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At least 991 records · Page 55

Space shuttle active-pogo-suppressor control design using linear quadratic regulator techniques

Two methods of active pogo suppression (stabilization) for the space shuttle vehicle were studied analytically. The basis for both approaches was the linear quadratic regulator, state space technique. The first approach minimized root-mean-square pump inlet pressure by using either fullstate feedback, partial-state feedback, or output feedback with a Kalman filter. The second approach increased the modal damping associated with the critical structural modes by using either full-state feedback or reconstructed state feedback. A number of implementable controls were found by both approaches. The designs were analyzed with respect to sensitivity, complexity, and controller energy requirements, as well as controller performance. Practical controllers resulting from the two design approaches tended to use pressure and flow as feedback variables for the minimum-rms method and structural accelerations or velocities for the modal control method. Both approaches are suitable for the design of active pogo-suppression controllers.

Lehtinen, B.↗

Solid surface wetting and the deployment of drops in microgravity

The complete or partial deployment of liquid samples in low gravity is primarily influenced by the interfacial properties of the specific liquid and solid materials used because the overwhelming bias of the Earth gravitational acceleration is removed. This study addresses the engineering aspects of injecting and deploying drops of prescribed volume into an acoustic positioning chamber in microgravity. The specific problems of interest are the design, testing, and implementation of injector tips to be used in a simultaneously retracting dual-injector system in the Drop Physics Module microgravity experiment facility. Prior to release, the liquid to be deployed must be retained within a restricted area at the very end of the injectors under dynamic stimuli from the continuous injection flow as well as from the stepped motion of the injectors. The final released drop must have a well determined volume and negligible residual linear or angular momentum. The outcome of Earth-based short-duration low gravity experiments had been the selection of two types of injector tips which were flown as back-up parts. They were successfully utilized during the USML-1 Spacelab mission as the primary tips. The combination of a larger contact surface, liquid pinning with a sharp edge, and selective coating of strategic tip surfaces with a non-wetting compound has allowed a significant increase in the success rate of deployment of simple and compound drops of aqueous solutions of glycerol and silicone oil. The diameter of the samples studied in the Drop Physics Module range between 0.3 and 2.7 cm. The tests conducted on-orbit with a manually operated small device have allowed the calibration of the volume deployed for a few drop sizes. The design for improved tips to be used during the next USML flight is based on these results.

Trinh, E. H.↗

Cell killing and chromatid damage in primary human bronchial epithelial cells irradiated with accelerated 56Fe ions

We examined cell killing and chromatid damage in primary human bronchial epithelial cells irradiated with high-energy 56Fe ions. Cells were irradiated with graded doses of 56Fe ions (1 GeV/nucleon) accelerated with the Alternating Gradient Synchrotron at Brookhaven National Laboratory. The survival curves for cells plated 1 h after irradiation (immediate plating) showed little or no shoulder. However, the survival curves for cells plated 24 h after irradiation (delayed plating) had a small initial shoulder. The RBE for 56Fe ions compared to 137Cs gamma rays was 1.99 for immediate plating and 2.73 for delayed plating at the D10. The repair ratio (delayed plating/immediate plating) was 1.67 for 137Cs gamma rays and 1.22 for 56Fe ions. The dose-response curves for initially measured and residual chromatid fragments detected by the Calyculin A-mediated premature chromosome condensation technique showed a linear response. The results indicated that the induction frequency for initially measured fragments was the same for 137Cs gamma rays and 56Fe ions. On the other hand, approximately 85% of the fragments induced by 137Cs gamma rays had rejoined after 24 h of postirradiation incubation; the corresponding amount for 56Fe ions was 37%. Furthermore, the frequency of chromatid exchanges induced by gamma rays measured 24 h after irradiation was higher than that induced by 56Fe ions. No difference in the amount of chromatid damage induced by the two types of radiations was detected when assayed 1 h after irradiation. The results suggest that high-energy 56Fe ions induce a higher frequency of complex, unrepairable damage at both the cellular and chromosomal levels than 137Cs gamma rays in the target cells for radiation-induced lung cancers.

