Engineering Papers⌕ Search

SEARCH · Engineering Papers

Results for “Differential”

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 37 records · Page 2

Studies of aircraft differential maneuvering. Report 75-27: Calculating of differential-turning barrier surfaces. Report 75-26: A user's guide to the aircraft energy-turn and tandem-motion computer programs. Report 75-7: A user's guide to the aircraft energy-turn hodograph program

The numerical analysis of composite differential-turn trajectory pairs was studied for 'fast-evader' and 'neutral-evader' attitude dynamics idealization for attack aircraft. Transversality and generalized corner conditions are examined and the joining of trajectory segments discussed. A criterion is given for the screening of 'tandem-motion' trajectory segments. Main focus is upon the computation of barrier surfaces. Fortunately, from a computational viewpoint, the trajectory pairs defining these surfaces need not be calculated completely, the final subarc of multiple-subarc pairs not being required. Some calculations for pairs of example aircraft are presented. A computer program used to perform the calculations is included.

Kelley, H. J.↗

Parallels between control PDE's (Partial Differential Equations) and systems of ODE's (Ordinary Differential Equations)

System theorists understand that the same mathematical objects which determine controllability for nonlinear control systems of ordinary differential equations (ODEs) also determine hypoellipticity for linear partial differentail equations (PDEs). Moreover, almost any study of ODE systems begins with linear systems. It is remarkable that Hormander's paper on hypoellipticity of second order linear p.d.e.'s starts with equations due to Kolmogorov, which are shown to be analogous to the linear PDEs. Eigenvalue placement by state feedback for a controllable linear system can be paralleled for a Kolmogorov equation if an appropriate type of feedback is introduced. Results concerning transformations of nonlinear systems to linear systems are similar to results for transforming a linear PDE to a Kolmogorov equation.

Hunt, L. R.↗

Differential geometry techniques for sets of nonlinear partial differential equations

An attempt is made to show that the Cartan theory of partial differential equations can be a useful technique for applied mathematics. Techniques for finding consistent subfamilies of solutions that are generically rich and well-posed and for introducing potentials or other usefully consistent auxiliary fields are introduced. An extended sample calculation involving the Korteweg-de Vries equation is given.

Estabrook, Frank B.↗

Differential response of the photosynthetic machinery to dehydration in older and younger resurrection plants

Abstract A group of vascular plants called homoiochlorophyllous resurrection plants evolved unique capabilities to protect their photosynthetic machinery against desiccation-induced damage. This study examined whether the ontogenetic status of the resurrection plant Craterostigma pumilum has an impact on how the plant responds to dehydration at the thylakoid membrane level to prepare cells for the desiccated state. Thus, younger plants (<4 months) were compared with their older (>6 months) counterparts. Ultrastructural analysis provided evidence that younger plants suppressed senescence-like programs that are realized in older plants. During dehydration, older plants degrade specific subunits of the photosynthetic apparatus such as the D1 subunit of PSII and subunits of the cytochrome b6f complex. The latter leads to a controlled down-regulation of linear electron transport. In contrast, younger plants increased photoprotective high-energy quenching mechanisms and maintained a high capability to replace damaged D1 subunits. It follows that depending on the ontogenetic state, either more degradation-based or more photoprotective mechanisms are employed during dehydration of Craterostigma pumilum.

Plant Sciences↗

Data for A Role for Differential Rubisco Activase Isoform Expression in C4 Bioenergy Grasses at High Temperature

Rubisco activase (Rca) facilitates the release of sugar-phosphate inhibitors at Rubisco catalytic sites during CO2 fixation. Most plant species express two Rca isoforms, the larger Rca-α and the shorter Rca-β, either by alternative splicing from a single gene or expression from separate genes. The mechanism of Rubisco activation by Rca isoforms has been intensively studied in C3 plants. However, the functional role of Rca in C4 plants where Rubisco and Rca are located in a much higher [CO2] compartment is less clear. In this study, we selected four C4 bioenergy grasses and the model C4 grass setaria ( Setaria viridis ) to investigate the role of Rca in C4 photosynthesis. All five C4 grass species contained two Rca genes, one encoding Rca-α and the other Rca-β, which were positioned closely together in the genomes. A variety of abiotic stress-related motifs were identified in the Rca-α promoter of each grass, and while the Rca-β gene was constantly highly expressed at ambient temperature, Rca-α isoforms were expressed only at high temperature but never surpassed 30% of Rca-β content. The pattern of Rca-α induction on transition to high temperature and reduction on return to ambient temperature was the same in all five C4 grasses. In sorghum ( Sorghum bicolor ), sugarcane ( Saccharum officinarum ), and setaria, the induction rate of Rca-α was similar to the recovery rate of photosynthesis and Rubisco activation at high temperature. This association between Rca-α isoform expression and maintenance of Rubisco activation at high temperature suggests that Rca-α has a functional thermo-protective role in carbon fixation in C4 grasses by sustaining Rubisco activation at high temperature.

