Engineering Papers⌕ Search

SEARCH · Engineering Papers

Results for “nonlinear 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 1,063 records · Page 59

Nonlinear Optimal Control of Electron Dynamics Within Hartree-Fock Theory

Consider the problem of determining the optimal applied electric field to drive a molecule from an initial state to a desired target state. For even moderately sized molecules, solving this problem directly using the exact equations of motion—the time-dependent Schrödinger equation (TDSE)—is numerically intractable. Here, we present a solution of this problem within time-dependent Hartree-Fock (TDHF) theory, a mean field approximation of the TDSE. Optimality is defined in terms of minimizing the total control effort while maximizing the overlap between desired and achieved target states. We frame this problem as an optimization problem constrained by the nonlinear TDHF equations; we solve it using trust region optimization with gradients computed via a custom-built adjoint state method. For three molecular systems, we show that with very small neural network parametrizations of the control, our method yields solutions that achieve desired targets within acceptable constraints and tolerances.

97 MATHEMATICS AND COMPUTING↗

A Modeling Toolkit for Comparing AC and DC Electrical Distribution Efficiency in Buildings

Recently, there has been considerable research interest in the potential for DC distribution systems in buildings instead of the traditional AC distribution systems. Due to the need for performing power conversions between DC and AC electricity, DC distribution may provide electrical efficiency advantages in some systems. To support comparative evaluations of AC-only, DC-only, and hybrid AC/DC distribution systems in buildings, a new modeling toolkit called the Building Electrical Efficiency Analysis Model (BEEAM) was developed and is described in this paper. To account for harmonics in currents or voltages arising from nonlinear devices, the toolkit implements harmonic power flow, along with nonlinear device behavioral descriptions derived from empirical measurements. This paper describes the framework, network equations, device representations, and an implementation of the toolkit in an open source software package, including a component library and graphical interface for creating circuits. Simulations of electrical behavior and device and system efficiencies using the toolkit are compared with experimental measurements of a small office environment in a variety of operating and load configurations. A detailed analysis of uncertainty estimation is also provided. Key findings were that a comparison of predicted versus measured efficiencies and power losses in the validation testbed using the initial toolkit implementation predicted device- and system-level efficiencies with reasonably good accuracy under both balanced and unbalanced AC scenarios. An uncertainty analysis also revealed that the maximum estimated error for system efficiency across all scenarios was 3%, and measured and modeled system efficiency agreed within the experimental uncertainty in approximately half of the scenarios. Based on the correspondence between simulation and measurement, the toolkit is proposed by the authors as a potentially useful tool for comparing efficiency in AC, DC, and hybrid AC/DC distribution systems in buildings.

DC distribution↗

Local imaging of diamagnetism in proximity-coupled niobium nanoisland arrays on gold thin films.

In this work, we study the effect of engineered disorder on the local magnetic response of proximity-coupled superconducting island arrays by comparing scanning superconducting quantum interference device (SQUID) susceptibility measurements to a model in which we treat the system as a network of one-dimensional (1D) superconductor-normal-metal-superconductor Josephson junctions, each with a Josephson coupling energy E-J determined by the junction length or distance between islands. We find that the disordered arrays exhibit a spatially inhomogeneous diamagnetic response which, for low local applied magnetic fields, is well described by this junction network model, and we discuss these results as they relate to inhomogeneous 2D superconductors. Our model of the static magnetic response of the arrays does not fully capture the onset of nonlinearity and dissipation with increasing applied field, as these effects are associated with vortex motion due to the dynamic nature of the scanning SQUID susceptometry measurement. This work demonstrates a model 2D superconducting system with engineered disorder, and it highlights the impact of dissipation on the local magnetic properties of 2D superconductors and Josephson junction arrays.

Bishop-Van Horn, Logan↗

Anisotropic Characterizations of Electrospun PAN Nanofiber Mats Using Design of Experiments

This paper deals with the dielectric and mechanical characterizations of polyacrylonitrile (PAN)-aligned electrospun nanofiber mats. A two factor three level full factorial experiment is conducted to understand the effect of various parameters on dielectric and mechanical responses. These responses are recorded against randomly oriented and aligned nanofiber mats. Improved properties of electrospun mats have applications in the field of energy storage and nanocomposite reinforcement. Dielectric and mechanical characterizations of PAN mats are vital, as the aligned electrospun mats were found to be useful in advanced energy and mechanical reinforcement applications. Therefore, it is paramount to understand the effects of system parameters to these properties. The design of experiment (DoE) includes two factors and three level full factorial experiments with concentrations of PAN solutions at 8 wt.%, 9 wt.%, and 10 wt.%, and speed of the rotating mandrel (collector) at 3 volt (V), 4 V, and 5 V inputs. The electric field intensity used in the experiment is 1 kV/cm. DoE is conducted to understand the nonlinear interactions of parameters to these responses. The dielectric and mechanical characterizations of 8 wt.%, 9 wt.%, and 10 wt.% with different speeds for the original and improved systems are discussed. It was observed that at 9 wt.% and at all mandrel speeds, the dielectric and tensile properties are optimum.

