13,054 research outputs found
Basic Understanding of Condensed Phases of Matter via Packing Models
Packing problems have been a source of fascination for millenia and their
study has produced a rich literature that spans numerous disciplines.
Investigations of hard-particle packing models have provided basic insights
into the structure and bulk properties of condensed phases of matter, including
low-temperature states (e.g., molecular and colloidal liquids, crystals and
glasses), multiphase heterogeneous media, granular media, and biological
systems. The densest packings are of great interest in pure mathematics,
including discrete geometry and number theory. This perspective reviews
pertinent theoretical and computational literature concerning the equilibrium,
metastable and nonequilibrium packings of hard-particle packings in various
Euclidean space dimensions. In the case of jammed packings, emphasis will be
placed on the "geometric-structure" approach, which provides a powerful and
unified means to quantitatively characterize individual packings via jamming
categories and "order" maps. It incorporates extremal jammed states, including
the densest packings, maximally random jammed states, and lowest-density jammed
structures. Packings of identical spheres, spheres with a size distribution,
and nonspherical particles are also surveyed. We close this review by
identifying challenges and open questions for future research.Comment: 33 pages, 20 figures, Invited "Perspective" submitted to the Journal
of Chemical Physics. arXiv admin note: text overlap with arXiv:1008.298
Co-Phased 360-Degree Profilometry of Discontinuous Solids with 2-Projectors and 1-Camera
Here we describe a co-phased 360-degree fringe-projection profilometer which
uses 2-projectors and 1-camera and can digitize discontinuous solids with
diffuse light surface. This is called co-phased because the two phase
demodulated analytic-signals from each projection are added coherently. This
360-degree co-phased profilometer solves the self-generated shadows cast by the
object discontinuities due to the angle between the camera and the single
white-light fringe projector in standard profilometry.Comment: 4 pages, 6 Figure
A critical examination of compound stability predictions from machine-learned formation energies
Machine learning has emerged as a novel tool for the efficient prediction of material properties, and claims have been made that machine-learned models for the formation energy of compounds can approach the accuracy of Density Functional Theory (DFT). The models tested in this work include five recently published compositional models, a baseline model using stoichiometry alone, and a structural model. By testing seven machine learning models for formation energy on stability predictions using the Materials Project database of DFT calculations for 85,014 unique chemical compositions, we show that while formation energies can indeed be predicted well, all compositional models perform poorly on predicting the stability of compounds, making them considerably less useful than DFT for the discovery and design of new solids. Most critically, in sparse chemical spaces where few stoichiometries have stable compounds, only the structural model is capable of efficiently detecting which materials are stable. The nonincremental improvement of structural models compared with compositional models is noteworthy and encourages the use of structural models for materials discovery, with the constraint that for any new composition, the ground-state structure is not known a priori. This work demonstrates that accurate predictions of formation energy do not imply accurate predictions of stability, emphasizing the importance of assessing model performance on stability predictions, for which we provide a set of publicly available tests
Faster ASV decomposition for orthogonal polyhedra using the Extreme Vertices Model (EVM)
The alternating sum of volumes (ASV) decomposition is a widely used
technique for converting a B-Rep into a CSG model. The obtained CSG
tree has convex primitives at its leaf nodes, while the contents of
its internal nodes alternate between the set union and difference
operators.
This work first shows that the obtained CSG tree T can also be
expressed as the regularized Exclusive-OR operation among all the
convex primitives at the leaf nodes of T, regardless the structure and
internal nodes of T. This is an important result in the case in which
EVM represented orthogonal polyhedra are used because in this model
the Exclusive-OR operation runs much faster than set union and
difference operations. Therefore this work applies this result to EVM
represented orthogonal polyhedra. It also presents experimental
results that corroborate the theoretical results and includes some
practical uses for the ASV decomposition of orthogonal polyhedra.Postprint (published version
The Average Projected Area Theorem - Generalization to Higher Dimensions
In 3-d the average projected area of a convex solid is 1/4 the surface area,
as Cauchy showed in the 19th century. In general, the ratio in n dimensions may
be obtained from Cauchy's surface area formula, which is in turn a special case
of Kubota's theorem. However, while these latter results are well-known to
those working in integral geometry or the theory of convex bodies, the results
are largely unknown to the physics community---so much so that even the 3-d
result is sometimes said to have first been proven by an astronomer in the
early 20th century! This is likely because the standard proofs in the
mathematical literature are, by and large, couched in terms of concepts that
are may not be familiar to many physicists. Therefore, in this work, we present
a simple geometrical method of calculating the ratio of average projected area
to surface area for convex bodies in arbitrary dimensions. We focus on a
pedagogical, physically intuitive treatment that it is hoped will be useful to
those in the physics community. We do discuss the mathematical background of
the theorem as well, pointing those who may be interested to sources that offer
the proofs that are standard in the fields of integral geometry and the theory
of convex bodies. We also provide discussion of the applications of the
theorem, especially noting that higher-dimensional ratios may be of use for
constructing observational tests of string theory. Finally, we examine the
limiting behavior of the ratio with the goal of offering intuition on its
behavior by pointing out a suggestive connection with a well-known fact in
statistics.Comment: 12 pages, 3 figures, submitted JGP after addition of discussion of
previous work on this topi
Mechanical testing of metallic foams for 3d model and simulation of cell distribution effects
Cellular materials have a bulk matrix with a larger number of voids named also cells. Metallic foams made by powder technology represent stochastic closed cells. The related inhomogeneity leads to a scattering of results both in terms of stressâstrain curves and maximum strength. Scattering is attributed to relative density variations and local cell discontinuities and it is confirmed also in case of dynamic loading. Finite element simulations through geometrical models that are able to capture the void morphology (named âmesoscale modelsâ), confirm these results and some efforts have been already done to quantify the relationship between shape irregularities and mechanical behavior. The aim of this paper is to present the dynamic characterization of an AA7075 closed cell material and to calibrate its mesoscale finite element model according to the related cell shape distribution. Specimens have been derived from a small ingot (45x45x100 mm) divided along sections so that morphological analysis and experimental tests have been carried out. Specimens extracted from a half of the ingot have been used for dynamic compression tests by means of a split Hopkinson bar, meanwhile specimens extracted from the other half of the ingot have been dissected for porosity distribution analyses carried out by means of image analysis. Stress-strain curves obtained from the mechanical tests have been discussed in terms of strain rate and statistical descriptors of the porosity. Successively a 3D-model of the specimen has been generated starting from the Voronoi algorithm, assigning as input the above-mentioned statistical distribution of the porosity. Due to the peculiarity of the cell morphology (e.g. single larger cells), stress-strain localization has been demonstrated as one of the reasons of the scattering found during the experiments. A material model, to reproduce the investigated foam mechanical behavior, has been calibrated. Despite the difference among experiments the material model is able to reproduce all of them. Difference between the model coefficients quantifies roughly the difference due to the local geometry of the cells
Bi-stability resistant to fluctuations
We study a simple micro-mechanical device that does not lose its snap-through
behavior in an environment dominated by fluctuations. The main idea is to have
several degrees of freedom that can cooperatively resist the de-synchronizing
effect of random perturbations. As an inspiration we use the power stroke
machinery of skeletal muscles, which ensures at sub-micron scales and finite
temperatures a swift recovery of an abruptly applied slack. In addition to
hypersensitive response at finite temperatures, our prototypical Brownian snap
spring also exhibits criticality at special values of parameters which is
another potentially interesting property for micro-scale engineering
applications
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