TY - BOOK
TI - Introduction to Partial Differential Equations
AU - Li, Z.
AU - Norris, L.
DA - 2019///
PY - 2019///
DO - 10.1142/12052
SP - 220
PB - World Scientific Publishing Company
ER -
TY - JOUR
TI - The use of Bayesian inference in the characterization of materials and thin films
AU - Jones, Jacob L.
AU - Broughton, Rachel
AU - Iamsasri, Thanakorn
AU - Fancher, Chris M.
AU - Wilson, Alyson G.
AU - Reich, Brian
AU - Smith, Ralph C.
T2 - ACTA CRYSTALLOGRAPHICA A-FOUNDATION AND ADVANCES
DA - 2019///
PY - 2019///
DO - 10.1107/S0108767319097940
VL - 75
SP - A211-A211
SN - 2053-2733
ER -
TY - JOUR
TI - DERIVATIVE-BASED GLOBAL SENSITIVITY ANALYSIS FOR MODELS WITH HIGH-DIMENSIONAL INPUTS AND FUNCTIONAL OUTPUTS
AU - Cleaves, Helen L.
AU - Alexanderian, Alen
AU - Guy, Hayley
AU - Smith, Ralph C.
AU - Yu, Meilin
T2 - SIAM JOURNAL ON SCIENTIFIC COMPUTING
AB - We present a framework for derivative-based global sensitivity analysis (GSA) for models with high-dimensional input parameters and functional outputs. We combine ideas from derivative-based GSA, random field representation via Karhunen--Loève expansions, and adjoint-based gradient computation to provide a scalable computational framework for computing the proposed derivative-based GSA measures. We illustrate the strategy for a nonlinear ODE model of cholera epidemics and for elliptic PDEs with application examples from geosciences and biotransport.
DA - 2019///
PY - 2019///
DO - 10.1137/19M1243518
VL - 41
IS - 6
SP - A3524-A3551
SN - 1095-7197
KW - global sensitivity analysis
KW - DGSMs
KW - functional Sobol' indices
KW - Karhunen-Loeve expansions
ER -
TY - JOUR
TI - An Augmented IB Method & Analysis for Elliptic BVP on Irregular Domains
AU - Li, Zhilin
AU - Dong, Baiying
AU - Tong, Fenghua
AU - Wang, Weilong
T2 - CMES-COMPUTER MODELING IN ENGINEERING & SCIENCES
AB - The immersed boundary method is well-known, popular, and has had vast areas of applications due to its simplicity and robustness even though it is only first order accurate near the interface. In this paper, an immersed boundary-augmented method has been developed for linear elliptic boundary value problems on arbitrary domains (exterior or interior) with a Dirichlet boundary condition. The new method inherits the simplicity, robustness, and first order convergence of the IB method but also provides asymptotic first order convergence of partial derivatives. Numerical examples are provided to confirm the analysis.
DA - 2019///
PY - 2019///
DO - 10.32604/cmes.2019.04635
VL - 119
IS - 1
SP - 63-72
SN - 1526-1506
KW - Immersed boundary method
KW - augmented approach
KW - convergence
KW - derivative computing
ER -
TY - JOUR
TI - Analysis of compartments-in-series models of liver metabolism as partial differential equations: the effect of dispersion and number of compartments
AU - Noorman, Marcella
AU - Allen, Richard
AU - Musante, Cynthia J.
AU - Banks, H. Thomas
T2 - MATHEMATICAL BIOSCIENCES AND ENGINEERING
AB - Non-alcoholic fatty liver disease is the most common cause of chronic liver disease. Precipitated by the build up of extra fat in the liver not caused by alcohol, it is still not understood why steatosis occurs where it does in the liver microstructure in non-alcoholic fatty liver disease. It is likely, however, that the location of steatosis is due, at least in part, to metabolic zonation (heterogeneity among liver cells in function and enzyme expression). Recently, there has been an influx of computational and mathematical models in order to investigate the relationship between metabolic zonation and steatosis in non-alcoholic fatty liver disease. Of interest among these models are "compartments-in-series" models. Compartments-in-series models include the spatial distribution of metabolite concentrations via series of compartments that are connected through some representation of blood flow. In this paper, we analyze one such model, focusing specifically at how the number of compartments and inclusion of dispersion in the flow affect simulation results. We find the number of compartments to have a much larger effect than the inclusion of dispersion, however this is likely due to numerical artifacts. Overall, we conclude that considering partial differential equations that are equivalent to compartments-in-series models would be beneficial both in computation and in theoretical analyses.
DA - 2019///
PY - 2019///
DO - 10.3934/mbe.2019052
VL - 16
IS - 3
SP - 1082-1114
SN - 1551-0018
KW - liver disease
KW - zonation
KW - computational inverse models
KW - dispersion in flows
KW - compartments-in-series models
ER -
TY - JOUR
TI - High-Resolution Positivity and Asymptotic Preserving Numerical Methods for Chemotaxis and Related Models
AU - Chertock, Alina
AU - Kurganov, Alexander
T2 - ACTIVE PARTICLES, VOL 2: ADVANCES IN THEORY, MODELS, AND APPLICATIONS
AB - Many microorganisms exhibit a special pattern formation at the presence of a chemoattractant, food, light, or areas with high oxygen concentration. Collective cell movement can be described by a system of nonlinear PDEs on both macroscopic and microscopic levels. The classical PDE chemotaxis model is the Patlak-Keller-Segel system, which consists of a convection-diffusion equation for the cell density and a reaction-diffusion equation for the chemoattractant concentration. At the cellular (microscopic) level, a multiscale chemotaxis models can be used. These models are based on a combination of the macroscopic evolution equation for chemoattractant and microscopic models for cell evolution. The latter is governed by a Boltzmann-type kinetic equation with a local turning kernel operator that describes the velocity change of the cells. A common property of the chemotaxis systems is their ability to model a concentration phenomenon that mathematically results in solutions rapidly growing in small neighborhoods of concentration points/curves. The solutions may blow up or may exhibit a very singular, spiky behavior. In either case, capturing such singular solutions numerically is a challenging problem and the use of higher-order methods and/or adaptive strategies is often necessary. In addition, positivity preserving is an absolutely crucial property a good numerical method used to simulate chemotaxis should satisfy: this is the only way to guarantee a nonlinear stability of the method. For kinetic chemotaxis systems, it is also essential that numerical methods provide a consistent and stable discretization in certain asymptotic regimes. In this paper, we review some of the recent advances in developing of high-resolution finite-volume and finite-difference numerical methods that possess the aforementioned properties of the chemotaxis-type systems.
DA - 2019///
PY - 2019///
DO - 10.1007/978-3-030-20297-2_4
SP - 109-148
SN - 2164-3725
ER -
TY - JOUR
TI - Model Input and Output Dimension Reduction Using Karhunen-Loeve Expansions With Application to Biotransport
AU - Alexanderian, Alen
AU - Reese, William
AU - Smith, Ralph C.
AU - Yu, Meilin
T2 - ASCE-ASME JOURNAL OF RISK AND UNCERTAINTY IN ENGINEERING SYSTEMS PART B-MECHANICAL ENGINEERING
AB - Abstract We consider biotransport in tumors with uncertain heterogeneous material properties. Specifically, we focus on the elliptic partial differential equation (PDE) modeling the pressure field inside the tumor. The permeability field is modeled as a log-Gaussian random field with a prespecified covariance function. We numerically explore dimension reduction of the input parameter and model output. Specifically, truncated Karhunen–Loève (KL) expansions are used to decompose the log-permeability field, as well as the resulting random pressure field. We find that although very high-dimensional representations are needed to accurately represent the permeability field, especially in presence of small correlation lengths, the pressure field is not sensitive to high-order KL terms of the input parameter. Moreover, we find that the pressure field itself can be represented accurately using a KL expansion with a small number of terms. These observations are used to guide a reduced-order modeling approach to accelerate computational studies of biotransport in tumors.
DA - 2019/12/1/
PY - 2019/12/1/
DO - 10.1115/1.4044317
VL - 5
IS - 4
SP -
SN - 2332-9025
ER -
TY - JOUR
TI - Application and Evaluation of Surrogate Models for Radiation Source Search
AU - Cook, Jared A.
AU - Smith, Ralph C.
AU - Hite, Jason M.
AU - Stefanescu, Razvan
AU - Mattingly, John
T2 - ALGORITHMS
AB - Surrogate models are increasingly required for applications in which first-principles simulation models are prohibitively expensive to employ for uncertainty analysis, design, or control. They can also be used to approximate models whose discontinuous derivatives preclude the use of gradient-based optimization or data assimilation algorithms. We consider the problem of inferring the 2D location and intensity of a radiation source in an urban environment using a ray-tracing model based on Boltzmann transport theory. Whereas the code implementing this model is relatively efficient, extension to 3D Monte Carlo transport simulations precludes subsequent Bayesian inference to infer source locations, which typically requires thousands to millions of simulations. Additionally, the resulting likelihood exhibits discontinuous derivatives due to the presence of buildings. To address these issues, we discuss the construction of surrogate models for optimization, Bayesian inference, and uncertainty propagation. Specifically, we consider surrogate models based on Legendre polynomials, multivariate adaptive regression splines, radial basis functions, Gaussian processes, and neural networks. We detail strategies for computing training points and discuss the merits and deficits of each method.
