Engineering Papers⌕ Search

SEARCH · Engineering Papers

Results for “linear systems”

Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.

At least 829 records · Page 46

Fast Solution of Fully Implicit Runge--Kutta and Discontinuous Galerkin in Time for Numerical PDEs, Part I: the Linear Setting

Fully implicit Runge--Kutta (IRK) methods have many desirable properties as time integration schemes in terms of accuracy and stability, but high-order IRK methods are not commonly used in practice with numerical PDEs due to the difficulty of solving the stage equations. This paper introduces a theoretical and algorithmic preconditioning framework for solving the systems of equations that arise from IRK methods applied to linear numerical PDEs (without algebraic constraints). Additionally, this framework also naturally applies to discontinuous Galerkin discretizations in time. Under quite general assumptions on the spatial discretization that yield stable time integration, the preconditioned operator is proven to have condition number bounded by a small, order-one constant, independent of the spatial mesh and time-step size, and with only weak dependence on number of stages/polynomial order; for example, the preconditioned operator for 10th-order Gauss IRK has condition number less than two, independent of the spatial discretization and time step. The new method can be used with arbitrary existing preconditioners for backward Euler-type time-stepping schemes and is amenable to the use of three-term recursion Krylov methods when the underlying spatial discretization is symmetric. The new method is demonstrated to be effective on various high-order finite-difference and finite element discretizations of linear parabolic and hyperbolic problems, demonstrating fast, scalable solution of up to 10th-order accuracy. The new method consistently outperforms existing block preconditioning approaches, and in several cases, the new method can achieve 4th-order accuracy using Gauss integration with roughly half the number of preconditioner applications and wallclock time as required using standard diagonally IRK methods.

97 MATHEMATICS AND COMPUTING↗

The MBARI-WEC: a power source for ocean sensing

Abstract Interest in wave energy converters to provide autonomous power to various ocean-bound systems, such as autonomous underwater vehicles, sensor systems, and even aquaculture farms, has grown in recent years. The Monterey Bay Aquarium Research Institute has developed and deployed a small two-body point absorber wave energy device suitable to such needs. This paper provides a description of the system to support future open-source access to the device and further the general development of similar wave energy systems. Additionally, to support future control design and system modification efforts, a set of hydrodynamic models are presented and cross-compared. To test the viability of using a linear frequency-domain admittance model for controller tuning, the linear model is compared against four WEC-Sim models of increasing complexity. The linear frequency-domain model is found to be generally adequate for capturing system dynamics, as the model agreement is good and the degree of nonlinearity introduced in the WEC-Sim models is generally less than 2.5%.

16 TIDAL AND WAVE POWER↗

Design Study of a Superconducting Quadrupole Magnet System Sustainable Under Dark Current Heating in ILC Main Linac

The International Linear Collider (ILC) main linac comprises a series of 12 m-long cryomodules. The cryomodule contains eight 9-cell superconducting (SC) RF (SRF) cavities and an SC quadrupole magnet combined with dipole correctors to focus and steer electron and positron beams. The magnets are installed between the SRF cavity string and at the longitudinal center of a common cryomodule/cryostat. These magnets are conductively cooled by pure aluminum channels thermally connected to a 2 K two-phase helium pipe for cooling the SRF cavities. A recent study shows that field-emitted electrons, so-called “dark current” initiated in the SRF cavities, are transmitted through the SRF cavity string and reach the SC magnet. The energy is inevitably absorbed in the SC coil due to the magnetic field, resulting in risks of a quench caused by the coil heating. We are investigating alternate magnet designs by using Nb $_{3}$ Sn or $\text{MgB}_{2}$ SC and by adding the dark current absorber surrounding the beam-pipe to realize sustainable magnet operation under the dark current heating. We report the design study of the magnet system and interfaces to the cryomodule accommodating it with the SRF cavities.

43 PARTICLE ACCELERATORS↗

COMSOL Models and Simulation Results for Closed-Loop Geothermal Systems with Thermal Enhancements

The Closed-Loop Geothermal Working Group and the National Renewable Energy Laboratory (NREL) have studied the performance of disc-shaped and linear thermal enhancements (conductive material introduced around a wellbore) in closed-loop geothermal systems. COMSOL models were developed to investigate the increase in heat production in systems with thermal enhancements compared to those without, across a range of scenarios. This dataset includes two example COMSOL models, a summary of the simulation results, and a link to an accompanying paper. Studied are idealized versions of two thermal enhancement designs: (1) existing or newly created fractures surrounding the wellbore, filled with highly conductive material, and (2) a 'fishbone structure,' where short wellbores are drilled radially outward from the main wellbore and filled with highly conductive material.

