Engineering Papers⌕ Search

SEARCH · Engineering Papers

Results for “Fractional operators”

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 19 records
All sourcesNASA NTRSDOE OSTI
NASA NTRS2002

Variable Order and Distributed Order Fractional Operators

Many physical processes appear to exhibit fractional order behavior that may vary with time or space. The continuum of order in the fractional calculus allows the order of the fractional operator to be considered as a variable. This paper develops the concept of variable and distributed order fractional operators. Definitions based on the Riemann-Liouville definitions are introduced and behavior of the operators is studied. Several time domain definitions that assign different arguments to the order q in the Riemann-Liouville definition are introduced. For each of these definitions various characteristics are determined. These include: time invariance of the operator, operator initialization, physical realization, linearity, operational transforms. and memory characteristics of the defining kernels. A measure (m2) for memory retentiveness of the order history is introduced. A generalized linear argument for the order q allows the concept of "tailored" variable order fractional operators whose a, memory may be chosen for a particular application. Memory retentiveness (m2) and order dynamic behavior are investigated and applications are shown. The concept of distributed order operators where the order of the time based operator depends on an additional independent (spatial) variable is also forwarded. Several definitions and their Laplace transforms are developed, analysis methods with these operators are demonstrated, and examples shown. Finally operators of multivariable and distributed order are defined in their various applications are outlined.

Lorenzo, Carl F.↗
DOE OSTI2022

A fractional model for anomalous diffusion with increased variability: Analysis, algorithms and applications to interface problems

Fractional equations have become the model of choice in several applications where heterogeneities at the microstructure result in anomalous diffusive behavior at the macroscale. Here, we introduce a new fractional operator characterized by a doubly-variable fractional order and possibly truncated interactions. Under certain conditions on the model parameters and on the regularity of the fractional order we show that the corresponding Poisson problem is well-posed. Additionally, we introduce a finite element discretization and describe an efficient implementation of the finite-element matrix assembly in the case of piecewise constant fractional order. Through several numerical tests, we illustrate the improved descriptive power of this new operator across media interfaces. Furthermore, we present one-dimensional and two-dimensional h-convergence results that show that the variable-order model has the same convergence behavior as the constant-order model.

97 MATHEMATICS AND COMPUTING↗
NASA NTRS2014

Autonomous Flight Rules Concept: User Implementation Costs and Strategies

The costs to implement Autonomous Flight Rules (AFR) were examined for estimates in acquisition, installation, training and operations. The user categories were airlines, fractional operators, general aviation and unmanned aircraft systems. Transition strategies to minimize costs while maximizing operational benefits were also analyzed. The primary cost category was found to be the avionics acquisition. Cost ranges for AFR equipment were given to reflect the uncertainty of the certification level for the equipment and the extent of existing compatible avionics in the aircraft to be modified.

Cotton, William B.↗
NASA NTRS1997

Performance Analysis of the NAS Y-MP Workload

This paper describes the performance characteristics of the computational workloads on the NAS Cray Y-MP machines, a Y-MP 832 and later a Y-MP 8128. Hardware measurements indicated that the Y-MP workload performance matured over time, ultimately sustaining an average throughput of 0.8 GFLOPS and a vector operation fraction of 87%. The measurements also revealed an operation rate exceeding 1 per clock period, a well-balanced architecture featuring a strong utilization of vector functional units, and an efficient memory organization. Introduction of the larger memory 8128 increased throughput by allowing a more efficient utilization of CPUs. Throughput also depended on the metering of the batch queues; low-idle Saturday workloads required a buffer of small jobs to prevent memory starvation of the CPU. UNICOS required about 7% of total CPU time to service the 832 workloads; this overhead decreased to 5% for the 8128 workloads. While most of the system time went to service I/O requests, efficient scheduling prevented excessive idle due to I/O wait. System measurements disclosed no obvious bottlenecks in the response of the machine and UNICOS to the workloads. In most cases, Cray-provided software tools were- quite sufficient for measuring the performance of both the machine and operating, system.