NASA Discipline Radiation Health↗

Track Structure and the Biological Effectiveness of Accelerated Particles for the Induction of Chromosome Damage

Track structure models predict that at a fixed value of LET, particles with lower charge number, Z will have a higher biological effectiveness compared to particles with a higher Z. In this report we investigated how track structure effects induction of chromosomal aberration in human cells. Human lymphocytes were irradiated in vitro with various energies of accelerated iron, silicon, neon, or titanium ions and chromosome damage was assessed in using three color FISH chromosome painting in chemically induced PCC samples collected a first cell division post irradiation. The LET values for these ions ranged from 30 to195 keV/micron. Of the particles studied, Neon ions have the highest biological effectiveness for induction of total chromosome damage, which is consistent with track structure model predictions. For complex-type exchanges 64 MeV/ u Neon and 450 MeV/u Iron were equally effective and induced the most complex damage. In addition we present data on chromosomes exchanges induced by six different energies of protons (5 MeV/u to 2.5 GeV/u). The linear dose response term was similar for all energies of protons suggesting that the effect of the higher LET at low proton energies is balanced by the production of nuclear secondaries from the high energy protons.

George, K.↗

The Biological Effectiveness of Accelerated Particles for the Induction of Chromosome Damage: Track Structure Effects and Cytogenetic Signatures of High-LET Exposure

Track structure models predict that at a fixed value of LET, particles with lower charge number, Z will have a higher biological effectiveness compared to particles with a higher Z. In this report we investigated how track structure effects induction of chromosomal aberration in human cells. Human lymphocytes were irradiated in vitro with various energies of accelerated iron, silicon, neon, or titanium ions and chromosome damage was assessed in using three color FISH chromosome painting in chemically induced PCC samples collected a first cell division post irradiation. The LET values for these ions ranged from 30 to 195 keV/micrometers. Of the particles studied, Neon ions have the highest biological effectiveness for induction of total chromosome damage, which is consistent with track structure model predictions. For complex-type exchanges 64 MeV/ u Neon and 450 MeV/u Iron were equally effective and induced the most complex damage. In addition we present data on chromosomes exchanges induced by six different energies of protons (5 MeV/u to 2.5 GeV/u). The linear dose response term was similar for all energies of protons suggesting that the effect of the higher LET at low proton energies is balanced by the production of nuclear secondaries from the high energy protons. All energies of protons have a much higher percentage of complex-type chromosome exchanges than gamma rays, signifying a cytogenetic signature for proton exposures.

George, K.↗

Accretion onto magnetized neutron stars - Normal mode analysis of the interchange instability at the magnetopause

Results are reported for a linearized hydromagnetic stability analysis of the magnetopause of an accreting neutron star. The magnetosphere is assumed to be slowly rotating, and the plasma just outside the magnetopause is assumed to be weakly magnetized. The plasma layer is assumed to be bounded above by a shock wave and to be thin compared with the radius of the magnetosphere. Under these circumstances, the growing modes are shown to be localized in the direction parallel to the zero-order magnetic field, but the structure of the modes is still similar to the flute mode. An expression for the growth rate at each magnetic latitude is obtained in terms of the magnitude of the gravitational acceleration normal to the surface, the azimuthal mode number, the radius of the magnetosphere, the height of the shock above the magnetopause, and the effective Atwood number which embodies the stabilizing effects of favorable curvature and magnetic tension. The effective Atwood number is calculated, and the stabilizing effects of viscosity and aligned flow parallel to the magnetopause are discussed.

Arons, J.↗

Broadening of looplike solar coronal transients

The broadening of the tops of nine outwardly expanding looplike coronal mass-ejection transients observed during 1973-1974 and 1980 has been examined. Five of the nine transients exhibit increased breadth with time (height); although the rates vary widely, no event shows an increase which can be fitted by a power-law form with a greater-than-linear increase with height. The breadth of four events decreases with height. When all nine events are considered together, the transient breadth with height is fitted with an expression h varies as R exp 0.48 with large scatter. In addition, measurements of the total observed loop length of the nine transients show that this length L varies as R exp 1.30. Both of these results are contrary to the predictions of one model of loop expulsion as a result of an assumed azimuthal magnetic field gradient. Finally, when combined with the facts that looplike mass ejections are usually associated with the occurrence of eruptive prominences, and that such mass ejections are generally accelerated through the corona, it is found that the observed variation of transient breadth with height contradicts some characteristics of self-similar fluid flow which have been ascribed to mass-ejection transients.

