Binder jetting additive manufacturing is an emerging technology with capability of processing a wide range of commercial materials, including metals and ceramics (316 SS, 420 SS, Inconel 625, Iron, ...Silica). In this project, aluminum oxide (Al2O3) powder was used for part fabrication. Various build parameters (e.g. layer thickness, saturation, particle size) were modified and different sintering profiles were investigated to achieve nearly full-density parts (~96%). The material's microstructure and physical properties were characterized. Full XRD, compression testing, and dielectric testing were conducted on all parts. Sintered alumina parts were achieved with an average compressive strength of 131.86MPa (16h sintering profile) and a dielectric constant of 9.47–5.65 for a frequency range of 20Hz to 1MHz. The complexity offered by additive processing aluminum oxide can be extended to the manufacturing of high value energy and environmental components for environmental systems (e.g. filters and membranes) or biomedical implants with integrated reticulated structures for improved osseointegration.
The purpose of this study was to perform a comparative analysis of powder-bed-based additive manufacturing (AM) technologies during the production of metallic components using Inconel 625 powder ...material. The AM technologies explored in this study include electron beam powder bed fusion (EPBF), laser powder bed fusion (LPBF), and binder jetting technology. Samples were fabricated in two build directions (X and Z build orientations) for this evaluation process, where all specimens underwent a hot isostatic pressing (HIP) post-process. The comparison was made in terms of microstructure and mechanical properties including ultimate tensile strength (UTS), yield strength (YS), percent elongation, and modulus of elasticity (E). Microstructural characterization showed evidence of equiaxed grain formation for binder jetting and LPBF parts, whereas EPBF parts displayed a more columnar grain formation parallel to the build direction. Six specimens were tested per technology, three built in the X orientation and three built in the Z orientation. All six specimens were built in a single run of each AM machine. Results indicated that all three technologies are capable of meeting the minimum requirements of the ASTM F3056-14 standard for parts produced in the X orientation, with properties that are similar to wrought Inconel 625. In the Z orientation, however, only LPBF was able to meet the minimum standard requirements. Through the comparative analysis of the mechanical properties, this work showed that LPBF outperformed the other technologies in a majority of the evaluated properties, followed by EPBF and binder jetting. An analysis of the fracture surfaces of tensile specimens was also performed, and it indicated ductile fracture (dimple rupture) for the specimens produced with all three of the AM technologies studied. Nevertheless, the characterization also showed certain differences in the fractured surfaces, such as the presence of un-sintered powder particles for the binder jetting processed Inconel 625, or the development of the so called woody structure for the EPBF processed material. This study can be used to determine distinct characteristics between the three powder-bed-based technologies for the fabrication of Inconel 625 that can further include other technologies and materials using similar approaches.
Judicious use of interval arithmetic, combined with careful pen and paper estimates, leads to effective strategies for computer assisted analysis of nonlinear operator equations. The method of radii ...polynomials is an efficient tool for bounding the smallest and largest neighborhoods on which a Newton-like operator associated with a nonlinear equation is a contraction mapping. The method has been used to study solutions of ordinary, partial, and delay differential equations such as equilibria, periodic orbits, solutions of initial value problems, heteroclinic and homoclinic connecting orbits in the category of functions. In the present work we adapt the method of radii polynomials to the analytic category. For ease of exposition we focus on studying periodic solutions in Cartesian products of infinite sequence spaces. We derive the radii polynomials for some specific application problems and give a number of computer assisted proofs in the analytic framework.