Bergeron, Robert J.↗
DOE OSTI2022

Advances in the long-pulse steady-state high beta H-mode scenario with active controls of divertor heat and particle fluxes in EAST

Since the last IAEA-Fusion Energy Conference, the Experimental Advanced Superconducting Tokamak (EAST) research program has been, in support of ITER and CFETR, focused on development in terms of the long-pulse steady-state (fully noninductive) high beta H-mode scenario with active controls of the stationary and transient divertor heat and particle fluxes. The operational domain of the steady-state H-mode plasma scenario has been significantly extended with ITER-like tungsten mono-block divertor, plasma control and heating schemes. EAST has achieved several important milestones in the development of high β p H-mode scenario and its key physics and technologies. A 60 s-scale long-pulse steady-state high β p H-mode discharge with the major normalized plasma parameters similar to the designed performance of the CFETR 1GW fusion power operation scenario has been successfully established and sustained by pure RF heating and current drive. Several feedback control schemes have been developed for a sustained detachment with good core confinement. This includes control of the total radiation power, target electron temperature, and particle flux measured using divertor Langmuir probes or a combination of the control of target electron temperature and AXUV radiation near the X point. The detachment feedback control schemes have been integrated with small-ELM regimes and high β p scenario via neon seeding, enabling a core and edge compatible integrated high-beta scenario applicable to long-pulse operations. ELM suppression has been achieved using various methods, including resonant magnetic perturbations and impurity seeding. Full suppression of ELMs by using n=4 RMPs has been demonstrated for ITER for the first time in low input torque plasmas in EAST. Finally, EAST has been operated with helium to support the ITER research requirements for the first time. For a long-pulse, high bootstrap current fraction operation, a new lower tungsten divertor with active water-cooling has been installed, along with improvements in the heating and current drive capability.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2024

Variable-spectrum mode control of high poloidal beta discharges

DIII-D experiments demonstrate that high pressure, broad current profile equilibria can be accessed in the high poloidal beta regime by optimizing the MHD mode control poloidal spectrum. A novel, variable spectrum (VS) magnetic feedback scheme implemented using the DIII-D internal non-axisymmetric coils (I-coils) facilitated access to reduced internal inductance $l$ i operation above the no-wall beta limit compared with both no feedback and fixed spectrum feedback. In addition, the VS feedback helped avoid beta collapses caused by marginally unstable resistive wall mode activity. The lower and upper I-coil rows were configured in two independent feedback loops, allowing the feedback field's poloidal spectrum to vary and track changes in the plasma mode structure as the edge safety factor q 95 varied from 11 to 6 during the discharges. The q 95 dependence of the measured phase difference between the lower and upper I-coil rows during VS feedback is qualitatively compatible with ideal MHD simulations of the least-stable plasma kink mode and with plasma response simulations that included kinetic modifications to ideal MHD. The VS feedback approach is a straightforward way to improve resilience to variations in mode structure that occur as plasma parameters change. The demonstrated expansion of the operating space to lower $l$ i is expected to improve the coupling of the plasma kink mode to external fields and beneficial wall eddy currents, and is compatible with high bootstrap fraction operation.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2025

Generalized fractional approach to solving partial differential equations with arbitrary dispersion relations

The dynamics of physical systems are typically modeled by partial differential equations (PDEs). Because of the complexity in physical systems, PDE models rely on approximations or limiting cases. To model the full complexity of physical systems, it is necessary to use multiscale approaches where appropriate models are used at each level. Alternatively, complexity can be directly tackled by fractional integrodifferential equations that must be derived for each system. Here, we argue that complexity can be restored in PDEs by describing them from a fractional calculus perspective. Rather than deriving a fractional integrodifferential equation, we reinterpret the dispersion relation of the system by use of the Riesz definition, which contains the required information relating the energy and momentum space of the system and thus fully describes their dynamics. The approach is demonstrated by two examples: the Landau–Lifshitz equation in a 1D ferromagnetic chain and a modified KdV equation supporting surface gravity waves or Euler dispersion. The presented approach is applicable to fluids, soft matter, and solid-state matter and can be readily generalized to higher dimensions and more complex systems. While numerical calculations are needed to determine the fractional operator, the approach is analytical and can be utilized to determine analytical solutions and investigate nonlinear problems.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2024

