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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.

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At least 505 records · Page 28
All sourcesNASA NTRSDOE OSTI
NASA NTRS2000

Neural Network Based Representation of UH-60A Pilot and Hub Accelerations

Neural network relationships between the full-scale, experimental hub accelerations and the corresponding pilot floor vertical vibration are studied. The present physics-based, quantitative effort represents an initial systematic study on the UH-60A Black Hawk hub accelerations. The NASA/Army UH-60A Airloads Program flight test database was used. A 'maneuver-effect-factor (MEF)', derived using the roll-angle and the pitch-rate, was used. Three neural network based representation-cases were considered. The pilot floor vertical vibration was considered in the first case and the hub accelerations were separately considered in the second case. The third case considered both the hub accelerations and the pilot floor vertical vibration. Neither the advance ratio nor the gross weight alone could be used to predict the pilot floor vertical vibration. However, the advance ratio and the gross weight together could be used to predict the pilot floor vertical vibration over the entire flight envelope. The hub accelerations data were modeled and found to be of very acceptable quality. The hub accelerations alone could not be used to predict the pilot floor vertical vibration. Thus, the hub accelerations alone do not drive the pilot floor vertical vibration. However, the hub accelerations, along with either the advance ratio or the gross weight or both, could be used to satisfactorily predict the pilot floor vertical vibration. The hub accelerations are clearly a factor in determining the pilot floor vertical vibration.

Kottapalli, Sesi↗
DOE OSTI2023

Considerations for realistic atmospheric environments: An application to corrosion testing

Measured salt compositions in dust collected over roughly the last decade from surfaces of in-service stainless-steel alloys at four locations around the United States are presented, along with the predicted brine compositions that would result from deliquescence of these salts. The salt compositions vary greatly from ASTM seawater and from laboratory salts (i.e., NaCl or MgCl 2 ) commonly used on corrosion testing. The salts contained relatively high amounts of sulfates and nitrates, evolved to basic pH values, and exhibited deliquescence relative humidity values (RH) higher than seawater. Additionally, inert dust in components were quantified and considerations for laboratory testing are presented. The observed dust compositions are discussed in terms of the potential corrosion behavior and are compared to commonly used accelerated testing protocols. Finally, ambient weather conditions and their influence on diurnal fluctuations in temperature (T) and RH on heated metal surfaces are evaluated and a relevant diurnal cycle for laboratory testing a heated surface has been developed. Suggestions for future accelerated tests are proposed that include exploration of the effects of inert dust particles on atmospheric corrosion, chemistry considerations, and realistic diurnal fluctuations in T and RH. Understanding mechanisms in both realistic and accelerated environments will allow development of a corrosion factor (i.e., scaling factor) for the extrapolation of laboratory-scale test results to real world applications.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2018

Cryogenic testing of the 2.1 GHz five-cell superconducting RF cavity with a photonic band gap coupler cell

We present results from cryogenic tests of the multi-cell superconducting radio frequency (SRF) cavity with a photonic band gap (PBG) coupler cell. Achieving high average beam currents is particularly desirable for future light sources and particle colliders based on SRF energy-recovery-linacs (ERLs). Beam current in ERLs is limited by the beam break-up instability, caused by parasitic higher order modes (HOMs) interacting with the beam in accelerating cavities. A PBG cell incorporated in an accelerating cavity can reduce the negative effect of HOMs by providing a frequency selective damping mechanism, thus allowing significantly higher beam currents. The multi-cell cavity was designed and fabricated of niobium. Two cryogenic (vertical) tests were conducted. The high unloaded Q-factor was demonstrated at a temperature of 4.2 K at accelerating gradients up to 3 MV/m. The measured value of the unloaded Q-factor was 1.55 × 10<8>, in agreement with prediction.

