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At least 1,117 records · Page 62

Fabric controls on fracture surface roughness of an architected rock material

Fluid flow through fractures is intimately linked to the fracture surfaces that define the void geometry through which fluids flow. Thus, an understanding of what controls fracture surface roughness is essential to the development of models for predicting fluid transport through fractured rock. The difficulty in predicting surface roughness arises from the complexity of rock which is inherently heterogeneous and nonuniform in composition, fabric, and structural components, even when samples are acquired from the same rock mass. Here, a benchmarked-simulation approach motivated from geo-architected 3D printed synthetic gypsum rocks is used to provide insight into the competing contributions from fabric and layering on fracture roughness formation. Simulation results from a discrete element model (Particle Flow Code, Itasca Consulting Group, Inc.) clearly indicate that the relative orientation between mineral layers and in-layer mineral fabric, and the variability in mineral bonding strengths determine whether anisotropic corrugated surfaces or isotropic surfaces are formed. Weak mineral layers oriented perpendicular to the applied load resulted in strong roughness anisotropy. Peak failure loads were found to vary up to 30% depending on the strength of the mineral fabric at the location of fracture initiation, which provides insight into the observed high variability in strength values of natural rock. The uniqueness of induced fracture roughness and peak failure load is intimately linked to layering, mineral fabric, and their distribution in the rock. These findings have important implications for any architected material fabricated through serial printing of layers with local compositional heterogeneity.

3D printed rock↗

Aerosol-Cloud Interactions From Aviation Soot Emissions

Current models estimate global aviation contributes approximately 5% to the total anthropogenic climate forcing, with aerosol-cloud interactions having the greatest effect. However, radiative forcing estimates from aviation aerosol-cloud interactions remain undetermined. There is an expected significant increase in aircraft emissions with aviation demand expected to rise by over 4% per year. Soot may play an important role in the ice nucleation of aircraft-induced cirrus formation due to a high emission rate, but the ice nucleating properties are poorly constrained. Understanding the microphysical processes leading to atmospheric ice crystal formation is crucial for the reliable parameterization of aerosol-cloud interactions in climate models due to their impact on precipitation and cloud radiative properties. Ice nucleation of aircraft-emitted soot is potentially affected by particle morphology with condensation of supercooled water occurring in pores followed by ice nucleation. However, soot has heterogeneous properties and undergoes atmospheric aging and oxidation that could change surface properties and contribute to complex ice nucleation processes. Further, this review synthesizes current knowledge of ice nucleation catalyzed by aviation in the cirrus regime and its effects on global radiative forcing. Further research is required to determine the ice nucleation and microphysical processes of cirrus cloud formation from aviation emissions in both controlled laboratory and field investigations to inform models for more accurate climate predictions and to provide efficient mitigation strategies.

54 ENVIRONMENTAL SCIENCES↗

Technical Evaluation of Accelerated Basin De-Inventory Material Addition to Sludge Batch 11 (Rev. 1)

