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- RPI SCOREC - Technical Reports

viscoelastic problem is based on recognizing that the measured displacement fields and the reconstructed material properties satisfy the appropriate equations of motion In the most general case these are the equations of conservation of momentum for the time harmonic response of an incompressible isotropic material in three dimensions Often approximations are introduced leading to simplified models that include the scalar Helmholtz equation anti plane shear plane stress and plane strain We consider each of these models as well as the original three dimensional time harmonic viscoelastic equations In each case we analyze the uniqueness of the inverse problem given single or multiple measurements We also develop and implement a unified variational method for solving all these problems With regards to the uniqueness of these problems we make the following observations 1 the problem of plane stress with a single measurement is identical to that of anti plane shear with two measurements 2 the problem of plane strain and the 3D problem share the same uniqueness properties and that these problems are more ill posed than those of plane stress and anti plane strain 3 in every case including more measurements helps considerably in reducing the space of possible solutions thus

Original URL path: http://www.scorec.rpi.edu/reports/view_report.php?id=566 (2015-07-15)

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imaging where the material modulus distributions are used to detect and or diagnose cancerous tumors We analyze the well posedness of the strong form of these problems and conclude that for the solution to exist the measured displacement field is required to satisfy rather restrictive compatibility conditions We propose a weak or a variational formulation and prove the existence and uniqueness of solutions under milder conditions on measured data This

Original URL path: http://www.scorec.rpi.edu/reports/view_report.php?id=567 (2015-07-15)

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The spatial distribution of these elastic parameters is determined by solving an inverse problem within the region of interest ROI This inverse problem solution requires the knowledge of the displacement fields at small and large strains The displacement fields are measured using a free hand ultrasound strain imaging technique wherein a linear array ultrasound transducer is positioned on the breast and radio frequency echo signals are recorded within the ROI

Original URL path: http://www.scorec.rpi.edu/reports/view_report.php?id=568 (2015-07-15)

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consider an inverse problem in linear elastostatics formulated as a constrained optimization problem We demonstrate well posedness of the linearized saddle point problem when the displacements are given in H2 and modulus field in H1 This higher than usual regularity requirement motivates the use of novel finite element spaces Here we choose a C1 quadratic B splines basis for the displacement field A consistent symmetric discretization in this space yields

Original URL path: http://www.scorec.rpi.edu/reports/view_report.php?id=569 (2015-07-15)

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a single frequency throughout the imaging domain The goal is to determine how the quantities 1 amplitude of displacement or alternatively 2 the displacement itself the average displacement the phase or the phase gradient change within a homogeneous stiff inclusion embedded within a homogeneous background The result are easily interpreted formulas that show the dependence on the radius of the inclusion the frequency and the stiffness contrast between the inclusion

Original URL path: http://www.scorec.rpi.edu/reports/view_report.php?id=570 (2015-07-15)

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the lack of a quantitative subgrid model to for the air entrainment process which plays a critical role in this problem In this paper we present in detail a computational multiphase fluid dynamics CMFD based approach for analyzing this problem The main ingredients of this approach are a comprehensive subgrid air entrainment model that predicts both the rate and location of the air entrainment and a two fluid transport model

Original URL path: http://www.scorec.rpi.edu/reports/view_report.php?id=571 (2015-07-15)

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is given a measured deformation field in a 2D domain Ω and seeks to reconstruct the pointwise distribution of material parameters within Ω Two classes of models are considered The simpler class is material models characterized by a single material parameter exemplified by the Neo Hookean model The second class of material models considered is characterized by two material parameters and includes a simplified Veronda Westmann model a Blatz model

Original URL path: http://www.scorec.rpi.edu/reports/view_report.php?id=572 (2015-07-15)

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LES formulation it is the strong form of these equations In the residual based variational multiscale RBVM formulation the basic idea is to split the solution and weighting function spaces into coarse and fine scale partitions Splitting the weighting functions in this way yields two sets of coupled equations one for the coarse or the resolved scales and another for the fine or the unresolved scales The equations for the fine scales are observed to be driven by the residual of the coarse scale solution projected onto the fine scale space These equations are solved approximately and the solution is substituted in the equations for the coarse scales In this way the effect of the unresolved scales on the resolved scales is modeled In this thesis we develop and test several LES models that are based on the RBVM formulation These include 1 The RBVM model which is extended to compressible flows for the first time 2 A new mixed model for compressible flows comprised of the RBVM model and the traditional Smagorinsky type eddy viscosity model In this model the RBVM term is used to model the cross stresses and the eddy viscosity is used to model the Reynolds

Original URL path: http://www.scorec.rpi.edu/reports/view_report.php?id=573 (2015-07-15)

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