SEARCH · Engineering Papers

Results for “mathematics of arrays”

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.

SourceResearch connectionFrom yearThrough year

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

At least 235 records · Page 13

All sources NASA NTRS DOE OSTI

DOE OSTI2023

An introduction to financial option pricing on a qudit-based quantum computer

The financial sector is anticipated to be one of the first industries to benefit from the increased computational power of quantum computers, in areas such as portfolio optimisation and risk management to financial derivative pricing. Financial mathematics, and derivative pricing in particular, are not areas quantum physicists are traditionally trained in despite the fact that they often have the raw technical skills needed to understand such topics. On the other hand, most quantum algorithms have largely focused on qubits, which are comprised of two discrete states, as the information carriers. However, discrete higher-dimensional qudits, in addition to possibly possessing increased noise robustness and allowing for novel error correction protocols in certain hardware implementations, also have logarithmically greater information storage and processing capacity. In the current NISQ era of quantum computing, a wide array of hardware paradigms are still being studied and any potential advantage a platform offers is worth exploring. Here we introduce the basic concepts behind financial derivatives for the unfamiliar enthusiast as well as outline in great detail the quantum algorithm routines needed to price a European option, the simplest derivative. This is done within the context of a quantum computer comprised of qudits and employing the natural higher-dimensional analogue of a qubit-based pricing algorithm with its various subroutines. From these pieces, one should relatively easily be able to tailor the scheme to more complex, realistic financial derivatives. Finally, the entire stack is numerically simulated with the results demonstrating how the qudit-based scheme's payoff quickly approaches that of both a similarly-resourced classical computer as well as the true payoff, within error, for a modest increase in qudit dimension.

Bornman, Nicholas↗

DOE OSTI2021

Multirate linearly-implicit GARK schemes

Many complex applications require the solution of initial-value problems where some components change fast, while others vary slowly. Multirate schemes apply different step sizes to resolve different components of the system, according to their dynamics, in order to achieve increased computational efficiency. The stiff components of the system, fast or slow, are best discretized with implicit base methods in order to ensure numerical stability. To this end, linearly implicit methods are particularly attractive as they solve only linear systems of equations at each step. This paper develops the Multirate GARK-ROS/ROW (MR-GARK-ROS/ROW) framework for linearly-implicit multirate time integration. The order conditions theory considers both exact and approximative Jacobians. The effectiveness of implicit multirate methods depends on the coupling between the slow and fast computations; an array of efficient coupling strategies and the resulting numerical schemes are analyzed. Multirate infinitesimal step linearly-implicit methods, that allow arbitrarily small micro-steps and offer extreme computational flexibility, are constructed. The new unifying framework includes existing multirate Rosenbrock(-W) methods as particular cases, and opens the possibility to develop new classes of highly effective linearly implicit multirate integrators.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2025

Enhancing Drinking Water Quality Modeling: Leveraging Physics Informed Neural Networks for Learning with Imperfect Reaction Models and Partial Data

Chemical kinetics models, typically formulated as systems of ordinary or partial differential equations, are valuable tools for simulating drinking water quality. However, these models often face inaccuracies due to discrepancies between the laboratory and the real-world conditions, as well as limitations in experimental analytical methods, hindering the accurate representation of the true underlying chemical mechanisms. In this study, we propose a Physics Informed Neural Network (PINN), using the eXtreme Theory of Functional Connections, to improve the prediction of chemical concentrations over time. The PINN method accounts for imperfect chemical models and incorporates partial data to improve predictions. Focusing on reactions describing water disinfection residual and disinfectant byproduct formation, which are crucial for public health and regulatory compliance, we demonstrate that the PINN model is able to accurately predict the concentrations of chemical species across various pH values. Notably, the model extends its accuracy to predict concentrations of chemical species not originally included in its training data. The developed method can be extended to a variety of chemical systems, offering a wide array of potential applications.

13 HYDRO ENERGY↗

DOE OSTI2026

Development of Advanced, Radiation Resistant, Optical-based Detector Technology for Future Experiments.