The Accelerated Basin De-inventory (ABD) program involves discarding spent nuclear fuel that is currently stored in L-Basin to the Defense Waste Processing Facility (DWPF) for vitrification. The first ABD discards will occur during the preparation of Sludge Batch (SB) 11. Savannah River Mission Completion has requested that the Savannah River National Laboratory assess the technical gaps related to the increased gadolinium poisoning requirement and the impacts of performing the Low Temperature Aluminum Dissolution (LTAD) process in Tank 51 with H-Canyon discards present. The following summarizes the evaluation of the impacts of increasing the quantity of gadolinium (and related topics) from what was previously evaluated in the SRNL studies of gadolinium-poisoned ABD material solubility, the overall ABD flowsheet review, and increasing the fissile mass loading in glass: 1) Based on literature surveys, there is no indication that organic interactions with gadolinium will be significant at the high pH (typically >13) conditions of the Concentration, Storage, and Transfer Facilities. Any interactions of gadolinium with organics in DWPF are not expected to adversely impact DWPF or downstream facilities. Thus, there is little-to-no residual risk from organic interactions with gadolinium [Gap closed]; 2) Adding depleted uranium to ABD material, targeting 235 U enrichment of 4.90% within each transfer window, will mitigate potential impacts from an increase in soluble 235 U enrichment during sludge washing and LTAD. The plan to take advantage of previous transfers and allow 235 U enrichment of >5% during the final transfer window carries a risk that Tank 51 supernate will have a 235 U enrichment of >5%, which should be evaluated for acceptance; 3) Increasing the gadolinium mass ratio to 3.0:1 Gd: 235 U(eq SLU ) should lead to the same or higher partitioning of gadolinium into the solid phase within the DWPF Chemical Process Cell, resulting in both liquid and solid phases with expected partitioning of Gd consistent with the prior solubility study [Gap closed for SB11]; 4) There are no expected impacts on DWPF melt temperature and melter operations due to the minimal ~0.2 weight percent (wt%) increase in Gd concentration relative to previous sludge batches [Gap closed for SB11]; 5) As observed previously, Gd is expected to enter the off-gas system via physical entrainment, but at a slightly higher concentration than what was observed for SB9 melter off-gas pluggage deposits (0.07 wt%) [Gap closed for SB11] ; 6) There are no expected impacts on DWPF recycle or the Recycle Collection Tank glycolate destruction process. [Gap closed for SB11]; 7) Gd is projected to be a trace component in the SB11 glass (<0.5 wt%) and can be ignored for process control. Trace components do not significantly impact glass durability, thus the conclusions of the previous Product Consistency Test evaluation at a fissile mass loading of 2,500 g fissile/m3 glass still applies to SB11. The ~0.1 wt% increase in Gd2O3 concentration relative to the previous study will not impact the predictability of SB11 glass with the DWPF Product Composition Control System (PCCS) models for durability or the acceptability of glass according to the Waste Acceptance Product Specifications (WAPS) criterion for product consistency [Gap closed for SB11]; 8) No additional Toxicity Characteristic Leaching Procedure testing is necessary for SB11 and the hazardous waste specification of the SB11 DWPF waste form is unchanged after the addition of the ABD stream [Gap closed for SB11]. The following summarizes the evaluation of the impacts of adding two-thirds of the ABD material to Tank 51 prior to LTAD: 1) The addition of two-thirds of the ABD increases overall aluminum mass from 1.39×10 4 kg to 1.64×10 4 kg (15.5% ABD Al). The form of the insoluble portion of the Al resulting from ABD addition should be the more readily dissolved Al(OH) 3 and amorphous forms. The portion of the ABD aluminum that is processed by LTAD is expected to be completely soluble, thus requiring that less of the boehmite in the sludge be dissolved to reach the same Al target in the SB. [Gap closed for SB11]; The expected LTAD impact on other components, as related primarily to the components in ABD, are discussed. Gd is expected to remain insoluble during LTAD and not impact the solubility of other components. [Gap closed for SB11]; The addition of two-thirds of the ABD increases overall projected SB11 uranium mass from 4,740 kg to 13,100 kg (63% ABD U) and the projected plutonium mass from 86.0 kg to 89.5 kg (3.9% ABD Pu). The addition of all of the ABD increases overall projected SB11 uranium mass from 4,740 kg to 16,100 kg (70% ABD U) and the projected plutonium mass from 86.0 kg to 90.4 kg (5.3% ABD Pu). The 235 U enrichment will be ≤5%. The fissile uranium will be adequately poisoned by Gd and the fissile Pu will be adequately poisoned by Fe from the sludge. [Gap closed for SB11]; There is a low risk that ABD addition will impact the rheology or pumpability of the slurry. There is a low but higher risk of ABD addition prior to LTAD impacting the settling rate; Based on the evaluation of adding two-thirds of the ABD material and all of the ABD material prior to the LTAD process, there is no volume or mass limit that would need to be imposed on ABD additions prior to LTAD. [Gap closed for SB11]. Revision 1 of this report addresses a variation on the ABD additions and LTAD strategy where sodium hydroxide additions for LTAD may be performed intermittently or concurrently with an ABD addition window. The proposed change does not alter the conclusions of this evaluation.

