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: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:The perivascular space (PVS) surrounds cerebral blood vessels and plays an important role in clearing waste products from the brain. Their anatomy and function have been described for arteries, but PVS around veins remain poorly characterized. Using in vivo 2-photon imaging in mice, we determined the size of the PVS around arteries and veins, and their connection with the subarachnoid space. After infusion of 70 kD FITC-dextran into the cerebrospinal fluid via the cisterna magna, labeled PVS were evident around arteries, but veins showed less frequent labeling of the PVS. The size of the PVS correlated with blood vessel size for both pial arteries and veins, but not for penetrating vessels. The PVS around pial arteries and veins was separated from the subarachnoid space by a thin meningeal layer, which did not form a barrier for the tracer. In vivo, FITC-dextran signal was observed adjacent to the vessel wall, but minimally within the wall itself. Post-mortem, there was a significant shift in the tracer's location within the arterial wall, extending into the smooth muscle layer. Taken together, these findings suggest that the PVS around veins has a limited role in the exchange of solutes between CSF and brain parenchyma.
| S-EPMC11291892 | biostudies-literature
Project description:Paradigmatic model systems, which are used to study the mechanical response of matter, are random networks of point-atoms, random sphere packings, or simple crystal lattices; all of these models assume central-force interactions between particles/atoms. Each of these models differs in the spatial arrangement and the correlations among particles. In turn, this is reflected in the widely different behaviours of the shear (G) and compression (K) elastic moduli. The relation between the macroscopic elasticity as encoded in G, K and their ratio, and the microscopic lattice structure/order, is not understood. We provide a quantitative analytical connection between the local orientational order and the elasticity in model amorphous solids with different internal microstructure, focusing on the two opposite limits of packings (strong excluded-volume) and networks (no excluded-volume). The theory predicts that, in packings, the local orientational order due to excluded-volume causes less nonaffinity (less softness or larger stiffness) under compression than under shear. This leads to lower values of G/K, a well-documented phenomenon which was lacking a microscopic explanation. The theory also provides an excellent one-parameter description of the elasticity of compressed emulsions in comparison with experimental data over a broad range of packing fractions.
| S-EPMC4702120 | biostudies-literature
Project description:Magnetoactive elastomers (MAEs) have gained significant attention in recent years due to their wide range of engineering applications. This paper investigates the important interplay between the particle microstructure and the sample shape of MAEs. A simple analytical expression is derived based on geometrical arguments to describe the particle distribution inside MAEs. In particular, smeared microstructures are considered instead of a discrete particle distribution. As a consequence of considering structured particle arrangements, the elastic free energy is anisotropic. It is formulated with the help of the rule of mixtures. We show that the enhancement of elastic moduli arises not only from the induced dipole-dipole interactions in the presence of an external magnetic field but also considerably from the change in the particle microstructure.
| S-EPMC8780743 | biostudies-literature