15 GEOTHERMAL ENERGY↗

An operator-based approach to topological photonics

Abstract Recently, the study of topological structures in photonics has garnered significant interest, as these systems can realize robust, nonreciprocal chiral edge states and cavity-like confined states that have applications in both linear and nonlinear devices. However, current band theoretic approaches to understanding topology in photonic systems yield fundamental limitations on the classes of structures that can be studied. Here, we develop a theoretical framework for assessing a photonic structure’s topology directly from its effective Hamiltonian and position operators, as expressed in real space, and without the need to calculate the system’s Bloch eigenstates or band structure. Using this framework, we show that nontrivial topology, and associated boundary-localized chiral resonances, can manifest in photonic crystals with broken time-reversal symmetry that lack a complete band gap, a result that may have implications for new topological laser designs. Finally, we use our operator-based framework to develop a novel class of invariants for topology stemming from a system’s crystalline symmetries, which allows for the prediction of robust localized states for creating waveguides and cavities.

97 MATHEMATICS AND COMPUTING↗

Losing Control of Your Linear Network? Try Resilience Theory

Resilience of cyber-physical networks to unexpected failures is a critical need widely recognized across domains. For instance, power grids, telecommunication networks, transportation infrastructures, and water treatment systems have all been subject to disruptive malfunctions and catastrophic cyberattacks. Following such adverse events, we investigate scenarios where a node of a linear network suffers a loss of control authority over some of its actuators. These actuators are not following the controller's commands and are instead producing undesirable outputs. The repercussions of such a loss of control can propagate and destabilize the whole network despite the malfunction occurring at a single node. To assess system vulnerability, we establish resilience conditions for networks with a subsystem enduring a loss of control authority over some of its actuators. Furthermore, we quantify the destabilizing impact on the overall network when such a malfunction perturbs a nonresilient subsystem. We illustrate our resilience conditions on two academic examples, on an islanded microgrid and on the linearized IEEE 39-bus system.

97 MATHEMATICS AND COMPUTING↗

A neural-network-enhanced parameter-varying framework for multi-objective model predictive control applied to buildings

Management of the electrical grid is becoming more complex due to the increased penetration of alternative energy generation technologies and a broadening diversity of electric loads. This complexity creates challenges in balancing demand and generation that can increase the potential for grid instabilities. One effective way to address this issue is to leverage previously unexploited demand flexibility through advanced control strategies. In this work, we propose an advanced control method, called adaptive neural parameter-varying model predictive control (ANPV-MPC), to control the temperature and energy consumption of a building via its Heating, Ventilation, and Air Conditioning system. ANPV-MPC combines key ideas in parameter-varying control, adaptive control, and online learning strategies to bridge the gap between computationally efficient linear model predictive control and more accurate nonlinear model predictive control. The novelty in ANPV-MPC is the use of a physics-inspired Bayesian neural network to estimate the coefficients of the parameter-varying linear control model. The Bayesian neural network additionally provides uncertainty estimates, triggering online training to capture evolving building system conditions. We show that ANPV-MPC can approximate the building system dynamics with a 28.39% higher accuracy than traditional linear model predictive control, resulting in 36.23% better control performance without increasing complexity of the optimal control problem. ANPV-MPC also adapts in real time to previously unseen conditions using online learning, further improving its performance.

24 POWER TRANSMISSION AND DISTRIBUTION↗

Proton Improvement Plan II Cryogenic Distribution System thermodynamic design

The Proton Improvement Plan – II (PIP-II) is a superconducting linear accelerator being built at Fermilab that will provide 800 MeV proton beams for neutrino production. The Linac requires cooling at 40 K, 5 K, and 2 K temperatures, which will be provided by cryogenic helium produced by a Helium Cryoplant and distributed by a Cryogenic Distribution System (CDS). Based primarily on the Linac heat load requirements at each temperature and the allowable pressure drop, we have made a preliminary thermodynamic design of the CDS. The design also incorporates special requirements such as controlled and/or fast cooldown of the superconducting RF cavities and their dual maximum allowable working pressures. This paper presents the overall features of the PIP-II CDS, sizing of helium process circuits, different operating modes, and calculated mass flow capacities that cater to these operating modes.

43 PARTICLE ACCELERATORS↗

Dynamically reconfigurable topological routing in nonlinear photonic systems

The propagation path of topologically protected states is bound to the interface between regions with different topology, and as such, the functionality of linear photonic devices leveraging these states is fixed during fabrication. Here, we propose a mechanism for dynamic control over a driven dissipative system’s local topology, yielding reconfigurable topological interfaces and thus tunable paths for protected routing. We illustrate our approach in non-resonantly pumped polariton lattices, where the nonlinear interaction between the polaritons and the exciton reservoir due to non-resonant pumping can yield picosecond-scale changes in the propagation paths of the chiral edge states. To analytically confirm the numerically observed topological dynamics, we generalize the spectral localizer framework to non-linear non-Hermitian Chern materials and apply this framework to a continuous model of the polariton system based on a driven-dissipative Gross-Pitaevskii equation. In doing so, we show that the local changes in the polariton lattice’s topology are captured by a local Chern marker. Looking forward, we anticipate such reconfigurable topological routing will enable the realization of novel classes of topological photonic devices.