43 PARTICLE ACCELERATORS↗
DOE OSTI2021

DeepMC: a deep learning method for efficient Monte Carlo beamlet dose calculation by predictive denoising in magnetic resonance-guided radiotherapy

Abstract Emerging magnetic resonance (MR) guided radiotherapy affords significantly improved anatomy visualization and, subsequently, more effective personalized treatment. The new therapy paradigm imposes significant demands on radiation dose calculation quality and speed, creating an unmet need for the acceleration of Monte Carlo (MC) dose calculation. Existing deep learning approaches to denoise the final plan MC dose fail to achieve the accuracy and speed requirements of large-scale beamlet dose calculation in the presence of a strong magnetic field for online adaptive radiotherapy planning. Our deep learning dose calculation method, DeepMC, addresses these needs by predicting low-noise dose from extremely noisy (but fast) MC-simulated dose and anatomical inputs, thus enabling significant acceleration. DeepMC simultaneously reduces MC sampling noise and predicts corrupted dose buildup at tissue-air material interfaces resulting from MR-field induced electron return effects. Here we demonstrate our model’s ability to accelerate dose calculation for daily treatment planning by a factor of 38 over traditional low-noise MC simulation with clinically meaningful accuracy in deliverable dose and treatment delivery parameters. As a post-processing approach, DeepMC provides compounded acceleration of large-scale dose calculation when used alongside established MC acceleration techniques in variance reduction and graphics processing unit-based MC simulation.

Engineering↗
DOE OSTI2014

Output correction factors for nine small field detectors in 6 MV radiation therapy photon beams: A PENELOPE Monte Carlo study

Purpose: To determine detector-specific output correction factors,k{sub Q} {sub c{sub l{sub i{sub n}}}} {sub ,Q} {sub m{sub s{sub r}}} {sup f{sub {sup {sub c}{sub l}{sub i}{sub n}{sub {sup ,f{sub {sup {sub m}{sub s}{sub r}{sub ,}}}}}}}} in 6 MV small photon beams for air and liquid ionization chambers, silicon diodes, and diamond detectors from two manufacturers. Methods: Field output factors, defined according to the international formalism published byAlfonso et al. [Med. Phys. 35, 5179–5186 (2008)], relate the dosimetry of small photon beams to that of the machine-specific reference field; they include a correction to measured ratios of detector readings, conventionally used as output factors in broad beams. Output correction factors were calculated with the PENELOPE Monte Carlo (MC) system with a statistical uncertainty (type-A) of 0.15% or lower. The geometries of the detectors were coded using blueprints provided by the manufacturers, and phase-space files for field sizes between 0.5 × 0.5 cm{sup 2} and 10 × 10 cm{sup 2} from a Varian Clinac iX 6 MV linac used as sources. The output correction factors were determined scoring the absorbed dose within a detector and to a small water volume in the absence of the detector, both at a depth of 10 cm, for each small field and for the reference beam of 10 × 10 cm{sup 2}. Results: The Monte Carlo calculated output correction factors for the liquid ionization chamber and the diamond detector were within about ±1% of unity even for the smallest field sizes. Corrections were found to be significant for small air ionization chambers due to their cavity dimensions, as expected. The correction factors for silicon diodes varied with the detector type (shielded or unshielded), confirming the findings by other authors; different corrections for the detectors from the two manufacturers were obtained. The differences in the calculated factors for the various detectors were analyzed thoroughly and whenever possible the results were compared to published data, often calculated for different accelerators and using the EGSnrc MC system. The differences were used to estimate a type-B uncertainty for the correction factors. Together with the type-A uncertainty from the Monte Carlo calculations, an estimation of the combined standard uncertainty was made, assigned to the mean correction factors from various estimates. Conclusions: The present work provides a consistent and specific set of data for the output correction factors of a broad set of detectors in a Varian Clinac iX 6 MV accelerator and contributes to improving the understanding of the physics of small photon beams. The correction factors cannot in general be neglected for any detector and, as expected, their magnitude increases with decreasing field size. Due to the reduced number of clinical accelerator types currently available, it is suggested that detector output correction factors be given specifically for linac models and field sizes, rather than for a beam quality specifier that necessarily varies with the accelerator type and field size due to the different electron spot dimensions and photon collimation systems used by each accelerator model.

