Collagen gels are used extensively for studying cell-matrix mechanical interactions and for making tissue equivalents, where these interactions lead to bulk deformation of the sparse network of long, highly entangled collagen fibrils and syneresis of the interstitial aqueous solution. We have used the confined compression test in conjunction with a biphasic theory to characterize collagen gel mechanics. A finite element method model based on our biphasic theory was used to analyze the experimental results. The results are qualitatively consistent with a viscoelastic collagen network, an inviscid interstitial solution, and significant frictional drag. Using DASOPT, a differential-algebraic equation solver coupled with an optimizing algorithm, the aggregate modulus for the collagen gel was estimated as 6.32 Pa, its viscosity as 6.6 ϫ 10 4 Pa s, and its interphase drag coefficient as 6.4 ϫ 10 9 Pa s m Ϫ2 in long-time ͑5 h͒ creep. Analysis of short-time ͑2 min͒ constant strain rate tests gave a much higher modulus ͑318.3 Pa͒, indicating processes that generate high resistance at short time but relax too quickly to be significant on a longer time scale. This indication of a relaxation spectrum in compression is consistent with that characterized in shear based on creep and dynamic testing. While Maxwell fluid behavior of the collagen network is exhibited in shear as in compression, the modulus measured in shear was larger. This is hypothesized to be due to microstructural properties of the network. Furthermore, parameter estimates based on the constant strain rate data were used to predict accurately the stress response to sinusoidal strain up to 15% strain, defining the linear viscoelastic limit in compression.

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A cylindrical shock wave produces this intricate flow pattern as it converges from outside sixteen circular obstacles and diffracts. Researchers are interested in the structure of the solution near the focus (green region). This high-resolution numerical solution was computed using adaptive overlapping meshes. Source: Center for Applied Scientific Computing, Lawrence Livermore National Laboratory. The panelists reported on science and engineering needs for each of these offices, and then discussed and identified mathematical advances that will be required if these challenges are to be met. A review of DOE challenges in energy, the environment and national security brings to light a broad and varied array of questions that the DOE must answer in the coming years. A representative subset of such questions includes: APPLIED MATHEMATICS AT THE U.S. DEPARTMENT OF ENERGY: Past, Present and a View to the FutureA• Can we predict the operating characteristics of a clean coal power plant?• How stable is the plasma containment in a tokamak?• How quickly is climate change occurring and what are the uncertainties in the predicted time scales?• How quickly can an introduced bio-weapon contaminate the agricultural environment in the US?• How do we modify models of the atmosphere and clouds to incorporate newly collected data of possibly of new types?• How quickly can the United States recover if part of the power grid became inoperable?Over the past half-century, the Applied Mathematics program in the U.S. Department of Energy's Office of Advanced Scientific Computing Research has made significant, enduring advances in applied mathematics that have been essential enablers of modern computational science. Motivated by the scientific needs of the Department of Energy and its predecessors, advances have been made in mathematical modeling, numerical analysis of differential equations, optimization theory, mesh generation for complex geometries, adaptive algorithms and other important mathematical areas. High-performance mathematical software libraries developed through this program have contributed as much or more to the performance of modern scientific computer codes as the high-performance computers on which these codes run. Funding from this program has assisted generations of graduate and postdoctoral students who have continued on to populate and contribute productively to research organizations in industry, universities and federal laboratories. The combination of these mathematical advances and the resulting software has enabled high-performance computers to be used for scientific discovery in ways that could only be imagined at the program's inception.Our nation, and indeed our world, face great challenges that must be addressed in coming years, and many of these will be addressed through the development of scientific understanding and engineering advances yet to be discovered. The U.S. Department of Energy (DOE) will play an essential role in providing science-based solutions to many of these problems, particularly those...

A general lattice Monte Carlo model is used for simulating the formation of Supported Lipid Bilayers (SLBs) from vesicle solutions. The model, based on a previously published paper, consists of adsorption, decomposition and lateral diffusion steps, and is derived from fundamental physical interactions and mass transport principles. The Monte Carlo simulation results are fit to experimental data at different vesicle bulk concentrations. A sensitivity analysis reveals that the process strongly depends on the bulk concentration C 0 , adsorption rate constant K and all vesicle radii parameters. A measure of "quality of coverage" is proposed. By this measure, the quality of the formed bilayers is found to increase with vesicle bulk concentration.1

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