12 MANAGEMENT OF RADIOACTIVE AND NON-RADIOACTIVE W↗

Feasibility of Adding Twitter Data to Aid Drought Depiction: Case Study in Colorado

The use of social media, such as Twitter, has changed the information landscape for citizens’ participation in crisis response and recovery activities. Given that drought progression is slow and also spatially extensive, an interesting set of questions arise, such as how the usage of Twitter by a large population may change during the development of a major drought alongside how the changing usage facilitates drought detection. For this reason, contemporary analysis of how social media data, in conjunction with meteorological records, was conducted towards improvement in the detection of drought and its progression. The research utilized machine learning techniques applied over satellite-derived drought conditions in Colorado. Three different machine learning techniques were examined: the generalized linear model, support vector machines and deep learning, each applied to test the integration of Twitter data with meteorological records as a predictor of drought development. It is found that the integration of data resources is viable given that the Twitter-based model outperformed the control run which did not include social media input. Eight of the ten models tested showed quantifiable improvements in the performance over the control run model, suggesting that the Twitter-based model was superior in predicting drought severity. Future work lies in expanding this method to depict drought in the western U.S.

54 ENVIRONMENTAL SCIENCES↗

The 32nd CDC: System identification using interval dynamic models

Motivated by the recent explosive development of results in the area of parametric robust control, a new technique to identify a family of uncertain systems is identified. The new technique takes the frequency domain input and output data obtained from experimental test signals and produces an 'interval transfer function' that contains the complete frequency domain behavior with respect to the test signals. This interval transfer function is one of the key concepts in the parametric robust control approach and identification with such an interval model allows one to predict the worst case performance and stability margins using recent results on interval systems. The algorithm is illustrated by applying it to an 18 bay Mini-Mast truss structure.

Keel, L. H.↗

Damage-mitigating control of space propulsion systems for high performance and extended life

Calculations are presented showing that a substantial improvement in service life of a reusable rocket engine can be achieved by an insignificant reduction in the system dynamic performance. The paper introduces the concept of damage mitigation and formulates a continuous-time model of fatigue damage dynamics. For control of complex mechanical systems, damage prediction and damage mitigation are carried out based on the available sensory and operational information such that the plant can be inexpensively maintained and safely and efficiently steered under diverse operating conditions. The results of simulation experiments are presented for transient operations of a reusable rocket engine.

Ray, Asok↗

Human Interfaces In Teleoperations And Virtual Environments

Conference report contains compilation of papers relating to interactions between humans and machines from perspectives of telepresence and sensorimotor adaptation, measurement and evaluation of performance, and design principles and predictive models. Topics discussed include neural networks, sensory technology, display, and feedback controls. Covers state of art of remote sensing and control by humans for space or other operations.

Durlach, Nathaniel I.↗

Generalized Predictive and Neural Generalized Predictive Control of Aerospace Systems

The research work presented in this thesis addresses the problem of robust control of uncertain linear and nonlinear systems using Neural network-based Generalized Predictive Control (NGPC) methodology. A brief overview of predictive control and its comparison with Linear Quadratic (LQ) control is given to emphasize advantages and drawbacks of predictive control methods. It is shown that the Generalized Predictive Control (GPC) methodology overcomes the drawbacks associated with traditional LQ control as well as conventional predictive control methods. It is shown that in spite of the model-based nature of GPC it has good robustness properties being special case of receding horizon control. The conditions for choosing tuning parameters for GPC to ensure closed-loop stability are derived. A neural network-based GPC architecture is proposed for the control of linear and nonlinear uncertain systems. A methodology to account for parametric uncertainty in the system is proposed using on-line training capability of multi-layer neural network. Several simulation examples and results from real-time experiments are given to demonstrate the effectiveness of the proposed methodology.