DA - 2019/12//
PY - 2019/12//
DO - 10.3390/a12120269
VL - 12
IS - 12
SP -
SN - 1999-4893
KW - surrogate modeling
KW - bayesian inference
KW - radiation source localization
ER -
TY - JOUR
TI - Stochastic Galerkin method for cloud simulation
AU - Chertock, A.
AU - Kurganov, A.
AU - Lukáčová-Medvid’ová, M.
AU - Spichtinger, P.
AU - Wiebe, B.
T2 - Mathematics of Climate and Weather Forecasting
AB - Abstract We develop a stochastic Galerkin method for a coupled Navier-Stokes-cloud system that models dynamics of warm clouds. Our goal is to explicitly describe the evolution of uncertainties that arise due to unknown input data, such as model parameters and initial or boundary conditions. The developed stochastic Galerkin method combines the space-time approximation obtained by a suitable finite volume method with a spectral-type approximation based on the generalized polynomial chaos expansion in the stochastic space. The resulting numerical scheme yields a second-order accurate approximation in both space and time and exponential convergence in the stochastic space. Our numerical results demonstrate the reliability and robustness of the stochastic Galerkin method. We also use the proposed method to study the behavior of clouds in certain perturbed scenarios, for examples, the ones leading to changes in macroscopic cloud pattern as a shift from hexagonal to rectangular structures.
DA - 2019/1/1/
PY - 2019/1/1/
DO - 10.1515/mcwf-2019-0005
VL - 5
IS - 1
SP - 65-106
OP -
SN - 2353-6438
UR - http://dx.doi.org/10.1515/mcwf-2019-0005
DB - Crossref
ER -
TY - JOUR
TI - A Mutual Information-Based Experimental Design Framework to Use High-Fidelity Nuclear Reactor Codes to Calibrate Low-Fidelity Codes
AU - Gordon, Natalie
AU - Gilkey, Lindsay
AU - Smith, Ralph C.
AU - Michaud, Isaac
AU - Williams, Brian
AU - Mousseau, Vincent
AU - Hooper, Russell
AU - Jones, Chris
T2 - NUCLEAR TECHNOLOGY
AB - Simulation-based nuclear reactor design requires highly efficient codes that quantify the requisite physics while having the efficiency required for optimization-based design and uncertainty quantification. To achieve the required accuracy and predictive capabilities, phenomenological parameters, often employed in closure relations or to quantify unmodeled or unresolved physics, must be calibrated for considered reactor conditions and designs. When available, experimental data with quantified observation errors are ideally employed for calibration. However, for many thermal-hydraulic, fuel, and Chalk River Unidentified Deposits modeling regimes, experimental data are prohibitively expensive or impossible to collect. For such cases, we demonstrate the use of a mutual information–based experimental design framework to employ validated high-fidelity codes to calibrate parameters in low-fidelity design codes. We demonstrate the use of the high-fidelity computational fluid dynamics package STAR-CCM+ to calibrate the turbulent mixing coefficient β in COBRA-TF (CTF). This includes the construction and verification of a surrogate for CTF, which permits the computationally intensive experimental design and Bayesian calibration steps. We also demonstrate Bayesian inference of parameter distributions for the Dittus-Boelter relation and propagation of these uncertainties through CTF to improve uncertainty bounds for computed maximum fuel temperatures.
DA - 2019/12/2/
PY - 2019/12/2/
DO - 10.1080/00295450.2019.1590073
VL - 205
IS - 12
SP - 1685-1696
SN - 1943-7471
KW - Mutual information
KW - experimental design
KW - Bayesian inference
ER -
TY - JOUR
TI - Real-time implementation and analysis of a modified energy based controller for the swing-up of an inverted pendulum on a cart
AU - Kennedy, Emese
AU - King, Ethan
AU - Tran, Hien
T2 - EUROPEAN JOURNAL OF CONTROL
AB - In this paper we derive a modified energy based swing-up controller using Lyapunov functions. During the derivation, all effort has been made to use a more complex dynamical model for the single inverted pendulum (SIP) system than the simplified model that is most commonly used. We consider the electrodynamics of the DC motor that drives the cart, and incorporate viscous damping friction as seen at the motor pinion. Furthermore, we use a new method to account for the limitation of having a cart-pendulum system with a finite track length. Two modifications to the controller are also discussed to make the method more appropriate for real-time implementation. One of the modifications improves robustness using a modified Lyapunov function for the derivation, while the other one incorporates viscous damping as seen at the pendulum axis. We present both simulation and real-time experimental results implemented in MATLAB Simulink.
DA - 2019/11//
PY - 2019/11//
DO - 10.1016/j.ejcon.2019.05.002
VL - 50
SP - 176-187
SN - 1435-5671
KW - Inverted pendulum
KW - Energy based control
KW - Lyapunov functions
KW - Real-time implementation
ER -
TY - JOUR
TI - Preface to the Special Issue in Memory of Professor Saul Abarbanel
T2 - Journal of Scientific Computing
DA - 2019/12//
PY - 2019/12//
DO - 10.1007/s10915-019-01084-0
UR - http://dx.doi.org/10.1007/s10915-019-01084-0
ER -
TY - JOUR
TI - LOCAL SENSITIVITY VIA THE COMPLEX-STEP DERIVATIVE APPROXIMATION FOR 1D PORO-ELASTIC AND PORO-VISCO-ELASTIC MODELS
AU - Banks, H. Thomas
AU - Bekele-Maxwell, Kidist
AU - Bociu, Lorena
AU - Noorman, Marcelle
AU - Guidiboni, Giovanna
T2 - MATHEMATICAL CONTROL AND RELATED FIELDS
AB - Poro-elastic systems have been used extensively in modeling fluid flow in porous media in petroleum and earthquake engineering. Nowadays, they are frequently used to model fluid flow through biological tissues, cartilages, and bones. In these biological applications, the fluid-solid mixture problems, which may also incorporate structural viscosity, are considered on bounded domains with appropriate non-homogeneous boundary conditions. The recent work in [12] provided a theoretical and numerical analysis of nonlinear poro-elastic and poro-viscoelastic models on bounded domains with mixed boundary conditions, focusing on the role of visco-elasticity in the material. Their results show that higher time regularity of the sources is needed to guarantee bounded solution when visco-elasticity is not present. Inspired by their results, we have recently performed local sensitivity analysis on the solutions of these fluid-solid mixture problems with respect to the boundary source of traction associated with the elastic structure [3]. Our results show that the solution is more sensitive to boundary datum in the purely elastic case than when visco-elasticity is present in the solid matrix. In this article, we further extend this work in order to include local sensitivities of the solution of the coupled system to the boundary conditions imposed on the Darcy velocity. Sensitivity analysis is the first step in identifying important parameters to control or use as control terms in these poro-elastic and poro-visco-elastic models, which is our ultimate goal.
DA - 2019/12//
PY - 2019/12//
DO - 10.3934/mcrf.2019044
VL - 9
IS - 4
SP - 623-642
SN - 2156-8499
KW - Sensitivity
KW - poro-elastic
KW - poro-visco-elastic
KW - biological tissues
KW - complex-step method
ER -
TY - JOUR
TI - A PARALLEL DOMAIN DECOMPOSITION METHOD FOR THE HELMHOLTZ EQUATION IN LAYERED MEDIA
AU - Heikkola, Erkki
AU - Ito, Kazufumi
AU - Toivanen, Jari
T2 - SIAM JOURNAL ON SCIENTIFIC COMPUTING
AB - An efficient domain decomposition method and its parallel implementation for the solution of the Helmholtz equation in three-dimensional layered media are considered. A modified trilinear finite element discretization scheme is applied to the equation system leading to fourth-order phase accuracy and thereby reducing the pollution error considerably. The resulting linear system is solved with the GMRES method using a multiplicative nonoverlapping domain decomposition preconditioner with layers defining the subdomains. This right preconditioner is constructed by embedding each layer into a rectangular domain and by employing a fast direct solver. Due to the construction of the preconditioner the iterations can be reduced to a subspace corresponding to the interfaces between the layers. Numerical experiments with several test cases demonstrate the effectiveness and scalability of the proposed method and ability to solve large-scale problems with up to billions of unknowns.
DA - 2019///
PY - 2019///
DO - 10.1137/18M1230906
VL - 41
IS - 5
SP - C505-C521
SN - 1095-7197
KW - Helmholtz equation
KW - domain decomposition method
KW - preconditioned iterative method
KW - ultrasonic tomography
KW - geological survey
ER -
TY - JOUR
TI - Analysis of Network Structure of Urban Bike-Sharing System: A Case Study Based on Real-Time Data of a Public Bicycle System
AU - Yao, Yi
AU - Zhang, Yifang
AU - Tian, Lixin
AU - Zhou, Nianxing
AU - Li, Zhilin
AU - Wang, Minggang
T2 - SUSTAINABILITY
AB - To better understand the characteristics of a bike-sharing system, we applied complex network methods to analyze the relationship between stations within the bike-sharing system. Firstly, using Gephi software, we constructed the public bicycle networks of different urban areas based on the real-time data of the Nanjing public bicycle system. Secondly, we analyzed and compared degree, strength, radiation distance, and community structure of the networks to understand the internal relations of the public bicycle system. The results showed that there were many stations with low usage of public bicycles. Furthermore, there was a geographical division between high-demand and low-demand areas for public bicycles. The usage of public bicycles at a station was not only related to land use but also related to the usage of bicycles at stations nearby. Moreover, the average service coverage of the public bicycle system was consistent with the original intention of “the first and last mile”, and public bicycles could meet different travel needs.
