Determination of horizon size in state-based peridynamics

Peridynamics is based on integro-differential equations and has a length scale parameter called horizon which gives peridynamics a non-local character. Currently, there are three main peridynamic formulations available in the literature including bond-based peridynamics, ordinary state-based peridynamics and non-ordinary state-based peridynamics. In this study, the optimum horizon size is determined for ordinary state-based peridynamics and non-ordinary state-based peridynamics formulations by using uniform and non-uniform discretisation under dynamic and static conditions. It is shown that the horizon sizes selected as optimum sizes for uniform discretisation can also be used for non-uniform discretisation without introducing significant error to the system. Moreover, a smaller horizon size can be selected for non-ordinary state-based formulation which can yield significant computational advantage. It is also shown that same horizon size can be used for both static and dynamic problems

Derivation of dual horizon state-based peridynamics formulation based on euler-lagrange equation

The numerical solution of peridynamics equations is usually done by using uniform spatial discretisation. Although implementation of uniform discretisation is straightforward, it can increase computational time significantly for certain problems. Instead, non-uniform discretisation can be utilised and different discretisation sizes can be used at different parts of the solution domain. Moreover, the peridynamic length scale parameter, horizon, can also vary throughout the solution domain. Such a scenario requires extra attention since conservation laws must be satisfied. To deal with these issues, dual-horizon peridynamics was introduced so that both non-uniform discretisation and variable horizon sizes can be utilised. In this study, dual-horizon peridynamics formulation is derived by using Euler–Lagrange equation for state-based peridynamics. Moreover, application of boundary conditions and determination of surface correction factors are also explained. Finally, the current formulation is verified by considering two benchmark problems including plate under tension and vibration of a plate

Unraveling the performance of dispersion-corrected functionals for the accurate description of weakly bound natural polyphenols

Long-range non-covalent interactions play a key role in the chemistry of natural polyphenols. We have previously proposed a description of supramolecular polyphenol complexes by the B3P86 density functional coupled with some corrections for dispersion. We couple here the B3P86 functional with the D3 correction for dispersion, assessing systematically the accuracy of the new B3P86-D3 model using for that the well-known S66, HB23, NCCE31, and S12L datasets for non-covalent interactions. Furthermore, the association energies of these complexes were carefully compared to those obtained by other dispersion-corrected functionals, such as B(3)LYP-D3, BP86-D3 or B3P86-NL. Finally, this set of models were also applied to a database composed of seven non-covalent polyphenol complexes of the most interest.FDM acknowledges financial support from the Swedish Research Council (Grant No. 621-2014-4646) and SNIC (Swedish National Infrastructure for Computing) for providing computer resources. The work in Limoges (IB and PT) is supported by the “Conseil Régional du Limousin”. PT gratefully acknowledges the support by the Operational Program Research and Development Fund (project CZ.1.05/2.1.00/03.0058 of the Ministry of Education, Youth and Sports of the Czech Republic). IB gratefully acknowledges financial support from “Association Djerbienne en France”

A peridynamic based machine learning model for one-dimensional and two-dimensional structures

With the rapid growth of available data and computing resources, using data-driven models is a potential approach in many scientific disciplines and engineering. However, for complex physical phenomena that have limited data, the data-driven models are lacking robustness and fail to provide good predictions. Theory-guided data science is the recent technology that can take advantage of both physics-driven and data-driven models. This study presents a novel peridynamics based machine learning model for one and two-dimensional structures. The linear relationships between the displacement of a material point and displacements of its family members and applied forces are obtained for the machine learning model by using linear regression. The numerical procedure for coupling the peridynamic model and the machine learning model is also provided. The numerical procedure for coupling the peridynamic model and the machine learning model is also provided. The accuracy of the coupled model is verified by considering various examples of a one-dimensional bar and two-dimensional plate. To further demonstrate the capabilities of the coupled model, damage prediction for a plate with a pre-existing crack, a two-dimensional representation of a three-point bending test, and a plate subjected to dynamic load are simulated

A Common and Unstable Copy Number Variant Is Associated with Differences in Glo1 Expression and Anxiety-Like Behavior

Glyoxalase 1 (Glo1) has been implicated in anxiety-like behavior in mice and in multiple psychiatric diseases in humans. We used mouse Affymetrix exon arrays to detect copy number variants (CNV) among inbred mouse strains and thereby identified a ∼475 kb tandem duplication on chromosome 17 that includes Glo1 (30,174,390–30,651,226 Mb; mouse genome build 36). We developed a PCR-based strategy and used it to detect this duplication in 23 of 71 inbred strains tested, and in various outbred and wild-caught mice. Presence of the duplication is associated with a cis-acting expression QTL for Glo1 (LOD>30) in BXD recombinant inbred strains. However, evidence for an eQTL for Glo1 was not obtained when we analyzed single SNPs or 3-SNP haplotypes in a panel of 27 inbred strains. We conclude that association analysis in the inbred strain panel failed to detect an eQTL because the duplication was present on multiple highly divergent haplotypes. Furthermore, we suggest that non-allelic homologous recombination has led to multiple reversions to the non-duplicated state among inbred strains. We show associations between multiple duplication-containing haplotypes, Glo1 expression and anxiety-like behavior in both inbred strain panels and outbred CD-1 mice. Our findings provide a molecular basis for differential expression of Glo1 and further implicate Glo1 in anxiety-like behavior. More broadly, these results identify problems with commonly employed tests for association in inbred strains when CNVs are present. Finally, these data provide an example of biologically significant phenotypic variability in model organisms that can be attributed to CNVs

E2F1 Regulates Cellular Growth by mTORC1 Signaling

During cell proliferation, growth must occur to maintain homeostatic cell size. Here we show that E2F1 is capable of inducing growth by regulating mTORC1 activity. The activation of cell growth and mTORC1 by E2F1 is dependent on both E2F1's ability to bind DNA and to regulate gene transcription, demonstrating that a gene induction expression program is required in this process. Unlike E2F1, E2F3 is unable to activate mTORC1, suggesting that growth activity could be restricted to individual E2F members. The effect of E2F1 on the activation of mTORC1 does not depend on Akt. Furthermore, over-expression of TSC2 does not interfere with the effect of E2F1, indicating that the E2F1-induced signal pathway can compensate for the inhibitory effect of TSC2 on Rheb. Immunolocalization studies demonstrate that E2F1 induces the translocation of mTORC1 to the late endosome vesicles, in a mechanism dependent of leucine. E2F1 and leucine, or insulin, together affect the activation of S6K stronger than alone suggesting that they are complementary in activating the signal pathway. From these studies, E2F1 emerges as a key protein that integrates cell division and growth, both of which are essential for cell proliferation