Results for “equation recovery” — Page 13

NASA NTRS1992

Optimal recovery from microburst wind shear

The flight path of a twin-jet transport aircraft is optimized in a microburst encounter during approach to landing. The objective is to execute an escape maneuver that maintains safe ground clearance and an adequate stall margin during the climb-out portion of the trajectory. A cost function penalizing rate of climb deviations from a nominal value and rate of elevator deflection produces qualitatively good results in a variety of microburst encounters. The optimal maneuver is a gradual pitch-up that ceases near the core of the microburst, followed by a slight reduction in pitch attitude in the tailwind area of the microburst. A minimum airspeed constraint in the optimization prevents excessive airspeed loss in very severe microbursts. The aircraft equations of motion include short-period dynamics, so that the optimization solves directly for the control surface deflections required to achieve the optimal flight paths.

Mulgund, Sandeep S.↗

NASA NTRS1989

ARISTOTELES: A European approach for an Earth gravity field recovery mission

Under contract of the European Space Agency a system study for a spaceborne gravity field recovery mission was performed, covering as a secondary mission objective geodetic point positioning in the cm range as well. It was demonstrated that under the given programmatic constraints including dual launch and a very tight development schedule, a six months gravity field mission in a 200 km near polar, dawn-dusk orbit is adequate to determine gravity anomalies to better than 5 mgal with a spatial resolution of 100 x 100 km half wavelength. This will enable scientists to determine improved spherical harmonic coefficients of the Earth gravity field equation to the order and degree of 180 or better.

Benz, R.↗

NASA NTRS1979

Observations of Pc 1-2 waves in the outer magnetosphere

High time resolution measurements made inside the magnetopause from L = 7 to L = 14 by the flux gate magnetometer aboard the Ogo 5 satellite, which demonstrate that the Pc 1-2 magnetic field oscillations are present in the outer magnetosphere, are examined. The solar wind dynamic pressure and the magnetospheric cold plasma were enhanced, and the IMF had a southward component 2 hours before the events, but there was no significant correlation between the time of the events and either storm recovery phase or substorm onset. The magnetic field perturbations in each event were transverse to the ambient field with amplitudes from 2 to 8 gamma, and most of the transverse perturbations showed left-handed polarization. Excursions into the magnetosheath during two events revealed a disturbed magnetic field with significant power in frequencies of minimum 0.1 Hz, and although the magnetosheath was a source of free energy for waves at Pc 1-2 frequencies, the data within the magnetosphere suggest that the observed pulsations were ion cyclotron waves generated at the geomagnetic equator at large radial distances.

Kaye, S. M.↗

NASA NTRS1983

A Unified Constitutive Relationship for the Time-dependent Behavior of Fast Breeder Alloys

Constitutive equations based on classical concepts of creep and plasticity generally rest on the assumption that the inelastic strain can be decomposed into two distinct and additive contributions, one time dependent (creep) and the other time dependent (plastic). It is suggested that an approach is to adopt a unified representation in which creep and plasticity are characterized as occurring simultaneously and interactively and time is an essential ingredient throughout. Examples of the inherent time dependency exhibited by some fast breeder alloys at elevated temperature are rate dependency under monotonic and cyclic straining, thermal recovery and strong creep-elasticity interaction. The stron influence of the recent history of plastic straining on stress relaxation is shown.