DA - 2019/10/1/
PY - 2019/10/1/
DO - 10.3390/su11195425
VL - 11
IS - 19
SP -
SN - 2071-1050
KW - sustainable mode of transportation
KW - bike-sharing system
KW - public bicycle
KW - complex network
KW - network structure
ER -
TY - JOUR
TI - Approximating Periodic Potential Energy Surfaces with Sparse Trigonometric Interpolation
AU - Morrow, Zachary
AU - Liu, Chang
AU - Kelley, C. T.
AU - Jakubikova, Elena
T2 - The Journal of Physical Chemistry B
AB - The potential energy surface (PES) describes the energy of a chemical system as a function of its geometry and is a fundamental concept in computational chemistry. A PES provides much useful information about the system, including the structures and energies of various stationary points, such as local minima, maxima, and transition states. Construction of full-dimensional PESs for molecules with more than 10 atoms is computationally expensive and often not feasible. Previous work in our group used sparse interpolation with polynomial basis functions to construct a surrogate reduced-dimensional PESs along chemically significant reaction coordinates, such as bond lengths, bond angles, and torsion angles. However, polynomial interpolation does not preserve the periodicity of the PES gradient with respect to angular components of geometry, such as torsion angles, which can lead to nonphysical phenomena. In this work, we construct a surrogate PES using trigonometric basis functions, for a system where the selected reaction coordinates all correspond to the torsion angles, resulting in a periodically repeating PES. We find that a trigonometric interpolation basis not only guarantees periodicity of the gradient but also results in slightly lower approximation error than polynomial interpolation.
DA - 2019/11/14/
PY - 2019/11/14/
DO - 10.1021/acs.jpcb.9b08210
VL - 123
IS - 45
SP - 9677-9684
UR - https://doi.org/10.1021/acs.jpcb.9b08210
ER -
TY - JOUR
TI - ADAPTION OF AKAIKE INFORMATION CRITERION UNDER LEAST SQUARES FRAMEWORKS FOR COMPARISON OF STOCHASTIC MODELS
AU - Banks, H. T.
AU - Joyner, Michele L.
T2 - QUARTERLY OF APPLIED MATHEMATICS
DA - 2019/12//
PY - 2019/12//
DO - 10.1090/qam/1542
VL - 77
IS - 4
SP - 831-859
SN - 1552-4485
KW - Continuous time Markov chain models
KW - CTMC
KW - stochastic differential equations
KW - SDE
KW - random differential equations
KW - RDE
KW - inverse problems
KW - model comparison techniques
KW - Akaike information criterion
KW - AIC
ER -
TY - JOUR
TI - Estimation of probability distributions of parameters using aggregate population data: analysis of a CAR T-cell cancer model
AU - Schacht, Celia
AU - Meade, Annabel
AU - Banks, H. T.
AU - Enderling, Heiko
AU - Abate-Daga, Daniel
T2 - MATHEMATICAL BIOSCIENCES AND ENGINEERING
AB - In this effort we explain fundamental formulations for aggregate data inverse problems requiring estimation of probability distribution parameters. We use as a motivating example a class of CAR T-call cancer models in mice. After ascertaining results on model stability and sensitivity with respect to parameters, we carry out first elementary computations on the question how much data is needed for successful estimation of probability distributions.
DA - 2019///
PY - 2019///
DO - 10.3934/mbe.2019365
VL - 16
IS - 6
SP - 7299-7326
SN - 1551-0018
KW - aggregate data
KW - CAR T-cell therapy
KW - cancer model
KW - inverse problems
KW - design of experiments
ER -
TY - JOUR
TI - Spatiotemporal characteristics of green travel: A classification study on a public bicycle system
AU - Yao, Yi
AU - Jiang, Xin
AU - Li, Zhilin
T2 - JOURNAL OF CLEANER PRODUCTION
AB - Understanding the characteristics of users and stations provides the foundation for a more efficient public bicycle system. Based on the real-time data of the Nanjing public bicycle system, we presented the spatiotemporal characteristics of users and stations combining data mining and geographic visualization. First, we analyzed users' gender, age, weekly flow, and time-segment flow, and classified the users into different types. In addition, we studied the cycling chains of certain users in details to understand the differences. Second, we analyzed the station distribution, station flow, station time-segment flow, and the surrounding environment, and studied the specific stations of different types to reveal the diverse characteristics. Moreover, we also explored the relationship between the user types and the station types. The results showed that public bicycles were mainly used for commuting or transferring, and social and economic activities around stations greatly influenced the use of public bicycles. However, the usage of the public bicycle system was still at a low level. Furthermore, different types of users had different cycling purposes, and different types of stations showed different characteristics of renting flow and returning flow. At last, we proposed different incentives and management measures for different types of users and stations.
DA - 2019/11/20/
PY - 2019/11/20/
DO - 10.1016/j.jclepro.2019.117892
VL - 238
SP -
SN - 1879-1786
KW - Green travel
KW - Public bicycle
KW - Spatiotemporal characteristics
KW - Clustering analysis
KW - Visualization analysis
ER -
TY - JOUR
TI - Optimization of processor allocation for domain decomposed Monte Carlo calculations
AU - Ellis, J. Austin
AU - Evans, Thomas M.
AU - Hamilton, Steven P.
AU - Kelley, C.T.
AU - Pandya, Tara M.
T2 - Parallel Computing
AB - Load imbalance plagues domain decomposed Monte Carlo calculations when sources are not uniform. Parallel efficiency for domain decomposed Monte Carlo transport calculations improves through a nonuniform allocation of processors over subdomains. We optimize the allocation with runtime diagnostics collected during a calibration step, then complete the full calculation. The diagnostic-based approach is compared to implicit filtering, an optimization algorithm for bound constrained noisy optimization problems. We consider both forward and hybrid radiation transport calculations to measure performance.
DA - 2019/9//
PY - 2019/9//
DO - 10.1016/j.parco.2019.06.001
VL - 87
SP - 77-86
J2 - Parallel Computing
LA - en
OP -
SN - 0167-8191
UR - http://dx.doi.org/10.1016/j.parco.2019.06.001
DB - Crossref
KW - Monte Carlo transport
KW - Load imbalance
KW - Domain decomposition
KW - Noisy optimization
ER -
TY - JOUR
TI - One-Dimensional/Two-Dimensional Coupling Approach with Quadrilateral Confluence Region for Modeling River Systems
T2 - Journal of Scientific Computing
DA - 2019/6/27/
PY - 2019/6/27/
DO - 10.1007/s10915-019-00985-4
UR - http://dx.doi.org/10.1007/s10915-019-00985-4
KW - Shallow water flow in river systems
KW - One-dimensional
KW - two-dimensional coupling
KW - Quadrilateral confluence region
KW - Well-balanced central-upwind scheme
ER -
TY - JOUR
TI - Global Sensitivity Analysis of Fractional-Order Viscoelasticity Models
AU - Miles, Paul R.
AU - Pash, Graham T.
AU - Smith, Ralph C.
AU - Oates, William S.
T2 - BEHAVIOR AND MECHANICS OF MULTIFUNCTIONAL MATERIALS XIII
AB - In this paper, we investigate hyperelastic and viscoelastic model parameters using Global Sensitivity Analysis (GSA). These models are used to characterize the physical response of many soft-elastomers, which are used in a wide variety of smart material applications. Recent research has shown the effectiveness of using fractionalorder calculus operators in modeling the viscoelastic response. The GSA is performed using parameter subset selection (PSS), which quantifies the relative parameter contributions to the linear and nonlinear, fractionalorder viscoelastic models. Calibration has been performed to quantify the model parameter uncertainty; however, this analysis has led to questions regarding parameter sensitivity and whether or not the parameters can be uniquely identified given the available data. By performing GSA we can determine which parameters are most influential in the model, and fix non-influential parameters at a nominal value. The model calibration can then be performed to quantify the uncertainty of the influential parameters.
DA - 2019///
PY - 2019///
DO - 10.1117/12.2514160
VL - 10968
SP -
SN - 1996-756X
KW - Viscoelasticity
KW - Global Sensitivity Analysis
KW - Fractional-Order Calculus
ER -
TY - JOUR
TI - Parameter-dependent Surrogate Model Development for PZT Bimorph Actuators Employed for Micro-air Vehicles
AU - Bravo, Nikolas
AU - Smith, Ralph C.
T2 - BEHAVIOR AND MECHANICS OF MULTIFUNCTIONAL MATERIALS XIII
AB - In the paper, we discuss the use of the homogenized energy model (HEM) to develop a dynamic mode decomposition surrogate model for a PZT bimorph actuator used for micro-air vehicles including Robobee. The HEM quantifies the nonlinear, hysteretic, and rate-dependent behavior inherent to PZT in highly dynamic operating regimes. Due to the computation complexity of the HEM, we must develop a surrogate model. The surrogate model must be parameter- and control-dependent to be able to perform inverse problems or uncertainty quantification in different driving regimes. In the literature, DMD can be adapted to address different control inputs. We will discuss using interpolation over the parameters to adapt the DMD to include parameter dependence. Finally, we will discuss the results and limitations of the new surrogate model.