Macqueen, R. M.↗

A finite element model of conduction, convection, and phase change near a solid/melt interface

Detailed understanding of heat transfer and fluid flow is required for many aerospace thermal systems. These systems often include phase change and operate over a range of accelerations or effective gravitational fields. An approach to analyzing such systems is presented which requires the simultaneous solution of the conservation laws of energy, momentum, and mass, as well as an equation of state. The variable property form of the governing equations are developed in two-dimensional Cartesian coordinates for a Newtonian fluid. A numerical procedure for solving the governing equations is presented and implemented in a computer program. The Galerkin form of the finite element method is used to solve the spatial variation of the field variables, along with the implicit Crank-Nicolson time marching algorithm. Quadratic Langrangian elements are used for the internal energy and the two components of velocity. Linear Lagrangian elements are used for the pressure. The location of the solid/liquid interface as well as the temperatures are determined form the calculated internal energy and pressure. This approach is quite general in that it can describe heat transfer without phase change, phase change with a sharp interface, and phase change without an interface. Analytical results from this model are compared to those of other researchers studying transient conduction, convection, and phase change and are found to be in good agreement. The numerical procedure presented requires significant computer resources, but this is not unusual when compared to similar studies by other researchers. Several methods are suggested to reduce the computational times.

Viterna, Larry A.↗

Precomputing Process Noise Covariance for Onboard Sequential Filters

Process noise is often used in estimation filters to account for unmodeled and mismodeled accelerations in the dynamics. The process noise covariance acts to inflate the state covariance over propagation intervals, increasing the uncertainty in the state. In scenarios where the acceleration errors change significantly over time, the standard process noise covariance approach can fail to provide effective representation of the state and its uncertainty. Consider covariance analysis techniques provide a method to precompute a process noise covariance profile along a reference trajectory using known model parameter uncertainties. The process noise covariance profile allows significantly improved state estimation and uncertainty representation over the traditional formulation. As a result, estimation performance on par with the consider filter is achieved for trajectories near the reference trajectory without the additional computational cost of the consider filter. The new formulation also has the potential to significantly reduce the trial-and-error tuning currently required of navigation analysts. A linear estimation problem as described in several previous consider covariance analysis studies is used to demonstrate the effectiveness of the precomputed process noise covariance, as well as a nonlinear descent scenario at the asteroid Bennu with optical navigation.

onboard↗

Solid Surface Wetting and the Deployment of Drops in Microgravity

The complete or partial deployment of liquid samples in low gravity is primarily influenced by the interfacial properties of the specific liquid and solid materials used because the overwhelming bias of the Earth gravitational acceleration is removed. This study addresses the engineering aspects of injecting and deploying drops of prescribed volume into an acoustic positioning chamber in microgravity. The specific problems of interest are the design, testing, and implementation of injector tips to be used in a simuttaneously retracting dual-injector system used in the Drop Physics Module microgravity experiment facility. Prior to release, the liquid to be deployed must be retained within a restricted area at the very end of the injectors even under dynamic stimuli due to continuous injection flow as well as to the stepped motion of the injectors, and the final released drop must have a well determined volume as well as negligible residual linear or angular momentum from the deployment process. The outcome of Earthbased short-duration low gravity experiments had been the selection of two types of injector tips which were flown as back-up parts and were successfully utilized during the USML-1 Spacelab mission. The combination of a larger contact surface, liquid pinning with a sharp edge, and selective coating of strategic tip surfaces with a non-wetting compound has allowed a significant increase in the success rate of deployment of simple and compound drops of aqueous solutions of glycerol and silicone oil. The diameter of the samples studied in the Drop Physics Module ranged between 0.3 and 2.7 cm. The tests conducted onsrbit with a manually operated small device have allowed the calibration of the volume deployed for a few drop sizes. The design for improved tips to be used during the next USML flight is based on these results.