Genomics↗

APOLLO: a facility-scale differentiable virtual accelerator at Fermilab FAST/IOTA

As the design complexity of modern accelerators grows, there is more interest in using advanced simulations that have fast execution time or yield additional insights like gradients. The FAST/IOTA facility has been working on implementing and experimentally validating an end-to-end digital twin that is both fast and gradient-aware, allowing for rapid prototyping of new software and experiments with minimal beam time costs. Our framework integrates physics and ML codes for linac and ring simulation through a set of generic interfaces between surrogate and physics-based sections. To reproduce device inputs and outputs, system state is exposed as a deterministic event loop in a specialized discrete event simulator architecture. Because Fermilab is undergoing control system transition, several APIs were implemented as final user interfaces - a fully asynchronous EPICS soft IOC, a gRPC-based Data Pool Manager (DPM), and legacy ACNET protocols. We discuss implementation details as well as challenges handling live data assimilation and future plans to extend modelling to main complex proton accelerators like PIPII and Booster.

Kuklev, Nikita [Fermilab]↗

Phospholipase D and phosphatidylinositol-4-phosphate 5-kinase 1 are involved in the regulation of oligodendrocyte morphological differentiation

Highlights: • PLD and PIP5K1 are involved in the regulation of oligodendroglial cell morphological differentiation. • Inhibition of PLD or PIP5K1 decreases differentiation or myelin marker expression. • PLD and PIP5K1 regulate differentiation of oligodendrocyte precursor cells. • Inhibition of PLD or PIP5K1 decreases differentiation marker expression of oligodendrocyte precursor cells. Oligodendroglial cells (oligodendrocytes) differentiate to form the myelin that wraps neuronal axons in the central nervous system (CNS). This myelin sheath supports the propagation of saltatory conduction and protects axons from physical stresses. When oligodendrocytes do not normally differentiate to myelinate axons, their key functions as oligodendrocytes in the CNS are severely impaired. The molecular mechanics that control differentiation still remain to be clarified. Arf6 belongs to the small GTPase family and is known to be a positive regulator of oligodendrocyte differentiation. Here, we show that the phospholipase D (PLD) and phosphatidylinositol-4-phosphate 5-kinase 1 (PIP5K1) molecules, the major effectors of Arf6, are involved in the regulation of oligodendrocyte differentiation. Knockdown of PLD1 or PIP5K type 1γ (PIP5K1C) by their respective specific siRNAs in mouse oligodendroglial FBD-102b cells inhibited morphological differentiation into structures bearing myelin-like processes; this finding is consistent with the concurrent changes in expression of differentiation and myelin marker proteins. Treatment with VU0155069 or UNC3230, specific inhibitors of PLD and PIP5K1, respectively, blunted morphological differentiation and decreased expression of myelin and differentiation marker proteins. Similar results have been obtained in studies using primary oligodendrocytes. These results suggest that the major Arf6 effector molecules PLD and PIP5K1 are among the molecules involved in the regulation of morphological differentiation in oligodendrocytes prior to myelination.

