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At least 91 records · Page 5

Highly compressible 3D periodic graphene aerogel microlattices

Graphene is a two-dimensional material that offers a unique combination of low density, exceptional mechanical properties, large surface area and excellent electrical conductivity. Recent progress has produced bulk 3D assemblies of graphene, such as graphene aerogels, but they possess purely stochastic porous networks, which limit their performance compared with the potential of an engineered architecture. Here we report the fabrication of periodic graphene aerogel microlattices, possessing an engineered architecture via a 3D printing technique known as direct ink writing. The 3D printed graphene aerogels are lightweight, highly conductive and exhibit supercompressibility (up to 90% compressive strain). Moreover, the Young’s moduli of the 3D printed graphene aerogels show an order of magnitude improvement over bulk graphene materials with comparable geometric density and possess large surface areas. Ultimately, adapting the 3D printing technique to graphene aerogels realizes the possibility of fabricating a myriad of complex aerogel architectures for a broad range of applications.

36 MATERIALS SCIENCE↗

AIR Algebraic Multigrid for a Space-Time Hybridizable Discontinuous Galerkin Discretization of Advection(-Diffusion)

This article investigates the efficiency, robustness, and scalability of approximate ideal restriction (AIR) algebraic multigrid as a preconditioner in the all-at-once solution of a space-time hybridizable discontinuous Galerkin discretization of advection-dominated flows. The motivation for this study is that the time-dependent advection-diffusion equation can be seen as a “steady” advection-diffusion problem in $(d+1)$-dimensions and AIR has been shown to be a robust solver for steady advection-dominated problems. Numerical examples demonstrate the effectiveness of AIR as a preconditioner for advection-diffusion problems on fixed and time-dependent domains, using both slab-by-slab and all-at-once space-time discretizations, and in the context of uniform and space-time adaptive mesh refinement. A closer look at the geometric coarsening structure that arises in AIR also explains why AIR can provide robust, scalable, space-time convergence on advective and hyperbolic problems, while most multilevel parallel-in-time schemes struggle with such problems.

97 MATHEMATICS AND COMPUTING↗

Target Formulation and Construction in Mesh Quality Improvement

In the Target-matrix Optimization Paradigm (TMOP), it’s long been understood that one must create a set of target matrices before the mesh can be optimized. But there is still no general method to create correct, effective targets in response to a specific mesh quality improvement goal. The TMOP literature describes how certain sets of target matrices can be used to control the shape or size of mesh elements, but those examples address only a fraction of the problems that can occur in mesh quality improvement and were not derived from a general framework for target matrix construction. In this work, a general method of target construction is introduced based on an independent set of geometric parameters which are intrinsic to the Jacobian matrices upon which TMOP is based. The parameters enable a systematic approach to target definition and construction. The approach entails two parts. The first part defines correspondences between available raw data (stuff about the mesh and/or the physical solution) and intermediate data (e.g., a field of error estimates). Once the correspondences are established, the raw data is processed into intermediate field data existing on mesh sample points. The second part is to create a model that represents the values of the geometric target parameters as functions of the intermediate data. The model is then tested numerically to establish model constants and effectiveness. This systematic approach to target construction is illustrated in a set of examples to show how it can be applied to common problems in mesh optimization such as equidistribution of geometric properties, preservation of existing good quality, and adaptation of the mesh to the solution. The result is a systematic method of target construction for TMOP which can be applied to a wide variety of planar and volume mesh quality improvement tasks.

97 MATHEMATICS AND COMPUTING↗

A Novel Deployable Telescope Baffle Using the Kresling Origami Fold

This report introduces a novel deployable origami baffle designed for telescopes and optical systems, which reduces stray light while maintaining high compactness ratios and low weight. This design leverages the planar nature of the end caps on a cylindrical Kresling origami fold to incorporate mounting points, deployable options, and baffle vanes. The adaptable nature of origami (number of faces, origami geometrical ratios, scaling, etc.) allows the design to easily conform to system requirements, including field of view, deployed length, stowed/deployed stability points, and available volume. Geometric ratios that exhibit bistability in both the stowed and deployed states are discussed in detail, as this results in a rigid structure that maintains its desired configuration. Several designs were conceptualized, and multiple small-scale prototypes were constructed. Potential applications include camera lens hoods, lightweight astronomy telescopes, and deployable baffles for space telescopes and optical systems.

