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Modeling laser attenuation in reacting flows using adaptive finite elements 55

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Modeling laser attenuation in reacting flows using adaptive ...

55th AIAA Aerospace sciences Meeting

作者： Bauman, Paul T. Adowski, Timothy R. Department of Mechanical and Aerospace Engineering Computational and Data-Enabled Science and Engineering University at Buffalo State University of New York BuffaloNY14260-4400 United States Department of Mechanical and Aerospace Engineering University at Buffalo State University of New York BuffaloNY14260-4400 United States

ISBN: (数字)9781624104473

ISBN: (纸本)9781624104473

In this work, we demonstrate the use of adaptive finite element analysis in low speed chemically reacting flows to compute the attenuation of laser intensity through an arbitrary path in the domain. We use adjoint-based error estimates to estimate the error in the computed intensity and drive adaptive mesh refinement. We discuss details of the implementation with the GRINS multiphysics framework, built on the libMesh finite element library. We present an example illustrating the adjoint solution and resulting adapted mesh for a laser attenuation quantity-of-interest in a two-dimensional reacting flow with heterogeneous carbon surface chemistry. © 2017 by Paul T. Bauman.

关键词： Chemically Reacting Flow Diode Lasers Adaptive Mesh Refinement Finite Element Formulation Doppler Broadening Beer Lambert Law Computing Thermal Boundary Condition Navier Stokes Equations Mathematical Models

Transient crosslinking kinetics optimize gene cluster interactions

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arXiv 2018年

作者： Walker, Benjamin Taylor, Dane Lawrimore, Josh Hult, Caitlin Adalsteinsson, David Bloom, Kerry Gregory Forest, M. Department of Mathematics University of North Carolina at Chapel Hill Department of Mathematics University at Buffalo State University of New York Computational and Data Enabled Science and Engineering University at Buffalo State University of New York Department of Microbiology and Immunology University of Michigan Medical School Department of Chemical Engineering University of Michigan Departments of Applied Physical Sciences and Biomedical Engineering University of North Carolina at Chapel Hill Department of Biology University of North Carolina at Chapel Hill

Our understanding of how chromosomes structurally organize and dynamically interact has been revolutionized through the lens of long-chain polymer physics. Major protein contributors to chromosome structure and dynamics are condensin and cohesin that stochastically generate loops within and between chains, and entrap proximal strands of sister chromatids. In this paper, we explore the ability of transient, protein-mediated, gene-gene crosslinks to induce clusters of genes, thereby dynamic architecture, within the highly repeated ribosomal DNA that comprises the nucleolus of budding yeast. We implement three approaches: live cell microscopy;computational modeling of the full genome during G1 in budding yeast, exploring four decades of timescales for transient crosslinks between 5kbp domains (genes) in the nucleolus on Chromosome XII;and, temporal network models with automated community (cluster) detection algorithms applied to the full range of 4D modeling datasets. The data analysis tools detect and track gene clusters, their size, number, persistence time, and their plasticity (deformation). Of biological significance, our analysis reveals an optimal mean crosslink lifetime that promotes pairwise and cluster gene interactions through "flexible" clustering. In this state, large gene clusters self-assemble yet frequently interact (merge and separate), marked by gene exchanges between clusters, which in turn maximizes global gene interactions in the nucleolus. This regime stands between two limiting cases each with far less global gene interactions: with shorter crosslink lifetimes, "rigid" clustering emerges with clusters that interact infrequently;with longer crosslink lifetimes, there is a dissolution of clusters. These observations are compared with imaging experiments on a normal yeast strain and two condensin-modified mutant cell strains. We apply the same image analysis pipeline to the experimental and simulated datasets, providing support for the modeling pred

关键词： Genes

GRINS: A multiphysics framework based on the libMesh finite element library

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GRINS: A multiphysics framework based on the libMesh finite ...

作者： Bauman, Paul T. Stogner, Roy H. Mechanical and Aerospace Engineering Computational and Data-Enabled Science and Engineering University at Buffalo State University of New York BuffaloNY14260-4400 United States Institute for Computational Engineering and Sciences University of Texas at Austin AustinTX78712 United States

This paper describes a flexible C++ software framework, called GRINS, for simulating complex multiphysics systems of partial differential equations using the finite element method. GRINS is designed to facilitate the rapid development and reuse of finite element formulation code as well as other features of complex simulations, including quantity-of-interest functionals, solvers, boundary conditions, initial conditions, and postprocessing. GRINS is built on the FEMSystem framework that is part of the libMesh finite element library. GRINS, through FEMSystem and libMesh, supports a number of contemporary algorithms and computing features including hybrid distributed and shared memory parallelism, parallel adaptive mesh refinement on unstructured grids, goal-oriented refinement driven by dual-weighted residual error estimates in quantities of interest, and adjoint-based parameter sensitivities. GRINS is deployed both as an application binary, allowing immediate use of existing features, and as a library to which the user may build and link a stand-alone application, extending the framework to their needs. Several examples demonstrate the effectiveness of the design, including uncertainty quantification applications. Planned developments are also discussed. © 2016 Society for Industrial and Applied Mathematics.