DA - 2019///
PY - 2019///
DO - 10.1117/12.2514246
VL - 10968
SP -
SN - 1996-756X
KW - Uncertainty Quantification
KW - PZT Bimorph
KW - Modeling
KW - Surrogate
KW - Homogenized Energy Model
ER -
TY - JOUR
TI - Incompressible limit of a continuum model of tissue growth with segregation for two cell populations
AU - Chertock, Alina
AU - Degond, Pierre
AU - Hecht, Sophie
AU - Vincent, Jean-Paul
T2 - Math. Biosci. Eng.
DA - 2019///
PY - 2019///
DO - https://doi-org.prox.lib.ncsu.edu/10.1007/s10915-019-00947-w
VL - 16
IS - 5
SP - 5804-5835
UR - https://doi.org/10.3934/mbe.2019290
ER -
TY - JOUR
TI - An asymptotic preserving scheme for kinetic chemotaxis models in two space dimensions
AU - Chertock, Alina
AU - Kurganov, Alexander
AU - Lukáčová-Medvid’ová, Mária
AU - Nur Özcan, Șeyma
T2 - Kinetic & Related Models
AB - In this paper, we study two-dimensional multiscale chemotaxis models based on a combination of the macroscopic evolution equation for chemoattractant and microscopic models for cell evolution. The latter is governed by a Boltzmann-type kinetic equation with a local turning kernel operator which describes the velocity change of the cells. The parabolic scaling yields a non-dimensional kinetic model with a small parameter, which represents the mean free path of the cells. We propose a new asymptotic preserving numerical scheme that reflects the convergence of the studied micro-macro model to its macroscopic counterpart-the Patlak-Keller-Segel system-in the singular limit. The method is based on the operator splitting strategy and a suitable combination of the higher-order implicit and explicit time discretizations. In particular, we use the so-called even-odd decoupling and approximate the stiff terms arising in the singular limit implicitly. We prove that the resulting scheme satisfies the asymptotic preserving property. More precisely, it yields a consistent approximation of the Patlak-Keller-Segel system as the mean-free path tends to 0. The derived asymptotic preserving method is used to get better insight to the blowup behavior of two-dimensional kinetic chemotaxis model.
DA - 2019///
PY - 2019///
DO - 10.3934/krm.2019009
VL - 12
IS - 1
SP - 195-216
SN - 1937-5077
UR - http://dx.doi.org/10.3934/krm.2019009
KW - Chemotaxis
KW - kinetic equations
KW - multiscale models
KW - asymptotic preserving (AP) methods
KW - operator splitting
ER -
TY - CONF
TI - A method of boundary equations for unsteady hyperbolic problems in 3D
AU - Petropavlovsky, S. V.
AU - Tsynkov, S. V.
AU - Turkel, E.
C2 - 2019///
C3 - Mathematics and Its Applications, Book of Abstracts for the International
Conference in honor of the 90th birthday of Sergei K. Godunov,
Novosibirsk, Russia, August 4-10, 2019
DA - 2019///
SP - 68
UR - https://stsynkov.math.ncsu.edu/publications/a82e_godunov90.pdf
ER -
TY - CONF
TI - A high order method of boundary operators for the 3D time-dependent wave equation
AU - Petropavlovsky, S. V.
AU - Tsynkov, S. V.
AU - Turkel, E.
C2 - 2019///
C3 - Book of Abstracts, The 14th International Conference on Mathematical
and Numerical Aspects of Wave Propagation, WAVES 2019,
Vienna University of Technology (TU Wien),
Vienna, Austria, August 25-30, 2019
DA - 2019///
SP - 363-365
UR - https://stsynkov.math.ncsu.edu/publications/Unsteady_DPM_waves2019_v6.pdf
ER -
TY - CONF
TI - Stochastic Models in Coordinate-Delay Synthetic Aperture Radar Imaging
AU - Gilman, Mikhail
AU - Tsynkov, Semyon
C2 - 2019///
C3 - Book of Abstracts, The 14th International Conference on Mathematical
and Numerical Aspects of Wave Propagation, WAVES 2019,
Vienna University of Technology (TU Wien),
Vienna, Austria, August 25-30, 2019
DA - 2019///
SP - 330-331
UR - https://stsynkov.math.ncsu.edu/publications/Dispersive_targets_Waves2019_v3_final.pdf
ER -
TY - JOUR
TI - Molecular Dynamics Simulations on Relaxed Reduced-Dimensional Potential Energy Surfaces
AU - Liu, Chang
AU - Kelley, C. T.
AU - Jakubikova, Elena
T2 - The Journal of Physical Chemistry A
AB - Molecular dynamics (MD) simulations with full-dimensional potential energy surfaces (PESs) obtained from high-level ab initio calculations are frequently used to model reaction dynamics of small molecules (i.e., molecules with up to 10 atoms). Construction of full-dimensional PESs for larger molecules is, however, not feasible since the number of ab initio calculations required grows rapidly with the increase of dimension. Only a small number of coordinates are often essential for describing the reactivity of even very large systems, and reduced-dimensional PESs with these coordinates can be built for reaction dynamics studies. While analytical methods based on transition-state theory framework are well established for analyzing the reduced-dimensional PESs, MD simulation algorithms capable of generating trajectories on such surfaces are more rare. In this work, we present a new MD implementation that utilizes the relaxed reduced-dimensional PES for standard microcanonical (NVE) and canonical (NVT) MD simulations. The method is applied to the pyramidal inversion of a NH3 molecule. The results from the MD simulations on a reduced, three-dimensional PES are validated against the ab initio MD simulations, as well as MD simulations on full-dimensional PES and experimental data.
DA - 2019/4/30/
PY - 2019/4/30/
DO - 10.1021/acs.jpca.9b02298
VL - 123
IS - 21
SP - 4543-4554
J2 - J. Phys. Chem. A
LA - en
OP -
SN - 1089-5639 1520-5215
UR - http://dx.doi.org/10.1021/acs.jpca.9b02298
DB - Crossref
ER -
TY - JOUR
TI - A gradient recovery-based adaptive finite element method for convection-diffusion-reaction equations on surfaces
AU - Xiao, Xufeng
AU - Feng, Xinlong
AU - Li, Zhilin
T2 - INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING
AB - Summary In this paper, we present an adaptive mesh refinement method for solving convection‐diffusion‐reaction equations on surfaces, which is a fundamental subproblem in many models for simulating the transport of substances on biological films and solid surfaces. The method considered is a combination of well‐known techniques: the surface finite element method, streamline diffusion stabilization, and the gradient recovery–based Zienkiewicz‐Zhu error estimator. The streamline diffusion method overcomes the instability issue of the finite element method for the dominance of the convection. The gradient recovery–based adaptive mesh refinement strategy enables the method to provide high‐resolution numerical solutions by relatively fewer degrees of freedom. Moreover, the implementation detail of a surface mesh refinement technique is presented. Various numerical examples, including the convection‐dominated diffusion problems with large variations of solutions, nearly singular solutions, discontinuous sources, and internal layers on surfaces, are presented to demonstrate the efficacy and accuracy of the proposed method.
DA - 2019/11/16/
PY - 2019/11/16/
DO - 10.1002/nme.6163
VL - 120
IS - 7
SP - 901-917
SN - 1097-0207
KW - adaptive strategy
KW - recovery-based error estimator
KW - streamline diffusion method
KW - surface convection-diffusion-reaction equations
KW - surface finite element method
ER -
TY - JOUR
TI - Cardiovascular dynamics during head-up tilt assessed via pulsatile and non-pulsatile models
AU - Williams, Nakeya D.
AU - Brady, Renee
AU - Gilmore, Steven
AU - Gremaud, Pierre
AU - Tran, Hien T.
AU - Ottesen, Johnny T.
AU - Mehlsen, Jesper
AU - Olufsen, Mette S.
T2 - Journal of Mathematical Biology
AB - This study develops non-pulsatile and pulsatile models for the prediction of blood flow and pressure during head-up tilt. This test is used to diagnose potential pathologies within the autonomic control system, which acts to keep the cardiovascular system at homeostasis. We show that mathematical modeling can be used to predict changes in cardiac contractility, vascular resistance, and arterial compliance, quantities that cannot be measured but are useful to assess the system's state. These quantities are predicted as time-varying parameters modeled using piecewise linear splines. Having models with various levels of complexity formulated with a common set of parameters, allows us to combine long-term non-pulsatile simulations with pulsatile simulations on a shorter time-scale. We illustrate results for a representative subject tilted head-up from a supine position to a [Formula: see text] angle. The tilt is maintained for 5 min before the subject is tilted back down. Results show that if volume data is available for all vascular compartments three parameters can be identified, cardiovascular resistance, vascular compliance, and ventricular contractility, whereas if model predictions are made against arterial pressure and cardiac output data alone, only two parameters can be estimated either resistance and contractility or resistance and compliance.
DA - 2019/5/31/
PY - 2019/5/31/
DO - 10.1007/s00285-019-01386-9
VL - 79
IS - 3
SP - 987-1014
J2 - J. Math. Biol.
LA - en
OP -
SN - 0303-6812 1432-1416
UR - http://dx.doi.org/10.1007/s00285-019-01386-9
DB - Crossref
KW - Cardiovascular dynamics modeling
KW - Head-up tilt
KW - Pulsatile versus non-pulsatile modeling
KW - Parameter estimation
KW - Orthostatic intolerance
ER -
TY - JOUR
TI - Active subspace analysis and uncertainty quantification for a polydomain ferroelectric phase-field model
AU - Leon, Lider S.
