722 research outputs found
An extended finite element method with smooth nodal stress
The enrichment formulation of double-interpolation finite element method
(DFEM) is developed in this paper. DFEM is first proposed by Zheng \emph{et al}
(2011) and it requires two stages of interpolation to construct the trial
function. The first stage of interpolation is the same as the standard finite
element interpolation. Then the interpolation is reproduced by an additional
procedure using the nodal values and nodal gradients which are derived from the
first stage as interpolants. The re-constructed trial functions are now able to
produce continuous nodal gradients, smooth nodal stress without post-processing
and higher order basis without increasing the total degrees of freedom. Several
benchmark numerical examples are performed to investigate accuracy and
efficiency of DFEM and enriched DFEM. When compared with standard FEM,
super-convergence rate and better accuracy are obtained by DFEM. For the
numerical simulation of crack propagation, better accuracy is obtained in the
evaluation of displacement norm, energy norm and the stress intensity factor
Very high energy emission from the hard spectrum sources HESS J1641-463, HESS J1741-302 and HESS J1826-130
A recent study of the diffuse -ray emission in the Central Molecular
Zone using very high energy (VHE, E 0.1 TeV) H.E.S.S. data suggests that
the Galactic Center (GC) is the most plausible supplier of Galactic
ultra-relativistic cosmic-rays (CRs) up to the knee at about 10 eV
(PeV). However, the GC might not be the only source capable to accelerate CRs
up to PeV energies in the Galaxy. Here we present H.E.S.S. data analysis
results and interpretation of three H.E.S.S. sources, with spectra extending
beyond 10 TeV and relatively hard spectral indices compared with the average
spectral index of H.E.S.S. sources, namely HESS J1641-463, HESS J1741-302 and
HESS J1826-130. Although the nature of these VHE -ray sources is still
open, their spectra suggest that the astrophysical objects producing such
emission must be capable of accelerating the parental particle population up to
energies of at least several hundreds of TeV. Assuming a hadronic scenario,
dense gas regions can provide rich target material for accelerated particles to
produce VHE -ray emission via proton-proton interactions followed by a
subsequent decay. Thus, detailed investigations of the interstellar
medium along the line of sight to all of these sources have been performed by
using data from available atomic and molecular hydrogen surveys. The results
point out the existence of dense interstellar gas structures coincident with
the best fit positions of these sources. One can find possible hadronic models
with CRs being accelerated close to the PeV energies to explain the
-ray emission from all of these sources, which opens up the possibility
that a population of PeV CR accelerators might be active in the Galaxy.Comment: 8 pages, 2 figures, in Proceedings of 35th ICRC, Busan (Korea) 201
HESS J1826130: A Very Hard -Ray Spectrum Source in the Galactic Plane
HESS J1826130 is an unidentified hard spectrum source discovered by
H.E.S.S. along the Galactic plane, the spectral index being = 1.6 with
an exponential cut-off at about 12 TeV. While the source does not have a clear
counterpart at longer wavelengths, the very hard spectrum emission at TeV
energies implies that electrons or protons accelerated up to several hundreds
of TeV are responsible for the emission. In the hadronic case, the VHE emission
can be produced by runaway cosmic-rays colliding with the dense molecular
clouds spatially coincident with the H.E.S.S. source.Comment: 6 pages, 3 figures, Proceedings of the 6th International Symposium on
High Energy Gamma-Ray Astronomy (Gamma2016), Heidelberg, German
Isogeometric analysis for functionally graded microplates based on modified couple stress theory
Analysis of static bending, free vibration and buckling behaviours of
functionally graded microplates is investigated in this study. The main idea is
to use the isogeometric analysis in associated with novel four-variable refined
plate theory and quasi-3D theory. More importantly, the modified couple stress
theory with only one material length scale parameter is employed to effectively
capture the size-dependent effects within the microplates. Meanwhile, the
quasi-3D theory which is constructed from a novel seventh-order shear
deformation refined plate theory with four unknowns is able to consider both
shear deformations and thickness stretching effect without requiring shear
correction factors. The NURBS-based isogeometric analysis is integrated to
exactly describe the geometry and approximately calculate the unknown fields
with higher-order derivative and continuity requirements. The convergence and
verification show the validity and efficiency of this proposed computational
approach in comparison with those existing in the literature. It is further
applied to study the static bending, free vibration and buckling responses of
rectangular and circular functionally graded microplates with various types of
boundary conditions. A number of investigations are also conducted to
illustrate the effects of the material length scale, material index, and
length-to-thickness ratios on the responses of the microplates.Comment: 57 pages, 14 figures, 18 table
A volume-averaged nodal projection method for the Reissner-Mindlin plate model
We introduce a novel meshfree Galerkin method for the solution of
Reissner-Mindlin plate problems that is written in terms of the primitive
variables only (i.e., rotations and transverse displacement) and is devoid of
shear-locking. The proposed approach uses linear maximum-entropy approximations
and is built variationally on a two-field potential energy functional wherein