Trinh, E. H.↗

Project Management Using Modern Guidance, Navigation and Control Theory

The idea of control theory and its application to project management is not new, however literature on the topic and real-world applications is not as readily available and comprehensive in how all the principals of Guidance, Navigation and Control (GN&C) apply. This paper will address how the fundamental principals of modern GN&C Theory have been applied to NASA's Constellation Space Suit project and the results in the ability to manage the project within cost, schedule and budget. A s with physical systems, projects can be modeled and managed with the same guiding principles of GN&C as if it were a complex vehicle, system or software with time-varying processes, at times non-linear responses, multiple data inputs of varying accuracy and a range of operating points. With such systems the classic approach could be applied to small and well-defined projects; however with larger, multi-year projects involving multiple organizational structures, external influences and a multitude of diverse resources, then modern control theory is required to model and control the project. The fundamental principals of G N&C stated that a system is comprised of these basic core concepts: State, Behavior, Control system, Navigation system, Guidance and Planning Logic, Feedback systems. The state of a system is a definition of the aspects of the dynamics of the system that can change, such as position, velocity, acceleration, coordinate-based attitude, temperature, etc. The behavior of the system is more of what changes are possible rather than what can change, which is captured in the state of the system. The behavior of a system is captured in the system modeling and if properly done, will aid in accurate system performance prediction in the future. The Control system understands the state and behavior of the system and feedback systems to adjust the control inputs into the system. The Navigation system takes the multiple data inputs and based upon a priori knowledge of the input, will develop a statistical-based weighting of the input to determine where the system currently is located. Guidance and Planning logic of the system with the understanding of where it is (provided by the navigation system) will in turn determine where it needs to be and how to get there. Lastly, the system Feedback system is the right arm of the control system to allow it to affect change in the overall system and therefore it is critical to not only correctly identify the system feedback inputs but also the system response to the feedback inputs. And with any systems project it is critical that the objective of the system be clearly defined for not only planning but to be used to measure performance and to aid in the guidance of the system or project.

Hill, Terry↗

Alleviation of whirl-flutter on a joined-wing tilt-rotor aircraft configuration using active controls

The feasibility of using active controls to delay the onset of whirl-flutter on a joined-wing tilt rotor aircraft was investigated. The CAMRAD/JA code was used to obtain a set of linear differential equations which describe the motion of the joined-wing tilt-rotor aircraft. The hub motions due to wing/body motion is a standard input to CAMRAD/JA and were obtained from a structural dynamics model of a representative joined-wing tilt-rotor aircraft. The CAMRAD/JA output, consisting of the open-loop system matrices, and the airframe free vibration motion were input to a separate program which performed the closed-loop, active control calculations. An eigenvalue analysis was performed to determine the flutter stability of both open- and closed-loop systems. Sensor models, based upon the feedback of pure state variables and based upon hub-mounted sensors, providing physically measurable accelerations, were evaluated. It was shown that the onset of tilt-rotor whirl-flutter could be delayed from 240 to above 270 knots by feeding back vertical and span-wise accelerations, measured at the rotor hub, to the longitudinal cyclic pitch. Time response calculations at a 270-knot cruise condition showed an active cyclic pitch control level of 0.009 deg, which equates to a very acceptable 9 pound active-control force applied at the rotor hub.

Vanaken, Johannes M.↗

Genetic and molecular dosimetry of HZE radiation (US-1 RADIAT)

In order to estimate radiation exposure in space, experiments were conducted during the 1st International Microgravity Laboratory (IML-1) mission in order to isolate genetic changes in animal cells caused by cosmic rays. The space measurements were evaluated against results from synthetic cosmic rays produced by particle accelerators on the ground. The biological material used was the tiny soil nematode, Caenorhabditis elegans. The measurements were made by thermoluminescent detectors and plastic nuclear track detectors. The development and the chromosome mechanics in microgravity were studied, and the mutagenesis induced by radiation exposure was analyzed. The results showed that there are no obvious differences in the development, behavior and chromosome mechanics, as a function of gravity unloading (reproduction, self-fertilization and mating of males with hermaphrodites, gross anatomy, symmetry and gametogenesis, pairing, disjoining and recombination of chromosomes). A variety of mutants were isolated, and it was noted that mutants isolated from regions of identified high particles were more severely affected than those isolated by random screening. Linear energy transfer particles seem to favor large scale genetic lesions.

