each agent will have a possibly different representation of the product best suited to the specific expertise it will implement (e.g., finite element analysis). The major difficulty will be in coordinating the various types of representations, making sure that they remain relatively consistent. The representations that may be used range from highly symbolic models (usually represented as graphs) to data structures representing, for example, geometry. Translation from one representation into another is a real problem and current standards are not sufficient to support this function. Special agents could be developed for this purpose. The problem of conflicting representations was considered in PACT (Gruber, 1992) where two representations were necessary: one for dynamic computations and the other for kinematics.
Applied Cognitive Work Analysis: A Pragmatic Methodology for Designing Revolutionary Cognitive Affordances
Published in Erik Hollnagel, Handbook of Cognitive Task Design, 2003
William C. Elm, Scott S. Potter, James W. Gualtieri, James R. Easter, Emilie M. Roth
The resulting FAN specifies the domain objectives and the functions that must be available and satisfied to achieve their goals. In turn, these functions may be abstract entities that need to have other, less abstract functions available and satisfied that they might be achieved. This creates a decomposition network of objectives or purposes that are linked together from abstract goals to specific means to achieve these goals. For example, in the case of engineered systems, such as a process plant, functional representations are developed that characterize the purposes for which the engineered system has been designed and the means structurally available for achieving those objectives. In the case of military command and control systems, the functional representations characterize the functional capabilities of individual weapon systems, maneuvers, or forces and the higher level goals related to military objectives.
Symmetry Groups of the Forward Master Equation for Stochastic Neutron Populations
Published in Nuclear Science and Engineering, 2022
Patrick F. O’Rourke, Scott D. Ramsey, Brian A. Temple
Next, we demonstrated a symmetry analysis of the definition of the PGF, which is an algebraic equation. We found the determining equations and supplemented the Lie group of the BPS solutions into said equation. This resulted in a factorial moment representation of the symmetry group, which was upward coupled for all except for . We then illustrated the global transformation of the survival probability for this Lie group. Interestingly, the BPS transform and the PGF definition transform for are identical and show that the extinction probability is scaled by the source strength. We showed the relation between , which essentially models the entire number distribution in -space, and the survival probability, which does the same but in -space, and how the source scaling invariance is conserved between the two quantities.
A simplified Bixon–Jortner–Plotnikov method for fast calculation of radiationless transfer rates in symmetric molecules
Published in Molecular Physics, 2023
A. I. Martynov, A. S. Belov, V. K. Nevolin
The operator of the non-adiabatic coupling is totally symmetric with respect to molecular point group operations. The consequence of this is that the non-adiabatic constant belongs to the same symmetry group representation as the product of WFs: . Valiev [30] also tried to associate the rate constants with representations of modes. Since only the modes with were taken into account in that work, the modeled IC in naphthalene and anthracene proceeded only via the A and B modes. This contradicts the zero displacement of non-totally symmetric modes according to Li [36].
Lie group method for constructing integrating factors of first-order ordinary differential equations
Published in International Journal of Mathematical Education in Science and Technology, 2023
The Lie group and Lie algebra were produced at the end of the nineteenth century. After decades of development, they became an important branch of mathematics in the 1970s. They are closely related to geometry, algebra, and analysis. The founder of Lie group theory, Marius Sophus Lie, was born on 17 December 1842 in the village Nordfjordeid in Norway (Ibragimov, 1992). Starting from 1857, he studied in Christiania (now Oslo), first in a grammar school and then (1859–1865) in a university. Later, he had a journey to Germany and France (1869–1870) and a meeting with Klein (which grew into a close friendship and a long-term partnership), Chasles, Jordan, and Darboux. During 1872–1886, Lie worked in the university of Christiania, and from 1886 to 1898 in the university of Leipzig. Lie died on 18 February 1899 in Christiania. The life, development of ideas, and work of this great Norwegian mathematician are discussed in detail in the excellent book of E.M. Polishchuk, ‘Sophus Lie’ (Nauka, Leningrad 1983). Lie's work has not received enough attention during his lifetime. It was not until the beginning of the twentieth century that his research results were carried forward due to their good applications in physics and geometry. For example, H. Weyl (1885–1955) studied the representation theory of the Lie group and used it in quantum mechanics. É. Cartan (1869–1951) used the Lie group in geometry to establish the Riemann symmetric space theory. We should also mention the use of the Lie group method for the differential equations arising in geometry, including motions in Riemannian manifolds, symmetric spaces, and invariant differential operators associated with them (see Olver, 1986 and the references therein).