Nonlinear Micromechanical Casimir Oscillator

The Casimir force between uncharged metallic surfaces originates from quantum mechanical zero point fluctuations of the electromagnetic field. We demonstrate that this quantum electrodynamical effect has a profound influence on the oscillatory behavior of microstructures when surfaces are in close proximity (<= 100 nm). Frequency shifts, hysteretic behavior and bistability caused by the Casimir force are observed in the frequency response of a periodically driven micromachined torsional oscillator.Comment: 4 pages, 4 figures; added and rearranged references; added comments on sensitivit

Frequency bands of strongly nonlinear homogeneous granular systems

Recent numerical studies on an infinite number of identical spherical beads in Hertzian contact showed the presence of frequency bands [ Jayaprakash, Starosvetsky, Vakakis, Peeters and Kerschen Nonlinear Dyn. 63 359 (2011)]. These bands, denoted here as propagation and attenuation bands (PBs and ABs), are typically present in linear or weakly nonlinear periodic media; however, their counterparts are not intuitive in essentially nonlinear periodic media where there is a complete lack of classical linear acoustics, i.e., in “sonic vacua.” Here, we study the effects of PBs and ABs on the forced dynamics of ordered, uncompressed granular systems. Through numerical and experimental techniques, we find that the dynamics of these systems depends critically on the frequency and amplitude of the applied harmonic excitation. For fixed forcing amplitude, at lower frequencies, the oscillations are large in amplitude and governed by strongly nonlinear and nonsmooth dynamics, indicating PB behavior. At higher frequencies the dynamics is weakly nonlinear and smooth, in the form of compressed low-amplitude oscillations, indicating AB behavior. At the boundary between the PB and the AB large-amplitude oscillations due to resonance occur, giving rise to collisions between beads and chaotic dynamics; this renders the forced dynamics sensitive to initial and forcing conditions, and hence unpredictable. Finally, we study asymptotically the near field standing wave dynamics occurring for high frequencies, well inside the AB

Microfluidics: Fluid physics at the nanoliter scale

Microfabricated integrated circuits revolutionized computation by vastly reducing the space, labor, and time required for calculations. Microfluidic systems hold similar promise for the large-scale automation of chemistry and biology, suggesting the possibility of numerous experiments performed rapidly and in parallel, while consuming little reagent. While it is too early to tell whether such a vision will be realized, significant progress has been achieved, and various applications of significant scientific and practical interest have been developed. Here a review of the physics of small volumes (nanoliters) of fluids is presented, as parametrized by a series of dimensionless numbers expressing the relative importance of various physical phenomena. Specifically, this review explores the Reynolds number Re, addressing inertial effects; the Péclet number Pe, which concerns convective and diffusive transport; the capillary number Ca expressing the importance of interfacial tension; the Deborah, Weissenberg, and elasticity numbers De, Wi, and El, describing elastic effects due to deformable microstructural elements like polymers; the Grashof and Rayleigh numbers Gr and Ra, describing density-driven flows; and the Knudsen number, describing the importance of noncontinuum molecular effects. Furthermore, the long-range nature of viscous flows and the small device dimensions inherent in microfluidics mean that the influence of boundaries is typically significant. A variety of strategies have been developed to manipulate fluids by exploiting boundary effects; among these are electrokinetic effects, acoustic streaming, and fluid-structure interactions. The goal is to describe the physics behind the rich variety of fluid phenomena occurring on the nanoliter scale using simple scaling arguments, with the hopes of developing an intuitive sense for this occasionally counterintuitive world

Current status of the Dynamical Casimir Effect

This is a brief review of different aspects of the so-called Dynamical Casimir Effect and the proposals aimed at its possible experimental realizations. A rough classification of these proposals is given and important theoretical problems are pointed out.Comment: 12 pages, the text corresponds to the final published version, except for the layout and reference styl

On the acoustical theory of the trumpet : is it sound? : a thesis presented in partial fulfilment of the requirements for the degree of Master of Science in Mathematics at Massey University, New Zealand

Newton's Second Law of Motion for one-dimensional inviscid flow of an incompressible fluid, in the absence of external forces, is often expressed in a form known as Bernoulli's equation: There are two distinct forms of Bernoulli's equation used in the system of equations which is commonly considered to describe sound production in a trumpet. The flow between the trumpeter's lips is, in the literature, assumed to be quasi-steady. From this assumption, the first term of the above Bernoulli equation is omitted, since it is then small in comparison to the other two terms. The flow within the trumpet itself is considered to consist of small fluctuations about some mean velocity and pressure. A linearized version of Bernoulli's equation (as used in the equations of linear acoustics) is then adequate to describe the flow. In this case it is the second term of the above equation which is neglected, and the first term is retained. Given that the flow between the trumpeter's lips is that same flow which enters the trumpet itself, a newcomer to the field of trumpet modelling might wonder whether the accepted model is really correct when these two distinct versions of the Bernoulli Equation are used side by side. This thesis addresses this question, and raises others that arise from a review of the standard theory of trumpet physics. The investigation comprises analytical and experimental components, as well as computational simulations. No evidence has been found to support the assumption of quasi-steady flow between the lips of a trumpeter. An alternative flow equation is proposed, and conditions given for its applicability. [NB: Mathematical/chemical formulae or equations have been omitted from the abstract due to website limitations. Please read the full text PDF file for a complete abstract.