The primary objective of this project has been to advance the design of high-performance electromagnetic (EM) calorimeters for future particle physics experiments, to identify and measure the timing, position and energy of electrons, positrons and gamma rays, particularly in high-luminosity environments with intense radiation and pileup conditions. To meet such challenges, the proposed research has focused on the development of ultra-compact, radiation-hard calorimeter modules, to provide excellent timing, spatial, and energy resolution. The work aligns with the DOE’s Basic Research Needs (BRN) for High Energy Physics (HEP) Instrumentation and the research team contributes actively to the Coordinating Panel on Advanced Detectors (CPAD) RDC9 calorimetry collaboration in the USA and the European Committee on Future Accelerators (ECFA) DRD-CALO calorimetry collaboration at CERN, the European Laboratory for Particle Physics located in Geneva, Switzerland. The research builds on the RADiCAL (radiation-hard, ultra-compact) modular sampling calorimeter approach, developed by the research team, which employs dense and very bright optical materials such as LYSO:Ce scintillator plates that are interleaved with very dense tungsten plates to minimize detector size while optimizing performance. The modules are comparable in size to a human index finger, dimensionally 14 mm x 14 mm in cross section and 135 mm in length. And despite the small size, the structure is capable of providing excellent timing and energy resolution. This is facilitated through the use of specialized quartz capillaries filled with wavelength-shifting filaments, positioned at various depths along the length of a module, to collect and guide light signals to silicon photomultipliers (SiPMs) which detect and convert the optical signals to electronic signals for analysis. The primary goals of this project have been: (1) Achieve a timing resolution to σ t ≤ 30 ps for high-energy electrons and photons, important for their association with specific events produced in colliding-beam experiments and for the detection of decays-in-flight of long-lived particles. The project has achieved this goal in beam tests of a single RADiCAL module at CERN, during which a timing resolution of σ t = 27 ps was measured for electrons of energy E = 150 GeV. Based upon a mathematical fit to the data measured over a broad energy range from low energy to high energy, a resolution of σ t ≤ 18 ps has been estimated for electrons of very high (TeV) energy. From these measurements and with further expected technical improvements, the timing resolution should reach σ t ≤ 10 ps, important for searches for discovery physics in upcoming and future experiments. (2) Achieve an energy resolution of σ E / E ≤ 10% / $\sqrt{E}$. The project has yet to achieve this goal, but is close to it, having measured a value of σ E / E ≤ 15.9% / $\sqrt{E}$ using a modular array. Ultimately, the resolution goal is expected to be reached by adjustments to material thicknesses within the modules, which will improve the sampling fraction to measure more precisely the shower energy for lower energy particles. The versatility of the modular RADiCAL approach enables the testing of advanced materials, photosensors and electronics, developed in collaboration with CPAD RDC and ECFA DRD-CALO groups. The structure can distinguish electrons, positrons and gamma rays from hadrons and muons and beam-induced backgrounds, making it a valuable tool in a variety of detector environments, including future circular colliders (FCC-ee, FCC-hh) proposed for the European Laboratory for Particle Physics (CERN), the muon-collider proposed for Fermi National Accelerator Laboratory (Fermilab), and searches for new physics in beam-dump, fixed target and forward-physics experiments. And, while designed with particle physics applications in mind, the technologies developed in this project have the potential for application more broadly in particle and nuclear physics, materials science, and medical physics, underscoring the far-reaching potential of this line of instrumentation research and development.