Robinson, D. N.↗

NASA NTRS2006

Self-Consistent Model of Magnetospheric Ring Current and Propagating Electromagnetic Ion Cyclotron Waves: Waves, Precipitating Ring Current Ions, and Thermal Electron Heating - 2

This paper is dedicated to further presentations and discussions of the results from our new global self-consistent theoretical model of interacting ring current ions and electromagnetic ion cyclotron waves [Khazanov et al., 2006; here referred to as Paper 1]. In order to adequately take into account the wave propagation and refraction in a multi-ion plasmasphere, we explicitly include the ray tracing equations in our previous self-consistent model and use the general form of the wave kinetic equation [for details see Paper 1]. To demonstrate the effects of the EMIC wave propagation and refraction on the RC proton precipitations and heating of the thermal plasmaspheric electrons we simulate the May 1998 storm. The main findings of our simulation can be summarized as follows. Firstly, the wave induced precipitations have a quite fine structure, and are highly organized by location of the plasmapause gradient. The strongest fluxes of about 4 (raised dot) 10(exp 6) [(cm (raised dot) s (raised dot) sr)(sup -l)] are observed during the main and early recovery phases of the storm. The very interesting and probably more important finding is that in a number of cases the most intense precipitating fluxes are not simply connected to the most intense EMIC waves. The character of the EMIC wave power spectral density distribution over the equatorial wave normal angle is an extremely crucial for the effectiveness of the RC ion scattering. Secondly, comparison of the global proton precipitating patterns with the results from other ring current model [Kozyra et al., 1997] reveals that although we observe a qualitative agreement between localizations of the wave induced fluxes in the models, there is no quantitative agreement between the magnitudes of these fluxes. These differences are mainly due to a qualitative difference between the characters of the EMIC wave power spectral density distributions over the equatorial wave normal angle. Finally, the two energy sources to the plasmaspheric electrons are considered; (i) the heat fluxes caused by the EMIC wave energy absorption due to Landau resonance, and (ii) the heat fluxes due to Coulomb energy degradation of the RC o(+) ions. The heat fluxes caused by the EMIC wave energy absorption due to Landau resonance are observed in the postnoon-premidnight MLT sector, and maximize at the magnitude of 10l1 (eV/(cm(sup 2)(raised dot) s) at L=3.25, MLT=22 at 3400 UT after 1 May, 0000 UT. The greatest Coulomb energy deposition rates are about 2 (raised dot) 10(sup 10)(eV/(cm(sup 2)(raised dot) s) and observed during two periods; 32-48 hours, and 76-86 hours after 1 May, 0000 UT. The theoretically derived spatial structure of the thermal electron heating caused by interaction of the RC with plasmasphere is strongly supported by concurrent and conjugate plasma measurements from the plasmasphere, the RC, and the topside ionosphere [Gurgiolo et al., 20051.

Khazanov, G. V.↗

NASA NTRS1977

An implementable digital adaptive flight controller designed using stabilized single-stage algorithms

An explicit adaptive controller, which makes direct use of on-line parameter identification, has been developed and applied to both the linearized and nonlinear equations of motion for the F-8 aircraft. This controller is composed of an on-line weighted least squares parameter identifier, a Kalman state filter, and a real model following control law designed using single-stage performance indices. The corresponding control gains are readily adjustable in accordance with parameter changes to ensure asymptotic stability if the conditions of perfect model following are satisfied, and stability in the sense of boundedness otherwise. Simulation experiments with realistic measurement noise indicate that the controller was effective in compensating for parameter variations and capable of rapid recovery from a set of erroneous initial parameter estimates which defined a set of destabilizing gains.

Alag, G.↗

NASA NTRSDate not supplied

Recommendations For Developing Space Suit Integrated Food Systems and Delivering Nutrition Before, During, and After Lunar Eva