Simultaneous enhancement of tritium burn efficiency and fusion power with low-tritium spin-polarized fuel

This study demonstrates that using spin-polarized deuterium-tritium (D-T) fuel with more deuterium than tritium can increase tritium burn efficiency (TBE) by at least an order of magnitude without compromising fusion power output, compared to unpolarized fuel. Although previous studies show that a low tritium fraction can enhance TBE, this strategy resulted in reduced fusion power density. The surprising improvement in TBE at fixed power reported here is due to the TBE increasing nonlinearly with decreasing tritium fraction but the fusion power density increasing roughly linearly with D-T cross section. A study is performed for an ARC-like tokamak producing 481 MW of fusion power with unpolarized 53:47 D-T fuel, finding the minimum startup tritium inventory (I startup,min ) is 0.69 kg. By spin-polarizing half of the fuel and using a 60:40 D-T mix, I startup,min is reduced to 0.08 kg, and fully spin-polarizing the fuel with a 63:37 D-T mix further reduces I startup,min to 0.03 kg. Some ARC-like scenarios are predicted to achieve plasma ignition with relatively modest spin polarization. These findings indicate that, with advancements in helium divertor pumping efficiency, TBE values of approximately 10%–40% could be achieved using low-tritium-fraction and spin-polarized fuel with minimal power loss. This would dramatically lower tritium startup inventory requirements and reduce the amount of on-site tritium. More generally than just for spin-polarized fuels, increased plasma performance can be used to increase TBE. This strongly motivates the development of spin-polarized fuels and low-tritium-fraction operation for burning plasmas.

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗
DOE OSTI2024

Full Scale HEPA Filter Encapsulation in Ultra-High-Performance Grout - Proof of Concept

The Hanford Tank Waste Treatment and Immobilization Plant (WTP) currently being constructed to treat radioactive waste, includes vitrification facilities for both the high-level waste (HLW) and low activity waste (LAW) fractions. Operation of the WTP will produce contaminated high-efficiency particulate air filters (HEPA), as part of the solid secondary waste (SSW) stream. The HEPA filters receive off-gas from the vessel vent header and primary off-gas treatment system in LAW Facility and remove particulate contaminants including 99 Tc and 129 I salts. The current disposal method for HEPA filters is encapsulation in metal containers using cementitious material (CM) and disposal in the Integrated Disposal Facility (IDF). Results from the 2017 IDF Performance Assessment (PA) WRPS (2018) demonstrated that while compliance is maintained for the 1000 year compliance period mandated by DOE O 435.1 and its accompanying manual, release of constituents from the HEPA filters result in exceedance of the performance objective imposed as the groundwater regulatory limit at later times. For example, at about 1500 years post-closure, solid secondary waste (SSW), including HEPA filters is predicted to become a dominant contributor to 99 Tc release and over the 10,000-year sensitivity analysis period, SSW is the dominant contributor of 129 I release to the groundwater. The estimated release could potentially be reduced if the HEPA filters are not compacted and waste containers could be distributed throughout a large space, thereby diluting the contaminant release. Additionally, a better cementitious material could be used to encapsulate the HEPA filters. One alternative method for disposal of contaminated HEPA filters is encapsulation of the filters in ultra high-performance grout (UHPG). UHPG is a variation of ultra-high-performance concrete (UHPC) is commonly used in the prestressed concrete industry for large structural members. Recent studies of UHPG show it has excellent properties for containing radionuclides such as 99 Tc and 129 I Nichols and Kaplan (2021). This report presents the results of the first attempt to encapsulate a clean, full-size HEPA filter in UHPG and evaluate the effectiveness of the immobilization process and final waste form. A full-scale proof-of-concept simulated waste form was prepared by encapsulating a HEPA filter in a 110-gallon stainless steel (SS) drum using UHPG. A change from Type I/II PC to Type 1L PLC was made after American Rock Products informed the team that they would no longer be using Type I/II by the end of 2024 and the northwest was phasing out Type I/II PC overall. Type I/II PC used in previous studies of UHPG for encapsulation (Nichols and Kaplan 2021). After the UHPG was cured both the scaled mockup and the full-scale simulated waste forms were sectioned for visual examination. UHPG completely encapsulated the filters and bonded to the external surfaces of materials comprising the filters. No cracks were observed in the sectioned waste forms.