47 OTHER INSTRUMENTATION↗

NASA NTRS2003

Effects of a Scanning Reflectarray Antenna on Modulated Data Modeled

The ferroelectric reflectarray is a new type of scanning antenna under development for space and ground communications and radar applications at the NASA Glenn Research Center. The reflectarray offers tremendous cost, gain, and efficiency advantages in comparison to the state-of-the-art phased arrays, but there is an inherent intersymbol interference (ISI) problem with digital communication data streams processed through the array because of the way the reflectarray is operated. This interference stems from the fact that the antenna beam is formed by the superposition of reflected waves from the array elements. The delays from the elements to the observation point of each wave differ. Ferroelectric phase shifters are designed to compensate for the modulo-2p phase differences so that the waves will constructively interfere at the sinusoidal carrier level; however, the delays of the integer-number multiple of the carrier period are not compensated for. This lack of compensation causes ISI in digital modulated signals. ISI has not been a problem with analog modulations and low-rate digital modulations since the distortion (or ISI) introduced is negligible. The problem becomes acute when the data rate gets higher, and the electrical size of the array gets bigger. Moreover, there are intrinsic transient effects associated with the phase shifters and the controller that executes the algorithm to direct the beam. That is, phase shifter updates to redirect the beam may be initiated simultaneously, but nonlinearity will cause different settling times. The ISI problem and other effects ultimately limit the size (gain) and data rate of the reflectarray. An ISI analysis was required to prove or disprove the suitability of the reflectarray antenna for high-rate digitally modulated signals and to give guidance for determining antenna parameters. In this research, the nature of the ISI of the reflectarray has been mathematically modeled.

Romanofsky, Robert R.↗

NASA NTRS2026

Mathematical Model of a Regenerative Fuel Cell for System Optimization

This thesis developed a system-level optimization model of a regenerative fuel cell (RFC) system for long-duration, off-world energy storage applications. Prior RFC design studies have typically been limited to reduced parameter sets and simplified constraints due to computational limitations relative to the number of relevant degrees of freedom. As a result, important nonlinear interactions between subsystems have not been fully captured. This work began to address that gap by developing a higher-fidelity, nonlinear optimization framework that incorporates a broader set of design variables and coupled constraints, enabling a multidimensional model that captures the coupled behavior of RFC subsystems and demonstrates the feasibility of applying optimization to such systems. An expanded system-level optimization approach was established that captures interactions between electrochemical performance, structural requirements, and storage design. This enabled a more comprehensive evaluation of trade-offs than conventional formulations. The model integrates four coupled subsystems: a fuel cell, an electrolyzer, reactant gas, and high-pressure storage tanks, and was formulated to accommodate a wide range of mission parameters, including operational time and required output power. It incorporates constraints on available solar array power, reactant mass balance between production and consumption, and pressure-dependent storage requirements. To enable reliable convergence, the optimization problem was reformulated to reduce dimensionality and improve numerical stability, with subsystem models organized for efficient evaluation. Problem dimensionality was reduced by consolidating lower-level design variables into higher-level representative quantities, and subsystem behavior was evaluated within the optimization loop. A multi-start initialization strategy was employed to mitigate sensitivity to local minima and improve solution quality, while nonlinear relationships were solved using robust numerical methods. The results showed that convergence was achieved across a range of required output power values. Specific energy reached a maximum at a critical mission power level, where the electrolyzer power matched the available solar input and operated near its voltage and current density limits. Beyond this point, further increases in required power resulted in less mass-efficient operation, increasing total system mass and reducing overall performance. The developed model represents an advancement in RFC system-level optimization by enabling analysis of a broader and more tightly coupled design space than previous considerations. While convergence behavior and computational cost remain challenges, the methods introduced improve solvability and allow inclusion of additional design variables with minimal loss of physical fidelity. However, the numerical results should not be interpreted as definitive design recommendations, as the model includes simplifying assumptions and omits several higher-order effects. Future work should extend this framework by incorporating additional subsystems and loss mechanisms, such as thermal management, parasitic power consumption, and reactant losses, to improve fidelity and ensure more representative design conclusions.

