ACME 2011 Proceedings of the 19 UK National Conference of the ...

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(a) Molecular dynamics simulation of water molecules (red and white) transported through a short (7,7) carbon nanotube (green lines), shown in cutaway, that is fixed between two graphene membranes (thin gold lines). The water is moving from an upstream to a downstream reservoir. Flow velocity (m/s) Figure 2: Water transport in carbon nanotubes. 5 4 3 2 1 0 0 5 10 15 20 25 30 CNT length (nm) (b) Molecular dynamics calculations of variation of water flow velocity with CNT length under 200 MPa pressure difference. The flow enhancement factors (relative to continuum flow expectations) are 71, 126, and 353 for the 5 nm, 12.5 nm and the 25 nm lengths, respectively. [3] Borg, M. K., Macpherson, G. B. and Reese, J. M., 2010, Controllers for imposing continuum-tomolecular boundary conditions in arbitrary fluid flow geometries, Mol. Sim., 36, 745-757. [4] Macpherson, G. B. and Reese, J. M., 2008, Molecular dynamics in arbitrary geometries: parallel evaluation of pair forces, Mol. Sim., 34, 97-115. [5] Lockerby, D. A., Reese, J. M. and Gallis, M. A., 2005, The usefulness of higher-order constitutive relations for describing the Knudsen layer, Phys. Fluids, 17, 100609. [6] Lockerby, D. A., Reese, J. M. and Gallis, M. A., 2005, Capturing the Knudsen layer in continuumfluid models of non-equilibrium gas flows, AAIA J., 43, 1391-1393. [7] Lockerby, D. A., Reese, J. M. and Struchtrup, H., 2009, Switching criteria for hybrid rarefied gas flow solvers, Proc. Roy. Soc. A, 465, 1581-1598. [8] Gu, X. J. and Emerson, D. R., 2009, A high-order moment approach for capturing non-equilibrium phenomena in the transition regime, J. Fluid Mech., 636, 177-216. [9] Brenner, H. and Ganesan, V., 2000, Molecular wall effects: are conditions at a boundary boundary conditions? Phys. Rev. E, 61, 6879-6897. [10] Macpherson, G. B. and Reese, J. M., 2006, Molecular dynamics for near surface flows in nano liquid and micro gas systems, 4th ASME Intl Conf Nanochannels, Microchannnels & Minichannels, ICNMM2006, 96170. [11] Lockerby, D. A., Reese, J. M., Emerson, D. R. and Barber R. W., 2004, Velocity boundary condition at solid walls in rarefied gas calculation, Phys. Rev. E, 70, 017303. 16
Proceedings of the 19 th UK Conference of the Association for Computational Mechanics in Engineering 5 - 6 April 2011, Heriot-Watt University, Edinburgh NON-INVASIVE AND INVERSE PROPERTY ESTIMATION OF ARTERIAL ELASTICITY *Amarpal S. Kapoor 1 , Perumal Nithiarasu 1 and Raoul Van Loon 1 1 Civil & Computational Engineering Centre, College of Engineering, Swansea University, Singleton Park, Swansea, SA2 8PP *A.S.Kapoor.568964@swansea.ac.uk Key Words: arterial elasticity; non-invasive; inverse property optimization; blood flow ABSTRACT A non-invasive, patient-specific method for the determination of in-vivo arterial elasticity is proposed here. Inverse property optimization, incorporating a 1D blood-flow model and Levenberg Marquardt Optimization render the possibility of accurately estimating the stiffness of arteries. We begin with a steady state analysis as a starting point, gradually implementing more realistic transient state conditions to finally result in a fully spatial and fully transient scheme. Various meshes representative of healthy and diseased arteries have been simulated successfully. Although the current methodology cannot be directly employed as a clinical practice at this point in time, it provides impetus to carry out work on an advanced level, i.e. 4D (3 spatial dimensions plus time). 1 INTRODUCTION A brief motivation for the above work is presented in this section. To have an accurate estimate of arterial elasticity is known to have an important significance in the medical fraternity. It has been long discovered that there is a direct relation between the stiffness of arteries and risk of cardiovascular events [1]. A prior knowledge of arterial elasticity can thus prove to be very important and there has been a rediscovery of this insight with the advent of modern computing framework. A variety of methods have been developed for assessing arterial properties [2]. Most of these methods rely on measuring the pulse wave velocity and assessing the arterial pressure waveforms. These methods provide a single value for the stiffness, which is not always true. Also there are several other factors like age, gender, disease states, smoking habits and possibly others which are not always taken into consideration with these methods. There is another class of methods for arterial elasticity estimation which rely on mechanical testing of specimens, taken from the body. There is an inherent change in material properties as the arteries are removed from the body and is not feasible as a clinical technique, owing to the invasive nature of this method. Moreover, classic risk factors fall short of making accurate predictions of cardiovascular diseases. This is therefore an attempt to develop an engineering based solution to the medical problem being discussed. 17
Page 1: ACME 2011 Proceedings of the 19 th
Page 4 and 5: First published 2011 by Heriot-Watt
Page 7 and 8: CONTENTS Invited Lectures CHALLENGE
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stress [MPa] 1 0 -1 -2 -3 -2.5 -2 -
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Proceedings of the 19 th UK Confere
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ecomes available, the material mode
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where ∂fin ∂UM force 2.5 2 1.5
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Practicallly, the perturbation fiel
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3 SIMULATING CONCRETE MESO-STRUCTUR
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¯K i is an approximation of the co
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h = 5.36 matrix 4.3 z P E f νf 0.9
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From the total hoop strainε θ , t
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3 EXTERIOR POINT ESHELBY BASED CRAC
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is applied uniformly on the edge to
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(a) (b) (c) (d) Figure 1: Influence
