Copyright (c) 2009 University of Pennsylvania All rights reserved. http://repository.upenn.edu/meam_papers Recent documents in Departmental Papers (MEAM) en-us Tue, 15 Sep 2009 23:32:54 PDT 3600 http://repository.upenn.edu/meam_papers/165 http://repository.upenn.edu/meam_papers/165 Mon, 14 Sep 2009 13:04:58 PDT This letter reports the implementation of ultrathin (100 nm) aluminum nitride (AlN) piezoelectric layers for the fabrication of vertically deflecting nanoactuators. The films exhibit an average piezoelectric coefficient (d31~−1.9 pC/N), which is comparable to its microscale counterpart. This allows vertical deflections as large as 40 nm from 18 µm long and 350 nm thick multilayer cantilever bimorph beams with 2 V actuation. Furthermore, in-plane stress and stress gradients have been simultaneously controlled. The films exhibit leakage currents lower than 2 nA/cm2 at 1 V, and have an average relative dielectric constant of approximately 9.2 (as in thicker films). These material characteristics and actuation results make the AlN nanofilms ideal candidates for the realization of nanoelectromechanical switches for low power logic applications. Nipun Sinha http://repository.upenn.edu/meam_papers/164 http://repository.upenn.edu/meam_papers/164 Tue, 26 May 2009 08:00:48 PDT We present a multigrid algorithm for the solution of source identification inverse problems constrained by variable-coefficient linear parabolic partial differential equations. We consider problems in which the inversion variable is a function of space only. We consider the case of L-2 Tikhonov regularization. The convergence rate of our algorithm is mesh-independent-even in the case of no regularization. This feature makes the method algorithmically robust to the value of the regularization parameter, and thus useful for the cases in which we seek high-fidelity reconstructions. The inverse problem is formulated as a PDE-constrained optimization. We use a reduced-space approach in which we eliminate the state and adjoint variables, and we iterate in the inversion parameter space using conjugate gradients. We precondition the Hessian with a V-cycle multigrid scheme. The multigrid smoother is a two-step stationary iterative solver that inexactly inverts an approximate Hessian by iterating exclusively in the high-frequency subspace (using a high-pass filter). We analyze the performance of the scheme for the constant coefficient case with full observations; we analytically calculate the spectrum of the reduced Hessian and the smoothing factor for the multigrid scheme. The forward and adjoint problems are discretized using a backward-Euler finite-difference scheme. The overall complexity of our inversion algorithm is O(NtN + N log(2) N), where N is the number of grid points in space and N-t is the number of time steps. We provide numerical experiments that demonstrate the effectiveness of the method for different diffusion coefficients and values of the regularization parameter. We also provide heuristics, and we conduct numerical experiments for the case with variable coefficients and partial observations. We observe the same complexity as in the constant-coefficient case. Finally, we examine the effectiveness of using the reduced-space solver as a preconditioner for a full-space solver. Santi S. Adavani http://repository.upenn.edu/meam_papers/163 http://repository.upenn.edu/meam_papers/163 Thu, 11 Dec 2008 12:25:20 PST State-of-the art algorithms for deformable image registration are based on the minimization of an image similarity functional that is regularized by adding a penalty term on the deformation map. The penalty function typically represents a smoothness regularization. In this article, we use a constrained optimization formulation in which the image similarity functional is coupled to a biophysical model. This formulation is pertinent when the data have been generated by imaging tissue that undergoes deformations due to an actual biophysical phenomenon. Such is the case of coregistering tumor-bearing brain images from the same individual. We present an approximate model that couples tumor growth with the mechanical deformations of the surrounding brain tissue. We consider primary brain tumors--in particular, gliomas. Glioma growth is modeled by a reaction-advection-diffusion PDE, with a two-way coupling with the underlying tissue elastic deformation. Tumor bulk, infiltration, and subsequent mass effects are not regarded separately but are captured by the model itself in the course of its evolution. Our formulation allows for updating the tumor diffusion coefficient following structural displacements caused by tumor growth/infiltration. Our forward problem implementation builds on the PETSc library of Argonne National Laboratory. Our reformulation results in a very small parameter space, and we use the derivative-free optimization library APPSPACK of Sandia National Laboratories. We test the forward model and the optimization framework by using landmark-based