42 ENGINEERING↗

Nematic Colloidal Micro‐Robots as Physically Intelligent Systems

Abstract Physically intelligent micro‐robotic systems exploit information embedded in micro‐robots, their colloidal cargo, and their milieu to interact, assemble, and form functional structures. Nonlinear anisotropic fluids such as nematic liquid crystals (NLCs) provide untapped opportunities to embed interactions via their topological defects, complex elastic responses, and ability to dramatically restructure in dynamic settings. Here a four‐armed ferromagnetic micro‐robot is designed and fabricated to embed and dynamically reconfigure information in the nematic director field, generating a suite of physical interactions for cargo manipulation. The micro‐robot shape and surface chemistry are designed to generate a nemato‐elastic energy landscape in the domain that defines multiple modes of emergent, bottom‐up interactions with passive colloids. Micro‐robot rotation expands the ability to sculpt interactions; the energy landscape around a rotating micro‐robot is dynamically reconfigured by complex far‐from‐equilibrium dynamics of the micro‐robot's companion topological defect. These defect dynamics allow transient information to be programmed into the domain and exploited. Robust micro‐robotic manipulation strategies are demonstrated that exploit these diverse modes of nemato‐elastic interaction to achieve cargo docking, transport, release, and assembly of complex reconfigurable structures at multi‐stable sites. Such structures are of great interest to future developments of LC‐based advanced optical device and micro‐manufacturing in anisotropic environments.

Yao, Tianyi↗

Optimal economic operation of liquid petroleum products pipeline systems

The majority of overland transport needs for crude petroleum and refined petroleum products are met using pipelines. Numerous studies have developed optimization methods for design of these systems in order to minimize construction costs while meeting capacity requirements. Here, we formulate problems to optimize the operations of existing single liquid commodity pipeline systems subject to physical flow and pump engineering constraints. The objectives are to maximize the economic value created for users of the system and to minimize operating costs. We present a general computational method for this class of continuous, non-convex nonlinear programs, and examine the use of pump operating settings and flow allocations as decision variables. Furthermore, the approach is applied to compute optimal operating regimes and perform engineering economic sensitivity analyses for a case study of a crude oil pipeline developed using publicly available data.

02 PETROLEUM↗

Real-time control of connected vehicles in signalized corridors using pseudospectral convex optimization

Recent advances in Connected and Automated Vehicle (CAV) technologies have opened up new opportunities to enable safe, efficient, and sustainable transportation systems. However, developing reliable and rapid speed control algorithms in highly dynamic environments with complex inter-vehicle interactions and nonlinear vehicle dynamics is still a daunting task. In this paper, we develop a novel speed control method for CAVs to produce optimal speed profiles that minimize the fuel consumption and avoid idling at signalized intersections. To this end, an optimal control problem is formulated using the information of the upcoming traffic signal to adapt vehicles' speeds to avoid frequent stop-and-go driving patterns. Here, by applying the pseudospectral discretization method and the sequential convex programming method, the computational efficiency is greatly improved, enabling potential real-time on-vehicle applications. In addition, the algorithm is implemented under a model predictive control framework to ensure online control with instant response for collision avoidance and robust vehicle coordination. The proposed algorithm is verified through numerical simulations of three different traffic scenarios. The convergence and accuracy of the proposed approach are demonstrated by comparing with a popular nonlinear solver. Furthermore, the benefit of the proposed method in both traffic mobility and fuel efficiency is validated using the speed profile determined from a traffic following model in a simulation software as the baseline.