42 ENGINEERING↗

The design and development of a two-dimensional adaptive truss structure

The functional model of a two dimensional adaptive truss structure which can purposefully change its geometrical configuration is introduced. The details of design and fabrication such as kinematic analysis, dynamic characteristics analysis and some test results are presented for the demonstration of this two dimensional truss concept.

Kuwao, Fumihiro↗

Intelligent adaptive structures

'Intelligent Adaptive Structures' (IAS) refers to structural systems whose geometric and intrinsic structural characteristics can be automatically changed to meet mission requirements with changing operational scenarios. An IAS is composed of actuators, sensors, and a control logic; these are integrated in a distributed fashion within the elements of the structure. The IAS concepts thus far developed for space antennas and other precision structures should be applicable to civil, marine, automotive, and aeronautical structural systems.

Wada, Ben K.↗

An Interpreted Language and System for the Visualization of Unstructured Meshes

We present an interpreted language and system supporting the visualization of unstructured meshes and the manipulation of shapes defined in terms of mesh subsets. The language features primitives inspired by geometric modeling, mathematical morphology and algebraic topology. The adaptation of the topology ideas to an interpreted environment, along with support for programming constructs such, as user function definition, provide a flexible system for analyzing a mesh and for calculating with shapes defined in terms of the mesh. We present results demonstrating some of the capabilities of the language, based on an implementation called the Shape Calculator, for tetrahedral meshes in R^3.

Moran, Patrick J.↗

Algebraic, geometric, and stochastic aspects of genetic operators

Genetic algorithms for function optimization employ genetic operators patterned after those observed in search strategies employed in natural adaptation. Two of these operators, crossover and inversion, are interpreted in terms of their algebraic and geometric properties. Stochastic models of the operators are developed which are employed in Monte Carlo simulations of their behavior.

Foo, N. Y.↗

Composite matrix construction for structured grid adaptive mesh refinement

Structured-grid adaptive mesh refinement (SAMR) is an approach to mesh generation that supports structured access to data and adaptive mesh refinement for discretized partial differential equations (PDEs). Solution algorithms often require that an inverse of an operator be applied, a system of algebraic equations must be solved, and this process is often the primary computational cost in an application. SAMR is well suited to geometric multigrid solvers, which can be effective, but often do not adapt well to complex geometry including material coefficients. Algebraic multigrid (AMG) is more robust in the face of complex geometry, in both boundary conditions and internal material interfaces. AMG requires a stored matrix linearization of the operator. We discuss an approach, and an implementation in the Chombo block-structured AMR framework, for constructing composite grid matrices from a SAMR hierarchy of grids for use in linear solvers in the PETSc numerical library. We consider a case study with the Chombo-based BISICLES ice sheet modeling application.

97 MATHEMATICS AND COMPUTING↗

Binding complexity and multiparty entanglement

We introduce “binding complexity”, a new notion of circuit complexity which quantifies the difficulty of distributing entanglement among multiple parties, each consisting of many local degrees of freedom. We define binding complexity of a given state as the minimal number of quantum gates that must act between parties to prepare it. To illustrate the new notion we compute it in a toy model for a scalar field theory, using certain multiparty entangled states which are analogous to configurations that are known in AdS/CFT to correspond to multiboundary wormholes. Pursuing this analogy, we show that our states can be prepared by the Euclidean path integral in (0 + 1)-dimensional quantum mechanics on graphs with wormhole-like structure. We compute the binding complexity of our states by adapting the Euler-Arnold approach to Nielsen’s geometrization of gate counting, and find a scaling with entropy that resembles a result for the interior volume of holographic multiboundary wormholes. We also compute the binding complexity of general coherent states in perturbation theory, and show that for “double-trace deformations” of the Hamiltonian the effects resemble expansion of a wormhole interior in holographic theories.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

Center for Tokamak Transient Simulations (RPI Unstructured Mesh Developments for FES SciDAC4 Partnerships) (Final Report)

