Propagation concept

Lammerts van Bueren, E.T. 2002. Organic Plant Breeding and Propagation Concepts and Strategies. PhD thesis, Wageningen Agricultural University. 

An excellent exposition of the propagator concept and role in quantum mechanics is given by... 

This chapter deals with the discussion and interpretation of approximate molecular electronic structure methods in terms of propagator concepts. Only situations with fixed nuclear frameworks are considered, and the discussion is limited to the description of states that are close in energy to the normal state of the system. We adopt the view that the main features of the electronic structure of such states can be developed in terms of atomic orbital representations of operators and that only valence shell orbitals need be considered. 

G. A. Aucar, Understanding NMR J-Couplings by the Theory of Polarization Propagators , Concepts Magn. Reson., A, 2008, 32A, 88. 

Aucar, G. A. (2008). Understanding NMR J-couplings by the theory of polarization propagators. Concepts in Magnetic Resonance Part A, 32, 88. 

We used the concept of sound velocity dispersion for explanation of the shift of pulse energy spectrum maximum, transmitted through the medium, and correlation of the shift value with function of medium heterogeneity. This approach gives the possibility of mathematical simulation of the influence of both medium parameters and ultrasonic field parameters on the nature of acoustic waves propagation in a given medium. 

Both the BO dynamics and Gaussian wavepacket methods described above in Section n separate the nuclear and electronic motion at the outset, and use the concept of potential energy surfaces. In what is generally known as the Ehrenfest dynamics method, the picture is still of semiclassical nuclei and quantum mechanical electrons, but in a fundamentally different approach the electronic wave function is propagated at the same time as the pseudoparticles. These are driven by standard classical equations of motion, with the force provided by an instantaneous potential energy function... 

The nebulization concept has been known for many years and is commonly used in hair and paint spays and similar devices. Greater control is needed to introduce a sample to an ICP instrument. For example, if the highest sensitivities of detection are to be maintained, most of the sample solution should enter the flame and not be lost beforehand. The range of droplet sizes should be as small as possible, preferably on the order of a few micrometers in diameter. Large droplets contain a lot of solvent that, if evaporated inside the plasma itself, leads to instability in the flame, with concomitant variations in instrument sensitivity. Sometimes the flame can even be snuffed out by the amount of solvent present because of interference with the basic mechanism of flame propagation. For these reasons, nebulizers for use in ICP mass spectrometry usually combine a means of desolvating the initial spray of droplets so that they shrink to a smaller, more uniform size or sometimes even into small particles of solid matter (particulates). 

Another important concept is that of the critical ignition volume. During the propagation of the combustion wave, the flame volume cannot continually grow beyond a critical value without an additional supply of energy. The condition that controls the critical volume for ignition is reached when the rate of increase of flame volume is less than the rate of increase of volume of the combustion products. In this condition a positive exchange of heat between the flame and the fresh mixture is achieved. 

This simple example Illustrates the important kinematic properties of shock waves, particularly the concepts of particle velocity and shock velocity. The particle velocity is the average velocity acquired by the beads. In this example, it is the piston velocity, v. The shock velocity is the velocity at which the disturbance travels down the string of beads. In general, at time n//2v, the disturbance has propagated to the nth bead. The distance the disturbance has traveled is therefore n d -b /), and the shock velocity is... 

The fluid mechanics origins of shock-compression science are reflected in the early literature, which builds upon fluid mechanics concepts and is more concerned with basic issues of wave propagation than solid state materials properties. Indeed, mechanical wave measurements, upon which much of shock-compression science is built, give no direct information on defects. This fluids bias has led to a situation in which there appears to be no published terse description of shock-compressed solids comparable to Kormer s for the perfect lattice. Davison and Graham described the situation as an elastic fluid approximation. A description of shock-compressed solids in terms of the benign shock paradigm might perhaps be stated as ... 

Other researchers have substantially advanced the state of the art of fracture mechanics applied to composite materials. Tetelman [6-15] and Corten [6-16] discuss fracture mechanics from the point of view of micromechanics. Sih and Chen [6-17] treat the mixed-mode fracture problem for noncollinear crack propagation. Waddoups, Eisenmann, and Kaminski [6-18] and Konish, Swedlow, and Cruse [6-19] extend the concepts of fracture mechanics to laminates. Impact resistance of unidirectional composites is discussed by Chamis, Hanson, and Serafini [6-20]. They use strain energy and fracture strength concepts along with micromechanics to assess impact resistance in longitudinal, transverse, and shear modes. 

This chapter presents fundamental concepts of comhnstion theory relating hoth to flame propagation and DDA technology. 

The combustion-flow interactions should be central in the computation of combustion-generated flow fields. This interaction is fundamentally multidimensional, and can only be computed by the most sophisticated numerical methods. A simpler approach is only possible if the concept of a gas explosion is drastically simplified. The consequence is that the fundamental mechanism of blast generation, the combustion-flow interaction, cannot be modeled with the simplified approach. In this case flame propagation must be formalized as a heat-addition zone that propagates at some prescribed speed. 

Over the years, this concept was refined in several ways. A scale dependency was modeled by the introduction of scale-dependent quenching of combustion. The first stage of the process was simulated by quasi-laminar flame propagation. In addition, three-dimensional versions of the code were developed (Hjertager 1985 Bakke 1986 Bakke and Hjertager 1987). Satisfactory agreement with experimental data was obtained. 

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