A Nonlinear Analysis of the Averaged Euler Equations

This paper develops the geometry and analysis of the averaged Euler equations for ideal incompressible flow in domains in Euclidean space and on Riemannian manifolds, possibly with boundary. The averaged Euler equations involve a parameter $\alpha$; one interpretation is that they are obtained by ensemble averaging the Euler equations in Lagrangian representation over rapid fluctuations whose amplitudes are of order $\alpha$. The particle flows associated with these equations are shown to be geodesics on a suitable group of volume preserving diffeomorphisms, just as with the Euler equations themselves (according to Arnold's theorem), but with respect to a right invariant $H^1$ metric instead of the $L^2$ metric. The equations are also equivalent to those for a certain second grade fluid. Additional properties of the Euler equations, such as smoothness of the geodesic spray (the Ebin-Marsden theorem) are also shown to hold. Using this nonlinear analysis framework, the limit of zero viscosity for the corresponding viscous equations is shown to be a regular limit, {\it even in the presence of boundaries}.Comment: 25 pages, no figures, Dedicated to Vladimir Arnold on the occasion of his 60th birthday, Arnold Festschrift Volume 2 (in press

Microelectromagnetic ferrofluid-based actuator

Computer simulations were used to investigate the performance of a microscale ferrofluid-based magnetic actuator developed for liquid dispensing in microfluidic channels. The actuation was based on the movement of a ferrofluid plug in a magnetic field gradient generated by on-chip effectively infinite parallel conductors. The movement, positioning, and retaining of ferrofluid plugs with different lengths at various locations along a microfluidic channel were investigated for two cases. In case (a), the magnetic field gradient was generated by a single conductor; when the ferrofluid reached its equilibrium position, the current was switched off and the nearest neighbor conductor was energized. A similar, consecutive on/off current switching was performed for case (b), where a set of conductors was energized simultaneously

Electroluminescence-detected magnetic-resonance study of polyparaphenylenevinylene (PPV)-based light-emitting diodes

The strong electroluminescence (EL)-detected magnetic resonance of PPV-based light emitting diodes is compared to the conductivity (sigma)- and photoluminescence (PL)-detected resonances. It provides direct evidence that polaron-to-singlet exciton conversion is responsible for the EL. In contrast to the narrow PL-enhancing resonance assigned to polaron recombination, strong EL- and sigma-quenching resonances are attributed to the spin-dependent polaron-to-bipolaron decay. The half-field EL- and sigma-detected resonances of two distinct triplet excitons is believed to result from triplet-triplet fusion to singlets

Design of high-magnetic field gradient sources for controlling magnetically induced flow of ferrofluids in microfluidic systems

The use of miniature electromagnets for ferrofluid-actuated liquid dispensing into microfluidic channels has been investigated by numerical simulations using the finite element method and measurements of fluid displacement and flow rate. The simulations illustrate the effect of structural and geometrical parameters of single and paired solenoid coils on the magnetic force experienced by the ferrofluid. Dual solenoids were used for extended fluid displacement. Ferrofluid positioning and flow rates were controlled also by using a solenoid with an iron core. The experimental measurements of fluidflow in capillaries were used to validate the modeling calculations. The results can be used as a basis for the development of on-chip ferrofluid-based devices integrated with microfluidic architectures

Electronic Structure of Lanthanum Hydrides with Switchable Optical Properties

Recent dramatic changes in the optical properties of LaH_{2+x} and YH_{2+x} films discovered by Huiberts et al. suggest their electronic structure is described best by a local model. Electron correlation is important in H^- -centers and in explaining the transparent insulating behavior of LaH_3. The metal-insulator transition at $x\sim 0.8$ takes place in a band of highly localized states centered on the $H$-vacancies in the LaH_3 structure.Comment: plain tex, 3 figure

Robust Signal Processing in Living Cells

Cellular signaling networks have evolved an astonishing ability to function reliably and with high fidelity in uncertain environments. A crucial prerequisite for the high precision exhibited by many signaling circuits is their ability to keep the concentrations of active signaling compounds within tightly defined bounds, despite strong stochastic fluctuations in copy numbers and other detrimental influences. Based on a simple mathematical formalism, we identify topological organizing principles that facilitate such robust control of intracellular concentrations in the face of multifarious perturbations. Our framework allows us to judge whether a multiple-input-multiple-output reaction network is robust against large perturbations of network parameters and enables the predictive design of perfectly robust synthetic network architectures. Utilizing the Escherichia coli chemotaxis pathway as a hallmark example, we provide experimental evidence that our framework indeed allows us to unravel the topological organization of robust signaling. We demonstrate that the specific organization of the pathway allows the system to maintain global concentration robustness of the diffusible response regulator CheY with respect to several dominant perturbations. Our framework provides a counterpoint to the hypothesis that cellular function relies on an extensive machinery to fine-tune or control intracellular parameters. Rather, we suggest that for a large class of perturbations, there exists an appropriate topology that renders the network output invariant to the respective perturbations