AU - Miles, Paul R.
AU - Smith, Ralph C.
AU - Oates, William S.
T2 - JOURNAL OF INTELLIGENT MATERIAL SYSTEMS AND STRUCTURES
AB - We perform parameter subset selection and uncertainty analysis for phase-field models that are applied to the ferroelectric material lead titanate. A motivating objective is to determine which parameters are influential in the sense that their uncertainties directly affect the uncertainty in the model response, and fix noninfluential parameters at nominal values for subsequent uncertainty propagation. We employ Bayesian inference to quantify the uncertainties of gradient exchange parameters governing 180° and 90° tetragonal phase domain wall energies. The uncertainties of influential parameters determined by parameter subset selection are then propagated through the models to obtain credible intervals when estimating energy densities quantifying polarization and strain across domain walls. The results illustrate various properties of Landau and electromechanical coupling parameters and their influence on domain wall interactions. We employ energy statistics, which quantify distances between statistical observations, to compare credible intervals constructed using a complete set of parameters against an influential subset of parameters. These intervals are obtained from the uncertainty propagation of the model input parameters on the domain wall energy densities. The investigation provides critical insight into the development of parameter subset selection, uncertainty quantification, and propagation methodologies for material modeling domain wall structure evolution, informed by density functional theory simulations.
DA - 2019/8//
PY - 2019/8//
DO - 10.1177/1045389X19853636
VL - 30
IS - 14
SP - 2027-2051
SN - 1530-8138
KW - Ferroelectric
KW - active subspace analysis
KW - uncertainty quantification
ER -
TY - JOUR
TI - Modeling Zika Virus Transmission Dynamics: Parameter Estimates, Disease Characteristics, and Prevention
AU - Rahman, Munsur
AU - Bekele-Maxwell, Kidist
AU - Cates, LeAnna L.
AU - Banks, H. T.
AU - Vaidya, Naveen K.
T2 - SCIENTIFIC REPORTS
AB - Abstract Because of limited data, much remains uncertain about parameters related to transmission dynamics of Zika virus (ZIKV). Estimating a large number of parameters from the limited information in data may not provide useful knowledge about the ZIKV. Here, we developed a method that utilizes a mathematical model of ZIKV dynamics and the complex-step derivative approximation technique to identify parameters that can be estimated from the available data. Applying our method to epidemic data from the ZIKV outbreaks in French Polynesia and Yap Island, we identified the parameters that can be estimated from these island data. Our results suggest that the parameters that can be estimated from a given data set, as well as the estimated values of those parameters, vary from Island to Island. Our method allowed us to estimate some ZIKV-related parameters with reasonable confidence intervals. We also computed the basic reproduction number to be from 2.03 to 3.20 across islands. Furthermore, using our model, we evaluated potential prevention strategies and found that peak prevalence can be reduced to nearly 10% by reducing mosquito-to-human contact by at least 60% or increasing mosquito death by at least a factor of three of the base case. With these preventions, the final outbreak-size is predicted to be negligible, thereby successfully controlling ZIKV epidemics.
DA - 2019/7/22/
PY - 2019/7/22/
DO - 10.1038/s41598-019-46218-4
VL - 9
SP -
SN - 2045-2322
ER -
TY - JOUR
TI - Sequential optimal positioning of mobile sensors using mutual information
AU - Schmidt, Kathleen
AU - Smith, Ralph C.
AU - Hite, Jason
AU - Mattingly, John
AU - Azmy, Yousry
AU - Rajan, Deepak
AU - Goldhahn, Ryan
T2 - STATISTICAL ANALYSIS AND DATA MINING
AB - Abstract Source localization, such as detecting a nuclear source in an urban area or ascertaining the origin of a chemical plume, is generally regarded as a well‐documented inverse problem; however, optimally placing sensors to collect data for such problems is a more challenging task. In particular, optimal sensor placement—that is, measurement locations resulting in the least uncertainty in the estimated source parameters—depends on the location of the source, which is typically unknown a priori . Mobile sensors are advantageous because they have the flexibility to adapt to any given source position. While most mobile sensor strategies designate a trajectory for sensor movement, we instead employ mutual information, based on Shannon entropy, to choose the next measurement location from a discrete set of design conditions.
DA - 2019/12//
PY - 2019/12//
DO - 10.1002/sam.11431
VL - 12
IS - 6
SP - 465-478
SN - 1932-1872
KW - Bayesian inference
KW - inverse problem
KW - mutual information
KW - sensor placement
KW - source localization
ER -
TY - JOUR
TI - Numerical Validations of the Tangent Linear Model for the Lorenz Equations
AU - Zhao, Tengjin
AU - Zhang, Jing
AU - Li, Zhilin
AU - Zhang, Zhiyue
T2 - CMES-COMPUTER MODELING IN ENGINEERING & SCIENCES
AB - The validity of the tangent linear model (TLM) is studied numerically using the example of the Lorenz equations in this paper. The relationship between the limit of the validity time of the TLM and initial perturbations for the Lorenz equations is investigated using the Monte Carlo sampling method. A new error function between the nonlinear and the linear evolution of the perturbations is proposed. Furthermore, numerical sensitivity analysis is carried to establish the relationship between parameters and the validity of the TLM, such as the initial perturbation, the prediction time, the time step size and so on, by the method of mathematical statistics.
DA - 2019///
PY - 2019///
DO - 10.32604/cmes.2019.04483
VL - 120
IS - 1
SP - 83-104
SN - 1526-1506
KW - Lorenz model
KW - tangent linear model
KW - nonlinear model
KW - Monte Carlo
ER -
TY - JOUR
TI - Surrogate-Based Robust Design for a Non-Smooth Radiation Source Detection Problem
AU - Stefanescu, Razvan
AU - Hite, Jason
AU - Cook, Jared
AU - Smith, Ralph C.
AU - Mattingly, John
T2 - ALGORITHMS
AB - In this paper, we develop and numerically illustrate a robust sensor network design to optimally detect a radiation source in an urban environment. This problem exhibits several challenges: penalty functionals are non-smooth due to the presence of buildings, radiation transport models are often computationally expensive, sensor locations are not limited to a discrete number of points, and source intensity and location responses, based on a fixed number of sensors, are not unique. We consider a radiation source located in a prototypical 250 m × 180 m urban setting. To address the non-smooth properties of the model and computationally expensive simulation codes, we employ a verified surrogate model based on radial basis functions. Using this surrogate, we formulate and solve a robust design problem that is optimal in an average sense for detecting source location and intensity with minimized uncertainty.
DA - 2019/6//
PY - 2019/6//
DO - 10.3390/a12060113
VL - 12
IS - 6
SP -
SN - 1999-4893
KW - robust design in the average sense
KW - Particle Swarm
KW - radial basis functions
KW - radiation source detection
ER -
TY - JOUR
TI - Uncertainty quantification of two-phase flow and boiling heat transfer simulations through a data-driven modular Bayesian approach
AU - Liu, Yang
AU - Dinh, Nam T.
AU - Smith, Ralph C.
AU - Sun, Xiaodong
T2 - INTERNATIONAL JOURNAL OF HEAT AND MASS TRANSFER
AB - In this paper, we present an approach to inversely quantify the uncertainty of MCFD simulations through a data-driven modular Bayesian inference. Both the model parameter uncertainty and the model form uncertainty are evaluated in the proposed approach. Considering the high-dimensionality of parameter space related to the solver, we performed a sensitivity analysis to reduce the input parameter dimension for the Bayesian inference. Based on the reduced parameter dimension, surrogate models based on Gaussian Process (GP) and Principal Component Analysis (PCA) are constructed to reduce the computational cost in the Bayesian inference. Two case studies based on the proposed approach are performed, focusing on two-phase flow dynamics and on wall boiling heat transfer, respectively. In case study I, we are able to construct a GP-based surrogate model based on 8 principal components to represent the total 208 MCFD solver outputs. Moreover, both cases show that the proposed approach is able to quantify and reduce the parameter uncertainties with the support of experimental measurements. The posterior uncertainties of investigated parameters have 50%-90% narrowed uncertainty ranges compared to their prior uncertainties. Furthermore, a forward uncertainty propagation of the MCFD solver with the obtained uncertainties shows that the agreement between the solver predictions and experimental measurements are significantly improved.
DA - 2019/8//
PY - 2019/8//
DO - 10.1016/j.ijheatmasstransfer.2019.04.075
VL - 138
SP - 1096-1116
SN - 1879-2189
ER -
TY - JOUR
TI - Incompressible limit of a continuum model of tissue growth with segregation for two cell populations
AU - Chertock, Alina
AU - Degond, Pierre
AU - Hecht, Sophie
AU - Vincent, Jean-Paul
T2 - MATHEMATICAL BIOSCIENCES AND ENGINEERING
AB - This paper proposes a model for the growth of two interacting populations of cells that do not mix. The dynamics is driven by pressure and cohesion forces on the one hand and proliferation on the other hand. Contrasting with earlier works which assume that the two populations are initially segregated, our model can deal with initially mixed populations as it explicitly incorporates a repul-sion force that enforces segregation. To balance segregation instabilities potentially triggered by the repulsion force, our model also incorporates a fourth order diffusion. In this paper, we study the influ-ence of the model parameters thanks to one-dimensional simulations using a finite-volume method for a relaxation approximation of the fourth order diffusion. Then, following earlier works on the single population case, we provide formal arguments that the model approximates a free boundary Hele Shaw type model that we characterise using both analytical and numerical arguments.
