3D-ink-extruded titanium scaffolds with porous struts and bioactive supramolecular polymers for orthopedic implants
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A method is reported to prepare siloxane microballoons that can be loaded into a direct ink write siloxane ink for 3D printing. The resulting structure is subjected to a solvent removal and supercritical drying process to provide a final printed siloxane having both macroscopic and microscopic porosity. Core-shell particles are generated by an emulsion template and phase separation process. Intra-strand closed-cell porosities can be achieved between 10 and 40 vol% thus facilitating additional compressive strain before lockup. Here short term compression set testing highlights the excellent shape retention properties of these elastomers, which have less than 8% relative compression set under load.
Limiting the injection rate to restrict the pressure below a threshold at a critical location can be an important goal of simulations that model the subsurface pressure between injection and extraction wells. The pressure is approximated by the solution of Darcy’s partial differential equation for a given permeability field. The subsurface permeability is modeled as a random field since it is known only up to statistical properties. This induces uncertainty in the computed pressure. Solving the partial differential equation for an ensemble of random permeability simulations enables estimating a probability distribution for the pressure at the critical location. These simulations are computationally expensive, and practitioners often need rapid online guidance for real-time pressure management. An ensemble of numerical partial differential equation solutions is used to construct a Gaussian process regression model that can quickly predict the pressure at the critical location as a function of the extraction rate and permeability realization. The Gaussian process surrogate analyzes the ensemble of numerical pressure solutions at the critical location as noisy observations of the true pressure solution, enabling robust inference using the conditional Gaussian process distribution. Our first novel contribution is to identify a sampling methodology for the random environment and matching kernel technology for which fitting the Gaussian process regression model scales as O ( n log n ) instead of the typical O ( n 3 ) rate in the number of samples n used to fit the surrogate. The surrogate model allows almost instantaneous predictions for the pressure at the critical location as a function of the extraction rate and permeability realization. Our second contribution is a novel algorithm to calibrate the uncertainty in the surrogate model to the discrepancy between the true pressure solution of Darcy’s equation and the numerical solution. Finally, although our method is derived for building a surrogate for the solution of Darcy’s equation with a random permeability field, the framework broadly applies to solutions of other partial differential equations with random coefficients.
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A nonlinear multigrid solver for two-phase flow and transport in a mixed fractional-flow velocity-pressure-saturation formulation is proposed. The solver, which is under the framework of the full approximation scheme (FAS), extends our previous work on nonlinear multigrid for heterogeneous diffusion problems. The coarse spaces in the multigrid hierarchy are constructed by first aggregating degrees of freedom, and then solving some local flow problems. The mixed formulation and the choice of coarse spaces allow us to assemble the coarse problems without visiting finer levels during the solving phase, which is crucial for the scalability of multigrid methods. Specifically, a natural generalization of the upwind flux can be evaluated directly on coarse levels using the precomputed coarse flux basis vectors. We find that the resulting solver is applicable to problems discretized on general unstructured grids. The performance of the proposed nonlinear multigrid solver in comparison with the standard single level Newton's method is demonstrated through challenging numerical examples. It is observed that the proposed solver is robust for highly nonlinear problems and clearly outperforms Newton's method in the case of high Courant-Friedrichs-Lewy (CFL) numbers.
Motivated by the synthesis of three-dimensional (3D) honeycomb carbon structures and the subsequent theoretical prediction of an energetically more favorable hexagonal carbon phase composed of 28 carbon atoms in the unit cell (hC28) with ordered pores, excellent mechanical properties, and metallic feature, we explore its potential for a Na-ion battery (NIB) anode material. Using density functional theory based calculations, we find that hC28 is a promising candidate whose specific capacity of 717 mAh/g is almost three times larger than that of hard carbon (~250 mAh/g). In addition, migration barrier of Na ions along the honeycomb channel is only 0.08 eV and the volume change during the charging/discharging process is merely 2.30%, which are much less than those of other carbon-based NIB anode materials. The average voltage is also low (0.36 eV) which can provide high operating voltage when connected to the cathode. Finally, these encouraging results would pave the way towards the development of hC28 as NIB anode with high capacity, excellent rate performance, low open-circuit voltage, and long-term cycle life.
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