Operations on stable moduli spaces.
Ontology highlight
ABSTRACT:
SUBMITTER: Galatius S
PROVIDER: S-EPMC7194281 | biostudies-literature | 2020
REPOSITORIES: biostudies-literature
Publications
Operations on stable moduli spaces.
Galatius Søren S Randal-Williams Oscar O
Research in the mathematical sciences 20200417 2
We construct certain operations on stable moduli spaces and use them to compare cohomology of moduli spaces of closed manifolds with tangential structure. We obtain isomorphisms in a stable range provided the <i>p</i>-adic valuation of the Euler characteristics agree, for all primes <i>p</i> not invertible in the coefficients for cohomology. ...[more]
Similar Datasets
Project description:We analyze 700 freshly-laid eggs from 58 species (22 families and 13 orders) across three orders of magnitude in egg mass. We study the elastic moduli using three metrics: (i) effective Young's modulus, EFEM, by a combined experimental and numerical method; (ii) elastic modulus, Enano, by nanoindentation, and (iii) theoretical Young's modulus, Etheory. We measure the mineral content by acid-base titration, and crystallographic characteristics by electron backscatter diffraction (EBSD), on representative species. We find that the mineral content ranges between 83.1% (Zebra finch) and 96.5% (ostrich) and is positively correlated with EFEM-23.28 GPa (Zebra finch) and 47.76 GPa (ostrich). The EBSD shows that eggshell is anisotropic and non-homogeneous, and different species have different degrees of crystal orientation and texture. Ostrich eggshell exhibits strong texture in the thickness direction, whereas chicken eggshell has little. Such anisotropy and inhomogeneity are consistent with the nanoindentation tests. However, the crystal characteristics do not appear to correlate with EFEM, as EFEM represents an overall "average" elasticity of the entire shell. The experimental results are consistent with the theoretical prediction of linear elasticity. Our comprehensive investigation into the elastic moduli of avian eggshell over broad taxonomic scales provides a useful dataset for those who work on avian reproduction.
| S-EPMC8533214 | biostudies-literature
Project description:Silicate and oxide glasses are often chemically doped with a variety of cations to tune for desirable properties in technological applications, but their performances are often limited by relatively lower mechanical and elastic properties. Finding a new route to synthesize silica-based glasses with high elastic and mechanical properties needs to be explored. Here, we report a dense SiO2-glass with ultra-high elastic moduli using sound velocity measurements by Brillouin scattering up to 72 GPa at 300 K. High-temperature measurements were performed up to 63 GPa at 750 K and 59 GPa at 1000 K. Compared to compression at 300 K, elevated temperature helps compressed SiO2-glass effectively overcome the kinetic barrier to undergo permanent densification with enhanced coordination number and connectivity. This hot compressed SiO2-glass exhibits a substantially high bulk modulus of 361-429 GPa which is at least 2-3 times greater than the metallic, oxide, and silicate glasses at ambient conditions. Its Poisson's ratio, an indicator for the packing efficiency, is comparable to the metallic glasses. Even after temperature quench and decompression to ambient conditions, the SiO2-glass retains some of its unique properties at compression and possesses a Poisson's ratio of 0.248(11). In addition to chemical alternatives in glass syntheses, coupled compression and heating treatments can be an effective means to enhance mechanical and elastic properties in high-performance glasses.
| S-EPMC9385850 | biostudies-literature
Project description:Modelling the mechanical response of silica glass is still challenging, due to the lack of knowledge concerning the elastic properties of intermediate states of densification. An extensive Brillouin Light Scattering study on permanently densified silica glasses after cold compression in diamond anvil cell has been carried out, in order to deduce the elastic properties of such glasses and to provide new insights concerning the densification process. From sound velocity measurements, we derive phenomenological laws linking the elastic moduli of silica glass as a function of its densification ratio. The found elastic moduli are in excellent agreement with the sparse data extracted from literature, and we show that they do not depend on the thermodynamic path taken during densification (room temperature or heating). We also demonstrate that the longitudinal sound velocity exhibits an anomalous behavior, displaying a minimum for a densification ratio of 5%, and highlight the fact that this anomaly has to be distinguished from the compressibility anomaly of a-SiO2 in the elastic domain.
| S-EPMC4246209 | biostudies-other
Project description:The bilayer bending modulus (Kc) is one of the most important physical constants characterizing lipid membranes, but precisely measuring it is a challenge, both experimentally and computationally. Experimental measurements on chemically identical bilayers often differ depending upon the techniques employed, and robust simulation results have previously been limited to coarse-grained models (at varying levels of resolution). This Communication demonstrates the extraction of Kc from fully atomistic molecular dynamics simulations for three different single-component lipid bilayers (DPPC, DOPC, and DOPE). The results agree quantitatively with experiments that measure thermal shape fluctuations in giant unilamellar vesicles. Lipid tilt, twist, and compression moduli are also reported.
| S-EPMC4183605 | biostudies-literature
Project description:Passive microrheology typically deduces shear elastic loss and storage moduli from displacement time series or mean-squared displacements (MSD) of thermally fluctuating probe particles in equilibrium materials. Common data analysis methods use either Kramers-Kronig (KK) transformation or functional fitting to calculate frequency-dependent loss and storage moduli. We propose a new analysis method for passive microrheology that avoids the limitations of both of these approaches. In this method, we determine both real and imaginary components of the complex, frequency-dependent response function χ(ω) = χ'(ω) + iχ''(ω) as direct integral transforms of the MSD of thermal particle motion. This procedure significantly improves the high-frequency fidelity of χ(ω) relative to the use of KK transformation, which has been shown to lead to artifacts in χ'(ω). We test our method on both model and experimental data. Experiments were performed on solutions of worm-like micelles and dilute collagen solutions. While the present method agrees well with established KK-based methods at low frequencies, we demonstrate significant improvement at high frequencies using our symmetric analysis method, up to almost the fundamental Nyquist limit.
