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.     

Electromagnetically induced polarization conversion

Electromagnetically induced transparency and polarization conversion due to interference between two polarization-selective plasmonic resonances coexisting in the same planar metamaterial are studied. The metasurface represents a periodic array of two topologically distinct metamolecules combined on the same substrate: i) monopole antennas connected to wires and supporting a high-Q resonance radiatively coupled to x-polarization, and ii) dipolar antennas supporting a low-Q resonance coupled to y-polarization. We demonstrate that due to the interaction between these modes through a capacitive coupling between the metamolecules, one can observe a circularly-polarized Electromagnetically Induced Transparency (EIT) and thereby achieve an efficient ultra-thin quarter-wave plate.     

Phoneme representation and classification in primary auditory cortex

A controversial issue in neurolinguistics is whether basic neural auditory representations found in many animals can account for human perception of speech. This question was addressed by examining how a population of neurons in the primary auditory cortex (A1) of the naive awake ferret encodes phonemes and whether this representation could account for the human ability to discriminate them. When neural responses were characterized and ordered by spectral tuning and dynamics, perceptually significant features including formant patterns in vowels and place and manner of articulation in consonants, were readily visualized by activity in distinct neural subpopulations. Furthermore, these responses faithfully encoded the similarity between the acoustic features of these phonemes. A simple classifier trained on the neural representation was able to simulate human phoneme confusion when tested with novel exemplars. These results suggest that A1 responses are sufficiently rich to encode and discriminate phoneme classes and that humans and animals may build upon the same general acoustic representations to learn boundaries for categorical and robust sound classification.