An exact solution is established pertaining to the dynamic response of an Euler-Bernoulli beam resting on a Winkler foundation with variable subgrade modulus. The solution is performed by employing the infinite power series method. Moreover, using the Frobenius theorem, the proposed method is extended in order to solve the problems wherein the variation of the modulus is not an analytic function. The solution procedure is demonstrated by several illustrative examples, and the correctness of the results has been ascertained by comparison with recognized solutions in the literature. Finally, it is shown that the proposed method of solution is directly applicable to the more general problem of beams on a variable-modulus Pasternak-type foundation.
A phenomenological model of visual perceptual dynamics is proposed based upon the cellular automata (CA) which considers the anatomical connections between visual areas of the macaque brain. Some other important characteristics of neural networks of the brain are also included in the model, such as the excitatory-inhibitory ratio of neural populations, synaptic delays, etc. A new form of "geometric mean interaction rules" among neural populations are also introduced which could be considered more realistic than the previous "arithmetic mean-based rules". This computational model is capable of showing interesting dynamical behaviors, seen in the visual perceptual states of the brain.
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