关键词： Multiphysics

An accurate front capturing scheme for tumor growth models with a free boundary limit

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arXiv 2017年

作者： Liu, Jian-Guo Tang, Min Wang, Li Zhou, Zhennan Department of Mathematics Department of Physics Duke University Department of Mathematics Institute of Natural Sciences MOE LSC Shanghai Jiao Tong University Department of Mathematics Computational and Data-Enabled Science and Engineering Program State University of New York Buffalo United States Department of Mathematics Duke University

We consider a class of tumor growth models under the combined effects of density-dependent pressure and cell multiplication, with a free boundary model as its singular limit when the pressure-density relationship becomes highly nonlinear. In particular, the constitutive law connecting pressure p and density ρ is p(ρ) = mm−1 ρm−1, and when m 1, the cell density ρ may evolve its support due to a pressure-driven geometric motion with sharp interface along the boundary of its support. The nonlinearity and degeneracy in the diffusion bring great challenges in numerical simulations, let alone the capturing of the singular free boundary limit. Prior to the present paper, there is lack of standard mechanism to numerically capture the front propagation speed as m 1. In this paper, we develope a numerical scheme based on a novel prediction-correction reformulation that can accurately approximate the front propagation even when the nonlinearity is extremely strong. We show that the semi-discrete scheme naturally connects to the free boundary limit equation as m → ∞, and with proper spacial discretization, the fully discrete scheme has improved stability, preserves positivity, and implements without nonlinear solvers. Finally, extensive numerical examples in both one and two dimensions are provided to verify the claimed properties and showcase good performance in various applications.35K55, 35B25, 76D27, 92C50 Copyright © 2017, The Authors. All rights reserved.

关键词： Tumors

Stability of stationary inverse transport equation in diffusion scaling

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arXiv 2017年

作者： Chen, Ke Li, Qin Wang, Li Mathematics Department University of Wisconsin-Madison 480 Lincoln Dr. MadisonWI53705 United States Department of Mathematics Computational and Data-Enabled Science and Engineering Program State University of New York at Buffalo 244 Mathematics Building BuffaloNY14206 United States

We consider the inverse problem of reconstructing the optical parameters for stationary radiative transfer equation (RTE) from velocity-averaged measurement. The RTE often contains multiple scales characterized by the magnitude of a dimensionless parameter-the Knudsen number (Kn). In the diffusive scaling (Kn 1), the stationary RTE is well approximated by an elliptic equation in the forward setting. However, the inverse problem for the elliptic equation is acknowledged to be severely ill-posed as compared to the well-posedness of inverse transport equation, which raises the question of how uniqueness being lost as Kn → 0. We tackle this problem by examining the stability of inverse problem with varying Kn. We show that, the discrepancy in two measurements is amplified in the reconstructed parameters at the order of Knp (p = 1 or 2), and as a result lead to ill-posedness in the zero limit of Kn. Our results apply to both continuous and discrete settings. Some numerical tests are performed in the end to validate these theoretical findings. Copyright © 2017, The Authors. All rights reserved.

关键词： Parameter estimation

A NEW NUMERICAL APPROACH TO INVERSE TRANSPORT EQUATION WITH ERROR ANALYSIS

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arXiv 2017年

作者： Li, Qin Shu, Ruiwen Wang, Li Mathematics Department University of Wisconsin-Madison 480 Lincoln Dr. MadisonWI53705 United States Department of Mathematics Computational and Data-Enabled Science and Engineering Program State University of New York at Buffalo 244 Mathematics Building BuffaloNY14206 United States

The inverse radiative transfer problem finds broad applications in medical imaging, atmospheric science, astronomy, and many other areas. This problem intends to recover the optical properties, denoted as absorption and scattering coefficient of the media, through the source-measurement pairs. A typical computational approach is to form the inverse problem as a PDE-constraint optimization, with the minimizer being the to-be-recovered coefficients. The method is tested to be efficient in practice, but lacks analytical justification: there is no guarantee of the existence or uniqueness of the minimizer, and the error is hard to quantify. In this paper, we provide a different algorithm by levering the ideas from singular decomposition analysis. Our approach is to decompose the measurements into three components, two out of which encode the information of the two coefficients respectively. We then split the optimization problem into two subproblems and use those two components to recover the absorption and scattering coefficients separately. In this regard, we prove the well-posedness of the new optimization, and the error could be quantified with better precision. In the end, we incorporate the diffusive scaling and show that the error is harder to control in the diffusive limit. Copyright © 2017, The Authors. All rights reserved.