DA - 2019///
PY - 2019///
DO - 10.3934/mbe.2019290
VL - 16
IS - 5
SP - 5804-5835
SN - 1551-0018
UR - http://dx.doi.org/10.3934/mbe.2019290
KW - tissue growth
KW - two cell populations
KW - incompressible limit
KW - free boundary problem
ER -
TY - JOUR
TI - Adaptive moving mesh upwind scheme for the two-species chemotaxis model
AU - Chertock, Alina
AU - Kurganov, Alexander
AU - Ricchiuto, Mario
AU - Wu, Tong
T2 - Computers & Mathematics with Applications
AB - Chemotaxis systems are used to model the propagation, aggregation and pattern formation of bacteria/cells in response to an external stimulus, usually a chemical one. A common property of all chemotaxis systems is their ability to model a concentration phenomenon—rapid growth of the cell density in small neighborhoods of concentration points/curves. More precisely, the solution may develop singular, spiky structures, or even blow up in finite time. Therefore, the development of accurate and computationally efficient numerical methods for the chemotaxis models is a challenging task. We study the two-species Patlak–Keller–Segel type chemotaxis system, in which the two species do not compete, but have different chemotactic sensitivities, which may lead to a significantly difference in cell density growth rates. This phenomenon was numerically investigated in Kurganov and Lukáčová-Medviďová (2014) and Chertock et al. (2018), where second- and higher-order methods on uniform Cartesian grids were developed. However, in order to achieve high resolution of the density spikes developed by the species with a lower chemotactic sensitivity, a very fine mesh had to be utilized and thus the efficiency of the numerical method was affected. In this work, we consider an alternative approach relying on mesh adaptation, which helps to improve the approximation of the singular structures evolved by chemotaxis models. We develop, in particular, an adaptive moving mesh (AMM) finite-volume semi-discrete upwind method for the two-species chemotaxis system. The proposed AMM technique allows one to increase the density of mesh nodes at the blowup regions. This helps to substantially improve the resolution while using a relatively small number of finite-volume cells.
DA - 2019/6//
PY - 2019/6//
DO - 10.1016/j.camwa.2019.01.021
VL - 77
IS - 12
SP - 3172-3185
J2 - Computers & Mathematics with Applications
LA - en
OP -
SN - 0898-1221
UR - http://dx.doi.org/10.1016/j.camwa.2019.01.021
DB - Crossref
KW - Two-species chemotaxis system
KW - Adaptive moving mesh (AMM) method
KW - Finite-volume upwind method
KW - Singular (spiky) solutions
ER -
TY - JOUR
TI - Compact High Order Accurate Schemes for the Three Dimensional Wave Equation
AU - Smith, F.
AU - Tsynkov, S.
AU - Turkel, E.
T2 - Journal of Scientific Computing
DA - 2019/5/6/
PY - 2019/5/6/
DO - 10.1007/s10915-019-00970-x
VL - 5
SP - 1–29
J2 - J Sci Comput
LA - en
OP -
SN - 0885-7474 1573-7691
UR - http://dx.doi.org/10.1007/s10915-019-00970-x
DB - Crossref
KW - Unsteady wave propagation
KW - Fourth order accurate approximation
KW - Small stencil
KW - Cartesian grid
KW - Implicit scheme
KW - Multigrid methods
ER -
TY - JOUR
TI - Detection of delayed target response in SAR
AU - Gilman, Mikhail
AU - Tsynkov, Semyon
T2 - Inverse Problems
AB - Delayed target response in synthetic aperture radar (SAR) imaging can be obscured by the range-delay ambiguity and speckle. To analyze the range-delay ambiguity, one extends the standard SAR formulation and allows both the target reflectivity and the image to depend not only on the coordinates, but also on the response delay. However, this still leaves the speckle unaccounted for. Yet speckle is commonly found in SAR images of extended targets, and a statistical approach is usually employed to describe it. We have developed a simple model of a delayed scatterer by modifying the random function that describes a homogeneous extended scatterer. Our model allows us to obtain a relation between the deterministic parameters of the target model and statistical moments of the SAR image. We assume a regular shape of the antenna trajectory, and our model targets are localized in at least one space-time coordinate; this permits analytical formulation for statistical moments of the image. The problem of reconstruction of coordinate-delay reflectivity function is reduced to that of discrimination between instantaneous and delayed scatterers; for the latter problem, the maximum likelihood based image processing procedure has been developed. We perform Monte-Carlo simulation and evaluate performance of the classification procedure for a simple dependence of scatterer reflectivity on the delay time.
DA - 2019/4/25/
PY - 2019/4/25/
DO - 10.1088/1361-6420/ab1c80
VL - 4
SP - 085005 (38pp)
J2 - Inverse Problems
OP -
SN - 0266-5611 1361-6420
UR - http://dx.doi.org/10.1088/1361-6420/ab1c80
DB - Crossref
KW - delayed scattering
KW - dispersive targets
KW - synthetic aperture radar
KW - speckle
KW - range-delay ambiguity
ER -
TY - JOUR
TI - A New Approach for Designing Moving-Water Equilibria Preserving Schemes for the Shallow Water Equations
AU - Cheng, Yuanzhen
AU - Chertock, Alina
AU - Herty, Michael
AU - Kurganov, Alexander
AU - Wu, Tong
T2 - JOURNAL OF SCIENTIFIC COMPUTING
DA - 2019/7//
PY - 2019/7//
DO - 10.1007/s10915-019-00947-w
VL - 80
IS - 1
SP - 538-554
SN - 1573-7691
UR - https://doi-org.prox.lib.ncsu.edu/10.1007/s10915-019-00947-w
KW - Shallow water equations
KW - Central-upwind scheme
KW - Well-balanced method
KW - Steady-state solutions (equilibria)
KW - Moving-water and still-water equilibria
ER -
TY - JOUR
TI - An asymptotic preserving scheme for the two-dimensional shallow water equations with Coriolis forces
AU - Liu, Xin
AU - Chertock, Alina
AU - Kurganov, Alexander
T2 - JOURNAL OF COMPUTATIONAL PHYSICS
AB - We consider the two-dimensional Saint-Venant system of shallow water equations with Coriolis forces. We focus on the case of a low Froude number, in which the system is stiff and conventional explicit numerical methods are extremely inefficient and often impractical. Our goal is to design an asymptotic preserving (AP) scheme, which is uniformly asymptotically consistent and stable for a broad range of (low) Froude numbers. The goal is achieved using the flux splitting proposed in [Haack et al., Commun. Comput. Phys., 12 (2012), pp. 955–980] in the context of isentropic Euler and Navier-Stokes equations. We split the flux into the stiff and nonstiff parts and then use an implicit-explicit approach: apply an explicit hyperbolic solver (we use the second-order central-upwind scheme) to the nonstiff part of the system while treating the stiff part of it implicitly. Moreover, the stiff part of the flux is linear and therefore we reduce the implicit stage of the proposed method to solving a Poisson-type elliptic equation, which is discretized using a standard second-order central difference scheme. We conduct a series of numerical experiments, which demonstrate that the developed AP scheme achieves the theoretical second-order rate of convergence and the time-step stability restriction is independent of the Froude number. This makes the proposed AP scheme an efficient and robust alternative to fully explicit numerical methods.
DA - 2019/8/15/
PY - 2019/8/15/
DO - 10.1016/j.jcp.2019.04.035
VL - 391
SP - 259-279
SN - 1090-2716
UR - https://doi-org.prox.lib.ncsu.edu/10.1016/j.jcp.2019.04.035
KW - Saint-Venant system of shallow water equations
KW - Coriolis forces
KW - Asymptotic preserving scheme
KW - Central-upwind scheme
KW - Flux splitting
KW - Implicit-explicit approach
ER -
TY - JOUR
TI - The influence of numerical error on parameter estimation and uncertainty quantification for advective PDE models
AU - Nardini, John T.
AU - Bortz, D. M.
T2 - INVERSE PROBLEMS
AB - Advective partial differential equations can be used to describe many scientific processes. Two significant sources of error that can cause difficulties in inferring parameters from experimental data on these processes include (i) noise from the measurement and collection of experimental data and (ii) numerical error in approximating the forward solution to the advection equation. How this second source of error alters parameter estimation and uncertainty quantification during an inverse problem methodology is not well understood. As a step towards a better understanding of this problem, we present both analytical and computational results concerning how a least squares cost function and parameter estimator behave in the presence of numerical error in approximating solutions to the underlying advection equation. We investigate residual patterns to derive an autocorrelative statistical model that can improve parameter estimation and confidence interval computation for first order methods. Building on our results and their general nature, we provide guidelines for practitioners to determine when numerical or experimental error is the main source of error in their inference, along with suggestions of how to efficiently improve their results.
DA - 2019/6//
PY - 2019/6//
DO - 10.1088/1361-6420/ab10bb
VL - 35
IS - 6
SP -
SN - 1361-6420
KW - inverse problems
KW - numerical analysis
KW - uncertainty quantification
KW - autocorrelation
ER -
TY - JOUR
TI - Population model for the decline of Homalodisca vitripennis (Hemiptera: Cicadellidae) over a ten-year period
AU - Banks, H. T.
