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This study discussed the influence of chemical composition on the conductivity and on some
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variations of the alloy chemical composition was investigated using Carl ZEISS Scanning
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... We end this section by mentioning that electrical and electromechanical engineering models may be also obtained using variational approaches like the mechanical ones[31]but we shall not consider here this aspect. The same might be valid in the case of thermofluidic models leading to equations of conservation laws. ...
Among the rather wide class of controlled systems with distributed parameters, the systems with propagation are a distinct class. They are not only described by hyperbolic partial differential equations - what may imply discontinuous solutions - but they represent the most natural way of introducing the time delay as a dynamical block in System and Control Theory - thus being a sound basis for it. On the other hand, all dynamical systems descriptions require what is called model validation: existence of solutions - representing in fact the rigorous proof that the set of solutions (trajectories) is not empty, the model thus having some sense; uniqueness - which is the illustration of our conception for some determinism in the natural phenomena (under identical causes, identical effects are to be observed) and well posedness - illustrating the fact that small errors in data will not result in "catastrophes" in the model. At the same time, there are two additional properties that are useful in model validation. First, some variables have such physical meanings that they have to be of definite sign along system's trajectories (e.g. pressures, absolute temperatures, substance concentrations, population number have to be at least nonnegative). Mathematically speaking, this means existence of some invariant sets and this property has to be obtained in a rigorous way (by proof). Second, it is quite obvious (at the physical level) that only stable steady states or trajectories can be observed or measured since the unstable ones are "destroyed" by the perturbations. This remark, due to N. G. ?Cetaev - one of the first followers of Liapunov and one of the classics of stability theory - clearly suggests that some inherent stability properties should characterize the models of natural (that is uncontrolled) processes. In this chapter the above philosophy will be illustrated on some cases of systems containing propagation blocks with dynamics boundary conditions. All aforementioned aspects will be discussed. In particular, stability and feedback stabilization will be tackled within the framework of the Liapunov approach via the Liapunov functional deduced from the energy identity which is but well known in the theory of the partial differential equations. The presentation will have application oriented, that is, all concepts and approaches will refer to various motivating engineering applications.
Some large-scale natural phenomena and unexpected experiments are analyzed. It is proved that they can be explained by gravitomagnetism existence and significant gravitomagnetic forces. On the same basis it is proved that a generator using the gravitational conservative forces source energy for work performance can exist and this does not contradict the energy conservation law.
A new solution of Maxwell's equations for gravitomagnetism, used in order to create the various models of phenomena (sand-devil, sea current, rotary stream, funnel, water soliton, water and sand tsunami, turbulent flows, additional (non-Newtonian) forces of celestial bodies’ interaction) is proposed.
A detailed proof for interested reader is given.
Experimental validations of the theory are considered.
Explanations of experiments that have not been justified until now are proposed.