Electrochemistry↗

DOE OSTI2021

Enabling modern data discovery for atmospheric measurements

The Atmospheric Radiation Measurement (ARM) user facility is a US Department of Energy Office of Science user facility that is managed and operated through a collaborative effort led by nine US Department of Energy national laboratories. The ARM Data Center, located at Oak Ridge National Laboratory, is responsible for the timely collection, processing, and delivery of data products to the scientific community. The ARM Data Center holds more than 11,000 data products, including metadata collected from field campaigns, instruments, value-added products, and principal investigator–contributed data. These data sets are checked for successful transfer (for most data, this transfer is carried out automatically via the network; however, some of the largest data sets and some of the most remote sites require manual shipping of hard disks) and both the data and metadata are processed to a standard format, which is an ARM-standardized structure, via the Network Common Data Form. The Network Common Data Form is a self-describing binary format with many compatible software tools. Once processed, the data are cataloged, stored in the ARM Data Archive, and made discoverable through association with an array of metadata-characterizing information, such as location and measurement classification. These metadata enable powerful search capabilities through the ARM Data Center Data Discovery interface. This paper discusses the workflow of how the new discovery system has been redesigned from user requirements and how the data are distributed to the scientific community.

54 ENVIRONMENTAL SCIENCES↗

DOE OSTI2024

Can mesoscale models capture the effect from cluster wakes offshore?

Long wakes from offshore wind turbine clusters can extend tens of kilometers downstream, affecting the wind resource of a large area. Given the ability of mesoscale numerical weather prediction models to capture important atmospheric phenomena and mechanisms relevant to wake evolution, they are often used to simulate wakes behind large wind turbine clusters and their impact over a wider region. Yet, uncertainty persists regarding the accuracy of representing cluster wakes via mesoscale models and their wind turbine parameterizations. Here, we evaluate the accuracy of the Fitch wind farm parameterization in the Weather Research and Forecasting model in capturing cluster-wake effects using two different options to represent turbulent mixing in the planetary boundary layer. To this end, we compare operational data from an offshore wind farm in the North Sea that is fully or partially waked by an upstream array against high-resolution mesoscale simulations. In general, we find that mesoscale models accurately represent the effect of cluster wakes on front-row turbines of a downstream wind farm. However, the same models may not accurately capture cluster-wake effects on an entire downstream wind farm, due to misrepresenting internal-wake effects.

17 WIND ENERGY↗

DOE OSTI2023

Developing new analysis tools for near surface radio-based neutrino detectors

The ARIANNA experiment is an Askaryan radio detector designed to measure high-energy neutrino induced cascades within the Antarctic ice. Ultra-high-energy neutrinos above 10 16 eV have an extremely low flux, so experimental data captured at trigger level need to be classified correctly to retain as much neutrino signal as possible. We first describe two new physics-based neutrino selection methods, or "cuts", (the updown and dipole cut) that extend the previously published analysis to a specialized ARIANNA station with 8 antenna channels, which is double the number used in the prior analysis. For a standard trigger with a threshold signal to noise ratio at 4.4, the new cuts produce a neutrino efficiency of > 95% per station-year of operation, while rejecting 99.93% of the background (corresponding to 53 remaining experimental background events). When the new cuts are combined with a previously developed cut using neutrino waveform templates, all background is removed at no change of efficiency. In addition, the neutrino efficiency is extrapolated to 1,000 station-years of operation, obtaining 91%. This work then introduces a new selection method (the deep learning cut) to augment the identification of neutrino events by using deep learning methods and compares the efficiency to the physics-based analysis. The deep learning cut gives 99% signal efficiency per station-year of operation while rejecting 99.997% of the background (corresponding to 2 remaining experimental background events), which are subsequently removed by the waveform template cut at no significant change in efficiency. Here the results of the deep learning cut were verified using measured cosmic rays which shows that the simulations do not introduce artifacts with respect to experimental data. The paper demonstrates that the background rejection and signal efficiency of near surface antennas meets the requirements of a large scale future array, as considered in baseline design of the radio component of IceCube-Gen2.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2020

Systems and methods for data storage and retrieval

A method includes directing a probe beam to a target that includes an array of data portions in a data storage medium arranged so that a beam area of the probe beam extends across a plurality of adjacent data portions, the array including a data portion subset with each data portion of the subset responsive to the probe beam to produce a response illumination, receiving the response illumination at a detector, and determining data values corresponding to the plurality of adjacent data portions based on the received response illumination. Apparatus and systems are also disclosed.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2021