Nelson, Gregory A.↗

Experimental Study of Large-Amplitude Faraday Waves in Rectangular Cylinders

Experiment on single-mode Faraday waves having two, thee, and four wavelengths across a rectangular cylinder of high aspect ratio is the subject of discussion. Previous experiments recently done by Henderson & Miles (1989) and by Lei Jiang et. a1 (1996) focused on Faraday waves with one and two wavelengths across rectangular cylinders. In this experimental study the waves steepness ranges from small at threshold levels to a large amplitude which according to Penny & Price theory (1952) approaches the maximum sustainable amplitude for a standing wave. The waves characteristics for small amplitudes are evaluated against an existing well known linear theory by Benjamin & Ursell (l954) and against a weakly nonlinear theory by J. Miles (1984) which includes the effect of viscous damping. The evaluation includes the wave neutral stability and damping rate. In addition, a wave amplitude differential equation of a linear theory including viscous effect by Cerda & Tirapegui (1998) is solved numerically to yield prediction of temporal profiles of both wave damping and wave formation at the threshold. An interesting finding from this exercise is that the fluid kinematic viscosity needs to increase ten times in order to obtain good agreement between the theoretical prediction and the experimental data for both wave damping and wave starting. For large amplitude waves, the experimental data are evaluated against the theory of Penny & Price which predicts wave characteristics of any amplitude up to the point at which the wave reaches its maximum amplitude attainable for a standing wave. The theory yields two criteria to show the maximum wave steepness, the vertical acceleration at the wave crest of half the earth gravity field acceleration and the including angle at the crest of 90 degrees. Comparison with experimental data shows close agreement for the wave crest acceleration but a large discrepancy for the including angle. Additional information is included in the original extended abstract.

Iek, Chanthy↗

Optimized Trajectory Correction Burn Placement for the NASA Artemis II Mission

The NASA Artemis II mission represents the first time humans plan to return to the lunar vicinity in over 50 years with a crew traveling to the Moon in the Orion spacecraft on a free return trajectory. This first crewed mission of the Artemis program will evaluate human-rated elements of Orion in preparation to sending astronauts to the lunar surface. The selected free-return cislunar trajectory profile that is reminiscent of the Apollo 8 mission that nominally requires no additional translational burns following the trans-lunar injection (TLI) burn. Due to crew activity, maneuver execution errors, navigation uncertainty, orbit insertion errors, disturbance accelerations, and other system limitations; periodic trajectory corrections burns are necessary to ensure proper entry interface (EI) conditions are satisfied for a safe return to Earth. Robust trajectory optimization techniques are utilized to determine the optimized placements for the Artemis II trajectory correction burns that accounts for the crew schedule, both the primary and backup navigation systems, targeting strategies and burn plan configurations, spacecraft venting, thruster selection, and the integrated GN&C performance.

Linear Covariance Analysis↗

A Simulated Spectrum of Convectively Generated Gravity Waves: Propagation from the Tropopause to the Mesopause and Effects on the Middle Atmosphere

This work evaluates the interaction of a simulated spectrum of convectively generated gravity waves with realistic middle atmosphere mean winds. The wave spectrum is derived from the nonlinear convection model described by Alexander et al. that simulated a two-dimensional midlatitude squall line. This spectrum becomes input to a linear ray tracing model for evaluation of wave propagation as a function of height through climatological background wind and buoyancy frequency profiles. The energy defined by the spectrum as a function of wavenumber and frequency is distributed spatially and temporally into wave packets for the purpose of estimating wave amplitudes at the lower boundary of the ray tracing model. A wavelet analysis provides an estimate of these wave packet widths in space and time. Without this redistribution of energies into wave packets the Fourier analysis alone inaccurately assumes the energy is evenly distributed throughout the storm model domain. The growth with height of wave amplitudes is derived from wave action flux conservation coupled to a convective instability saturation condition. Mean flow accelerations and wave energy dissipation profiles are derived from this analysis and compared to parameterized estimates of gravity wave forcing, providing a measure of the importance of the storm source to global gravity wave forcing. The results suggest that a single large convective storm system like the simulated squall line could provide a significant fraction of the zonal mean gravity wave forcing at some levels, particularly in the mesosphere. The vertical distributions of mean flow acceleration and energy dissipation do not much resemble the parameterized profiles in form because of the peculiarities of the spectral properties of the waves from the storm source. The ray tracing model developed herein provides a tool for examining the role of convectively generated waves in middle atmosphere physics.