Kelkar, Atul G.↗

Rapid adaptation to Coriolis force perturbations of arm trajectory

1. Forward reaching movements made during body rotation generate tangential Coriolis forces that are proportional to the cross product of the angular velocity of rotation and the linear velocity of the arm. Coriolis forces are inertial forces that do not involve mechanical contact. Virtually no constant centrifugal forces will be present in the background when motion of the arm generates transient Coriolis forces if the radius of body rotation is small. 2. We measured the trajectories of arm movements made in darkness to a visual target that was extinguished as movement began. The reaching movements were made prerotation, during rotation at 10 rpm in a fully enclosed rotating room, and postrotation. During testing the subject was seated at the center of the room and pointed radially. Neither visual nor tactile feedback about movement accuracy was present. 3. In experiment 1, subjects reached at a fast or slow rate and their hands made contact with a horizontal surface at the end of the reach. Their initial perrotary movements were highly significantly deviated relative to prerotation in both trajectories and end-points in the direction of the transient Coriolis forces that had been generated during the reaches. Despite the absence of visual and tactile feedback about reaching accuracy, all subjects rapidly regained straight movement trajectories and accurate endpoints. Postrotation, transient errors of opposite sign were present for both trajectories and endpoints. 4. In a second experiment the conditions were identical except that subjects pointed just above the location of the extinguished target so that no surface contact was involved. All subjects showed significant initial perrotation deviations of trajectories and endpoints in the direction of the transient Coriolis forces. With repeated reaches the trajectories, as viewed from above, again became straight, but there was only partial restoration of endpoint accuracy, so that subjects reached in a straight line to the wrong place. Aftereffects of opposite sign were transiently present in the postrotary movements. 5. These observations fail to support current equilibrium point models, both alpha and lambda, of movement control. Such theories would not predict endpoint errors under our experimental conditions, in which the Coriolis force is absent at the beginning and end of a movement. Our results indicate that detailed aspects of movement trajectory are being continuously monitored on the basis of proprioceptive feedback in relation to motor commands. Adaptive compensations can be initiated after one perturbation despite the absence of either visual or tactile feedback about movement trajectory and endpoint error. Moreover, movement trajectory and end-point can be remapped independently.(ABSTRACT TRUNCATED AT 400 WORDS).

Non-NASA Center↗

Introducing GFWED: The Global Fire Weather Database

The Canadian Forest Fire Weather Index (FWI) System is the mostly widely used fire danger rating system in the world. We have developed a global database of daily FWI System calculations, beginning in 1980, called the Global Fire WEather Database (GFWED) gridded to a spatial resolution of 0.5 latitude by 2-3 longitude. Input weather data were obtained from the NASA Modern Era Retrospective-Analysis for Research and Applications (MERRA), and two different estimates of daily precipitation from rain gauges over land. FWI System Drought Code calculations from the gridded data sets were compared to calculations from individual weather station data for a representative set of 48 stations in North, Central and South America, Europe, Russia,Southeast Asia and Australia. Agreement between gridded calculations and the station-based calculations tended to be most different at low latitudes for strictly MERRA based calculations. Strong biases could be seen in either direction: MERRA DC over the Mato Grosso in Brazil reached unrealistically high values exceeding DCD1500 during the dry season but was too low over Southeast Asia during the dry season. These biases are consistent with those previously identified in MERRAs precipitation, and they reinforce the need to consider alternative sources of precipitation data. GFWED can be used for analyzing historical relationships between fire weather and fire activity at continental and global scales, in identifying large-scale atmosphereocean controls on fire weather, and calibration of FWI-based fire prediction models.

bias↗

Modeling of Multicomponent Trace Contaminant Adsorption on Activated Carbon

Modeling of multicomponent trace contaminant adsorption on activated carbon for spacecraft life support applications presents challenges due to the very low contaminant concentrations in cabin air coupled with very strong adsorption of heavier components such as cyclic polydimethylsiloxanes. Both gas-phase and solid-phase micropore mass transfer resistances can be important, and competitive interactions between adsorbed components can result in behavior such as roll-up where lighter components displaced by heavier components have a higher concentration at the outlet than at the inlet. This paper describes the further development of a dynamic trace contaminant adsorption model based on Ideal Adsorbed Solution Theory (IAST). Alternative 1-dimensional and 2-dimensional versions of the model are described with different mass transfer resistance and driving force assumptions. Optimization of solution methods for speed and stability is also described. Mass balance equations are scaled to provide sensitivity over the wide range of component concentrations in cabin air. Model parameters are estimated from isotherm and breakthrough test data on single adsorbate and binary adsorbate systems. Multicomponent results are compared against predictions of a heritage model used extensively by NASA for trace contaminant control system (TCCS) carbon bed sizing. Finally, efforts to implement the model in a second software platform for wider access are described.