62 RADIOLOGY AND NUCLEAR MEDICINE↗
DOE OSTI2015

SU-C-304-03: Experimental Investigation On the Accuracy of Plastic Scintillation Dosimeters in Small Fields

Purpose: To investigate the accuracy of the Exradin W1 (SI) and of an “in-house” plastic scintillation dosimeter (CHUQ PSD) in small radiation fields. Methods: Output factor (OF) measurements with the W1 and CHUQ PSD were performed for field sizes of 0.5 x 0.5, 1 x 1 and 2 x 2 cm{sup 2}. Both detectors were placed parallel to the central axis (CAX) in water. The spectrum discrimination calibration method was performed in each set-up to account for the Cerenkov (CRV) signal created in the fiber. The OFs were compared to the expected field factors in water derived using i) Monte Carlo (MC) simulations of an accurate accelerator model and ii) microLion (PTW) and D1V diode (SI) OFs. MC-derived correction factors were applied to both the microLion and D1V OFs. For the CHUQ PSD the calibration was repeated in water (// CAX), solid water (perpendicular to CAX) and under a shielded configuration. The signal was collected using a spectrometer (wavelength range = 185–1100 nm). Spectral analysis was performed to evaluate potential changes of the spectral distributions under the various calibration set-up configurations. Results: The W1 OFs presented an over-response for the 0.5 x 0.5 cm{sup 2} in the range of 3 – 4.1% relative to the expected field factor. The CHUQ PSD presented an under-response in the range of 1.5 – 2.7%, without accounting for volume averaging. The CRV spectra under the various calibration procedures appeared similar to each other and only minor changes were observed to the respective OFs. Conclusion: The W1 and CHUQ PSD can be used in small fields down to a 1 x 1 cm{sup 2} field size. Discrepancies were encountered between the two detectors for the smallest field size of 0.5 x 0.5 cm{sup 2} with the CHUQ PSD exhibiting a closer agreement to the expected field factor. Funding sources: 1) Alexander S. Onassis Public Benefit Foundation in Greece and 2) CREATE Medical Physics Research Training Network grant of the Natural Sciences and Engineering Research Council, Grant number: 432290, RGPIN-2014-06475.

46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗
DOE OSTI2015

Analysis of Anderson Acceleration on a Simplified Neutronics/Thermal Hydraulics System

ABSTRACT A standard method for solving coupled multiphysics problems in light water reactors is Picard iteration, which sequentially alternates between solving single physics applications. This solution approach is appealing due to simplicity of implementation and the ability to leverage existing software packages to accurately solve single physics applications. However, there are several drawbacks in the convergence behavior of this method; namely slow convergence and the necessity of heuristically chosen damping factors to achieve convergence in many cases. Anderson acceleration is a method that has been seen to be more robust and fast converging than Picard iteration for many problems, without significantly higher cost per iteration or complexity of implementation, though its effectiveness in the context of multiphysics coupling is not well explored. In this work, we develop a one-dimensional model simulating the coupling between the neutron distribution and fuel and coolant properties in a single fuel pin. We show that this model generally captures the convergence issues noted in Picard iterations which couple high-fidelity physics codes. We then use this model to gauge potential improvements with regard to rate of convergence and robustness from utilizing Anderson acceleration as an alternative to Picard iteration.

Toth, Alex↗
NASA NTRS2012

Properties of Ground Level Enhancement Events and the Associated Solar Eruptions During Solar Cycle 23