42 ENGINEERING↗

Dynamics of coupled thermoacoustic modes: Noise and frequency spacing effects

Practical combustion systems consist of multiple thermoacoustic modes that are linearly stable or unstable at a wide range of frequencies. When coupled, the modal interactions are a strong function of the frequency spacing between them – having very significant implications on interpretation of linear stability or instability of modes from experimental data. Frequency spacing between the modes particularly influences the stability and existence of potential limit cycle solutions. In this paper, we extend earlier deterministic studies to include the effects of noise, studying how deterministic dynamics change with the addition of noise and the simultaneous impact of frequency spacing (i.e., closely, or widely spaced). Specifically, this paper characterizes three key effects of noise, which are (1) distribution of limit cycle amplitudes (“diffusion”), (2) shift in the average limit cycle amplitudes (“noise induced drift”), and (3) introduction of new bifurcations that are not present in the deterministic system. Key conclusions from this work are that in highly noisy practical environments, a deterministic/ low noise analysis will not be sufficient to explain even critical qualitative features of the system – such as existence of stable limit cycles or their amplitudes. Furthermore, the nature of noise-induced effects on nonlinear modal interactions can be fundamentally different for degenerate, closely spaced, and widely spaced modes.

42 ENGINEERING↗

The Role of Stratigraphy and Loading History in Generating Complex Compaction Bands in Idealized Field-Scale Settings

The Buckskin Gulch locality in Utah is a landmark example of compaction localization. The outcrop of this locality involves distinct stratigraphic heterogeneity and was exposed to complex loading history. It features multiple sets of deformation bands with different kinematics and orientation. Similar formations were seen in the Valley of Fire, Nevada, and the Orange quarry, France, among other localities. The formation of such complex structures, their propagation mechanisms, and frequency is affected by numerous local and ambient factors whose impacts are not yet fully understood. The simulation of the above-mentioned localities is not feasible because of the limited amount of available information. This work, instead, investigates from a geomechanics standpoint how the interplay among material nonlinearity, outcrop stratigraphy, and loading history interconnects with specific spatiotemporal patterns of compaction band propagation. Our study shows that the system stratigraphy can be responsible for the emergence of coexisting compaction bands with different inclination and kinematics. Specifically, we show that stiffness contrasts induce nonlocal stress changes which may favor the initiation of secondary structures with different compaction localization characteristics. Furthermore, systems of inclined compaction bands induced by burial increase display secondary, noncontemporaneous sets of vertical compaction bands under the effects of postburial shortening. Our results indicate that stages of intermediate burial decrease prior to tectonic shortening can promote the formation of such complex systems. Despite the simplifications involved in our analyses, these findings show how geomechanics computations complement field observations and could provide a mechanics-based validation of site-specific reconstruction hypothesis.

58 GEOSCIENCES↗

Accelerating kinetic plasma simulations with machine-learning-generated initial conditions

Computational models of plasma technologies often solve for the system operating conditions by time-stepping an initial value problem to a quasi-steady solution. However, the strongly nonlinear and multi-timescale nature of plasma dynamics often necessitate millions, or even hundreds of millions, of steps to reach convergence, reducing the effectiveness of these simulations for computer-aided engineering. We consider acceleration of kinetic plasma simulations via data-driven machine-learning-generated initial conditions, which initialize the simulations close to their final quasi-steady-state, thereby reducing the number of steps to reach convergence. Three machine-learning models are developed to predict the density and ion kinetic profiles of capacitively coupled plasma discharges relevant to the microelectronics industry. The models are trained on kinetic simulations over a range of device operating frequencies and pressures. Best performance was observed when simulations were initialized with ion kinetic profiles generated by a convolutional neural network, reducing the mean number of steps to reach convergence by 17.1× when compared to initialization with a zero-dimensional global model. We also outline a workflow for continuous data-driven model improvement and simulation speedup, with the aim of generating sufficient data for full device digital twins.

Artificial neural networks↗

Optimizing Vehicle Fleet and Assignment for Concentrating Solar Power Plant Heliostat Washing

Concentrating solar power central-receiver plants use thousands of sun-tracking mirrors, i.e., heliostats, to reflect sunlight to a central receiver, which collects and uses the heat to generate electricity. Over time, soiling reduces the reflectivity of the heliostats and, therefore, the efficiency of the system. Current industry practice sends vehicles to wash heliostats in an ad hoc fashion. We present a mixed-integer nonlinear program that determines wash vehicle fleet size, mix, and assignment of wash crews to heliostats to minimize the sum of (i) the revenues lost due to heliostat soiling, (ii) the costs of hiring wash crews and operating the vehicles, and (iii) the costs of purchasing wash vehicles. We establish conditions for convexity of the objective function, and then propose a decomposition method that enables near-optimal solutions to the wash vehicle fleet sizing and assignment problem on the order of a couple of minutes. Furthermore, these solutions yield hundreds of thousands of dollars in savings per year over current industry practices.