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On each subdomain, we then have to
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( i�1) ( i�1) �Un�1 � ε
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� ~ � 1 ψ ~ � � ~ (2) �
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For the case of uni-axial tension,
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3 Numerical results Preliminary num
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The coefficients An cannot be deriv
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The spatial semi-discretisation is
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3 CRITICAL TIME STEP INCREASED WITH
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v/vo 2E-05 1.5E-05 1E-05 5E-06 0 -3
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3 RESULTS AND DISCUSSION Fig. 1a sh
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Model updating from eigenvalue and
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1. If R = ω 2 n, there is no eigen
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F = ´ Ω STv CSv dΩ A = ´ Γ U
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Fig. 3 Wall normal pressure in the
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contact contact (ii). f ≈ f ( d,
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In the analysis of the incident P-w
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elow a certain threshold. In both t
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K/d 2 Effective Permeability 0.0032
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METHOD 2 (Mellor and Herring Type)
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(a) Free Surface Profile from Janos
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2 IMMERSED FLUID SOLVER Consider th
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References [1] R. Mittal and G. Iac
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a second impact on the forward fuse
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Acknowledgement L. Papagiannis is f
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acceptable probability throughout t
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algorithm was then responsible for
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strategy of saving the computationa
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(a) (b) Figure 5. Comparison of (a)
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Thermal load step i i i i Update ,
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Displacement (mm) Conclusions 45 40
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load carrying of the structure to b
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compressive stress field between co
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Unbonded flexible pipes and risers
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Figure 2: (a) Riser configuration (
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Furthermore the total strain varies
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Displacement 14 12 10 8 6 4 2 0 Mem
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As this project was in the conceptu
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kg and additional mass to represent
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1 Step make box 2 Step make cylinde
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element method. The solid model is
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just new element classes) without t
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Fig.4. Frame model and the displace
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capacities to meet with such demand
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esponses. Severe cases are to be co
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2 Numerical results In this section
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the frequency intially increases un
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and F (R) = ⎡ ⎢ ⎣ ... UαT (R
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Merit function g 10 1 10 0 10 -1 10
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2 STRUCTURAL CHARACTERISTICS OF PTM
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Fig. 5. Simplified FE model of a PT
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general the computational results o
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References [1] Ainsworth M, Oden JT
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Error Cause Interpolation Error Ele
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(a) Before Improvement (b) After Im
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een applied to FE fluid flow proble
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Acknowledgements Figure 2: Flowchar
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1 1 ′′ 1 ′′′ 3 ′′ 2
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3 COMBINING SHAPE FUNCTIONS The exp
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electron current). For the case of
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electron concentration (1/cm 3 ) x
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2 CONSERVATION LAW FOR A MOVING CV
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5 NUMERICAL RESULTS A 1-D cellular
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FEM can be found in [3]. In this pa
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h Y 1 0 −1 −2 −3 −4 −5
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applications. The partition of unit
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1.1 1.05 1 0.95 0.9 0.85 0.8 0.75 2
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2 NURBS BASIS FUNCTIONS NURBS are a
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4 RESULTS To illustrate the isoBEM
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290
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1 1 2 { σ ( ξ, s) } = [ D] { ε (
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4.4 Example 4 - A single edge crack
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