Solar cycle 23 witnessed the most complete set of observations of coronal mass ejections (CMEs) associated with the Ground Level Enhancement (GLE) events. We present an overview of the observed properties of the GLEs and those of the two associated phenomena, viz., flares and CMEs, both being potential sources of particle acceleration. Although we do not find a striking correlation between the GLE intensity and the parameters of flares and CMEs, the solar eruptions are very intense involving X-class flares and extreme CME speeds (average approx. 2000 km/s). An M7.1 flare and a 1200 km/s CME are the weakest events in the list of 16 GLE events. Most (80 %) of the CMEs are full halos with the three non-halos having widths in the range 167 to 212 degrees. The active regions in which the GLE events originate are generally large: 1290 msh (median 1010 msh) compared to 934 msh (median: 790 msh) for SEP-producing active regions. For accurate estimation of the CME height at the time of metric type II onset and GLE particle release, we estimated the initial acceleration of the CMEs using flare and CME observations. The initial acceleration of GLE-associated CMEs is much larger (by a factor of 2) than that of ordinary CMEs (2.3 km/sq s vs. 1 km/sq s). We confirmed the initial acceleration for two events for which CME measurements are available in the inner corona. The GLE particle release is delayed with respect to the onset of all electromagnetic signatures of the eruptions: type II bursts, low frequency type III bursts, soft X-ray flares and CMEs. The presence of metric type II radio bursts some 17 min (median: 16 min; range: 3 to 48 min) before the GLE onset indicates shock formation well before the particle release. The release of GLE particles occurs when the CMEs reach an average height of approx 3.09 R(sub s) (median: 3.18 R (sub s) ; range: 1.71 to 4.01 R (sub s) ) for well-connected events (source longitude in the range W20–W90). For poorly connected events, the average CME height at GLE particle release is ∼66 % larger (mean: 5.18 R (sub s) ; median: 4.61 R (sub s) ; range: 2.75–8.49 R (sub s) ). The longitudinal dependence is consistent with shock accelerations because the shocks from poorly connected events need to expand more to cross the field lines connecting to an Earth observer. On the other hand, the CME height at metric type II burst onset has no longitudinal dependence because electromagnetic signals do not require magnetic connectivity to the observer. For several events, the GLE particle release is very close to the time of first appearance of the CME in the coronagraphic field of view, so we independently confirmed the CME height at particle release. The CME height at metric type II burst onset is in the narrow range 1.29 to 1.8 R(sub s), with mean and median values of 1.53 and 1.47 R(sub s). The CME heights at metric type II burst onset and GLE particle release correspond to the minimum and maximum in the Alfven speed profile. The increase in CME speed between these two heights suggests an increase in Alfvenic Mach number from 2 to 3. The CME heights at GLE particle release are in good agreement with those obtained from the velocity dispersion analysis, including the source longitude dependence. We also discuss the implications of the delay of GLE particle release with respect to complex type III bursts by approx 18 min (median: 16 in; range: 2 to 44 min) for the flare acceleration mechanism. A similar analysis is also performed on the delay of particle release relative to the hard X-ray emission.

Geomagnetic Storms↗
DOE OSTI2021

A physics-based model for frost buildup under turbulent flow using direct numerical simulations

We present a new model for frost buildup under turbulent (and laminar) flow using direct numerical simulations. The physical model consists of two layers, the air and the frost. The air layer is fully resolved and consists of solving for the velocity, temperature, and vapor mass fraction fields. The frost layer thickness is resolved using conservation of mass and energy. Both phases are dynamically coupled using the immersed boundary method. Three-dimensional simulations are conducted in an open-channel configuration. A number of challenges need to be overcome to make these simulations feasible. First, to enforce far-field conditions of zero gradient and prescribed mean temperature and humidity, a source term is added to the energy and transport equations in the flow solver. Second, the mean frost thickness is subtracted after each time step to ensure a constant mean flow thickness and level of turbulence in the numerical domain. Third, a slow-time acceleration approach, which accelerates the frost buildup by a predetermined factor, is employed to bridge the gap between the fast turbulent and slow frost buildup time scales. Finally, a frost densification scheme is used to overcome the difficulties of vertically varying frost properties. The model is validated by comparing the frost thickness and frost thickness buildup rate over a period of one hour from a cooled flat plate experiment. As a result, both quantities compare favorably with experiments.

32 ENERGY CONSERVATION, CONSUMPTION, AND UTILIZATI↗
DOE OSTI2022

Detection of multi-reference character imbalances enables a transfer learning approach for virtual high throughput screening with coupled cluster accuracy at DFT cost

Appropriately identifying and treating molecules and materials with significant multi-reference (MR) character is crucial for achieving high data fidelity in virtual high-throughput screening (VHTS). Despite development of numerous MR diagnostics, the extent to which a single value of such a diagnostic indicates the MR effect on a chemical property prediction is not well established. We evaluate MR diagnostics for over 10 000 transition-metal complexes (TMCs) and compare to those for organic molecules. We observe that only some MR diagnostics are transferable from one chemical space to another. By studying the influence of MR character on chemical properties (i.e., MR effect) that involve multiple potential energy surfaces (i.e., adiabatic spin splitting, ΔE H–L , and ionization potential, IP), we show that differences in MR character are more important than the cumulative degree of MR character in predicting the magnitude of an MR effect. Motivated by this observation, we build transfer learning models to predict CCSD(T)-level adiabatic ΔE H–L and IP from lower levels of theory. By combining these models with uncertainty quantification and multi-level modeling, we introduce a multi-pronged strategy that accelerates data acquisition by at least a factor of three while achieving coupled cluster accuracy (i.e., to within 1 kcal mol –1 MAE) for robust VHTS.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2024