The goal of this project was the development of unstructured mesh technologies for fusion simulation codes” for FES SciDAC partnerships and to integrate those technologies into the simulation workflows of those partnerships. Specific developments were executed in support of the following FES SciDAC4 partnerships: Partnership Center for High‐fidelity Boundary Plasma Simulation (HBPS), Center for Integrated Simulation of Fusion Relevant RF (RF‐SciDAC), Center for Plasma Surface Interactions: Predicting the Performance and Impact of Dynamic PFC Surfaces (PSI2), and Center for Tokamak Transient Simulations (CTTS). The key unstructured mesh development areas addressed in this project include (i) methods to most effectively perform PIC calculations on unstructured meshes; (ii) creating meshes for fusion systems accounting for any desired level of geometric complexity and providing physics aware mesh configurations, (iii) adapting unstructured meshes to control the discretization errors, (iv) executing unstructured mesh calculations on GPU accelerated systems, (v) supporting physics/application‐specific PIC operations including surface/wall interactions of particles, (vi) providing infrastructure tools to support the interactions of solvers with unstructured meshes, and (vii) providing advanced methods for coupling plasma physics codes.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

Investigation of finite element: ABC methods for electromagnetic field simulation

The mechanics of wave propagation in the presence of obstacles is of great interest in many branches of engineering and applied mathematics like electromagnetics, fluid dynamics, geophysics, seismology, etc. Such problems can be broadly classified into two categories: the bounded domain or the closed problem and the unbounded domain or the open problem. Analytical techniques have been derived for the simpler problems; however, the need to model complicated geometrical features, complex material coatings and fillings, and to adapt the model to changing design parameters have inevitably tilted the balance in favor of numerical techniques. The modeling of closed problems presents difficulties primarily in proper meshing of the interior region. However, problems in unbounded domains pose a unique challenge to computation, since the exterior region is inappropriate for direct implementation of numerical techniques. A large number of solutions have been proposed but only a few have stood the test of time and experiment. The goal of this thesis is to develop an efficient and reliable partial differential equation technique to model large three dimensional scattering problems in electromagnetics.

Chatterjee, A.↗

Simulated annealing reconstruction and characterization of the three-dimensional microstructure of a LiCoO{sub 2} Lithium-ion battery cathode

We adapt the simulated annealing approach for reconstruction of the 3D microstructure of a LiCoO{sub 2} cathode from a commercial Li-ion battery. The real size distribution curve of LiCoO{sub 2} particles is applied to regulate the reconstruction process. By discretizing a 40 × 40 × 40 μm cathode volume with 8,000,000 numerical cubes, the cathode involving three individual phases: 1) LiCoO{sub 2} as active material, 2) pores or electrolyte, and 3) additives (polyvinylidene fluoride + carbon black) is reconstructed. The microstructural statistical properties required in the reconstruction process are extracted from 2D focused ion beam/scanning electron microscopy images or obtained by analyzing the powder mixture used to make the cathode. Characterization of the reconstructed cathode gives important structural and transport properties including the two-point correlation functions, volume-specific surface area between phases, tortuosity and geometrical connectivity of individual phase. - Highlights: • Simulated annealing approach is adapted for 3D reconstruction of LiCoO{sub 2} cathode. • Real size distribution of LiCoO{sub 2} particles is applied in reconstruction process. • Reconstructed cathode accords with real one at important statistical properties. • Effective electrode-characterization approaches have been established. • Extensive characterization gives important structural properties, say, tortuosity.

36 MATERIALS SCIENCE↗

Generation and adaptation of 3-D unstructured grids for transient problems

Grid generation and adaptive refinement techniques suitable for the simulation of strongly unsteady flows past geometrically complex bodies in 3-D are described. The grids are generated using the advancing front technique. Emphasis is placed not to generate elements that are too small, as this would severely increase the cost of simulations with explicit flow solvers. The grids are adapted to an evolving flowfield using simple h-refinement. A grid change is performed every 5 to 10 timesteps, and only one level of refinement/coarsening is allowed per mesh change.

Loehner, Rainald↗

Real time computer controlled weld skate

A real time, adaptive control, automatic welding system was developed. This system utilizes the general case geometrical relationships between a weldment and a weld skate to precisely maintain constant weld speed and torch angle along a contoured workplace. The system is compatible with the gas tungsten arc weld process or can be adapted to other weld processes. Heli-arc cutting and machine tool routing operations are possible applications.