similarity functions and by applying it to brain tumor data from clinical and animal studies. State-of-the-art registration algorithms fail in such problems due to excessive deformations. We compare our results with previous work in our group, and we observed up to 50% improvement in landmark deformation prediction. We present preliminary validation results in which we were able to reconstruct deformation fields using four degrees of freedom. Our study demonstrates the validity of our formulation and points to the need for richer datasets and fast optimization algorithms. Cosmina Hogea http://repository.upenn.edu/meam_papers/162 http://repository.upenn.edu/meam_papers/162 Wed, 26 Nov 2008 08:39:57 PST In this article, we propose new parallel algorithms for the construction and 2:1 balance refinement of large linear octrees on distributed memory machines. Such octrees are used in many problems in computational science and engineering, e.g., object representation, image analysis, unstructured meshing, finite elements, adaptive mesh refinement, and N-body simulations. Fixed-size scalability and isogranular analysis of the algorithms using an MPI-based parallel implementation was performed on a variety of input data and demonstrated good scalability for different processor counts (1 to 1024 processors) on the Pittsburgh Supercomputing Center's TCS-1 AlphaServer. The results are consistent for different data distributions. Octrees with over a billion octants were constructed and balanced in less than a minute on 1024 processors. Like other existing algorithms for constructing and balancing octrees, our algorithms have ϑ (N log N) work and ϑ (N) storage complexity. Under reasonable assumptions on the distribution of octants and the work per octant, the parallel time complexity is ϑ (N/np log np log(N/np) + np log np), where N is the size of the final linear octree and np is the number of processors. Hari Sundar http://repository.upenn.edu/meam_papers/161 http://repository.upenn.edu/meam_papers/161 Wed, 26 Nov 2008 08:16:44 PST Equilibrium adhesion states are analyzed for nonlinear spherical caps adhered to a rigid substrate under the influence of adhesive tractions that depend on the local separation between the shell and substrate. Transitions between bistable snapped-in and snapped-out configurations are predicted as a function of four nondimensional parameters representing the adhesive energy, the undeformed shell curvature, the range of the adhesive interactions, and the magnitude of an externally applied load. Nonuniform energy and traction fields associated with free-edge boundary conditions are calculated to better understand localized phenomena such as the diffusion of impurities into a bonded interface and the diffusion of receptors in the cell membrane. The linear Griffith approximations commonly used in the literature are shown to be limited to shells with a small height to thickness ratio and short-range adhesive interactions. External loading is found to alter the adhered configurations and the spatial distributions of both adhesive and elastic energies. An important implication of the latter analysis is the theoretical prediction of the pull-off force, which is shown to depend not only on the interface properties, but also on the geometric and material parameters of the shell and on both the magnitude and type of external loading. Richard M. Springman http://repository.upenn.edu/meam_papers/160 http://repository.upenn.edu/meam_papers/160 Tue, 25 Nov 2008 13:24:29 PST A solid solution can spontaneously separate into phases that self-assemble into patterns. This process can be guided via external fields to form ordered micro- and nanostructures. In this paper, we demonstrate that notions of interaction energies provide powerful insights into the coupling of these fields with the properties of the alloy. A phase-field model is developed that incorporates chemical, interfacial, and elastic energies, including heterogeneous elastic properties, and couples naturally to externally imposed mechanical fields. Aggregation in bulk and in thin films under patterned external load is investigated. The kinetics and morphology of phase separation are shown to depend significantly on elastic properties of the system, which include elastic heterogeneity and the misfit or transformation strain. Eshelby-type asymptotic estimates for interaction energies are shown to be very useful in understanding and predicting the trends observed from the simulations. John L. Bassani http://repository.upenn.edu/meam_papers/159 http://repository.upenn.edu/meam_papers/159 Mon, 20 Oct 2008 09:32:49 PDT We have numerically investigated the axisymmetric motion of a finite-sized nearly occluding air bubble through a shear-thinning Casson fluid flowing in blood vessels of circular cross section. The numerical solution entails solving a two-layer fluid model - a cell-free layer and a non-Newtonian core together with the gas bubble. This problem is of interest to the field of