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At least 397 records · Page 22

Magnetic tweezers with high permeability electromagnets for fast actuation of magnetic beads

As a powerful and versatile scientific instrument, magnetic tweezers have been widely used in biophysical research areas, such as mechanical cell properties and single molecule manipulation. If one wants to steer bead position, the nonlinearity of magnetic properties and the strong position dependence of the magnetic field in most magnetic tweezers lead to quite a challenge in their control. In this article, we report multi-pole electromagnetic tweezers with high permeability cores yielding high force output, good maneuverability, and flexible design. For modeling, we adopted a piece-wise linear dependence of magnetization on field to characterize the magnetic beads. We implemented a bi-linear interpolation of magnetic field in the work space, based on a lookup table obtained from finite element simulation. The electronics and software were custom-made to achieve high performance. In addition, the effects of dimension and defect on structure of magnetic tips also were inspected. In a workspace with size of 0.1 × 0.1 mm{sup 2}, a force of up to 400 pN can be applied on a 2.8 μm superparamagnetic bead in any direction within the plane. Because the magnetic particle is always pulled towards a tip, the pulling forces from the pole tips have to be well balanced in order to achieve control of the particle’s position. Active video tracking based feedback control is implemented, which is able to work at a speed of up to 1 kHz, yielding good maneuverability of the magnetic beads.

36 MATERIALS SCIENCE↗

Highly non-linear solid core photonic crystal fiber with one nano hole

The numerical study of newly designed solid core photonic crystal fiber (SCPCF) having three hexagonal air hole rings in cladding region and one small nano hole at the center are presented. By using full vectorial finite element method (FV-FEM), we analyses the optical properties like effective area, nonlinearity and confinement loss of the proposed PCF. Results show that the change in core diameter controls the effective area, nonlinearity and confinement loss. A low effective area (3.34 µm{sup 2}), high nonlinearity (36.34 W{sup −1}km{sup −1}) and low confinement loss (0.00106 dB/km) are achieved at the communication wavelength 1.55 µm for the SCPCF having core air hole diameter 0.10 µm, cladding air holes diameter 1.00 µm and pitch 2.50 µm. This type of PCF is very useful in non-linear applications such as supercontinuum generation, four wave mixing, second harmonic generation etc.

36 MATERIALS SCIENCE↗

SU-F-207-05: Excess Heat Corrections in a Prototype Calorimeter for Direct Realization of CT Absorbed Dose to Phantom

Purpose: To reconcile air kerma and calorimetry measurements in a prototype calorimeter for obtaining absorbed dose in diagnostic CT beams. While corrections for thermal artifacts are routine and generally small in calorimetry of radiotherapy beams, large differences in relative stopping powers of calorimeter materials at the lower energies typical of CT beams greatly magnify their effects. Work-to-date on the problem attempts to reconcile laboratory measurements with modeling output from Monte Carlo and finite-element analysis of heat transfer. Methods: Small thermistor beads were embedded in a polystyrene (PS) core element of 1 cm diameter, which was inserted into a cylindrical HDPE phantom of 30 cm diameter and subjected to radiation in a diagnostic CT x-ray imaging system. Resistance changes in the thermistors due to radiation heating were monitored via lock-in amplifier. Multiple 3-second exposures were recorded at 8 different dose-rates from the CT system, and least-squares fits to experimental data were compared to an expected thermal response obtained by finite-element analysis incorporating source terms based on semi-empirical modeling and Monte Carlo simulation. Results: Experimental waveforms exhibited large thermal artifacts with fast time constants, associated with excess heat in wires and glass, and smaller steps attributable to radiation heating of the core material. Preliminary finite-element analysis follows the transient component of the signal qualitatively, but predicts a slower decay of temperature spikes. This was supplemented by non-linear least-squares fits incorporating semi-empirical formulae for heat transfer, which were used to obtain dose-to-PS in reasonable agreement with the output of Monte Carlo calculations that converts air kerma to absorbed dose. Conclusion: Discrepancies between the finite-element analysis and our experimental data testify to the very significant heat transfer correction required for absorbed dose calorimetry of diagnostic CT beams. The results obtained here are being used to refine both simulations and design of calorimeter core components.

