Horizon problem remediation via deformed phase space

We investigate the effects of a special kind of dynamical deformation between the momenta of the scalar field of the Brans–Dicke theory and the scale factor of the FRW metric. This special choice of deformation includes linearly a deformation parameter. We trace the deformation footprints in the cosmological equations of motion when the BD coupling parameter goes to infinity. One class of the solutions gives a constant scale factor in the late time that confirms the previous result obtained via another approach in the literature. This effect can be interpreted as a quantum gravity footprint in the coarse grained explanation. The another class of the solutions removes the big bang singularity, and the accelerating expansion region has an infinite temporal range which overcomes the horizon problem. After this epoch, there is a graceful exiting by which the universe enters in the radiation dominated era.     

Prediction of rheological behavior of MWCNTs–SiO2/EG–water non-Newtonian hybrid nanofluid by designing new correlations and optimal artificial neural networks

In this paper, at the first, new correlations were proposed to predict the rheological behavior of MWCNTs–SiO₂/EG–water non-Newtonian hybrid nanofluid using different sets of experimental data for the viscosity, consistency and power law indices. Then, based on minimum prediction errors, two optimal artificial neural network models (ANNs) were considered to forecast the rheological behavior of the non-Newtonian hybrid nanofluid. One hundred and ninety-eight experimental data were employed for predicting viscosity (Model I). Two sets of forty-two experimental data also were considered to predict the consistency and power law indices (Model II). The data sets were divided to training and test sets which contained respectively 80 and 20% of data points. Comparisons between the correlations and ANN models showed that ANN models were much more accurate than proposed correlations. Moreover, it was found that the neural network is a powerful instrument in establishing the relationship between a large numbers of experimental data. Thus, this paper confirmed that the neural network is a reliable method for predicting the rheological behavior of non-Newtonian nanofluids in different models.

     

Measurement of the thermal conductivity of MWCNT-CuO/water hybrid nanofluid using artificial neural networks (ANNs)

Journal of Thermal Analysis and Calorimetry - In this paper, artificial neural networks (ANNs) are developed to predict the thermal conductivity ( $$k_{\text{nf}}$$ ) of multi-walled carbon...     

Linear and non-linear vibration and frequency response analyses of microcantilevers subjected to tip-sample interaction

Despite their simple structure and design, microcantilevers are receiving increased attention due to their unique sensing and actuation features in many MEMS and NEMS. Along this line, a non-linear distributed-parameters modeling of a microcantilever beam under the influence of a nanoparticle sample is studied in this paper. A long-range Van der Waals force model is utilized to describe the microcantilever-particle interaction along with an inextensibility condition for the microcantilever in order to derive the equations of motion in terms of only one generalized coordinate. Both of these considerations impose strong nonlinearities on the resultant integro-partial equations of motion. In order to provide an understanding of non-linear characteristics of combined microcantilever-particle system, a geometrical function is wisely chosen in such a way that natural frequency of the linear model exactly equates with that of non-linear model. It is shown that both approaches are reasonably comparable for the system considered here. Linear and non-linear equations of motion are then investigated extensively in both frequency and time domains. The simulation results demonstrate that the particle attraction region can be obtained through studying natural frequency of the system consisting of microcantilever and particle. The frequency analysis also proves that the influence of nonlinearities is amplified inside the particle attraction region through bending or shifting the frequency response curves. This is accompanied by sudden changes in the vibration amplitude estimated very closely by the non-linear model, while it cannot be predicted by the best linear model at all.     

Wave propagation and breaking in multidimensional magnetogasdynamic flows

Summary The theory of shocks evolving from weak discontinuities is applied to magnetogasdynamics and worked out in detail for two situations: a spherical disturbance propagating into a uniform magnetic field, and a planar disturbance propagating in the field of a current-carrying wire. For both cases, shock formation is delayed as the magnetoacoustic speed of propagation approaches the Alfvén speed. This agrees with the fact that Alfvén waves do not steepen to form shocks.

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Résumé On applique à la magnétogasdynamique la théorie des ondes de choc produites par l'évolution des discontinuités faibles. On présente des résultats sur la formation de chocs par des ondes magnétoacoustiques. Lorsque la vitesse de propagation de ces ondes se rapproche de la vitesse d'Alfvén, l'apparition des chocs est retardée, en accord avec le résultat bien connu que les ondes d'Alfvén ne se transforment pas pour former des chocs.

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Research supported in part by Grant No. AFOSR-73-2561.