rheology and for gas embolism studies in health sciences. The numerical method is based on a modified front-tracking method. The viscosity expression in the Casson model for blood (bulk fluid) includes the hematocrit [the volume fraction of red blood cells (RBCs)] as an explicit parameter. Three different flow Reynolds numbers, Reapp=ΡlUmaxd/µapp, in the neighborhood of 0.2, 2, and 200 are investigated. Here, Ρl is the density of blood, Umax is the centerline velocity of the inlet Casson profile, d is the diameter of the vessel, and µapp is the apparent viscosity of whole blood. Three different hematocrits have also been considered: 0.45, 0.4, and 0.335. The vessel sizes considered correspond to small arteries, and small and large arterioles in normal humans. The degree of bubble occlusion is characterized by the ratio of bubble to vessel radius (aspect ratio), λ, in the range 0.9 ≤ λ≤1.05. For arteriolar flow, where relevant, the Fahraeus-Lindqvist effects are taken into account. Both horizontal and vertical vessel geometries have been investigated. Many significant insights are revealed by our study: (i) bubble motion causes large temporal and spatial gradients of shear stress at the "endothelial cell" (EC) surface lining the blood vessel wall as the bubble approaches the cell, moves over it, and passes it by; (ii) rapid reversals occur in the sign of the shear stress (+ → - → +) imparted to the cell surface during bubble motion; (iii) large shear stress gradients together with sign reversals are ascribable to the development of a recirculation vortex at the rear of the bubble; (iv) computed magnitudes of shear stress gradients coupled with their sign reversals may correspond to levels that cause injury to the cell by membrane disruption through impulsive compression and stretching; and (v) for the vessel sizes and flow rates investigated, gravitational effects are negligible. Karthik Mukundakrishnan http://repository.upenn.edu/meam_papers/158 http://repository.upenn.edu/meam_papers/158 Tue, 14 Oct 2008 13:03:50 PDT When an AC electric field was applied across a small gap between two metal electrodes elevated above a surface, rhodamine-phalloidin-labeled actin filaments were attracted to the gap and became suspended between the two electrodes. The variance 〈s2(x)〉 of each filament's horizontal, lateral displacement was measured as a function of electric field intensity and position along the filament. 〈s2(x)〉 markedly decreased as the electric field intensity increased. Hypothesizing that the electric field induces tension in the filament, we estimated the tension using a linear, Brownian dynamic model. Our experimental method provides a novel means for trapping and manipulating biological filaments and for probing the surface conductance and mechanical properties of single polymers. Mark E. Arsenault http://repository.upenn.edu/meam_papers/157 http://repository.upenn.edu/meam_papers/157 Tue, 26 Aug 2008 06:00:38 PDT Recognizing useful modular robot configurations composed of hundreds of modules is a significant challenge. Matching a new modular robot configuration to a library of known configurations is essential in identifying and applying control schemes. We present three different algorithms to address the problem of (a) matching and (b) mapping new robot configurations onto a library of known configurations. The first method solves the problem using graph isomorphisms and can identify configurations that share the same underlying graph structure, but have different port connections amongst the modules. The second approach compares graph spectra of configuration matrices to find a permutation matrix that maps a given configuration to a known one. The third algorithm exploits the unique structure of the problem for the particular robots used in our research to achieve impressive gains in performance and speed over existing techniques, especially for larger configurations. With these three algorithms, this paper presents novel solutions to the problem of configuration recognition and sheds light on theoretical and practical issues for long-term advances in this important area of modular robotics. Results and examples are provided to compare the performance of the three algorithms and discuss their relative advantages. Michael Park http://repository.upenn.edu/meam_papers/156 http://repository.upenn.edu/meam_papers/156 Wed, 16 Jul 2008 11:42:03 PDT Although time-periodic fluid flows sometimes produce mixing via Lagrangian chaos, the additional contribution to mixing caused by nonperiodicity has not been quantified experimentally. Here, we do so for a quasi-two-dimensional flow generated by electromagnetic forcing. Several distinct measures of mixing are found to vary continuously with the Reynolds number, with no evident change in magnitude or slope at the onset of nonperiodicity. Furthermore, the scaled probability distributions of the mean Lyapunov exponent have the same form in the periodic and nonperiodic flow states. M. J. Twardos