60 APPLIED LIFE SCIENCES↗

Bringing Trimmed Serendipity Methods to Computational Practice in Firedrake

We present an implementation of the trimmed serendipity finite element family, using the open-source finite element package Firedrake. The new elements can be used seamlessly within the software suite for problems requiring H 1 , H (curl), or H (div)-conforming elements on meshes of squares or cubes. To test how well trimmed serendipity elements perform in comparison to traditional tensor product elements, we perform a sequence of numerical experiments including the primal Poisson, mixed Poisson, and Maxwell cavity eigenvalue problems. Overall, we find that the trimmed serendipity elements converge, as expected, at the same rate as the respective tensor product elements, while being able to offer significant savings in the time or memory required to solve certain problems.

97 MATHEMATICS AND COMPUTING↗

NDT System for Metal Components in Concrete Structures (Final Report)

Steel reinforcements embedded within concrete can corrode and crack, leading to weakening of the structures, and existing NDT (non-destructive testing) techniques do not provide the full picture. Condition assessment is critical in evaluating these structures in order to ensure safe, long-term operation of the nuclear power plants. Improved NDT techniques are needed as the nation’s generating stations age and require action based on increasingly critical inspection data. The power industry uses eddy current test (ECT) during in-service inspections to detect and monitor defects such as cracks and corrosion in metals, particularly metal pipes. However, the detection of defects in the reinforcing steel embedded in concrete is far more challenging for numerous reasons. Primary among them is the concrete layer’s thickness, which prevents the ability to have a close proximity between sensor and metallic sample. One solution to this problem is to create a higher sensitivity technique which can inspect at depth, with good spatial resolution and excellent directional sensitivity, to isolate the metal buried deep in the concrete and characterize defects in the metal. The goal of the phase II research program was to study and develop a new reinforced concrete NDT technology based on anisotropic magnetoresistive (AMR) sensors designed specifically for ECT of steel reinforcements in concrete. The first technical objective was to demonstrate the capability of inspecting steel reinforcement structures, including metal rebar and tensioning cable at or below 6” of depth embedded in concrete. Another objective was to be able to confidently identify multiple layers of reinforcements at varying depths. In addition, the technique needed to be able to provide condition assessment of the metal, providing data on the structure and positioning of the steel members, material loss, and detection of the presence of breaks. An important part of the research and development was aimed at achieving superior performance compared to existing technology. The ability to detect corrosion breaks in unbonded multi-wire and multi-strand tendons was another important objective. The final objective that led to a successful program was to build a complete prototype portable scanning system capable of demonstrating the probe performance in the field. All of these objectives were met, which provided data for the system development work going forward. RMD worked with the engineering firm Simpson Gumpertz & Heger to develop a detailed problem definition for concrete structures and the necessary sensor specifications. In addition, we developed finite element simulation models for the eddy current based NDT system through the analysis of the electromagnetic (EM) properties of sample materials and the orientation of the transmitter, sensor array (receivers), metal, and intervening materials like concrete and air. Based on the modeling and specifications, we designed and fabricated prototype sensor modules. We then acquired and fabricated test samples to characterize and optimize the sensors. Finally, we built a complete prototype for testing on actual concrete structures. This new NDT technology has high promise for greatly improving capabilities in the inspection of steel reinforcements within concrete structures, such as rebar, liners, anchors, and prestressing cables. This method could be valuable in the maintenance of nuclear power plants, and many other structures critical to our nation’s infrastructure.

42 ENGINEERING↗

Space-Time Finite Element Tensor Network Approach for the Time-Dependent Convection–Diffusion–Reaction Equation with Variable Coefficients

In this paper, we present a new space-time Galerkin-like method, where we treat the discretization of spatial and temporal domains simultaneously. This method utilizes a mixed formulation of the tensor-train (TT) and quantized tensor-train (QTT) (please see Section Tensor-Train Decomposition), designed for the finite element discretization (Q1-FEM) of the time-dependent convection–diffusion–reaction (CDR) equation. We reformulate the assembly process of the finite element discretized CDR to enhance its compatibility with tensor operations and introduce a low-rank tensor structure for the finite element operators. Recognizing the banded structure inherent in the finite element framework’s discrete operators, we further exploit the QTT format of the CDR to achieve greater speed and compression. Additionally, we present a comprehensive approach for integrating variable coefficients of CDR into the global discrete operators within the TT/QTT framework. The effectiveness of the proposed method, in terms of memory efficiency and computational complexity, is demonstrated through a series of numerical experiments, including a semi-linear example.

