Hierarchical Methods: Hierarchy and Hierarchical Asymptotic by V. Kulish

By V. Kulish

Everybody is present in a global surrounded via desktop. desktops verify our specialist job and penetrate more and more deeper into our way of life. Therein we additionally want more and more sophisticated c- puter expertise. occasionally we expect that the following iteration of c- puter will fulfill all our desires, giving us desire that almost all of our pressing difficulties can be solved very quickly. despite the fact that, the longer term comes and il- sions burn up. This phenomenon happens and vanishes sporadically, and, most likely, is a primary legislation of our lifestyles. adventure exhibits that certainly ‘systematically last’ difficulties are regularly of a posh tech- logical nature (the production of latest iteration of specifically excellent - croschemes, parts of reminiscence, and so on. ). yet allow us to be aware that among those difficulties there are continually ones solved by way of our in simple terms highbrow efforts by myself. growth during this path doesn't require the discovery of any ‘superchip’ or different related parts. you will need to observe that the consequences bought during this manner quite often change into extra major than the ‘fruits’ of proper technological growth. The hierarchical asymptotic analytical–numerical equipment may be - garded as result of such ‘purely highbrow efforts’. Their software permits us to simplify basically computing device calculational techniques and, hence, to lessen the calculational time required. it's seen that this situation is particularly appealing to any laptop user.

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Additional resources for Hierarchical Methods: Hierarchy and Hierarchical Asymptotic Methods in Electrodynamics, Volume 1

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7 HIERARCHICAL METHODS Waves with Negative, Zero and Positive Energy Performing corresponding calculational for the considered model of sound wave in an elastic medium, we can obtain the well known expression for the wave energy density [27]: where is the wave energy in an elementary volume is the medium density; A and are the wave amplitude and the frequency, respectively. It seems at first sight that the wave energy should be a quite positive-determined quantity, because As is widely known, the energy describes the ability of bodies to work.

Each model can reflect certain peculiarity of the system only. In other words, each complex system can be modeled by various methods. In the general theory of systems this statement is called the principle of ability to model. A number of consequences follow from it. The most important is that each particular group of properties of some complex system can be studied by specific theoretical model. Let us mention that two types of such models can be constructed. They are particular models and the total one.

However, we have not any contradiction in this case. The point is that the physical behavior of the weak nonlinear systems at relatively small observational intervals (for instance, during one or a few oscillations) turns out to be almost the same as a ‘purely linear’ equivalent system. The essential difference appears only in the course of a large number of oscillations. In other words, we can regard the weak nonlinear system as some slowly evolving (equivalent) linear system. It means that the system amplitude and frequency in this case are slowly varying parameters (variables) of the weak linear system.

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