Discrete Quantum Transitions, Duality: Emergence of Physical Structures and Occurrence of Observed Formations (Hidden Properties of Mathematical Physics Equations)

With the help of skew-symmetric differential forms, the hidden properties of the mathematical physics equations that describe discrete quantum transitions and emergence the physical structures are investigated. It is shown that the mathematical physics equations possess a unique property. They can describe discrete quantum transitions, emergence of physical structures and occurrence observed formations. However, such a property possesses only equations on which no additional conditions, namely, the conditions of integrability, are imposed. The intergrability conditions are realized from the equations themselves. Just under realization of integrability conditions double solutions to the mathematical physics equations, which describe discrete transitions and so on, are obtained. The peculiarity consists in the fact that the integrability conditions do not directly follow from the mathematical physics equations;they are realized under the description of evolutionary process. The hidden properties of differential equations were discovered when studying the integrability of differential equations of mathematical physics that depends on the consistence between the derivatives in differential equations along different directions and on the consistence of equations in the set of equations. The results of this work were obtained with the help of skew-symmetric differential forms that possess a nontraditional mathematical apparatus such as nonidentical relations, degenerate transformations and the transition from nonintegrable manifolds to integrable structures. Such results show that mathematical physics equations can describe quantum processes.

Behavior of reinforced concrete structural walls with various opening locations: experiments and macro model

Two experimental tests of three-storied reinforced concrete structural walls having large openings were performed.Based on an original macro model,a multiple modified macro-model was proposed to develop a simple method to design a reinforced concrete structural wall with large openings and various opening locations.The interaction between reinforcement ties and concrete struts formed along the perimeter of openings was neglected in the original model.However,the strut-and-tie node was proposed to take account of such interaction in the proposed model.The predicted behavior of two specimens using such a proposed model was compared with the experimental results.It is shown that the behavior of structural walls with large openings could be modeled well using the proposed model.Moreover,the study indicates that the proposed model is applicable even in cases of multi-story structural walls having large openings and various opening locations.