14 SOLAR ENERGY↗

Josephson dynamics in two-dimensional ring-shaped condensates

We investigate Josephson transport in a fully closed, two-dimensional superfluid circuit formed by a ring-shaped 87 Rb Bose-Einstein condensate that contains two optical barriers acting as movable weak links. Translating these barriers at controlled speeds imposes a steady bias current, enabling direct mapping of the current-chemical-potential (𝐼−Δ⁢𝜇) characteristics. For narrow junctions (𝑤 ≈ 1µ⁢m), the circuit exhibits a pronounced dc branch that terminates at a critical current 𝐼 𝑐 = 9⁢(1) × 10 3 s −1 ; above this threshold, the system switches to an ac, resistive regime. Classical-field simulations that include the moving barriers quantitatively reproduce both the nonlinear 𝐼−Δ⁢𝜇 curve and the measured 𝐼 𝑐 , validating the underlying microscopic picture. Analysis of the ensuing phase dynamics shows that dissipation is mediated by the nucleation and traversal of vortex-antivortex pairs through the junctions, while the bulk condensate remains globally phase locked—direct evidence of the ring's topological constraint enforcing quantized circulation. These results establish a cold-atom analog of a superconducting quantum interference device in which Josephson dynamics can be resolved at the single-vortex level, providing a versatile platform for atomtronic circuit elements, nonreciprocal Josephson devices, and on-chip Sagnac interferometers for multiaxis rotation sensing.

74 ATOMIC AND MOLECULAR PHYSICS↗

Theory of the charge density wave in A V 3 Sb 5 kagome metals

The family of metallic kagome compounds AV 3 Sb 5 (A = K, Rb, Cs) was recently discovered to exhibit both superconductivity and charge order. The nature of the charge density wave (CDW) phase is presently unsettled, which complicates the interpretation of the superconducting ground state. In this paper, we use group theory and density functional theory (DFT) to derive and solve a phenomenological Landau model for this CDW state. The DFT results reveal three unstable phonon modes with the same in-plane momentum but different out-of-plane momenta, whose frequencies depend strongly on the electronic temperature. This is indicative of an electronically driven CDW, stabilized by features of the in-plane electronic dispersion. Motivated by the DFT analysis, we construct a Landau free-energy expansion for coupled CDW order parameters with wave vectors at the M and L points of the hexagonal Brillouin zone. We find an unusual trilinear term coupling these different order parameters, which can promote the simultaneous condensation of both CDWs even if the two modes are not nearly degenerate. We classify the different types of coupled multi-Q CDW orders, focusing on those that break the sixfold rotational symmetry and lead to a unit-cell doubling along all three crystallographic directions, as suggested by experiments. Here, we determine a region in parameter space, characterized by large nonlinear Landau coefficients, where these phases—dubbed staggered trihexagonal and staggered Star of David—are the leading instabilities of the system. Finally, we discuss the implications of our results for the kagome metals.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

Third-order Hall effect in the surface states of a topological insulator

Time reversal and inversion symmetric materials fail to yield linear and nonlinear responses since they possess net zero Berry curvature. However, higher-order Hall response can be generated in these systems upon constraining the crystalline symmetries. Motivated by the recently discovered third-order Hall (TOH) response mediated by Berry connection polarizability, namely, the variation of the Berry connection with respect to an applied electric field, here, we investigate the existence of such a Hall effect in the surface states of hexagonal warped topological insulators (e.g., Bi 2 Te 3 ) under the application of only electric field. Using the semiclassical Boltzmann formalism, we investigate the effect of tilt and hexagonal warping on the Berry connection polarizability tensor and, consequently, the TOH effect, provided the Dirac cone remains gapless. We find that the magnitude of the response increases significantly with increasing tilt strength and warping, and therefore, they can provide the tunability of this effect. In addition, we also explore the effect of chemical doping on the TOH response in this system. Interestingly, we show, based on the symmetry analysis, that the TOH can be the leading-order response in this system, which can directly be verified in experiments.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

Toward fusion plasma scenario planning for NSTX-U using machine-learning-accelerated models