60 APPLIED LIFE SCIENCES↗

Decision Aid for Conjunction Risk Mitigation by Differential Drag

In the previous five years, the rate of conjunctions that the NASA Conjunction Assessment Risk Analysis (CARA) team processed and analyzed has more than tripled. (NASA CARA, 2024) New missions in the early development phases are now required to plan for dealing with conjunctions under the present space environment, and also projecting forward into a future likely with even further increased utilization of the space environment. Some missions are investigating the possibility of using differential drag to remediate conjunctions without expending limited fuel or for missions without propulsive capabilities. The NASA CARA team studied the historical record of conjunctions to evaluate the circumstances under which differential drag may be successfully applied and have developed a series of tables to use as a decision aid for missions considering differential drag. Currently, if a CARA-protected mission with maneuvering capabilities is predicted to have a conjunction with probability of collision (Pc) greater than 7E-5 (the default value of the ‘yellow threshold’, which may have some other value agreed by CARA and the mission during the Orbital Collison Avoidance Planning (OCAP) process), CARA will use its Maneuver Trade Space (MTS) tool to evaluate and recommend options for the timing and magnitude of a risk mitigation maneuver (RMM), based on the mission’s capabilities. If the conjunction’s Pc is greater than 1E-4, the ‘red threshold’, then an RMM must be executed per NASA Procedural Requirements (NPR) 8079.1 (NASA, 2023), although missions may execute an RMM even if the Pc is lower. The magnitude of the maneuver is typically a few cm/s, and CARA estimates how many will be required for the mission’s nominal lifetime – typically a few per year – during the OCAP process, to inform the mission’s delta-V requirement. For traditional satellites, this is usually smaller than other requirements for orbit insertion, maintenance, and disposal, but for CubeSats or other small satellite missions, a propulsion system may not provide much more than a few cm/s of delta-V or may not fit at all within the available budget of money, time, size, weight, and/or power (SWaP). Conversely, CubeSats often have deployable solar panels, which offer the capacity to have much higher areas facing some directions than others. Such a mission can instead use ‘differential drag’ to remediate a conjunction -- in other words, change its drag area (usually increasing) to deviate from the predicted collision course. This is how Planet’s Dove spacecraft maintain their formations and remediate conjunction risks without having on-board propulsion (Foster, et al., 2017) (Griffith, et al., 2021). CARA has been developing improvements to MTS to support differential-drag for NASA's missions -- where it is effective. CARA records all conjunctions of their protected payloads, with historical records starting in 2005 (with significant conjunction events starting to occur on or after 2013). From this record, approximately 7,300 had a Pc greater than 1E-4 at 3 days prior to the time of closest approach, the time analyzed for differential drag efficacy. Of those, approximately 4,300 had fully-defined covariance matrices stored for both the primary and secondary objects; this set of conjunctions is the basis for the analysis of this work. CARA’s MTS tool was used to propagate the primary satellite forward from that decision point with varying degrees of increase to ballistic coefficient (BC). Because these conjunctions came from multiple missions, the nondimensional ‘delta-BC’ factor was used to quantify and normalize the increase in ballistic coefficient, defined as follows: Delta-BC = BC_new / BC_old - 1 Positive delta-BC factors represent an increase in drag compared to the nominal attitude, while negative delta-BC factors (to a minimum of -1) represent a decrease in drag. At the conclusion of the differential-drag ‘maneuver’, the Pc was recalculated to evaluate whether or not the conjunction was mitigated (Pc < 3E-6). These results were then binned and sorted along several axes, including altitude, amount of delta-BC, and (pre-maneuver) rate of energy dissipation (EDR), to identify underlying patterns. The altitude plot is shown in Figure 1. To validate this analysis, we consulted the record of a NASA mission which uses differential drag to maintain its orbit and remediate conjunction risk. CARA’s empirical record of the mission’s orbit history suggests it achieves a delta-BC of 2.2. Of the twenty-one RMM plans that were submitted by this mission, eighteen were matched with conjunctions in the historical record; of those, twelve were successfully remediated (final measured Pc < 3E-6), and six were not. This is consistent with the expected efficacy for missions orbiting at that altitude. We are presently simulating this mission’s RMMs with MTS; this work is ongoing, but so far, the MTS results are qualitatively in agreement with the empirical results -- correctly predicting that a maneuver would or would not remediate a conjunction, if not exactly matching the final post-remediation Pc value. We found that differential drag was most successful for satellites with perigees below 560 km, and which could adopt an average delta-BC of 2 or greater (that is, increasing their ballistic coefficient by a factor of 3). However, this is a difficult threshold for a mission to clear; very few spacecraft are capable of adopting a high-drag configuration for 72 hours continuously. Planet’s Dove spacecraft use differential drag to remediate conjunctions (Griffith, et al., 2021), and they have a maximum delta-BC factor of 9, but in practice (with mission and charging constraints) they achieve a time-averaged delta-BC that is closer to 2 (Foster, et al., 2017). A mission’s differential drag utility strongly depends on the operational constraints that has the capacity to limit the time-averaged delta-BC. A mission with a high maximum delta-BC of 5 or more can have an effective delta-BC of less than 1 due to operational constraints such as instrument and solar panel pointing, especially if this constraint results in holding an intermediate drag value for most of its orbit. CARA has developed tables that can be used as decision aids to advise missions-in-development about the best way to utilize their differential drag capabilities. For missions below 560 km with the operational flexibility to devote multiple days to holding a high-drag configuration (or a sufficiently high drag ratio to compensate for limitations on that time), they are -- more likely than not -- able to successfully remediate high-risk conjunctions. Conversely, missions that do not meet these exacting criteria -- most missions -- can instead be advised to use on-board propulsion systems to perform RMMs, or to turn their minimum-area face towards the approach vector, thereby reducing Pc at the moment of conjunction due to the decreased Hard-Body Radius (HBR), that is a strongly correlated variable in the Pc calculations. (NASA, 2023)

conjunction assessment↗