Voltage and temperature effects on low cobalt lithium-ion battery cathode degradation

Degradation of low cobalt lithium-ion cathodes was tested using a full factorial combination of upper cut-off voltage (4.0 V and 4.3 V vs. Li/Li + ) and operating temperature (25 °C and 60 °C). Half-cell batteries were analyzed with electrochemical and microstructural characterization methods. Electrochemical performance was assessed with galvanostatic cycling, cyclic voltammetry (CV), and electrochemical impedance spectroscopy (EIS) supported by distribution of relaxation times (DRT) analysis. Electrode microstructure was characterized with scanning electron microscopy (SEM), X-ray diffraction (XRD), and X-ray absorption near edge structure (XANES) imaging. Higher cut-off voltage cycling shows presence of NiO x formation, a low diffusivity rock-salt phase, in both CV and XRD data. XRD patterns confirmed that the rock-salt phase was beginning to form at the low cut-off voltage at high temperature, but in much lower intensity than at the high cut-off voltage. Higher temperature accelerates degradation processes at both voltages. Degradation factors at high temperature include NiO x formation, cathode material dissolution, and electrolyte decomposition. SEM analysis suggests that supporting phases may isolate and disconnect active material particles reducing capacity retention and battery life cycle. DRT analysis and XANES imaging show that both high temperature samples revealed a NiO x phase based on an increased diffusive impedance and a visible shift in the XANES spectra. The low cut-off voltage, high temperature sample showed a split peak and shift to lower energies indicating early formation of the NiO x phase. The diffusive impedance, which hinders intercalation and deintercalation, is driven by the formation of the NiO x phase. While primarily driven by cut-off voltage, elevated temperature also contributes to this degradation mechanism.

electrochemical impedance spectroscopy↗
DOE OSTI2018

Direct observation of dislocation structure evolution in SRF cavity niobium using electron channeling contrast imaging

Two major goals of superconducting radio frequency cavity research and development are achieving higher accelerating gradient and gaining the highest quality factor, a measure of efficiency. However, the consistent improvement of these performance metrics is restricted by many factors, one of which is microstructural defects, such as dislocation substructures within the material. In this work, dislocation evolution is compared in four samples extracted from a 2.8 mm thick large-grain niobium slice, with tensile axes chosen to generate specific dislocation structures during subsequent deformation. The four samples are (1) as-extracted, (2) extracted and annealed, (3) extracted and then deformed to 40% tensile strain, and (4) extracted, annealed at 800 °C 2 h, and then deformed to 40% strain. Electron channeling contrast imaging was performed on all samples to characterize initial dislocation density and dislocation structure evolution due to annealing and deformation, and related to the mechanical behavior observed in stress-strain curves. A fundamental understanding of dislocation evolution in niobium is necessary to develop computational models to simulate cavity forming, which could enable new processing methods for cavity fabrication to be identified that could lead to improved performance.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2025

Machine learning-accelerated path integral molecular dynamics simulations of reactive organic electrolytes

Hydrogen bonded electrolytes that exhibit accelerated proton transport via sequential reactive hops have drawn interest for their promise in clean energy applications. Molecular dynamics simulations of these electrolytes offer the opportunity to uncover microscopic mechanistic details that could be used to design and tune the properties of candidate electrolyte technologies. However, accurately modeling the proton transfer reactions and transport properties that give rise to high charge conductivites in these electrolytes proves computationally challenging because of the need to perform lengthy condensed phase simulations, treating both the electronic and nuclear degrees of freedom quantum mechanically. In this paper, we demonstrate that such a modeling task can be efficiently achieved with the use of density functional theory (DFT)-trained machine learning potentials (MLP) to accelerate path integral molecular dynamics (PIMD) simulations. We highlight the practical utility of this approach by using it to benchmark how closely PIMD simulations employing different DFT exchange–correlation functionals reproduce the composition-dependent densities, diffusion coefficients, and electrical conductivities of mixtures consisting of imidazole and levulinic acid. Even with the speedup afforded by our MLPs, PIMD simulations remain quite expensive. Furthermore, in order to render PIMD more computationally tractable, we introduce and benchmark the accuracy of a ring polymer contraction approach that leverages a computationally efficient short-range MLP to accelerate our PIMD simulations by an additional factor of four.