12 MANAGEMENT OF RADIOACTIVE AND NON-RADIOACTIVE W↗
NASA NTRS1981

Local effects of partly cloudy skies on solar and emitted radiations

Solar radiation measurements are made on a routine basis. Global solar, atmospheric emitted, downwelled diffuse solar, and direct solar radiation measurement systems are fully operational with the first two in continuous operation. Fractional cloud cover measurements are made from GOES imagery or from ground based whole sky photographs. Normalized global solar irradiance values for partly cloudy skies were correlated to fractional cloud cover.

Whitney, D. A.↗
NASA NTRS1987

Numerical analysis of discrete fractional integrodifferential structural dampers

This paper develops solution algorithms enabling the handling of the dynamic response of nonlinear structures contained discretely attached dampers modeled by fractional integrodifferential operators of the Grunwald-Liouville-Riemann type. The development consists of two levels of formulation, namely: (1) numerical approximations of fractional operators and, (2) the establishment of global level implicit schemes enabling the solution to nonlinear structural formulations. To generalize the overall results, error estimates are derived for the fractional operator approximation algorithm. These enable an ongoing optimization of solution efficiency for a given error tolerance. To benchmark the scheme, the results of several numerical experiments are presented. These illustrate the numerical characteristics of the overall formulation.

Padovan, Joseph↗
NASA NTRS1987

Finite element analysis of steady and transiently moving/rolling nonlinear viscoelastic structure. I - Theory

In a three-part series of papers, a generalized finite element analysis scheme is developed to handle the steady and transient response of moving/rolling nonlinear viscoelastic structure. This paper considers the development of the moving/rolling element strategy, including the effects of large deformation kinematics and viscoelasticity modeled by fractional integrodifferential operators. To improve the solution strategy, a special hierarchical constraint procedure is developed for the case of steady rolling/translating, as well as a transient scheme involving the use of a Grunwaldian representation of the fractional operator.

Padovan, Joe↗
DOE OSTI2025

Moment method and continued fraction expansion in Floquet operator Krylov space

Recursion methods such as Krylov techniques map complex dynamics to an effective noninteracting problem in one dimension. For example, the operator Krylov space for Floquet dynamics can be mapped to the dynamics of an edge operator of the one-dimensional Floquet inhomogeneous transverse field Ising model (ITFIM), where the latter, after a Jordan-Wigner transformation, is a Floquet model of noninteracting Majorana fermions and the couplings correspond to Krylov angles. We present an application of this showing that a moment method exists where given an autocorrelation function, one can construct the corresponding Krylov angles and from that the corresponding Floquet ITFIM. Consequently, when no solutions for the Krylov angles are obtained, it indicates that the autocorrelation is not generated by unitary dynamics. We highlight this by studying certain special cases: stable m-period dynamics derived using the method of continued fractions, exponentially decaying, and power-law decaying stroboscopic dynamics. Remarkably, our examples of stable m-period dynamics correspond to m-period edge modes for the Floquet ITFIM where, deep in the chain, the couplings correspond to a critical phase. Furthermore our results pave the way to engineer Floquet systems with desired properties of edge modes and also provide examples of persistent edge modes in gapless Floquet systems.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
NASA NTRS1986

Balancing High-Speed Rotors at Low Speed

Flexible balancing reduces vibrations at operating speeds. Highspeed rotors in turbomachines dynamically balanced at fraction of operating rotor speed. New method takes into account rotor flexible rather than rigid.