AU - Banks, John E.
AU - Cody, Natalie G.
AU - Hoddle, Mark S.
AU - Meade, Annabel E.
T2 - JOURNAL OF BIOLOGICAL DYNAMICS
AB - The glassy-winged sharpshooter, Homalodisca vitripennis (Germar), is an invasive pest which presents a major economic threat to grape industries in California, because it spreads a disease-causing bacterium, Xylella fastidiosa. In this note we develop a time and temperature dependent mathematical model to analyze aggregate population data for H. vitripennis from a 10-year study consisting of biweekly monitoring of H. vitripennis populations on unsprayed citrus, during which H. vitripennis decreased significantly. This model was fitted to the aggregate H. vitripennis time series data using iterative reweighted weighted least squares (IRWLS) with assumed probability distributions for certain parameter values. Results indicate that the H. vitripennis model fits the phenological and temperature data reasonably well, but the observed population decrease may possibly be attributed to factors other than the abiotic effect of temperature. A key factor responsible for this decline but not analyzed here could be biotic, for example, potentially parasitism of H. vitripennis eggs by Cosmocomoidea ashmeadi. A biological control program targeting H. vitripennis utilizing the mymarid egg parasitoid Cosmocomoidea (formerly Gonatocerus) ashmeadi (Girault) is described.
DA - 2019/1/1/
PY - 2019/1/1/
DO - 10.1080/17513758.2019.1616839
VL - 13
IS - 1
SP - 422-446
SN - 1751-3766
KW - Population model
KW - data fitting
KW - inverse problems
KW - weighted least squares
KW - generalized least squares
KW - biological control
KW - Homalodisca vitripennis
KW - Gonatocerus ashmeadi
KW - Cosmocomoidea ashmeadi
KW - density dependence
ER -
TY - JOUR
TI - Uncertainty analysis of dielectric elastomer membranes under electromechanical loading
AU - Gao, W.
AU - Miles, P. R.
AU - Moura, A. G.
AU - Hussaini, M. Y.
AU - Oates, W. S.
T2 - SMART MATERIALS AND STRUCTURES
AB - The uncertainty in modeling finite deformation membrane electromechanics is analyzed by comparing low and high fidelity models against data on the dielectric elastomer VHB 4910. Both models include electrically and mechanically induced stress during transverse deformation of the membranes. The low fidelity model approximates deformation to be homogeneous while the high fidelity model includes a more accurate kinematic assumption of inhomogeneous deformation. We illustrate the importance of model fidelity with regards to parameter uncertainty and the associated propagation of errors in predicting membrane forces and charges in realistic actuator configurations. Both the low and high fidelity models are shown to accurately predict membrane forces and charges under different applied displacements and voltages. However, there are significant differences in the estimation of the dielectric constant used to model the membrane electromechanics. Bayesian statistics are used to quantify the uncertainty of the modeling approaches in light of both force–displacement and charge–voltage measurements. We quantify the hyperelastic, electromechanical coupling, and dielectric model uncertainties self-consistently using all mechanical and electrical experiments conducted on the 3M elastomer VHB 4910. We conclude that the low fidelity model is useful for system dynamic and control applications yet is limited in self-consistent predictions of both forces and charges from applied displacements and voltages. In comparison, the high fidelity model provides a more accurate description of the electromechanical coupling and dielectric constitutive behavior, but requires more computational power due to finite element discretization. In addition, the high fidelity modeling illustrates that a deformation dependent dielectric constant is necessary to self-consistently simulate both force–displacement and charge–voltage data.
DA - 2019/5//
PY - 2019/5//
DO - 10.1088/1361-665X/aaedea
VL - 28
IS - 5
SP -
SN - 1361-665X
KW - Bayesian uncertainty
KW - dielectric elastomer
KW - membranes
KW - hyperelastic
ER -
TY - JOUR
TI - IMMUNOSUPPRESSANT TREATMENT DYNAMICS IN RENAL TRANSPLANT RECIPIENTS: AN ITERATIVE MODELING APPROACH
AU - Murad, Neha
AU - Tran, H. T.
AU - Banks, H. T.
AU - Everett, R. A.
AU - Rosenberg, Eric S.
T2 - DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS-SERIES B
AB - Finding the optimal balance between over-suppression and under-suppression of the immune response is difficult to achieve in renal transplant patients, all of whom require lifelong immunosuppression. Our ultimate goal is to apply control theory to adaptively predict the optimal amount of immunosuppression; however, we first need to formulate a biologically realistic model. The process of quantitively modeling biological processes is iterative and often leads to new insights with every iteration. We illustrate this iterative process of modeling for renal transplant recipients infected by BK virus. We analyze and improve on the current mathematical model by modifying it to be more biologically realistic and amenable for designing an adaptive treatment strategy.
DA - 2019/6//
PY - 2019/6//
DO - 10.3934/dcdsb.2018274
VL - 24
IS - 6
SP - 2781-2797
SN - 1553-524X
KW - Inverse problem
KW - infection dynamics
KW - differential equations
KW - renal transplantation
KW - immunosuppression therapy
KW - iterative modeling process
KW - BKV
ER -
TY - JOUR
TI - Gradient-Free Construction of Active Subspaces for Dimension Reduction in Complex Models with Applications to Neutronics
AU - Coleman, Kayla D.
AU - Lewis, Allison
AU - Smith, Ralph C.
AU - Williams, Brian
AU - Morris, Max
AU - Khuwaileh, Bassam
T2 - SIAM-ASA JOURNAL ON UNCERTAINTY QUANTIFICATION
AB - Recent developments in the field of reduced-order modeling---and, in particular, active subspace construction---have made it possible to efficiently approximate complex models by constructing low-order response surfaces based upon a small subspace of the original high-dimensional parameter space. These methods rely upon the fact that the response tends to vary more prominently in a few dominant directions defined by linear combinations of the original inputs, allowing for a rotation of the coordinate axis and a consequent transformation of the parameters. In this paper, we discuss a gradient-free active subspace algorithm that is feasible for high-dimensional parameter spaces where finite-difference techniques are impractical. This analysis extends the gradient-free algorithm introduced in [A. Lewis, R. Smith, and B. Williams, Comput. Math. Appl., 72 (2016), pp. 1603--1615] in two significant ways: (i) we introduce an initialization algorithm to identify lower-dimensional subspaces of influential directions to seed the gradient-free algorithm for high-dimensional problems, and (ii) we analyze dimension selection criteria to verify the algorithms. We illustrate the initialized gradient-free active subspace algorithm for a neutronics example implemented with SCALE6.1 for input dimensions up to 7700.
DA - 2019///
PY - 2019///
DO - 10.1137/16M1075119
VL - 7
IS - 1
SP - 117-142
SN - 2166-2525
KW - gradient-free active subspaces
KW - neutronics applications
ER -
TY - JOUR
TI - An optimal control approach for blood pressure regulation during head-up tilt
AU - Williams, Nakeya D.
AU - Mehlsen, Jesper
AU - Tran, Hien T.
AU - Olufsen, Mette S.
T2 - BIOLOGICAL CYBERNETICS
AB - This paper presents an optimal control approach to modeling effects of cardiovascular regulation during head-up tilt (HUT). Many patients who suffer from dizziness or light-headedness are administered a head-up tilt test to explore potential deficits within the autonomic control system, which maintains the cardiovascular system at homeostasis. This system is complex and difficult to study in vivo, and thus we propose to use mathematical modeling to achieve a better understanding of cardiovascular regulation during HUT. In particular, we show the feasibility of using optimal control theory to compute physiological control variables, vascular resistance and cardiac contractility, quantities that cannot be measured directly, but which are useful to assess the state of the cardiovascular system. A non-pulsatile lumped parameter model together with pseudo- and clinical data are utilized in the optimal control problem formulation. Results show that the optimal control approach can predict time-varying quantities regulated by the cardiovascular control system. Our results compare favorable to our previous study using a piecewise linear spline approach, less a priori knowledge is needed, and results were obtained at a significantly lower computational cost.
DA - 2019/4//
PY - 2019/4//
DO - 10.1007/s00422-018-0783-9
VL - 113
IS - 1-2
SP - 149-159
SN - 1432-0770
KW - Cardiovascular dynamics modeling
KW - Head-up tilt
KW - Non-pulsatile model
KW - Orthostatic intolerance
KW - Optimal control
ER -
TY - JOUR
TI - Parameter subset selection techniques for problems in mathematical biology
AU - Olsen, Christian Haargaard
AU - Ottesen, Johnny T.
AU - Smith, Ralph C.
AU - Olufsen, Mette S.
T2 - BIOLOGICAL CYBERNETICS
AB - Patient-specific models for diagnostics and treatment planning require reliable parameter estimation and model predictions. Mathematical models of physiological systems are often formulated as systems of nonlinear ordinary differential equations with many parameters and few options for measuring all state variables. Consequently, it can be difficult to determine which parameters can reliably be estimated from available data. This investigation highlights pitfalls associated with practical parameter identifiability and subset selection. The latter refer to the process associated with selecting a subset of parameters that can be identified uniquely by parameter estimation protocols. The methods will be demonstrated using five examples of increasing complexity, as well as with patient-specific model predicting arterial blood pressure. This study demonstrates that methods based on local sensitivities are preferable in terms of computational cost and model fit when good initial parameter values are available, but that global methods should be considered when initial parameter value is not known or poorly understood. For global sensitivity analysis, Morris screening provides results in terms of parameter sensitivity ranking at a much lower computational cost.