Wall, W. A., Jr.↗

Using an external surrogate for predictor model training in real-time motion management of lung tumors

Purpose: Precise prediction of respiratory motion is a prerequisite for real-time motion compensation techniques such as beam, dynamic couch, or dynamic multileaf collimator tracking. Collection of tumor motion data to train the prediction model is required for most algorithms. To avoid exposure of patients to additional dose from imaging during this procedure, the feasibility of training a linear respiratory motion prediction model with an external surrogate signal is investigated and its performance benchmarked against training the model with tumor positions directly. Methods: The authors implement a lung tumor motion prediction algorithm based on linear ridge regression that is suitable to overcome system latencies up to about 300 ms. Its performance is investigated on a data set of 91 patient breathing trajectories recorded from fiducial marker tracking during radiotherapy delivery to the lung of ten patients. The expected 3D geometric error is quantified as a function of predictor lookahead time, signal sampling frequency and history vector length. Additionally, adaptive model retraining is evaluated, i.e., repeatedly updating the prediction model after initial training. Training length for this is gradually increased with incoming (internal) data availability. To assess practical feasibility model calculation times as well as various minimum data lengths for retraining are evaluated. Relative performance of model training with external surrogate motion data versus tumor motion data is evaluated. However, an internal–external motion correlation model is not utilized, i.e., prediction is solely driven by internal motion in both cases. Results: Similar prediction performance was achieved for training the model with external surrogate data versus internal (tumor motion) data. Adaptive model retraining can substantially boost performance in the case of external surrogate training while it has little impact for training with internal motion data. A minimum adaptive retraining data length of 8 s and history vector length of 3 s achieve maximal performance. Sampling frequency appears to have little impact on performance confirming previously published work. By using the linear predictor, a relative geometric 3D error reduction of about 50% was achieved (using adaptive retraining, a history vector length of 3 s and with results averaged over all investigated lookahead times and signal sampling frequencies). The absolute mean error could be reduced from (2.0 ± 1.6) mm when using no prediction at all to (0.9 ± 0.8) mm and (1.0 ± 0.9) mm when using the predictor trained with internal tumor motion training data and external surrogate motion training data, respectively (for a typical lookahead time of 250 ms and sampling frequency of 15 Hz). Conclusions: A linear prediction model can reduce latency induced tracking errors by an average of about 50% in real-time image guided radiotherapy systems with system latencies of up to 300 ms. Training a linear model for lung tumor motion prediction with an external surrogate signal alone is feasible and results in similar performance as training with (internal) tumor motion. Particularly for scenarios where motion data are extracted from fluoroscopic imaging with ionizing radiation, this may alleviate the need for additional imaging dose during the collection of model training data.

60 APPLIED LIFE SCIENCES↗

An adaptive Hessian approximated stochastic gradient MCMC method

Bayesian approaches have been successfully integrated into training deep neural networks. One popular family is stochastic gradient Markov chain Monte Carlo methods (SG-MCMC), which have gained increasing interest due to their ability to handle large datasets and the potential to avoid overfitting. Although standard SG-MCMC methods have shown great performance in a variety of problems, they may be inefficient when the random variables in the target posterior densities have scale differences or are highly correlated. Here, we present an adaptive Hessian approximated stochastic gradient MCMC method to incorporate local geometric information while sampling from the posterior. The idea is to apply stochastic approximation (SA) to sequentially update a preconditioning matrix at each iteration. The preconditioner possesses second-order information and can guide the random walk of a sampler efficiently. Instead of computing and saving the full Hessian of the log posterior, we use limited memory of the samples and their stochastic gradients to approximate the inverse Hessian-vector multiplication in the updating formula. Moreover, by smoothly optimizing the preconditioning matrix via SA, our proposed algorithm can asymptotically converge to the target distribution with a controllable bias under mild conditions. To reduce the training and testing computational burden, we adopt a magnitude-based weight pruning method to enforce the sparsity of the network. Our method is user-friendly and demonstrates better learning results compared to standard SG-MCMC updating rules. The approximation of inverse Hessian alleviates storage and computational complexities for large dimensional models. Numerical experiments are performed on several problems, including sampling from 2D correlated distribution, synthetic regression problems, and learning the numerical solutions of heterogeneous elliptic PDE. The numerical results demonstrate great improvement in both the convergence rate and accuracy.

97 MATHEMATICS AND COMPUTING↗

The application of model-referenced adaptive control to robotic manipulators

The achievement of quality dynamic performance in manipulator systems is difficult using conventional control methods because of both the inherent geometric nonlinearities of these systems and the dependence of the system dynamics on the characteristics of manipulated objects. A model-referenced adaptive control law is developed for maintaining uniformly good performance over a wide range of motions and payloads. The effectiveness of the approach is demonstrated in several simulations and the system stability as a function of input is investigated. Also developed is a 'learning signal' approach designed to minimize initial transients arising from abrupt changes in the inertial payload.

Dubowsky, S.↗