Giordano, J.↗
NASA NTRS2018

Identification of Safety Metrics for Airport Surface Operations

A large fraction of safety incidents occurs on the ground during airport surface operations. Although these incidents are mostly non-fatal with a few exceptions, they are high profile incidents that remain a source of concern for the National Transportation Safety Board (NTSB), the Federal Aviation Administration (FAA), major airlines, and other stakeholders of the National Airspace System (NAS). These incidents have historically been mitigated by implementing changes to regulations, policies, and procedures over time. This approach has minimized but not eliminated the risk of occurrences. It is thus important to develop integrated techniques to assess, model, and prevent these incidents by analyzing the risk and likelihood of occurrence and communicating results of the analysis to decision-making personnel who can mitigate and prevent incidents in real time. The research presented in this report builds on prior work of researchers at the NASA Ames Research Center who developed an automated framework, Real-Time Safety Monitoring (RTSM), to enable monitoring and prediction of the safety of the NAS. In the RTSM framework, hazards to flight are translated to safety metrics such as wake vortex encounters or loss of separation, that can be modeled and analyzed offline and also predicted and monitored in real time (online). The intent of this report is to integrate predictable incidents that occur during surface and ground operations into the safety portfolio of the RTSM project by (i) identifying suitable information sources from which ground incidents can be studied, (ii) developing safety metrics correlated with surface operations, and (iii) recommending suitable data sources that can be quantified and used for the computation of pertinent safety metrics.

ground operations↗
NASA NTRS2018

Identification of Safety Metrics for Airport Surface Operations

A large fraction of safety incidents occurs on the ground during airport surface operations. Although these incidents are mostly non-fatal with a few exceptions, they are high profile incidents that remain a source of concern for the National Transportation Safety Board (NTSB), the Federal Aviation Administration (FAA), major airlines, and other stakeholders of the National Airspace System (NAS). These incidents have historically been mitigated by implementing changes to regulations, policies, and procedures over time. This approach has minimized but not eliminated the risk of occurrence of safety incidents. It is thus important to develop integrated techniques to assess, model, and prevent these incidents by analyzing the risk and likelihood of occurrence and communicating results of the analysis to decision-making personnel who can mitigate and prevent incidents in real time. The work presented in this paper builds on a previously developed architecture for safety, Real-Time Safety Monitoring (RTSM), to enable monitoring and prediction of the safety of the NAS. In the RTSM framework, hazards to flight are translated to safety metrics such as wake vortex encounters or loss of separation, that can be modeled and analyzed offline and also predicted and monitored in real time (online). The intent of this paper is to integrate predictable incidents that occur during surface and ground operations into the safety portfolio of the RTSM project by (i) identifying suitable information sources from which ground incidents can be studied, (ii) developing safety metrics correlated with surface operations, and (iii) recommending suitable data sources that can be quantified and used for the computation of pertinent safety metrics.

safety↗
DOE OSTI2021

Identifiability and predictability of integer- and fractional-order epidemiological models using physics-informed neural networks

Here we analyze a plurality of epidemiological models through the lens of physics-informed neural networks (PINNs) that enable us to identify time-dependent parameters and data-driven fractional differential operators. In particular, we consider several variations of the classical susceptible-infectious-removed (SIR) model by introducing more compartments and fractional-order and time-delay models. We report the results for the spread of COVID-19 in New York City, Rhode Island and Michigan states and Italy, by simultaneously inferring the unknown parameters and the unobserved dynamics. For integer-order and time-delay models, we fit the available data by identifying time-dependent parameters, which are represented by neural networks. In contrast, for fractional differential models, we fit the data by determining different time-dependent derivative orders for each compartment, which we represent by neural networks. We investigate the structural and practical identifiability of these unknown functions for different datasets, and quantify the uncertainty associated with neural networks and with control measures in forecasting the pandemic.

60 APPLIED LIFE SCIENCES↗