Kevin E Lange↗

Static and Forced Oscillation Wind Tunnel Tests of A Tandem Propeller Configuration

A series of static and forced oscillation tests were conducted using a tandem propeller configuration in the NASA Langley 12-Foot Low-Speed Tunnel. The primary objectives were to quantify the effect of aerodynamic interactions on propeller thrust and identify conditions where the effect is most significant. A secondary objective was to obtain a preliminary data set from dynamic testing to assess the impact of angular rate on thrust performance. This paper presents analysis of the experimental data, which includes propeller performance measurements and qualitative flow visualization. The static results show that the rear propeller in the tandem configuration can experience thrust degradations greater than 30%. The extent of the wake interaction is a function of the hub separation distance and the advance ratio of the front propeller. Forced oscillation results showed that the front propeller exhibited primarily linear behavior across the conditions tested, whereas the rear propeller exhibited dynamic nonlinearity in the region of significant thrust degradation. These results are intended to support high-fidelity modeling research, particularly for flight dynamics simulation development to aid trajectory prediction, control design, and identification of hazardous conditions for multirotor vehicles.

Aerodynamic Interactions↗

Band Energy Dependence of Defect Formation in the Topological Semimetal Cd3As2

Cadmium Arsenide (Cd3As2) is a prototypical Dirac semimetal that manifests topological properties in a 3D bulk material. In defect-free Cd3As2, the Fermi level lies at a minimum in the density of states at the Dirac point, but experimentally it forms with excess electron carriers and an elevated EF, thereby masking the topological features. To computationally study the self-doping of Cd3As2, we combine density functional theory (DFT) calculations for defect formation energies with quasi-particle self-consistent GW (QSGW) electronic structure calculations. We demonstrate an innate dependence of the point defect formation energies on carrier concentrations and use the QSGW calculated density of states to extrapolate formation energies to arbitrary electron concentrations. This approach allows the quantitative modeling of thermodynamic defect equilibria in topological semimetals and is used to predict how Cd3As2 growth conditions affect the position of EF relative to the Dirac point.

CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS↗

Assessing time-dependent temperature profile predictions using reduced transport models for high performing NSTX plasmas

Time-dependent, predictive simulations were performed with the 1.5D tokamak integrated modeling code TRANSP on a large set of well-analyzed, high performing discharges from the National Spherical Torus Experiment (NSTX) in order to evaluate how well modern reduced transport models can reproduce experimentally observed temperature profiles in spherical tokamaks. Overall, it is found that simulations using the Multi-Mode Model (MMM) more consistently agree with the NSTX observations than those using the Trapped Gyro-Landau Fluid (TGLF) model, despite TGLF requiring orders of magnitude greater computational cost. When considering all examined discharges, MMM has median overpredictions of electron temperature (T e ) and ion temperature (T i ) profiles of 28% and 27%, respectively, relative to the experiment. TGLF overpredicts T e by 46%, with much larger variance than MMM, and underpredicts T i by 25%. As the ratio of kinetic to magnetic field pressure (β) is increased across NSTX discharges, TGLF predicts lower T e and significant flattening of the T i profile, conflicting with NSTX observations. When using an electrostatic version of TGLF, both T e and T i are substantially overpredicted, underscoring the importance of electromagnetic turbulence in the high β spherical tokamak regime. Additionally, calculations with neural net surrogate models for TGLF were performed outside of TRANSP with a time slice flux matching transport solver, finding better agreement with experiment than the TRANSP simulations, highlighting the impact of different transport solvers and simulation techniques. Furthermore, the reasonable agreement with experiment of temperature profiles predicted by MMM motivates a more detailed examination of the sensitivities of the TRANSP simulations with MMM to different NSTX plasma regimes in a companion paper (Lestz et al Plasma Phys. Control. Fusion 67 105030), in preparation for self-consistent, time-dependent predictive modeling of NSTX-U scenarios.