Thirty-one structurally diverse marketed central nervous system (CNS)-active drugs, one active metabolite, and seven non-CNS-active compounds were tested in three P-glycoprotein (P-gp) in vitro ...assays: transwell assays using MDCK, human MDR1-MDCK, and mouse Mdr1a-MDCK cells, ATPase, and calcein AM inhibition. Additionally, the permeability for these compounds was measured in two in vitro models: parallel artificial membrane permeation assay and apical-to-basolateral apparent permeability in MDCK. The exposure of the same set of compounds in brain and plasma was measured in P-gp knockout (KO) and wild-type (WT) mice after subcutaneous administration. One drug and its metabolite, risperidone and 9-hydroxyrisperidone, of the 32 CNS compounds, and 6 of the 7 non-CNS drugs were determined to have positive efflux using ratio of ratios in MDR1-MDCK versus MDCK transwell assays. Data from transwell studies correlated well with the brain-to-plasma area under the curve ratios between P-gp KO and WT mice for the 32 CNS compounds. In addition, 3300 Pfizer compounds were tested in MDR1-MDCK and Mdr1a-MDCK transwell assays, with a good correlation (R(2) = 0.92) between the efflux ratios in human MDR1-MDCK and mouse Mdr1a-MDCK cells. Permeability data showed that the majority of the 32 CNS compounds have moderate to high passive permeability. This work has demonstrated that in vitro transporter assays help in understanding the role of P-gp-mediated efflux activity in determining the disposition of CNS drugs in vivo, and the transwell assay is a valuable in vitro assay to evaluate human P-gp interaction with compounds for assessing brain penetration of new chemical entities to treat CNS disorders.
We study polynomial expansions of local unstable manifolds attached to equilibrium solutions of parabolic partial differential equations. Due to the smoothing properties of parabolic equations, these ...manifolds are finite dimensional. Our approach is based on an infinitesimal invariance equation and recovers the dynamics on the manifold in addition to its embedding. The invariance equation is solved, to any desired order in space and time, using a Newton scheme on the space of formal Fourier–Taylor series. Under mild non-resonance conditions we show that the formal series converge in some small enough neighborhood of the equilibrium. An a-posteriori computer assisted argument is given which, when successful, provides mathematically rigorous convergence proofs in explicit and much larger neighborhoods. We give example computations and applications.
The set of transverse homoclinic intersections for a saddle-focus equilibrium in the planar equilateral restricted four-body problem admits certain simple homoclinic orbits which form the skeleton of ...the complete homoclinic intersection—or homoclinic web. In the present work, the planar restricted four-body problem is viewed as an invariant subsystem of the spatial problem, and the influence of this planar homoclinic skeleton on the spatial dynamics is studied from a numerical point of view. Starting from the vertical Lyapunov families emanating from saddle-focus equilibria, we compute the stable/unstable manifolds of these spatial periodic orbits and look for intersections between these manifolds near the fundamental planar homoclinics. In this way, we are able to continue all of the basic planar homoclinic motions into the spatial problem as homoclinics for appropriate vertical Lyapunov orbits which, by the Smale tangle theorem, suggest the existence of chaotic motions in the spatial problem. While the saddle-focus equilibrium solutions in the planar problems occur only at a discrete set of energy levels, the cycle-to-cycle homoclinics in the spatial problem are robust with respect to small changes in energy.
We describe a method for computing an atlas for the stable or unstable manifold attached to an equilibrium point and implement the method for the saddle-focus libration points of the planar ...equilateral restricted four-body problem. We employ the method at the maximally symmetric case of equal masses, where we compute atlases for both the stable and unstable manifolds. The resulting atlases are comprised of thousands of individual chart maps, with each chart represented by a two-variable Taylor polynomial. Post-processing the atlas data yields approximate intersections of the invariant manifolds, which we refine via a shooting method for an appropriate two-point boundary value problem. Finally, we apply numerical continuation to some of the BVP problems. This breaks the symmetries and leads to connecting orbits for some nonequal values of the primary masses.
This paper develops validated computational methods for studying infinite dimensional stable manifolds at equilibrium solutions of parabolic PDEs, synthesizing disparate errors resulting from ...numerical approximation. To construct our approximation, we decompose the stable manifold into three components: a finite dimensional slow component, a fast-but-finite dimensional component, and a strongly contracting infinite dimensional “tail”. We employ the parameterization method in a finite dimensional projection to approximate the slow-stable manifold, as well as the attached finite dimensional invariant vector bundles. This approximation provides a change of coordinates which largely removes the nonlinear terms in the slow stable directions. In this adapted coordinate system we apply the Lyapunov-Perron method, resulting in mathematically rigorous bounds on the approximation errors. As a result, we obtain significantly sharper bounds than would be obtained using only the linear approximation given by the eigendirections. As a concrete example we illustrate the technique for a 1D Swift-Hohenberg equation.
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