Wong, Stephan [Sandia National Laboratories (SNL-N↗

Energy storage systems for electrical microgrids with pulsed power loads

Pulsed power loads (PPLs) are highly non-linear and can cause significant stability and power quality issues in an electrical microgrid. According to the present invention, many of these issues can be mitigated by an Energy Storage System (ESS) that offsets the PPL. The ESS can maintain a constant bus voltage and decouple the generation sources from the PPL. For example, the ESS specifications can be obtained with an ideal, band-limited hybrid battery and flywheel system.

Weaver, Wayne W.↗

Low-Cost X-Ray CT System for Imaging of Roots

The goal of this project was to develop and demonstrate an innovative, low cost, field deployable, stationary 3D x-ray computed tomography (CT) system that will image total root phenotypes with a micron size resolution at a throughput of hundreds of plants per cycle. This system is based on UHV’s unique low cost linear x-ray tube technology and sophisticated reconstruction & image segmentation algorithms developed at University of Massachusetts, Lowel and University of Nottingham; and was tested for several types of soils at University of Wisconsin and Texas A&M University. Currently, no technologies exist that have been designed to image roots in complex media such as agricultural field conditions. Due to its small size, high resolution & fast imaging of fine roots, low power consumption, large penetration depth (i.e. ability to see through several feet of soil) and ease of field deployability, this CT system will increase the speed and efficacy of discovery, field translation, and deployment of improved crops and systems that improve soil carbon accumulation and storage, decrease N2O emissions, and improve water efficiency leading towards advancements that could mitigate 10% of the total US Greenhouse gases. This degree of imaging in the field has never been available and would be invaluable to scientists in understanding how environmental conditions and phenotypic variations contribute to carbon deposition through root development.

54 ENVIRONMENTAL SCIENCES↗

Nonlinear Elimination Applied to Radiation Diffusion

We apply a nonlinearly preconditioned, quasi-Newton framework to accelerate the numerical solution of the thermal radiative transfer (TRT) equations. This framework was inspired by the unpublished method that has existed for years in Teton, Lawrence Livermore National Laboratory’s deterministic TRT code. In this paper, we cast this iteration scheme within a formal nonlinear preconditioning framework and compare its performance against other iteration schemes in the framework. With proper choices of iteration controls for the various levels of the solver, we can recover the standard linearized one-step method, a full nonlinear Newton scheme, as well as the method in Teton. In brief, the nonlinear preconditioning TRT scheme formally eliminates the material temperature equation from the nonlinear system in a nonlinear analog of a Schur complement. This nonlinear elimination step involves solving a decoupled nonlinear equation for each spatial degree of freedom and is therefore inexpensive. By applying a quasi-Newton iteration scheme on the new system, we obtain a three-level iteration scheme that is at least as efficient as commonly used TRT schemes. The new method allows full convergence to the nonlinear backward Euler time-discretized system, increasing accuracy and robustness, while using a similar number of linear iterations as the more common linearized one-step methods Eq. (4).

77 NANOSCIENCE AND NANOTECHNOLOGY↗

Computing partition functions in the one-clean-qubit model

We present a method to approximate partition functions of quantum systems using mixed-state quantum computation. For positive-semidefinite Hamiltonians, our method has an expected running-time that is almost linear in [M/( ε rel Z )] 2 , where M is the dimension of the quantum system, Z is the partition function, and ε rel is the relative precision. It is based on approximations of the exponential operator as linear combinations of certain operators related to block-encoding of Hamiltonians or Hamiltonian evolutions. The trace of each operator is estimated using a standard algorithm in the one-clean-qubit model. For large values of Z , our method may run faster than exact classical methods, whose complexities are polynomial in M . We also prove that a version of the partition function estimation problem within additive error is complete for the so-called DQC1 complexity class, suggesting that our method provides a superpolynomial speedup for certain parameter values. Overall, to attain a desired relative precision, we develop a classical procedure based on a sequence of approximations within predetermined additive errors that may be of independent interest.