DA - 2019/4//
PY - 2019/4//
DO - 10.1007/s00422-018-0784-8
VL - 113
IS - 1-2
SP - 121-138
SN - 1432-0770
KW - Parameter identifiability
KW - Parameter subset selection
KW - Parameter estimation
KW - Modeling
ER -
TY - JOUR
TI - A direct method for accurate solution and gradient computations for elliptic interface problems
AU - Chen, Xiaohong
AU - Feng, Xiufang
AU - Li, Zhilin
T2 - NUMERICAL ALGORITHMS
DA - 2019/3//
PY - 2019/3//
DO - 10.1007/s11075-018-0503-5
VL - 80
IS - 3
SP - 709-740
SN - 1572-9265
KW - Elliptic interface problem
KW - Accurate solution and gradient computation
KW - Variable coefficient with discontinuities
KW - Convergence proof
KW - Discrete Green's function
KW - Discrete elliptic maximum principle
KW - Compact finite difference scheme
ER -
TY - JOUR
TI - Optimal control of immunosuppressants in renal transplant recipients susceptible to BKV infection
AU - Murad, Neha
AU - Tran, H. T.
AU - Banks, H. T.
T2 - OPTIMAL CONTROL APPLICATIONS & METHODS
AB - Summary Kidney transplant recipients are put on a lifelong regime of immunosuppressants to prevent the body from rejecting the allograft. Suppressing the immune system renders the body susceptible to infections. The key to a successful transplant is to ensure the immune system is sufficiently suppressed to prevent organ rejection but adequately strong to fight infections. Finding the optimal balance between over and undersuppression of the immune response is crucial in preventing allograft failure. In this paper, we design a feedback control formulation to predict the optimal amount of immunosuppression required by renal transplant recipients in the context of infections caused by BK virus. We use a receding horizon control methodology to construct the feedback control. Data, as they are currently collected, provide information for only some model states, so we use nonlinear Kalman filtering to estimate the remaining model states for feedback control. We conclude that, using the presented methodology, an individualized adaptive treatment schedule can be built for renal transplant recipients.
DA - 2019/3//
PY - 2019/3//
DO - 10.1002/oca.2478
VL - 40
IS - 2
SP - 292-309
SN - 1099-1514
KW - BK virus
KW - immunosuppression
KW - Kalman filtering
KW - optimal feedback control
KW - receding horizon control
KW - renal transplant
ER -
TY - JOUR
TI - Convergence of the EDIIS Algorithm for Nonlinear Equations
AU - Chen, Xiaojun
AU - Kelley, C. T.
T2 - SIAM Journal on Scientific Computing
AB - The Energy Direct Inversion on the Iterative Subspace (EDIIS) algorithm was designed to globalize Anderson acceleration, a method for improving the performance of fixed point iteration. The motivating application is electronic structure computations. In this paper we prove a convergence result for that algorithm and illustrate the theory with a computational example.
DA - 2019/1//
PY - 2019/1//
DO - 10.1137/18M1171084
VL - 41
IS - 1
SP - A365-A379
J2 - SIAM J. Sci. Comput.
LA - en
OP -
SN - 1064-8275 1095-7197
UR - http://dx.doi.org/10.1137/18M1171084
DB - Crossref
KW - nonlinear equations
KW - Anderson acceleration
KW - EDIIS
ER -
TY - JOUR
TI - Ecosystem function in predator-prey food webs-confronting dynamic models with empirical data
AU - Curtsdotter, Alva
AU - Banks, H. Thomas
AU - Banks, John E.
AU - Jonsson, Mattias
AU - Jonsson, Tomas
AU - Laubmeier, Amanda N.
AU - Traugott, Michael
AU - Bommarco, Riccardo
T2 - JOURNAL OF ANIMAL ECOLOGY
AB - Most ecosystem functions and related services involve species interactions across trophic levels, for example, pollination and biological pest control. Despite this, our understanding of ecosystem function in multitrophic communities is poor, and research has been limited to either manipulation in small communities or statistical descriptions in larger ones. Recent advances in food web ecology may allow us to overcome the trade-off between mechanistic insight and ecological realism. Molecular tools now simplify the detection of feeding interactions, and trait-based approaches allow the application of dynamic food web models to real ecosystems. We performed the first test of an allometric food web model's ability to replicate temporally nonaggregated abundance data from the field and to provide mechanistic insight into the function of predation. We aimed to reproduce and explore the drivers of the population dynamics of the aphid herbivore Rhopalosiphum padi observed in ten Swedish barley fields. We used a dynamic food web model, taking observed interactions and abundances of predators and alternative prey as input data, allowing us to examine the role of predation in aphid population control. The inverse problem methods were used for simultaneous model fit optimization and model parameterization. The model captured >70% of the variation in aphid abundance in five of ten fields, supporting the model-embodied hypothesis that body size can be an important determinant of predation in the arthropod community. We further demonstrate how in-depth model analysis can disentangle the likely drivers of function, such as the community's abundance and trait composition. Analysing the variability in model performance revealed knowledge gaps, such as the source of episodic aphid mortality, and general method development needs that, if addressed, would further increase model success and enable stronger inference about ecosystem function. The results demonstrate that confronting dynamic food web models with abundance data from the field is a viable approach to evaluate ecological theory and to aid our understanding of function in real ecosystems. However, to realize the full potential of food web models, in ecosystem function research and beyond, trait-based parameterization must be refined and extended to include more traits than body size.
DA - 2019/2//
PY - 2019/2//
DO - 10.1111/1365-2656.12892
VL - 88
IS - 2
SP - 196-210
SN - 1365-2656
KW - agricultural pests
KW - allometry
KW - body mass
KW - conservation biological control
KW - herbivore suppression
KW - multitrophic functioning
KW - predator-prey interactions
KW - species traits
ER -
TY - JOUR
TI - Direct implementation of high order BGT artificial boundary conditions
AU - Medvinsky, M.
AU - Tsynkov, S.
AU - Turkel, E.
T2 - Journal of Computational Physics
AB - Local artificial boundary conditions (ABCs) for the numerical simulation of waves have been successfully used for decades (most notably, the boundary conditions due to Engquist & Majda, Bayliss, Gunzburger & Turkel, and Higdon). The basic idea behind these boundary conditions is that they cancel several leading terms in an expansion of the solution. The larger the number of terms canceled, the higher the order of the boundary condition and, in turn, the smaller the reflection error due to truncation of the original unbounded domain by an artificial outer boundary. In practice, however, the use of local ABCs has been limited to low orders (first and second), because higher order boundary conditions involve higher order derivatives of the solution, which may harm well-posedness and cause numerical instabilities. They are also difficult to implement especially in finite elements. A prominent exception is the development of local high order ABCs based on auxiliary variables. In the current paper, we implement high order Bayliss–Turkel ABCs directly — with no auxiliary variables yet no discrete approximation of the constituent high order derivatives either. Instead, we represent the solution at the boundary as an expansion with respect to a continuous basis. For the spherical artificial boundary, the basis consists of eigenfunctions of the Beltrami operator (spherical harmonics), which enable replacing the high order derivatives in the ABCs with powers of the corresponding eigenvalues. The continuous representation at the boundary is coupled to higher order compact finite differences inside the domain by the method of difference potentials (MDP). It maintains high order accuracy even when the boundary is not aligned with the discretization grid.
DA - 2019/1//
PY - 2019/1//
DO - 10.1016/j.jcp.2018.09.040
VL - 376
SP - 98-128
J2 - Journal of Computational Physics
LA - en
OP -
SN - 0021-9991
UR - http://dx.doi.org/10.1016/j.jcp.2018.09.040
DB - Crossref
KW - Propagation of waves over unbounded regions
KW - Helmholtz equation
KW - Spherical artificial boundary
KW - Expansion with respect to continuous basis
KW - Method of difference potentials (MDP)
KW - Beltrami operator
ER -
TY - JOUR
TI - PARAMETER IDENTIFICATION AND SENSITIVITY ANALYSIS FOR A PHYTOPLANKTON COMPETITION MODEL
AU - Stojsavljevic, Thomas
AU - Pinter, Gabriella
AU - Lauko, Istvan
AU - Myers, Nicholas
T2 - QUARTERLY OF APPLIED MATHEMATICS
AB - Phytoplankton live in a complex environment with two essential resources, light and nutrients, forming various gradients. Light supplied from above is never homogeneously distributed in a body of water due to refraction and absorption from biomass present in the ecosystem and other sources. Nutrients in turn are typically supplied from below mixed-up by diffusion from the benthic region. Here we present a model of two phytoplankton species competing in a deep freshwater lake for light and two nutrients, one of which is assumed to be preferred. The model is comprised of a system of non- linear, non-local partial differential equations with appropriate boundary conditions. The parameter space of the model is analyzed for parameter identifiability - the ability for a parameterâs true value to be recovered through optimization, and for global sensitivity - the influence a parameter has on model response. The results of these analyses are interpreted within their biological context.
DA - 2019/3//
PY - 2019/3//
DO - 10.1090/qam/1514
VL - 77
IS - 1
SP - 1-18
SN - 1552-4485
ER -