INTRODUCTION Artemis missions will include a higher tempo and frequency of extravehicular activities (EVAs) than any previous space program. Because of the physical demands expected from the crew, future space suit designs are required to incorporate nutritional support to the astronauts during lunar surface EVAs lasting longer than 4 hours. The purpose of this project was to provide recommendations to aid the development of an in-suit system that can adequately, safely, and acceptably deliver nutrition to a crewmember while confined to a space suit during EVA. METHODS Physiological, logistical, and engineering aspects of potential in-suit nutrition approaches were assessed through literature reviews, assessments of commercial off the shelf (COTS) foods, suit volumetric modeling, and feedback from subject matter experts and crewmembers. Key driving factors in the development of in-suit nutrition requirements included how much and what type of nutrition should be included, what food formulations are appropriate and safe, what are inherent limitations of space suits, what are the potential risks to the crewmember in the suit, and what practices and preferences from astronauts should be considered. Design references were conceptualized and assessed for strengths and limitations as potential in-suit nutrition systems for surface EVA. RESULTS Acute exogenous energy demands vary greatly depending on activity intensity and duration, and partial energy replenishment (i.e., 60–80 kcal∙hr-1 of EVA, or 460–680 kcal for EVAs lasting up to 8 hours) during activities could improve performance, safety, and recovery. COTS foods capable of providing these energy requirements exist; however, no COTS foods have been identified that pass NASA flight standards for microbiological safety and stability. In-suit nutrition delivery design references that were considered included in-suit concepts for a prefilled drink bag, a hydratable drink bag, and a solid food stick. In addition, a helmet feed port concept was considered for use with drink bags external to the suit. Volumetric models of the in-suit drink bag concepts, based on xEMU dimensions, indicate challenges of fitting formulations > 200 ml (equating to approximately 200 kcal). Astronaut feedback on the four concepts indicated that despite some individual preferences for inclusion of solid foods and helmet port designs, the prefilled drink bag concept was the most preferred. A prefilled drink bag can only be used if food safety and stability can be ensured, possibly requiring advancements in food delivery hardware. CONCLUSION The ability to meet the increased need for nutrition during surface EVAs through provision of nutrients in the suited configuration would benefit overall crew health, performance, and morale, and thus increase the likelihood of mission success. It is recommended that in-suit nutrition capabilities provide at least 400–600 kcal within the suit during EVAs lasting > 4 hours and that suit designs include a dedicated volume for food grade nutrition systems. The developed food system should either allow for 1) installation of prefilled (sealed sterile) liquid nutrition in the suit and provide a mechanism to break the seal at the time that consumption is desired or 2) demonstrate that the unsealed food product shelf life allows for safe consumption after at least 12 hours of EVA.

E L Dillon↗

NASA NTRSDate not supplied

Recommendations for Developing Space Suit Integrated Food Systems and Delivering Nutrition Before, During, and After Lunar EVA

INTRODUCTION Artemis missions will include a higher tempo and frequency of extravehicular activities (EVAs) than any previous space program. Because of the physical demands expected from the crew, future space suit designs are required to incorporate nutritional support to the astronauts during lunar surface EVAs lasting longer than 4 hours. The purpose of this project was to provide recommendations to aid the development of an in-suit system that can adequately, safely, and acceptably deliver nutrition to a crewmember while confined to a space suit during EVA. METHODS Physiological, logistical, and engineering aspects of potential in-suit nutrition approaches were assessed through literature reviews, assessments of commercial off the shelf (COTS) foods, suit volumetric modeling, and feedback from subject matter experts and crewmembers. Key driving factors in the development of in-suit nutrition requirements included how much and what type of nutrition should be included, what food formulations are appropriate and safe, what are inherent limitations of space suits, what are the potential risks to the crewmember in the suit, and what practices and preferences from astronauts should be considered. Design references were conceptualized and assessed for strengths and limitations as potential in-suit nutrition systems for surface EVA. RESULTS Acute exogenous energy demands vary greatly depending on activity intensity and duration, and partial energy replenishment (i.e., 60–80 kcal∙hr-1 of EVA, or 460–680 kcal for EVAs lasting up to 8 hours) during activities could improve performance, safety, and recovery. COTS foods capable of providing these energy requirements exist; however, no COTS foods have been identified that pass NASA flight standards for microbiological safety and stability. In-suit nutrition delivery design references that were considered included in-suit concepts for a prefilled drink bag, a hydratable drink bag, and a solid food stick. In addition, a helmet feed port concept was considered for use with drink bags external to the suit. Volumetric models of the in-suit drink bag concepts, based on xEMU dimensions, indicate challenges of fitting formulations > 200 ml (equating to approximately 200 kcal). Astronaut feedback on the four concepts indicated that despite some individual preferences for inclusion of solid foods and helmet port designs, the prefilled drink bag concept was the most preferred. A prefilled drink bag can only be used if food safety and stability can be ensured, possibly requiring advancements in food delivery hardware. CONCLUSION The ability to meet the increased need for nutrition during surface EVAs through provision of nutrients in the suited configuration would benefit overall crew health, performance, and morale, and thus increase the likelihood of mission success. It is recommended that in-suit nutrition capabilities provide at least 400–600 kcal within the suit during EVAs lasting > 4 hours and that suit designs include a dedicated volume for food grade nutrition systems. The developed food system should either allow for 1) installation of prefilled (sealed sterile) liquid nutrition in the suit and provide a mechanism to break the seal at the time that consumption is desired or 2) demonstrate that the unsealed food product shelf life allows for safe consumption after at least 12 hours of EVA.