convection–diffusion–reaction equation↗

PDE-constrained Optimization under Uncertainty

Uncertainty is pervasive in all science and engineering applications. Incorporating uncertainty in physical models is therefore both natural and vital. In doing so, we often arrive at parametric systems of partial differential equations (PDEs). When passing from simulation to optimization, we obtain (typically nonconvex) infinite-dimensional optimization problems that, upon discretization, result in extremely large-scale nonlinear programs. For example, consider a linear elliptic PDE on a two- dimensional domain with a single random coeffcient. If we sampled the random input with 10,000 realizations of the coeffcient, the resulting optimization problem would have 10,000 PDE constraints. Furthermore, discretizing each PDE with piecewise linear finite elements on a 100X100 uni- form quadrilateral mesh results in 100,000,000 degrees of freedom. As a result, the critical components for ensuring mesh-independent performance of numerical optimization methods in the deterministic setting, for example, solution regularity and generalized differentiability, are even more critical in the stochastic setting.

42 ENGINEERING↗

Model's sparse representation based on reduced mixed GMsFE basis methods

In this paper, we propose a model's sparse representation based on reduced mixed generalized multiscale finite element (GMsFE) basis methods for elliptic PDEs with random inputs. A typical application for the elliptic PDEs is the flow in heterogeneous random porous media. Mixed generalized multiscale finite element method (GMsFEM) is one of the accurate and efficient approaches to solve the flow problem in a coarse grid and obtain the velocity with local mass conservation. When the inputs of the PDEs are parameterized by the random variables, the GMsFE basis functions usually depend on the random parameters. This leads to a large number degree of freedoms for the mixed GMsFEM and substantially impacts on the computation efficiency. In order to overcome the difficulty, we develop reduced mixed GMsFE basis methods such that the multiscale basis functions are independent of the random parameters and span a low-dimensional space. To this end, a greedy algorithm is used to find a set of optimal samples from a training set scattered in the parameter space. Reduced mixed GMsFE basis functions are constructed based on the optimal samples using two optimal sampling strategies: basis-oriented cross-validation and proper orthogonal decomposition. Although the dimension of the space spanned by the reduced mixed GMsFE basis functions is much smaller than the dimension of the original full order model, the online computation still depends on the number of coarse degree of freedoms. To significantly improve the online computation, we integrate the reduced mixed GMsFE basis methods with sparse tensor approximation and obtain a sparse representation for the model's outputs. The sparse representation is very efficient for evaluating the model's outputs for many instances of parameters. To illustrate the efficacy of the proposed methods, we present a few numerical examples for elliptic PDEs with multiscale and random inputs. In particular, a two-phase flow model in random porous media is simulated by the proposed sparse representation method.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

Proximal Galerkin: A Structure-Preserving Finite Element Method for Pointwise Bound Constraints

The proximal Galerkin finite element method is a high-order, low iteration complexity, nonlinear numerical method that preserves the geometric and algebraic structure of pointwise bound constraints in infinite-dimensional function spaces. This paper introduces the proximal Galerkin method and applies it to solve free boundary problems, enforce discrete maximum principles, and develop a scalable, mesh-independent algorithm for optimal design with pointwise bound constraints. This paper also introduces the latent variable proximal point (LVPP) algorithm, from which the proximal Galerkin method derives. When analyzing the classical obstacle problem, we discover that the underlying variational inequality can be replaced by a sequence of second-order partial differential equations (PDEs) that are readily discretized and solved with, e.g., the proximal Galerkin method. Throughout this work, we arrive at several contributions that may be of independent interest. These include (1) a semilinear PDE we refer to as the entropic Poisson equation; (2) an algebraic/geometric connection between high-order positivity-preserving discretizations and certain infinite-dimensional Lie groups; and (3) a gradient-based, bound-preserving algorithm for two-field, density-based topology optimization. The complete proximal Galerkin methodology combines ideas from nonlinear programming, functional analysis, tropical algebra, and differential geometry and can potentially lead to new synergies among these areas as well as within variational and numerical analysis. Open-source implementations of our methods accompany this work to facilitate reproduction and broader adoption.

97 MATHEMATICS AND COMPUTING↗

Fast Multilevel Solvers for a Class of Discrete Fourth Order Parabolic Problems

In this paper, we study fast iterative solvers for the solution of fourth order parabolic equations discretized by mixed finite element methods. We propose to use consistent mass matrix in the discretization and use lumped mass matrix to construct efficient preconditioners. We provide eigenvalue analysis for the preconditioned system and estimate the convergence rate of the preconditioned GMRes method. Furthermore, we show that these preconditioners only need to be solved inexactly by optimal multigrid algorithms. Our numerical examples indicate that the proposed preconditioners are very efficient and robust with respect to both discretization parameters and diffusion coefficients. We also investigate the performance of multigrid algorithms with either collective smoothers or distributive smoothers when solving the preconditioner systems.