Lestz, J. B. [General Atomics, San Diego, CA (Unit↗

Project Management Using Modern Guidance, Navigation and Control Theory

Implementing guidance, navigation, and control (GN&C) theory principles and applying them to the human element of project management and control is not a new concept. As both the literature on the subject and the real-world applications are neither readily available nor comprehensive with regard to how such principles might be applied, this paper has been written to educate the project manager on the "laws of physics" of his or her project (not to teach a GN&C engineer how to become a project manager) and to provide an intuitive, mathematical explanation as to the control and behavior of projects. This paper will also address how the fundamental principles of modern GN&C were applied to the National Aeronautics and Space Administration's (NASA) Constellation Program (CxP) space suit project, ensuring the project was managed within cost, schedule, and budget. A project that is akin to a physical system can be modeled and managed using the same over arching principles of GN&C that would be used if that project were a complex vehicle, a complex system(s), or complex software with time-varying processes (at times nonlinear) containing multiple data inputs of varying accuracy and a range of operating points. The classic GN&C theory approach could thus be applied to small, well-defined projects; yet when working with larger, multiyear projects necessitating multiple organizational structures, numerous external influences, and a multitude of diverse resources, modern GN&C principles are required to model and manage the project. The fundamental principles of a GN&C system incorporate these basic concepts: State, Behavior, Feedback Control, Navigation, Guidance and Planning Logic systems. The State of a system defines the aspects of the system that can change over time; e.g., position, velocity, acceleration, coordinate-based attitude, and temperature, etc. The Behavior of the system focuses more on what changes are possible within the system; this is denoted in the state of the system. The behavior of a system, as captured in the system modeling, when properly done will aid in accurately predicting future system performance. The Feedback Control system understands the state and behavior of the system and uses feedback to adjust control inputs into the system. The feedback, which is the right arm of the Control system, allows change to be affected in the overall system; it therefore is important to not only correctly identify the system feedback inputs, but also the system response to the feedback inputs. The Navigation system takes multiple data inputs and based on a priori knowledge of the inputs, develops a statistically based weighting of the inputs and measurements to determine the system's state. Guidance and Planning Logic of the system, complete with an understanding of where the system is (provided by the Navigation system), will in turn determine where the system needs to be and how to get it there. With any system/project, it is critical that the objective of the system/project be clearly defined -- not only to plan but to measure performance and to aid in guiding the system or the project. The system principles discussed above, which can be and have been applied to the current CxP space suit development project, can also be mapped to real-world constituents, thus allowing project managers to apply systems theories that are well defined in engineering and mathematics to a discipline (i.e., Project Management) that historically has been based in personal experience and intuition. This mapping of GN&C theory to Project Management will, in turn, permit a direct, methodical approach to Project Management, planning and control providing a tool to help predict (and guide) performance and an understanding of the project constraints, how the project can be controlled, and the impacts to external influences and inputs. This approach, to a project manager, flows down to the three bottom-line variables of cost, schedule, and scope ando the needed control of these three variables to successfully perform and complete a project.

Hill, Terry R.↗

The influence of the rotor wake on rotorcraft stability and control

The effect of the time-averaged rotor wake flowfield on the aerodynamic behavior of the tail rotor and fixed tail surfaces is discussed. The flowfield at the location of these surfaces is predicted by two wake models, a simplified flat wake model and an accurate free wake model. Both models are shown to give similar predictions of the flowfield in the vicinity of the empennage that are generally in agreement with experiment. The contributions of these aerodynamic interactions to the helicopter stability derivatives are described and control responses using different wake models are compared with flight test.

Curtiss, H. C., Jr.↗

Forward sensitivity analysis and mode dependent control for closure modeling of Galerkin systems

Model reduction by projection-based approaches is often associated with losing some of the important features that contribute towards the dynamics of the retained scales. As a result, a mismatch occurs between the predicted trajectories of the original system and the truncated one. We put forth a framework to apply a continuous time control signal in the latent space of the reduced order model (ROM) to account for the effect of truncation. We set the control input using parameterized models by following energy transfer principles. Our methodology relies on observing the system behavior in the physical space and using the projection operator to restrict the feedback signal into the latent space. Then, we leverage the forward sensitivity method (FSM) to derive relationships between the feedback and the desired mode-dependent control. We test the performance of the proposed approach using two test cases, corresponding to viscous Burgers and vortex merger problems at high Reynolds number. Results show that the ROM trajectory with the applied FSM control closely matches its target values in both the data-dense and data-sparse regimes.

97 MATHEMATICS AND COMPUTING↗

Small error dynamics and the predictability of atmospheric flows

In this paper, linear small-error theory is applied to the study of weather predictability. A simple baroclinic shear model and a barotropic channel model with a localized jet are used as examples. It is shown that increase in error on synoptic forecast time scales is controlled by rapidly growing perturbations that are not of normal mode form. Unpredictable regimes are not necessarily associated with larger exponential growth rates than are relatively more predictable regimes. Model problems illustrating baroclinic and barotropic dynamics suggest that asymptotic measures of divergence in phase space, while applicable in the limit of infinite time, may not be appropriate over time intervals addressed by present synoptic forecast.

Farrell, Brian F.↗