关键词： Recovery

data-driven brain network models predict individual variability in behavior

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arXiv 2018年

作者： Bansal, Kanika Medaglia, John D. Bassett, Danielle S. Vettel, Jean M. Muldoon, Sarah F. Department of Mathematics University at Buffalo BuffaloNY United States U.S. Army Research Laboratory Aberdeen Proving GroundMD United States Department of Biomedical Engineering Columbia University New YorkNY United States Department of Psychology Drexel University PhiladelphiaPA United States Department of Neurology Perelman School of Medicine University of Pennsylvania PhiladelphiaPA United States Department of Biomedical Engineering University of Pennsylvania PhiladelphiaPA United States Department of Electrical and Systems Engineering University of Pennsylvania PhiladelphiaPA United States Department of Physics and Astronomy University of Pennsylvania PhiladelphiaPA United States Department of Psychological and Brain Sciences University of California Santa BarbaraCA United States Computational and Data-Enabled Science and Engineering Program University at Buffalo-SUNY BuffaloNY United States

The relationship between brain structure and function has been probed using a variety of approaches, but how the underlying structural connectivity of the human brain drives behavior is far from understood. To investigate the effect of anatomical brain organization on human task performance, we use a data-driven computational modeling approach and explore the functional effects of naturally occurring structural differences in brain networks. We construct personalized brain network models by combining anatomical connectivity estimated from diffusion spectrum imaging of individual subjects with a nonlinear model of brain dynamics. By performing computational experiments in which we measure the excitability of the global brain network and spread of synchronization following a targeted computational stimulation, we quantify how individual variation in the underlying connectivity impacts both local and global brain dynamics. We further relate the computational results to individual variability in the subjects' performance of three language-demanding tasks both before and after transcranial magnetic stimulation to the left-inferior frontal gyrus. Our results show that task performance correlates with either local or global measures of functional activity, depending on the complexity of the task. By emphasizing differences in the underlying structural connectivity, our model serves as a powerful tool to predict individual differences in task performances, to dissociate the effect of targeted stimulation in tasks that differ in cognitive complexity, and to pave the way for the development of personalized therapeutics. Copyright © 2018, The Authors. All rights reserved.

关键词： Digital storage

Stability of Inverse Transport Equation in Diffusion Scaling And Fokker-Planck Limit

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arXiv 2017年

作者： Chen, Ke LI, Qin Wang, Li Mathematics Department University of Wisconsin-Madison 480 Lincoln Dr. MadisonWI53705 United States Mathematics Department and Wisconsin Institute of Discovery University of Wisconsin-Madison 480 Lincoln Dr. MadisonWI53705 United States Department of Mathematics Computational and Data-Enabled Science and Engineering Program State University of New York at Buffalo 244 Mathematics Building BuffaloNY14206 United States

We consider the inverse problem of reconstructing the scattering and absorption coefficients using boundary measurements for a time dependent radiative transfer equation (RTE). As the measurement is mostly polluted by errors, both experimental and computational, an important question is to quantify how the error is amplified in the process of reconstruction. In the forward setting, the solution to the RTE behaves differently in different regimes, and the stability of the inverse problem vary accordingly. In particular, we consider two scalings in this paper. The first one concerns with a diffusive scaling whose macroscopic limit is a diffusion equation. In this case, we showed, following the similar approach as in [Chen, Li and Wang, arXiv:1703.00097], that the stability degrades when the limit is taken. The second one considers a highly forward peaked scattering, wherein the scattering operator is approximated by a Fokker-Planck operator as a limit. In this case, we showed that a fully recover of the scattering coefficient is less possible in the limit, whereas obtaining a rescaled version of the scattering coefficient becomes more practice friendly. Copyright © 2017, The Authors. All rights reserved.

关键词： Inverse problems

Enabling the statistical calibration of active nitridation of graphite by atomic nitrogen 45

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Enabling the statistical calibration of active nitridation o...

45th AIAA Thermophysics Conference, 2015

作者： Bauman, Paul T. University at Buffalo State University of New York BuffaloNY14260-4400 United States Department of Mechanical and Aerospace Engineering Computational and Data-Enabled Science and Engineering United States

ISBN: (数字)9781624103612

ISBN: (纸本)9781624103612

A workow is presented for using PDE-based models to simulate an experimental setup for inferring properties associated with carbon nitridation. The eventual goal is the statistical calibration of the parameters associated with the active nitridation of graphite carbon;this work is a stepping stone in this direction. Simple catalycity models are used to illustrate the the calibration workow. This study builds from previous work where it was determined that a one-dimensional model used was inadequate to represent the physical mechanisms at work. The experimental work is briey recapitulated and the mathematical model used for data reduction is presented. Details of the statistical calibration procedure and all assumptions are discussed. Results of the calibration procedure for the simple catalytic model will be presented and discussed. Extensions underway are highlighted. © 2015, American Institute of Aeronautics and Astronautics Inc. All Rights Reserved.

关键词： Aluminum nitride