97 MATHEMATICS AND COMPUTING↗

Liquid Crystal Orientation and Shape Optimization for the Active Response of Liquid Crystal Elastomers

Liquid crystal elastomers (LCEs) are responsive materials that can undergo large reversible deformations upon exposure to external stimuli, such as electrical and thermal fields. Controlling the alignment of their liquid crystals mesogens to achieve desired shape changes unlocks a new design paradigm that is unavailable when using traditional materials. While experimental measurements can provide valuable insights into their behavior, computational analysis is essential to exploit their full potential. Accurate simulation is not, however, the end goal; rather, it is the means to achieve their optimal design. Such design optimization problems are best solved with algorithms that require gradients, i.e., sensitivities, of the cost and constraint functions with respect to the design parameters, to efficiently traverse the design space. In this work, a nonlinear LCE model and adjoint sensitivity analysis are implemented in a scalable and flexible finite element-based open source framework and integrated into a gradient-based design optimization tool. To display the versatility of the computational framework, LCE design problems that optimize both the material, i.e., liquid crystal orientation, and structural shape to reach a target actuated shapes or maximize energy absorption are solved. Multiple parameterizations, customized to address fabrication limitations, are investigated in both 2D and 3D. The case studies are followed by a discussion on the simulation and design optimization hurdles, as well as potential avenues for improving the robustness of similar computational frameworks for applications of interest.

42 ENGINEERING↗

Uniform Subspace Correction Preconditioners for Discontinuous Galerkin Methods with hp-Refinement

In this paper, we develop subspace correction preconditioners for discontinuous Galerkin (DG) discretizations of elliptic problems with hp-refinement. These preconditioners are based on the decomposition of the DG finite element space into a conforming subspace, and a set of small nonconforming edge spaces. The conforming subspace is preconditioned using a matrix-free low-order refined technique, which in this work, we extend to the hp-refinement context using a variational restriction approach. The condition number of the resulting linear system is independent of the granularity of the mesh h, and the degree of the polynomial approximation p. The method is amenable to use with meshes of any degree of irregularity and arbitrary distribution of polynomial degrees. Furthermore, numerical examples are shown on several test cases involving adaptively and randomly refined meshes, using both the symmetric interior penalty method and the second method of Bassi and Rebay (BR2).

97 MATHEMATICS AND COMPUTING↗

HygroThermFEM v1.0

HygroThermFEM is a Finite Element Method-based numerical calculation engine for solving 2-D heat and moisture transfer problems. This numerical engine is used in the THERM software tool, and its primary purpose is for the analysis of building envelopes (e.g., windows, walls, roofs, foundations, etc.). However, the engine can also be used for any heat and moisture transfer problems that require solving fundamental 2-D energy and mass transfer equations. Fluid flow solutions (Navier-Stokes momentum equations) are not included, but the correlations for various convection heat transfer situations are provided, including the translation of complex cavity geometries into those for which correlations are applicable. The calculation engine is written in C++ and includes an API for connecting to third-party tools.

Vidanovic, Dragan [Lawrence Berkeley National Labo↗

Mathematical and Numerical Analyses of Peridynamics for Multiscale Materials Modeling

We have treated the modeling, analysis, numerical analysis, and algorithmic development for nonlocal models of diffusion and mechanics. Variational formulations were developed and finite element methods were developed based on those formulations for both steady state and time dependent problems. Obstacle problems and optimization problems for the nonlocal models were also treated and connections made with fractional derivative models.