Alexander, Joan↗

A Simulated Spectrum of Convectively Generated Gravity Waves: Propagation from the Tropopause to the Mesopause and Effects on the Middle Atmosphere

This work evaluates the interaction of a simulated spectrum of convectively generated gravity waves with realistic middle atmosphere mean winds. The wave spectrum is derived from the nonlinear convection model described by Alexander et al. [1995] that simulated a two-dimensional midlatitude squall line. This spectrum becomes input to a linear ray tracing model for evaluation of wave propagation as a function of height through climatological background wind and buoyancy frequency profiles. The energy defined by the spectrum as a function of wavenumber and frequency is distributed spatially and temporally into wave packets for the purpose of estimating wave amplitudes at the lower boundary of the ray tracing model. A wavelet analysis provides an estimate of these wave packet widths in space and time. Without this redistribution of energies into wave packets the Fourier analysis alone inaccurately assumes the energy is evenly distributed throughout the storm model domain. The growth with height of wave amplitudes is derived from wave action flux conservation coupled to a convective instability saturation condition. Mean flow accelerations and wave energy dissipation profiles are derived from this analysis and compared to parameterized estimates of gravity wave forcing, providing a measure of the importance of the storm source to global gravity wave forcing. The results suggest that a single large convective storm system like the simulated squall line could provide a significant fraction of the zonal mean gravity wave forcing at some levels, particularly in the mesosphere. The vertical distributions of mean flow acceleration and energy dissipation do not much resemble the parameterized profiles in form because of the peculiarities of the spectral properties of the waves from the storm source. The ray tracing model developed herein provides a tool for examining the role of convectively generated waves in middle atmosphere physics.

Alexander, M. Joan↗

Augmenting Parametric Optimal Ascent Trajectory Modeling with Graph Theory

It has been well documented that decisions made in the early stages of Conceptual and Pre-Conceptual design commit up to 80% of total Life-Cycle Cost (LCC) while engineers know the least about the product they are designing [1]. Once within Preliminary and Detailed design however, making changes to the design becomes far more difficult to enact in both cost and schedule. Primarily this has been due to a lack of detailed data usually uncovered later during the Preliminary and Detailed design phases. In our current budget-constrained environment, making decisions within Conceptual and Pre-Conceptual design which minimize LCC while meeting requirements is paramount to a program's success. Within the arena of launch vehicle design, optimizing the ascent trajectory is critical for minimizing the costs present within such concerns as propellant, aerodynamic, aeroheating, and acceleration loads while meeting requirements such as payload delivered to a desired orbit. In order to optimize the vehicle design its constraints and requirements must be known, however as the design cycle proceeds it is all but inevitable that the conditions will change. Upon that change, the previously optimized trajectory may no longer be optimal, or meet design requirements. The current paradigm for adjusting to these updates is generating point solutions for every change in the design's requirements [2]. This can be a tedious, time-consuming task as changes in virtually any piece of a launch vehicle's design can have a disproportionately large effect on the ascent trajectory, as the solution space of the trajectory optimization problem is both non-linear and multimodal [3]. In addition, an industry standard tool, Program to Optimize Simulated Trajectories (POST), requires an expert analyst to produce simulated trajectories that are feasible and optimal [4]. In a previous publication the authors presented a method for combatting these challenges [5]. In order to bring more detailed information into Conceptual and Pre-Conceptual design, knowledge of the effects originating from changes to the vehicle must be calculated. In order to do this, a model capable of quantitatively describing any vehicle within the entire design space under consideration must be constructed. This model must be based upon analysis of acceptable fidelity, which in this work comes from POST. Design space interrogation can be achieved with surrogate modeling, a parametric, polynomial equation representing a tool. A surrogate model must be informed by data from the tool with enough points to represent the solution space for the chosen number of variables with an acceptable level of error. Therefore, Design Of Experiments (DOE) is used to select points within the design space to maximize information gained on the design space while minimizing number of data points required. To represent a design space with a non-trivial number of variable parameters the number of points required still represent an amount of work which would take an inordinate amount of time via the current paradigm of manual analysis, and so an automated method was developed. The best practices of expert trajectory analysts working within NASA Marshall's Advanced Concepts Office (ACO) were implemented within a tool called multiPOST. These practices include how to use the output data from a previous run of POST to inform the next, determining whether a trajectory solution is feasible from a real-world perspective, and how to handle program execution errors. The tool was then augmented with multiprocessing capability to enable analysis on multiple trajectories simultaneously, allowing throughput to scale with available computational resources. In this update to the previous work the authors discuss issues with the method and solutions.

Patrick D Dees↗