Tuning Electrogenerated Chemiluminescence Intensity Enhancement Using Hexagonal Lattice Arrays of Gold Nanodisks

Electrogenerated chemiluminescence (ECL) microscopy shows promise as a technique for mapping chemical reactions on single nanoparticles. The technique’s spatial resolution is limited by the quantum yield of the emission and the diffusive nature of the ECL process. To improve signal intensity, ECL dyes have been coupled with plasmonic nanoparticles, which act as nanoantennas. Here, we characterize the optical properties of hexagonal arrays of gold nanodisks and how they impact the enhancement of ECL from the coreaction of tris(2,2'-bipyridyl)dichlororuthenium(II) hexahydrate and tripropylamine. Here, we find that varying the lattice spacing results in a 23-fold enhancement of ECL intensity because of increased dye-array near-field coupling as modeled using finite element method simulations.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

DOE OSTI2021

DPC Disposal Thermal Scoping Analysis

This is a progress report on thermal modeling for dual-purpose canister (DPCs) direct disposal that covers several available calculation methods and addresses creep and temperature-dependent properties in a salt repository. Three modeling approaches are demonstrated: A semi-analytical calculation method that uses linear solutions with superposition and imaging, to represent a central waste package in a larger array; A finite difference model of coupled thermal creep, implemented in FLAC2D; and An integrated finite difference thermal-hydrologic modeling approach for repositories in different generic host media, implemented in PFLOTRAN. These approaches are at different levels of maturity, and future work is expected to add refinements and establish the best applications for each.

12 MANAGEMENT OF RADIOACTIVE AND NON-RADIOACTIVE W↗

DOE OSTI2022

Vector-Matrix Multiplication Engine for Neuromorphic Computation with a CBRAM Crossbar Array [Slides]

The core function of many neural network algorithms is the dot product, or vector matrix multiply (VMM) operation. Crossbar arrays utilizing resistive memory elements can reduce computational energy in neural algorithms by up to five orders of magnitude compared to conventional CPUs. Moving data between a processor, SRAM, and DRAM dominates energy consumption. By utilizing analog operations to reduce data movement, resistive memory crossbars can enable processing of large amounts of data at lower energy than conventional memory architectures.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2022

Future energy infrastructure, energy platform and energy storage

Today fossil energy dominates energy consumption across the world. There has been an increasing momentum to reduce fossil energy consumption and increase renewable energy utilization to more than 70%. Such high penetrations of distributed renewable resources bring large uncertainty and complexity that cannot be easily handled by the current infrastructure. For the last two decades, telecommunication industry has gone through a similar transition from centralized to distributed systems, and more recently to platform approaches, which become the corner stone of today’s vibrant platform economy. Based on telecommunication history, we believe that a platform-based approach, called the energy platform, is a viable solution for addressing the renewable energy challenges. The energy platform consists of an array of computational algorithms, sensing and control technologies for key industry, energy generators and users to jointly manage and control the complex energy infrastructure. It includes the following key components: (1) the hardware and software to generate, store, control and transmit electricity/data (the energy cloud), (2) the digital platforms and tools for key energy producers, digital, service and communication industry to share the assets, participate in and manage the complex infrastructure, and for customers to participate in energy transactions, (3) the transaction platform for new service and business models. Additionally, the energy platform requires breakthroughs in large scale energy storage and many other areas including efficient power electronics, sensors and controls, new mathematical and computational tools, and deep integration of energy technologies and information sciences to control and stabilize such complex chaotic systems.

