Modeling Heterogeneous Materials via Two-Point Correlation Functions: II. Algorithmic Details and Applications

In the first part of this series of two papers, we proposed a theoretical formalism that enables one to model and categorize heterogeneous materials (media) via two-point correlation functions S2 and introduced an efficient heterogeneous-medium (re)construction algorithm called the "lattice-point" algorithm. Here we discuss the algorithmic details of the lattice-point procedure and an algorithm modification using surface optimization to further speed up the (re)construction process. The importance of the error tolerance, which indicates to what accuracy the media are (re)constructed, is also emphasized and discussed. We apply the algorithm to generate three-dimensional digitized realizations of a Fontainebleau sandstone and a boron carbide/aluminum composite from the two- dimensional tomographic images of their slices through the materials. To ascertain whether the information contained in S2 is sufficient to capture the salient structural features, we compute the two-point cluster functions of the media, which are superior signatures of the micro-structure because they incorporate the connectedness information. We also study the reconstruction of a binary laser-speckle pattern in two dimensions, in which the algorithm fails to reproduce the pattern accurately. We conclude that in general reconstructions using S2 only work well for heterogeneous materials with single-scale structures. However, two-point information via S2 is not sufficient to accurately model multi-scale media. Moreover, we construct realizations of hypothetical materials with desired structural characteristics obtained by manipulating their two-point correlation functions.Comment: 35 pages, 19 figure

Effective approach to the Nagaoka regime of the two dimensional t-J model

We argue that the t-J model and the recently proposed Ising version of this model give the same physical picture of the Nagaoka regime for J/t << 1. In particular, both models are shown to give compatible results for a single Nagaoka polaron as well as for a Nagaoka bipolaron. When compared to the standard t-J or t-Jz models, the Ising version allows for a numerical analysis on much larger clusters by means of classical Monte Carlo simulations. Taking the advantage of this fact, we study the low doping regime of t-J model for J/t << 1 and show that the ground state exhibits phase separation into hole-rich ferromagnetic and hole-depleted antiferromagnetic regions. This picture holds true up to a threshold concentration of holes, \delta < \delta_t ~ 0.44 \sqrt{J/t}. Analytical calculations show that \delta_t=\sqrt{J/2\pi t}.Comment: 10 pages, 10 figures, revte

Topology Optimization and 3D printing of Large Deformation Compliant Mechanisms for Straining Biological Tissues

This paper presents a synthesis approach in a density-based topology optimization setting to design large deformation compliant mechanisms for inducing desired strains in biological tissues. The modelling is based on geometrical nonlinearity together with a suitably chosen hypereleastic material model, wherein the mechanical equilibrium equations are solved using the total Lagrangian finite element formulation. An objective based on least-square error with respect to target strains is formulated and minimized with the given set of constraints and the appropriate surroundings of the tissues. To circumvent numerical instabilities arising due to large deformation in low stiffness design regions during topology optimization, a strain-energy based interpolation scheme is employed. The approach uses an extended robust formulation i.e. the eroded, intermediate and dilated projections for the design description as well as variation in tissue stiffness. Efficacy of the synthesis approach is demonstrated by designing various compliant mechanisms for providing different target strains in biological tissue constructs. Optimized compliant mechanisms are 3D-printed and their performances are recorded in a simplified experiment and compared with simulation results obtained by a commercial software.Comment: 23 pages, 14 figure

Physical examination tests of the shoulder: a systematic review and meta-analysis of diagnostic test performance

Background: Physical examination tests of the shoulder (PETS) are clinical examination maneuvers designed to aid the assessment of shoulder complaints. Despite more than 180 PETS described in the literature, evidence of their validity and usefulness in diagnosing the shoulder is questioned. Methods: This meta-analysis aims to use diagnostic odds ratio (DOR) to evaluate how much PETS shift overall probability and to rank the test performance of single PETS in order to aid the clinician’s choice of which tests to use. This study adheres to the principles outlined in the Cochrane guidelines and the PRISMA statement. A fixed effect model was used to assess the overall diagnostic validity of PETS by pooling DOR for different PETS with similar biomechanical rationale when possible. Single PETS were assessed and ranked by DOR. Clinical performance was assessed by sensitivity, specificity, accuracy and likelihood ratio. Results: Six thousand nine-hundred abstracts and 202 full-text articles were assessed for eligibility; 20 articles were eligible and data from 11 articles could be included in the meta-analysis. All PETS for SLAP (superior labral anterior posterior) lesions pooled gave a DOR of 1.38 [1.13, 1.69]. The Supraspinatus test for any full thickness rotator cuff tear obtained the highest DOR of 9.24 (sensitivity was 0.74, specificity 0.77). Compression-Rotation test obtained the highest DOR (6.36) among single PETS for SLAP lesions (sensitivity 0.43, specificity 0.89) and Hawkins test obtained the highest DOR (2.86) for impingement syndrome (sensitivity 0.58, specificity 0.67). No single PETS showed superior clinical test performance. Conclusions: The clinical performance of single PETS is limited. However, when the different PETS for SLAP lesions were pooled, we found a statistical significant change in post-test probability indicating an overall statistical validity. We suggest that clinicians choose their PETS among those with the highest pooled DOR and to assess validity to their own specific clinical settings, review the inclusion criteria of the included primary studies. We further propose that future studies on the validity of PETS use randomized research designs rather than the accuracy design relying less on well-established gold standard reference tests and efficient treatment options

Ultrawide phononic band gap for combined in-plane and out-of-plane waves

We consider two-dimensional phononic crystals formed from silicon and voids, and present optimized unit cell designs for (1) out-of-plane, (2) in-plane and (3) combined out-of-plane and in-plane elastic wave propagation. To feasibly search through an excessively large design space (10e40 possible realizations) we develop a specialized genetic algorithm and utilize it in conjunction with the reduced Bloch mode expansion method for fast band structure calculations. Focusing on high symmetry plain-strain square lattices, we report unit cell designs exhibiting record values of normalized band-gap size for all three categories. For the combined polarizations case, we reveal a design with a normalized band-gap size exceeding 60%.Comment: 4 pages, 1 figure, submitted for journal publicatio