97 MATHEMATICS AND COMPUTING↗

Linear Velocity Problems Part 2: Thermodynamic Considerations

A compressible polytropic gas, in one dimensional planar, cylindrical, or spherical coordinate systems, is examined through four thermodynamic properties: mass density, pressure, specific internal energy (SIE), and entropy, under the assumptions that the fluid velocity is linearly proportional to the radial coordinate and that the Euler gas dynamics equations assert a self similar solution class. The behavior of the thermodynamics is almost entirely determined by an arbitrary function that results from the derivation of the density distribution. Through physical and other arguments, the arbitrary function can be plotted spatially with time profiles, providing a deeper understanding of the system and how the arbitrary function affects the behavior of the compressible gas.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

First results from a high-frame-rate, multi-GHz ionizing particle detection system geared toward accelerator diagnostic applications

An integrated detection system, consists of a thin diamond sensor incorporated into a compact signal loop, coupled in turn to an application-specific integrated circuit readout chip, has been tested for the first time, using ps-duration electron pulses from the Next Linear Collider Test Accelerator at the SLAC National Accelerator Laboratory. For readout frame rates as high as 120 kHz, the detection system is shown to achieve a linear dynamic range of 10 3 and a bandwidth of 4–5 GHz, with no ringing seen on the tail of the output pulse. These results represent the best-performing multi-GHz ionizing particle detection system achieved to date.

Ferezghi, Mohammadreza Mohseni [University of Cali↗

Synergistic data analytics for electromechanical oscillation in electric power systems

Accurate real-time estimation of the four electromechanical oscillation properties, i.e., dominant oscillation modes, mode shapes, participation factors, and coherent groups, is of great importance to assess and mitigate potential electromechanical oscillations in interconnected power systems. While eigenvalue analysis can realize such estimation, it requires precise linearized dynamic models and accurate parameters, which are highly difficult to obtain in practice. Data fusion-based modal estimation methods can extract the properties of electromechanical oscillations from measurement data without the power system model and parameters, but most of the time only one or two property assessments can be accomplished each time. To overcome this challenge, this paper presents a synergistic data analytics solution to characterize the dynamic behaviors of electromechanical oscillations from real-time measurement data. Here, the proposed method uses optimized variable projection, and it is capable of estimating all four electromechanical oscillation behavior properties from measured responses. Case studies are performed using the simulated measurement data of a 16-generator 68-bus test system and the field measurements collected by the PMUs deployed in the Yunnan Power Grid. The results demonstrate that the proposed synergistic data analytics solution can achieve satisfactory performance in capturing the properties of electromechanical oscillations from measurement data and exhibit strong robustness against measurement noise when compared with existing measurement-based methods.

42 ENGINEERING↗

Microscopic dynamics underlying the stress relaxation of arrested soft materials

Arrested soft materials such as gels and glasses exhibit a slow stress relaxation with a broad distribution of relaxation times in response to linear mechanical perturbations. Although this macroscopic stress relaxation is an essential feature in the application of arrested systems as structural materials, consumer products, foods, and biological materials, the microscopic origins of this relaxation remain poorly understood. Here, we elucidate the microscopic dynamics underlying the stress relaxation of such arrested soft materials under both quiescent and mechanically perturbed conditions through X-ray photon correlation spectroscopy. By studying the dynamics of a model associative gel system that undergoes dynamical arrest in the absence of aging effects, we show that the mean stress relaxation time measured from linear rheometry is directly correlated to the quiescent superdiffusive dynamics of the microscopic clusters, which are governed by a buildup of internal stresses during arrest. We also show that perturbing the system via small mechanical deformations can result in large intermittent fluctuations in the form of avalanches, which give rise to a broad non-Gaussian spectrum of relaxation modes at short times that is observed in stress relaxation measurements. These findings suggest that the linear viscoelastic stress relaxation in arrested soft materials may be governed by nonlinear phenomena involving an interplay of internal stress relaxations and perturbation-induced intermittent avalanches.

36 MATERIALS SCIENCE↗

Assessment of operational availability for the PIP-II Superconducting Radio Frequency linear accelerator facility

Operational availability is a critical performance measure for an accelerator facility in modern time. A high availability enables the facility to serve a wide range of users simultaneously. Consequently, besides pure accelerator physics considerations, newly proposed accelerator facilities account for the availability and reliability aspects in the design phases. It allows incorporation of appropriate mitigation strategies for the most vulnerable systems in the machine and therefore, minimizes unscheduled interruptions during the operation. This report lays out a methodology for the availability assessment of the complete particle accelerator facility and presents an initial assessment of the availability of the newly proposed Proton Improvement Plan-II (PIP-II) accelerator facility at Fermilab. The paper describes a comprehensive reliability model of the PIP-II facility that comprises not only 800 MeV linear accelerator (linac) system but also essential utility systems in the form of cryogenic, water, power and air systems. The paper details estimations of the availability of the PIP-II facility for two operational modes i.e. the nominal operational mode featuring 800 MeV beam and critical operational mode involving operation with the lowest objective beam energy of 600 MeV.

43 PARTICLE ACCELERATORS↗