Abstract. We develop stochastic mixed finite element methods for spatially adaptive simulations of fluid-structure interactions when subject to thermal fluctuations. To account for thermal fluctuations, we introduce a discrete fluctuation-dissipation balance condition to develop compatible stochastic driving fields for our discretization. We perform analysis that shows our condition is sufficient to ensure results consistent with statistical mechanics. We show the Gibbs-Boltzmann distribution is invariant under the stochastic dynamics of the semi-discretization. To generate efficiently the required stochastic driving fields, we develop a Gibbs sampler based on iterative methods and multigrid to generate fields with O(N ) computational complexity. Our stochastic methods provide an alternative to uniform discretizations on periodic domains that rely on Fast Fourier Transforms. To demonstrate in practice our stochastic computational methods, we investigate within channel geometries having internal obstacles and no-slip walls how the mobility/diffusivity of particles depends on location. Our methods extend the applicability of fluctuating hydrodynamic approaches by allowing for spatially adaptive resolution of the mechanics and for domains that have complex geometries relevant in many applications. Introduction. We develop general computational methods for applications involving the microscopic mechanics of spatially extended elastic bodies within a fluid that are subjected to thermal fluctuations. Motivating applications include the study of the microstructures of complex fluids [17], lipid bilayer membranes [28,32,48], and micro-mechanical devices [37,29]. Even in the deterministic setting, the mechanics of fluid-structure interactions pose a number of difficult and long-standing challenges owing to the rich behaviors that can arise from the interplay of the fluid flow and elastic stresses of the microstructures [19,42]. To obtain descriptions tractable for analysis and simulations, approximations are often introduced into the fluid-structure coupling. For deterministic systems, many spatially adaptive numerical methods have been developed for approximate fluid-structure interactions [25,35,26,39,2,30]. In the presence of thermal fluctuations, additional challenges arise from the need to capture in computational methods the appropriate propagation of fluctuations throughout the discretized system to obtain results consistent with statistical mechanics. In practice, challenges arise from the very different dissipative properties of the discrete operators relative to their continuum differential counterparts. These issues have important implications for how stochastic fluctuations should be handled in the discrete setting. Even when it is possible to formulate stochastic driving fields in a well-founded manner consistent with statistical mechanics, these Gaussian random
We investigate the kinetics of supported lipid bilayer formation by the adsorption and rupture of uncharged phosphatidylcholine lipid vesicles on to a solid substrate. We model the adsorption process taking into account the distinct vesicle rupture events and growth processes. This includes (i) the initial adhesion and vesicle rupture that nucleates bilayer islands, (ii) the growth and merger of bilayer islands, (iii) enhanced adhesion of vesicles to the bilayer edge, and (iv) the final desorption of excess vesicles from the substrate.These simulation studies give insight into prior experimental observations of adsorption in which an overloading of lipid on the solid substrate occurs before formation of the final supported lipid bilayer. Our model provides an explanation for the features of the interesting universal master curve that was observed for the surface fluorescence intensity in the experimental investigations of Weirich et al.
Albuquerque, NM 87185Sumrnmary Packaged LSI and hybrid devices used in high reliability military and space applications must pass a rigorous series of screens defined by Method 5004 of Mil Standard 883B. One of ;these screens is the Particle Impact Noise Detection (PIND) test. This test uses a very sensitive acoustic transducer to listen for particles within the package while the package is vibrated and shocked. We have used SEM, EDAX, and optical microscopy to analyze the particles from PIND failures.From these analyses we have identified the primary sources of PIND failures and have developed procedures that yield a low reject rate at PIND test.The device used in this investigation was a 1 K RAM die eutectically attached to a 24-pin leadless hermetic package (LHP). The package is solder sealed in a belt furnace with a gold-tin eutectic preform and a gold-plated cover.We have recovered the particles from PIND test failures by placing lead tape over a punched hole in the gold plated Kovar lid.The package is then vibrated until the particles pass through the hole and are attached to the adhesive on the tape.From the analyses we have identified many sources of particles that cause PIND test failures; the main source being the gold-tin solder preform used in the sealing process. We have investigated the effect of sealing materials, furnace temperature, furnace ambient, and package orientation on the number of gold-tin solder spheres.The best results were obtained with a nonoxidizing furnace ambient with the packages placed lid down and angled at 45 degrees during sealing. These improved assembly processes have lead to PIND test yields of better than 90 percent.
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