A polynomial regularity lemma for semi-algebraic hypergraphs and its applications in geometry and property testing

Fox, Gromov, Lafforgue, Naor, and Pach proved a regularity lemma for semi-algebraic $k$-uniform hypergraphs of bounded complexity, showing that for each $\epsilon>0$ the vertex set can be equitably partitioned into a bounded number of parts (in terms of $\epsilon$ and the complexity) so that all but an $\epsilon$-fraction of the $k$-tuples of parts are homogeneous. We prove that the number of parts can be taken to be polynomial in $1/\epsilon$. Our improved regularity lemma can be applied to geometric problems and to the following general question on property testing: is it possible to decide, with query complexity polynomial in the reciprocal of the approximation parameter, whether a hypergraph has a given hereditary property? We give an affirmative answer for testing typical hereditary properties for semi-algebraic hypergraphs of bounded complexity

Exploring property driven design fabrication through materials testing and software development

Thesis (S.B.)--Massachusetts Institute of Technology, Dept. of Mechanical Engineering, 2010.This electronic version was submitted by the student author. The certified thesis is available in the Institute Archives and Special Collections.Cataloged from student submitted PDF version of thesis. Vita.Includes bibliographical references (p. 33).Since its introduction in the late 1980s, layered manufacturing has become an increasingly efficient and common means to delivering functional and visually representative prototypes in relatively short amounts of time from previously prepared Computer-Aided Design files. However, most layered manufacturing technologies today produce only single material, constant property prototypes from a limited array of materials. In this project, we explore a different approach to layer manufacturing, namely, a layered manufacturing product that, while using a single material, produces an entity of varying material properties. Materials testing of PMC®-724 demonstrate the material's capacity to possess a range of Shore A Hardness over a range of elasticity, illustrating the potential for printing with variable property materials. Moreover, we will also explore a new approach to fabrication that challenges the concept of Computer- Aided Manufacturing (CAM) by introducing a software application that, rather than providing a means of digitizing the geometry of a completed design, allows engineers and designers to create and design structures that are defined at various points by their material behavior as opposed to their geometry. As a proof of concept demonstration, a mono-material, variable property shoe sole will be printed using property-mapped polyurethane elastomer PMC®-724 with the new software.by Mindy Eng.S.B

Magnetorheological landing gear: 2. Validation using experimental data

Aircraft landing gears are subjected to a wide range of excitation conditions with conflicting damping requirements. A novel solution to this problem is to implement semi-active damping using magnetorheological (MR) fluids. In part 1 of this contribution, a methodology was developed that enables the geometry of a flow mode MR valve to be optimized within the constraints of an existing passive landing gear. The device was designed to be optimal in terms of its impact performance, which was demonstrated using numerical simulations of the complete landing gear system. To perform the simulations, assumptions were made regarding some of the parameters used in the MR shock strut model. In particular, the MR fluid's yield stress, viscosity, and bulk modulus properties were not known accurately. Therefore, the present contribution aims to validate these parameters experimentally, via the manufacture and testing of an MR shock strut. The gas exponent, which is used to model the shock strut's nonlinear stiffness, is also investigated. In general, it is shown that MR fluid property data at high shear rates are required in order to accurately predict performance prior to device manufacture. Furthermore, the study illustrates how fluid compressibility can have a significant influence on the device time constant, and hence on potential control strategies

Ballistic Impact Testing of Aluminum 2024 and Titanium 6Al-4V for Material Model Development

An experimental program is underway to develop a consistent set of material property and impact test data, and failure analysis, for a variety of materials that can be used to develop improved impact failure and deformation models. Unique features of this set of data are that all material property information and impact test results are obtained using identical materials, the test methods and procedures are extensively documented and all of the raw data is available. This report describes ballistic impact testing which has been conducted on aluminum (Al) 2024 and titanium (Ti) 6Al-4vanadium (V) sheet and plate samples of different thicknesses and with different types of projectiles, one a regular cylinder and one with a more complex geometry incorporating features representative of a jet engine fan blade

MeshPipe: a Python-based tool for easy automation and demonstration of geometry processing pipelines

The popularization of inexpensive 3D scanning, 3D printing, 3D publishing and AR/VR display technologies have renewed the interest in open-source tools providing the geometry processing algorithms required to clean, repair, enrich, optimize and modify point-based and polygonal-based models. Nowadays, there is a large variety of such open-source tools whose user community includes 3D experts but also 3D enthusiasts and professionals from other disciplines. In this paper we present a Python-based tool that addresses two major caveats of current solutions: the lack of easy-to-use methods for the creation of custom geometry processing pipelines (automation), and the lack of a suitable visual interface for quickly testing, comparing and sharing different pipelines, supporting rapid iterations and providing dynamic feedback to the user (demonstration). From the user's point of view, the tool is a 3D viewer with an integrated Python console from which internal or external Python code can be executed. We provide an easy-to-use but powerful API for element selection and geometry processing. Key algorithms are provided by a high-level C library exposed to the viewer via Python-C bindings. Unlike competing open-source alternatives, our tool has a minimal learning curve and typical pipelines can be written in a few lines of Python code.Peer ReviewedPostprint (published version

The use of simulated body fluid (SBF) for assessing materials bioactivity in the context of tissue engineering: Review and challenges

Some special implantable materials are defined as “bioactive” if they can bond to living bone, forming a tight and chemically‐stable interface. This property, which is inherent to some glass compositions, or can be induced by applying appropriate surface treatments on otherwise bio‐inert metals, can be evaluated in vitro by immersion studies in simulated body fluid (SBF), mimicking the composition of human plasma. As a result, apatite coating may form on the material surface, and the presence of this bone‐like “biomimetic skin” is considered predictive of bone‐bonding ability in vivo. This review article summarizes the story and evolution of in vitro bioactivity testing methods using SBF, highlighting the influence of testing parameters (e.g., formulation and circulation of the solution) and material‐related parameters (e.g., composition, geometry, texture). Suggestions for future methodological refinements are also provided at the end of the paper