Chemical bonding↗
DOE OSTI2017

An alternative to the Λcdm model: the case of scale invariance

The hypothesis is made that, at large scales where general relativity may be applied, empty space is scale invariant. This establishes a relation between the cosmological constant and the scale factor λ of the scale-invariant framework. This relation brings major simplifications in the scale-invariant equations for cosmology, which contain a new term, depending on the derivative of the scale factor, that opposes gravity and produces an accelerated expansion. The displacements due to the acceleration term make a high contribution Ω{sub λ} to the energy density of the universe, satisfying an equation of the form Ω{sub m}+Ω{sub k}+Ω{sub λ}=1. The models do not demand the existence of unknown particles. There is a family of flat models with different density parameters Ω{sub m}<1. Numerical integrations of the cosmological equations for different values of the curvature and density parameter k and Ω{sub m} are performed. The presence of even tiny amounts of matter in the universe tends to kill scale invariance. The point is that for Ω{sub m}=0.3 the effect is not yet completely killed. Models with non-zero density start explosively with a braking phase followed by a continuously accelerating expansion. Several observational properties are examined, in particular the distances, the m–z diagram, and the Ω{sub m} versus Ω{sub λ} plot. Comparisons with observations are also performed for the Hubble constant H{sub 0} versus Ω{sub m}, for the expansion history in the plot H(z)/(z+1) versus redshift z, and for the transition redshift from braking to acceleration. These first dynamical tests are satisfied by scale-invariant models, which thus deserve further study.

79 ASTRONOMY AND ASTROPHYSICS↗
NASA NTRS1976

Crack propagation and arrest in pressurized containers

The problem of crack propagation and arrest in a finite volume cylindrical container filled with pressurized gas is considered. It is assumed that the cylinder contains a symmetrically located longitudinal part-through crack with a relatively small net ligament. The net ligament suddenly ruptures initiating the process of fracture propagation and depressurization in the cylinder. Thus the problem is a coupled gas dynamics and solid mechanics problem the exact formulation of which does not seem to be possible. The problem is reduced to a proper initial value problem by introducing a dynamic fracture criterion which relates the crack acceleration to the difference between a load factor and the corresponding strength parameter. The results indicate that generally in gas filled cylinders fracture arrest is not possible unless the material behaves in a ductile manner and the container is relatively long.

Erdogan, F.↗
NASA NTRS1977

Crack propagation and arrest in pressurized containers

The problem of crack propagation and arrest in a finite volume cylindrical container filled with pressurized gas is considered. It is assumed that the cylinder contains a symmetrically located longitudinal part-through crack with a relatively small net ligament. The net ligament suddenly ruptures initiating the process of fracture propagation and depressurization in the cylinder. The problem is formulated by making two major assumptions, namely, that the shell problem is quasi-static and the gas dynamics problem is one-dimensional. The problem is reduced to a proper initial value problem by introducing a dynamic fracture criterion which relates the crack acceleration to the difference between a load factor and the corresponding strength parameter. The main results are demonstrated by considering two examples, an aluminum cylinder which may behave in a quasi-brittle manner, and a steel cylinder which undergoes ductile fracture. The results indicate that generally in gas-filled cylinders fracture arrest is not possible unless the material behaves in a ductile manner and the container is relatively long.

Erdogan, F.↗
NASA NTRS1982

Analysis and design of steady transonic flow over airfoils by the method of parametric differentiation

The results reported here are based on applying the method of parametric differentiation (MPD) to transform the nonlinear differential equation governing small-disturbance transonic flow to a linear equation. Implicit approximate factorization and monotone methods were used to accelerate convergence of the linear problem by an order of magnitude over successive line over-relaxation. The relative merits of using MPD are discussed in comparison to conventional small-disturbance applications. Several MPD analyses are performed on an array of airfoils. A design procedure utilizing MPD is discussed and demonstrated for two nonlifting cases.

Halt, D. W.↗