Filtering Aspects of Practical Test-Functions and the Ergodic Hypothesis

Doboga, Flavia; Toma, Ghiocel; Pusca, Stefan; Ghelmez, Mihaela A.; Morarescu, Cristian

doi:10.1007/11424857_60

Cited by 2 publications

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“…The shape of the output signal (obtained by numerical simulations in Matlab based on Runge-Kutta functions) will be analyzed, being shown that for very short range alternating inputs an external observer could notice (in certain condition) the existence of two distinct envelopes corresponding to two distinct structural patterns inside the material. Such aspect differs to the oscillations of unstable type second order systems studied using difference equations [4], and they differs also yo previous studies of the same author [5] where the frequency response of such systems to alternating inputs was studied (in conjunction with the ergodic hypothesis).…”

Section: Introductioncontrasting

confidence: 64%

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Different Structural Patterns Created by Short Range Variations of Internal Parameters

Doboga¹

2007

Computational Science – ICCS 2007

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Abstract. This papers presents properties of spatial linear systems described by a certain physical quantity generated by a differential equation. This quantity can be represented by internal electric or magnetic field inside the material, by concentration or by similar physical or chemical quantities. A specific differential equation generates this quantity considering as input the spatial alternating variations of an internal parameter. As a consequence, specific spatial linear variations of the observable output physical quantity appear. It is shown that in case of very short range variations of this internal parameters, systems described by a differential equation able to generate a practical test-function exhibit an output which appears to an external observer under the form of two distinct envelopes. These can be considered as two distinct structural patterns located in the same material along a certain linear axis.

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Section: Introductioncontrasting

confidence: 64%

“…These can be considered as two distinct structural patterns located in the same material along a certain linear axis. By this study, a fundamental new interpretation based on spatial aspects has been obtained for graphics previously obtained for non-linear equations of evolution [5] (the novelty of this study being justified).…”

Section: Discussionmentioning

confidence: 87%

Different Structural Patterns Created by Short Range Variations of Internal Parameters

Doboga¹

2007

Computational Science – ICCS 2007

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Vanishing Waves on Closed Intervals and Propagating Short‐Range Phenomena

Toma

Doboga

2008

Mathematical Problems in Engineering

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This study presents mathematical aspects of wave equation considered on closed space intervals. It is shown that a solution of this equation can be represented by a certain superposition of traveling waves with null values for the amplitude and for the time derivatives of the resulting wave in the endpoints of this interval. Supplementary aspects connected with the possible existence of initial conditions for a secondorder differential system describing the amplitude of these localized oscillations are also studied, and requirements necessary for establishing a certain propagation direction for the wave rejecting the possibility of reverse radiation are also presented. Then it is shown that these aspects can be extended to a set of adjacent closed space intervals, by considering that a certain traveling wave propagating from an endpoint to the other can be defined on each space interval and a specific mathematical law which can be approximated by a differential equation describes the amplitude of these localized traveling waves as related to the space coordinates corresponding to the middle point of the interval. Using specific differential equations, it is shown that the existence of such propagating law for the amplitude of localized oscillations can generate periodical patterns and can explain fracture phenomena inside materials as well.

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Filtering Aspects of Practical Test-Functions and the Ergodic Hypothesis

Cited by 2 publications

References 1 publication

Different Structural Patterns Created by Short Range Variations of Internal Parameters

Different Structural Patterns Created by Short Range Variations of Internal Parameters

Vanishing Waves on Closed Intervals and Propagating Short‐Range Phenomena

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