One of the most promising devices for realizing power production through nuclear fusion is the tokamak. To maximize performance, it is preferable that tokamak reactors achieve advanced operating scenarios characterized by good plasma confinement, improved magnetohydrodynamic (MHD) stability, and a largely non-inductively driven plasma current. Such scenarios could enable steady-state reactor operation with high \emph{fusion gain} --- the ratio of produced fusion power to the external power provided through the plasma boundary. Precise and robust control of the evolution of the plasma boundary shape as well as the spatial distribution of the plasma current, density, temperature, and rotation will be essential to achieving and maintaining such scenarios. The complexity of the evolution of tokamak plasmas, arising due to nonlinearities and coupling between various parameters, motivates the use of model-based control algorithms that can account for the system dynamics. In this work, a learning-based accelerated model trained on data from the National Spherical Torus Experiment Upgrade (NSTX-U) is employed to develop planning and control strategies for regulating the density and temperature profile evolution around desired trajectories. The proposed model combines empirical scaling laws developed across multiple devices with neural networks trained on empirical data from NSTX-U and a database of first-principles-based computationally intensive simulations. The reduced execution time of the accelerated model will enable practical application of optimization algorithms and reinforcement learning approaches for scenario planning and control development. An initial demonstration of applying optimization approaches to the learning-based model is presented, including a strategy for mitigating the effect of leaving the finite validity range of the accelerated model. The approach shows promise for actuator planning between experiments and in real-time.

machine learning↗

Finite deformation implementation of a mixed-mode single-integral type cohesive zone with reorienting surfaces of separation

To model material ductile failure and crack propagation, cohesive zone elements can be embedded along potential fracture paths in a finite element simulation. When damage criteria are met, elements in the mesh decohere, simulating the formation and propagation of a crack. In this paper, we present a novel computational algorithm based on finite deformation theory, essential to modeling crack initiation and growth in solids undergoing large deformations. This new algorithm was formulated within a Lagrangian frame of reference to extend previous cohesive zone algorithms to include modeling crack growth in finite deformation contexts. The local coordinate system, necessary for defining an embedded cohesive zone, is constructed based upon the current configuration and is updated within the nonlinear iteration process, thereby resulting in the convergence of the solution for a growing crack in a large deformation quasi-static setting. The model’s accuracy was demonstrated by comparing finite element model simulation results with the analytic case of a constant surface separation, as shown in the verification examples. The power and efficacy of the algorithm to capture large deformations during crack growth were then demonstrated with a double cantilever beam example case. It indicates that the model can be applied to a variety of physical circumstances for predicting crack initiation and growth with delamination and fracture.

42 ENGINEERING↗

TRUST End-of-Year Report

The objective of the Delivery Environments (DE) Testbeds to Reduce Uncertainties in Simulations and Tests (TRUST) work package is to quantify and help increase confidence in specific areas of computational and experimental capabilities that are applicable to current and future delivery environments. More complete quantification of confidence in experimental and computational capabilities and the sufficient increase of confidence in those capabilities is critical to improving weapons engineering design, qualification, and assessment efforts that are critical to the current and future stockpile. Staff development will include cross-discipline training to provide engineers with experience in both numerical simulations and experimental methods. This work will use and provide feedback on analysis tools and experimental results databases for efficient and responsive engineering which are currently under development: engineering common model framework (ECMF), engineering quantification of margins and uncertainties (EQMU), and the test information management system (TIMS). TRUST includes four testbeds and their associated engineering analysis baseline models (EABMs): 1. contact thermal conductivity (CTC); 2. nonlinear dynamics (ND); 3. sensors in environments for accelerometers (SEA); 4. sensors in environments for fiber optic displacement gages (SEFOD).

42 ENGINEERING↗

Design of double- and multi-bend achromat lattices with large dynamic aperture and approximate invariants

A numerical method to design nonlinear double- and multi-bend achromat (DBA and MBA) lattices with approximate invariants of motion is investigated. The search for such nonlinear lattices is motivated by Fermilab’s Integrable Optics Test Accelerator (IOTA), whose design is based on an integrable Hamiltonian system with two invariants of motion. While it may not be possible to design an achromatic lattice for a dedicated synchrotron light source storage ring with one or more exact invariants of motion, it is possible to tune the sextupoles and octupoles in existing DBA and MBA lattices to produce approximate invariants. In our procedure, the lattice is tuned while minimizing the turn-by-turn fluctuations of the Courant-Snyder actions J x and J y at several distinct amplitudes, while simultaneously minimizing diffusion of the on-energy betatron tunes. The resulting lattices share some important features with integrable ones, such as a large dynamic aperture, trajectories confined to invariant tori, robustness to resonances and errors, and a large amplitude-dependent tune-spread. Compared to the nominal NSLS-II lattice, the single- and multi-bunch instability thresholds are increased and the bunch-by-bunch feedback gain can be reduced.

43 PARTICLE ACCELERATORS↗