| S-EPMC5954977 | biostudies-literature
Project description:At present, limited functional data exists regarding the application and use of biomechanical and imaging technologies for oral implant osseointegration assessment. The objective of this investigation was to determine the functional apparent moduli (FAMs) that could predict the dynamics of oral implant osseointegration. Using an in vivo dental implant osseous healing model, two FAMs, functional bone apparent modulus (FBAM), and composite tissue apparent modulus (FCAM), of the selected peri-implant structures were calculated via microcomputed tomography (micro-CT) and finite element (FE) simulations in order to support this concept. Results showed significant sensitivity between FAMs and micro-CT parameters, especially between bone mineral density and FBAM, while at extraction defect sites the strongest correlations existed between bone-implant contact and FCAM. Significant enhancement of FCAM indicated progressive functional repair during early osseointegration. Further, the resultant interfacial resistance was predicted by bone mineral content (BMC) and FBAM within a approximately 200 microm peri-implant thickness, while the extraction defects gave zones of approximately 575 microm and 200 microm for BMC and FCAM, respectively. These results suggest that the function of dental implant support can be predicted from a peri-implant structural zone. We conclude that FAMs can be used to predict the dynamics of dental implant osseointegration in vivo.
| S-EPMC2881481 | biostudies-literature
Project description:A number of highly curved membranes in vivo, such as epithelial cell microvilli, have the relatively high sphingolipid content associated with "raft-like" composition. Given the much lower bending energy measured for bilayers with "nonraft" low sphingomyelin and low cholesterol content, observing high curvature for presumably more rigid compositions seems counterintuitive. To understand this behavior, we measured membrane rigidity by fluctuation analysis of giant unilamellar vesicles. We found that including a transmembrane helical GWALP peptide increases the membrane bending modulus of the liquid-disordered (Ld) phase. We observed this increase at both low-cholesterol fraction and higher, more physiological cholesterol fraction. We find that simplified, commonly used Ld and liquid-ordered (Lo) phases are not representative of those that coexist. When Ld and Lo phases coexist, GWALP peptide favors the Ld phase with a partition coefficient of 3-10 depending on mixture composition. In model membranes at high cholesterol fractions, Ld phases with GWALP have greater bending moduli than the Lo phase that would coexist.
| S-EPMC5961461 | biostudies-literature
Project description:Controlling mechanical properties of polymeric biomaterials, including the elastic modulus, is critical to direct cell behavior, such as proliferation and differentiation. Dityrosine photocrosslinking is an attractive and simple method to prepare materials that exhibit a wide range of elastic moduli by rapidly crosslinking tyrosyl-containing polymers. However, high concentrations of commonly used oxidative crosslinking reagents, such as ruthenium-based photoinitiators and persulfates, present cytotoxicity concerns. We found the elastic moduli of materials prepared by crosslinking an artificial protein with tightly controlled tyrosine molarity can be modulated up to 40 kPa by adjusting photoinitiator and persulfate concentrations. Formulations with various concentrations of the crosslinking reagents were able to target a similar material elastic modulus, but excess unreacted persulfate resulted in cytotoxic materials. Therefore, we identified a systematic method to prepare non-cytotoxic photocrosslinked polymeric materials with targeted elastic moduli for potential biomaterials applications in diverse fields, including tissue engineering and 3D bioprinting.
| S-EPMC7082925 | biostudies-literature
Project description:Microtubules play a number of important mechanical roles in almost all cell types in nearly all major phylogenetic trees. We have used a molecular mechanics approach to perform tensile tests on individual tubulin monomers and determined values for the axial and circumferential moduli for all currently known complete sequences. The axial elastic moduli, in vacuo, were found to be 1.25 GPa and 1.34 GPa for alpha- and beta-bovine tubulin monomers. In the circumferential direction, these moduli were 378 MPa for alpha- and 460 MPa for beta-structures. Using bovine tubulin as a template, 269 homologous tubulin structures were also subjected to simulated tensile loads yielding an average axial elastic modulus of 1.10 +/- 0.14 GPa for alpha-tubulin structures and 1.39 +/- 0.68 GPa for beta-tubulin. Circumferentially the alpha- and beta-moduli were 936 +/- 216 MPa and 658 +/- 134 MPa, respectively. Our primary finding is that that the axial elastic modulus of tubulin diminishes as the length of the monomer increases. However, in the circumferential direction, no correlation exists. These predicted anisotropies and scale dependencies may assist in interpreting the macroscale behavior of microtubules during mitosis or cell growth. Additionally, an intergenomic approach to investigating the mechanical properties of proteins may provide a way to elucidate the evolutionary mechanical constraints imposed by nature upon individual subcellular components.
| S-EPMC2553145 | biostudies-literature
Project description:In this work, the authors have demonstrated the use of machine learning (ML) models in the prediction of bulk modulus for High Entropy Alloys (HEA). For the first time, ML has been used for optimizing the composition of HEA to achieve enhanced bulk modulus values. A total of 12 ML algorithms were trained to classify the elemental composition as HEA or non-HEA. Among these models, Gradient Boosting Classifier (GBC) was found to be the most accurate, with a test accuracy of 78%. Further, six regression models were trained to predict the bulk modulus of HEAs, and the best results were obtained by LASSO Regression model with an R-square value of 0.98 and an adjusted R-Square value of 0.97 for the test data set. This work effectively bridges the gap in the discovery and property analysis of HEAs. By accelerating material discovery via providing alternate means for designing virtual alloy compositions having favourable bulk modulus for respective applications, this work opens new avenues of applications of HEAs.
| S-EPMC10665368 | biostudies-literature