97 MATHEMATICS AND COMPUTING↗

Numerical Integration of Viscoelastic Models

Accurate modeling of viscoelasticity remains an important consideration for a variety of materials (e.g. polymers and inorganic glasses). As such, over the previous decades a substantial body of work has been dedicated to developing appropriate constitutive models for viscoelasticity ranging from initial considerations of linear thermoviscoelasticity to more complex non-linear formulations incorporating fictive temperatures or potential energy clocks including the use of both internal state variable(ISV) and hereditary integral representations. Nonetheless, relatively limited (in comparison to plasticity) attention has been paid to the numerical integration of such schemes. In terms of integral based formulations, Taylor et al. first considered the problem of the integration of a linear viscoelasticity model. That work focused on the integration of the hereditary integrals and demonstrated improved performance of the new scheme with a custom finite element code over an existing finite difference reference. Chambers and Becker, using a free volume based shift factor, also considered the integration of the hereditary integrals and the impact on the problem of a pressurized thick-walled cylinder and developed an adaptive scheme to bound the error. Chambers later developed three-point Gauss and composite integration schemes for the hereditary integrals and noted improved accuracy. With respect to ISV-based schemes, formulations for the non-linear Schapery model have been proposed. However, in those efforts greater attention was paid to convergence of the non-linear solution scheme than impact of numerical integration. Various authors (e.g. Holzapfel and Simo and Hughes) have also studied the use of convolution integrals with differential forms of ISVs for temperature-independent formulations. Regardless, while the "potential energy clock" (PEC) and "simplified potential energy clock"(SPEC) models have been used to study a variety of non-linear responses (e.g.), limited attention has been paid to the numerical performance. As will be discussed later, the "clock" at the center of the formulations includes temperature and complex history dependence making the numerical integration of such a model even more challenging. Thus, in the current work an initial effort towards characterizing the numerical integration of the constitutive model through simplified problems is performed. To that end, in Section 2 the theory of the model is briefly presented while the numerical integration is discussed in Section 3. Results of various studies characterizing the numerical behavior and performance are then given in Section 4. Finally, some concluding remarks and thoughts for follow on works are provided in Section 5.

36 MATERIALS SCIENCE↗

Bilevel parameter optimization for learning nonlocal image denoising models

We propose a bilevel optimization approach for the estimation of parameters in nonlocal image denoising models. The parameters we consider are both the space-dependent fidelity weight and weights within the kernel of the nonlocal operator. In both cases we investigate the differentiability of the solution operator in function spaces and derive a first order optimality system that characterizes local minima. For the numerical solution of the problems, we propose a second-order trust-region algorithm in combination with a finite element discretization of the nonlocal denoising models and we introduce a computational strategy for the solution of the resulting dense linear systems. Several experiments illustrate the applicability and effectiveness of our approach.

97 MATHEMATICS AND COMPUTING↗

An finite element analysis surrogate model with boundary oriented graph embedding approach for rapid design

Abstract In this work, we present a boundary oriented graph embedding (BOGE) approach for the graph neural network to assist in rapid design and digital prototyping. The cantilever beam problem has been solved as an example to validate its potential of providing physical field results and optimized designs using only 10 ms. Providing shortcuts for both boundary elements and local neighbor elements, the BOGE approach can embed unstructured mesh elements into the graph and performs an efficient regression on large-scale triangular-mesh-based finite element analysis (FEA) results, which cannot be realized by other machine-learning-based surrogate methods. It has the potential to serve as a surrogate model for other boundary value problems. Focusing on the cantilever beam problem, the BOGE approach with 3-layer DeepGCN model achieves the regression with mean square error (MSE) of 0.011 706 (2.41% mean absolute percentage error) for stress field prediction and 0.002 735 MSE (with 1.58% elements having error larger than 0.01) for topological optimization. The overall concept of the BOGE approach paves the way for a general and efficient deep-learning-based FEA simulator that will benefit both industry and Computer Aided Design (CAD) design-related areas.

42 ENGINEERING↗

A point-centered arbitrary Lagrangian Eulerian hydrodynamic approach for tetrahedral meshes

We present a three dimensional (3D) arbitrary Lagrangian Eulerian (ALE) hydrodynamic scheme suitable for modeling complex compressible flows on tetrahedral meshes. The new approach stores the conserved variables (mass, momentum, and total energy) at the nodes of the mesh and solves the conservation equations on a control volume surrounding the point. This type of an approach is termed a point-centered hydrodynamic (PCH) method. The conservation equations are discretized using an edge-based finite element (FE) approach with linear basis functions. All fluxes in the new approach are calculated at the center of each tetrahedron. A multidirectional Riemann-like problem is solved at the center of the tetrahedron. The advective fluxes are calculated by solving a 1D Riemann problem on each face of the nodal control volume. A 2-stage Runge–Kutta method is used to evolve the solution forward in time, where the advective fluxes are part of the temporal integration. The mesh velocity is smoothed by solving a Laplacian equation. The details of the new ALE hydrodynamic scheme are discussed. Results from a range of numerical test problems are presented.

97 MATHEMATICS AND COMPUTING↗