25 ENERGY STORAGE↗

NASA NTRS1983

Finite Element Analysis of a Deployable Space Structure

The dynamic characteristics of the Solar Array Flight Experiment (SAFE) structure during deployment and retraction are investigated. The SAFE structure consists of a deployable mast with an attached solar blanket designed with accordion type folds to permit packaging in a small volume. The planar form of the blanket geometry during deployment is maintained by a blanket tension/guidewire system. Structurally, the mast is modeled as an Euler beam column with inplane and out of plane bending and finite torsional stiffness. For out of plane motion, the blanket is modeled as a distributed mass uniformly supported by the three guidewires. For inplane motion the blanket displacements are assumed to vary linearly from the mast base to the mast tip. The mathematical model uses a virtual work formulation, required because the axial loading on the mast is nonconservative, combined with assumed beam modes to derive the differential equations of motion. Consideration of the time dependent boundary conditions results in an infinite set of ODE with time dependent coefficients. Finally, correlation of mast tip accelerations to mast base bending moments for specified modal motions are indicated.

Weeks, G. E.↗

DOE OSTI2020

Field Programmable Gate Arrays for Enhancing the Speed and Energy Efficiency of Quantum Dynamics Simulations

We present the first application of field programmable gate arrays (FPGAs) as new, customizable hardware architectures for carrying out fast and energy-efficient quantum dynamics simulations of large chemical/material systems. Instead of tailoring the software to fixed hardware, which is the typical case for writing quantum chemistry code for central processing units (CPUs) and graphics processing units (GPUs), FPGAs allow us to directly customize the underlying hardware (even at the level of specific electrical signals in the circuit) to give a truly optimized computational performance for quantum dynamics calculations. By offloading the most intensive and repetitive calculations onto an FPGA, we show that the computational performance of our real-time electron dynamics calculations can even exceed that of optimized commercial mathematical libraries running on high-performance GPUs. In addition to this impressive computational speedup, we show that FPGAs are immensely energy-efficient and consume 4 times less energy than modern GPU or CPU architectures. These energy savings are a practical and important metric for supercomputing centers (many of which exceed over $1 million in power costs alone), as exascale computing capabilities become more widespread and commonplace. Taken together, the implementation techniques and performance metrics of our study demonstrate that FPGAs could play a promising role in upcoming quantum chemistry and materials science applications, particularly for the acceleration and energy-efficient execution of quantum dynamics calculations.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

DOE OSTI2022

Multi-qubit entanglement and algorithms on a neutral-atom quantum computer

Gate model quantum computers promise to solve currently intractable computational problems if they can be operated at scale with long coherence times and high fidelity logic. Neutral atom hyperfine qubits provide inherent scalability due to their identical characteristics, long coherence times, and ability to be trapped in dense multi-dimensional arrays. Combined with the strong entangling interactions provided by Rydberg states, all the necessary characteristics for quantum computation are available. Here we demonstrate several quantum algorithms on a programmable gate model neutral atom quantum computer in an architecture based on individual addressing of single atoms with tightly focused optical beams scanned across a two-dimensional array of qubits. Preparation of entangled Greenberger-Horne-Zeilinger (GHZ) states with up to 6 qubits, quantum phase estimation for a chemistry problem, and the Quantum Approximate Optimization Algorithm (QAOA) for the MaxCut graph problem are demonstrated. These results highlight the emergent capability of neutral atom qubit arrays for universal, programmable quantum computation, as well as preparation of non-classical states of use for quantum enhanced sensing.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2020

ZFP Hardware Implementation

As core counts increase in new HPC systems with comparatively little increase in memory bandwidth, the trend is an effective decrease in memory bandwidth per core. Other bandwidth limitations in HPC systems exist between CPU and GPU memory, between system nodes, and between node memory and storage. Compression of floating-point data has the potential to reduce data movement and pressure across these communication channels. Furthermore, it has the potential to reduce the footprint of floating-point arrays stored in memory. ZFP, implemented in software, is gaining traction as an effective method in floating-point compression; however, performance gains are limited to the spare compute cycles available before reaching the bandwidth limitations of the communication channel. A hardware implementation of ZFP has the potential to raise the bar on performance. From the inception of ZFP, it was designed to accommodate a hardware implementation.

42 ENGINEERING↗