the shear strain, written in terms of the primitive variables, is computed via
a volume-averaged nodal projection operator that is constructed from the
Kirchhoff constraint of the three-field mixed weak form. The stability of the
method is rendered by adding bubble-like enrichment to the rotation degrees of
freedom. Some benchmark problems are presented to demonstrate the accuracy and
performance of the proposed method for a wide range of plate thicknesses
Guaranteed error bounds in homogenisation: an optimum stochastic approach to preserve the numerical separation of scales
This paper proposes a new methodology to guarantee the accuracy of the homogenisation schemes that are traditionally employed to approximate the solution of PDEs with random, fast evolving diffusion coefficients. More precisely, in the context of linear elliptic diffusion problems in randomly packed particulate composites, we develop an approach to strictly bound the error in the expectation and second moment of quantities of interest, without ever solving the fine-scale, intractable stochastic problem. The most attractive feature of our approach is that the error bounds are computed without any integration of the fine-scale features. Our computations are purely macroscopic, deterministic and remain tractable even for small scale ratios. The second contribution of the paper is an alternative derivation of modelling error bounds through the Prager–Synge hypercircle theorem. We show that this approach allows us to fully characterise and optimally tighten the interval in which predicted quantities of interest are guaranteed to lie. We interpret our optimum result as an extension of Reuss–Voigt approaches, which are classically used to estimate the homogenised diffusion coefficients of composites, to the estimation of macroscopic engineering quantities of interest. Finally, we make use of these derivations to obtain an efficient procedure for multiscale model verification and adaptation
Application of smooth particle hydrodynamics method for modelling blood flow with thrombus formation
Thrombosis plays a crucial role in atherosclerosis or in haemostasis when a blood vessel is injured. This article focuses on using a meshless particle-based Lagrangian numerical technique, the smoothed particles hydrodynamic (SPH) method, to study the flow behaviour of blood and to explore the flow parameters that induce formation of a thrombus in a blood vessel. Due to its simplicity and effectiveness, the SPH method is employed here to simulate the process of thrombogenesis and to study the effect of various blood flow parameters. In the present SPH simulation, blood is modelled by two sets of particles that have the characteristics of plasma and of platelet, respectively. To simulate coagulation of platelets which leads to a thrombus, the so-called adhesion and aggregation mechanisms of the platelets during this process are modelled by an inter-particle force model. The transport of platelets in the flowing blood, platelet adhesion and aggregation processes are coupled with viscous blood flow for various low Reynolds number scenarios. The numerical results are compared with the experimental observations and a good agreement is found between the simulated and experimental results
Discovery of the VHE gamma-ray source HESS J1641-463
A new TeV source, HESS J1641-463, has been serendipitously discovered in the
Galactic plane by the High Energy Stereoscopic System (H.E.S.S.) at a
significance level of 8.6 standard deviations. The observations of HESS
J1641-463 were performed between 2004 and 2011 and the source has a moderate
flux level of 1.7% of the Crab Nebula flux at E > 1 TeV. HESS J1641-463 has a
rather hard photon index of 1.99 +- 0.13_stat +- 0.20_sys. HESS J1641-463 is
positionally coincident with the radio supernova remnant SNR G338.5+0.1, but no
clear X-ray counterpart has been found in archival Chandra observations of the
region. Different possible VHE production scenarios will be discussed in this
contribution.Comment: 5 pages, 5 figures, 2012 Fermi Symposium proceedings - eConf C12102
Mathematical investigation of normal and abnormal wound healing dynamics:local and non-local model
The movement of cells during (normal and abnormal) wound healing is the result of biomechanical interactions that combine cell responses with growth factors as well as cell-cell and cell-matrix interactions (adhesion and remodelling). It is known that cells can communicate and interact locally and non-locally with other cells inside the tissues through mechanical forces that act locally and at a distance, as well as through long non-conventional cell protrusions. In this study, we consider a non-local partial differential equation model for the interactions between fibroblasts, macrophages and the extracellular matrix (ECM) via a growth factor (TGF-β) in the context of wound healing. For the non-local interactions, we consider two types of kernels (i.e., a Gaussian kernel and a cone-shaped kernel), two types of cell-ECM adhesion functions (i.e., adhesion only to higher-density ECM vs. adhesion to higher-/lower-density ECM) and two types of cell proliferation terms (i.e., with and without decay due to overcrowding). We investigate numerically the dynamics of this non-local model, as well as the dynamics of the localised versions of this model (i.e., those obtained when the cell perception radius decreases to 0). The results suggest the following: (i) local models explain normal wound healing and non-local models could also explain abnormal wound healing (although the results are parameter-dependent); (ii) the models can explain two types of wound healing, i.e., by primary intention, when the wound margins come together from the side, and by secondary intention when the wound heals from the bottom up.</p
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