space suit↗

NASA NTRS1993

Design of a recovery system for a reentry vehicle

Engineers are often required to design decelerator systems which are deployed in cross-wind orientations. If the system is not designed to minimize 'line sail', damage to the parachutes could result. A Reentry Vehicle Analysis Code (RVAC) and an accompanying graphics animation software program (DISPLAY) are presented in this paper. These computer codes allow the user to quickly apply the Purvis line sail modeling technique to any vehicle and then observe the relative motion of the vehicle, nose cap, suspension lines, pilot and drogue bags and canopies on a computer screen. Data files are created which allow plots of velocities, spacial positions, and dynamic pressures versus time to be generated. The code is an important tool for the design engineer because it integrates two degrees of freedom (DOF) line sail equations with a three DOF model of the reentry body and jettisoned nose cap to provide an animated output.

Von Eckroth, Wulf↗

NASA NTRS1983

Correlations Between Metallurgical Characterization Studies, Exploratory Mechanical Tests, and Continuum Mechanics Approaches to Constitutive Equations

Austenitic stainless steels, such as types 316 and 304, are widely used as pressure vessel materials in the temperature range of 425 to 650 C. Stainless steel specimens were tested to rupture at two different stress levels sigma and sigma 2 sigma 1 sigma 2) to establish the normal stain-time behavior. A subsequent test was performed in which the specimen was crept at the higher stress (sigma 1) to the beginning of the secondary stage of creep, presumed to be the strain/time conditions at which a steady state microstructure is developed, and then the stress was reduced to the lower level (sigma 2). The associated microstructure, and significance of this microstructure on the creep strain-hardening model for variable uniaxial loads were assesed and found to be consistent with the use of creep-recovery models at high stresses and temperatures and strain-hardening models at low stresses and tempertures.

Moteff, J.↗

NASA NTRS2021

Depletion & Recovery of the O3 Layer Observed from Space Over the Past 50 Years of the Anthropocene

This year we are celebrating the 50th anniversary of the launch of the backscatter UV (BUV) instrument on NASA’s Nimbus-4 satellite. Since then 10 more advanced instruments, but based on the same basic measurement principle, have been launched on polar orbiting NASA and NOAA satellites. The datasets produced by these instruments are unique for they have captured the period before the onset of the decline of the ozone layer due to manmade chemicals, the declining period, and the present slow recovery period. This period includes the rapid development of the iconic anthropocene era feature called the “Ozone Hole” . However, stitching together data from 11 separate satellite instruments to create a homogeneous record has presented many challenges. The first two NASA instruments suffered considerable degradation after launch that required the development of novel techniques to characterize their calibration. The next 7 instruments were launched on NOAA’s polar orbiting weather satellites that were not designed for long-term monitoring of climate variables. In particular, they didn’t have the station keeping capabilities needed to maintain a stable equator crossing time. Drifting orbits not only stress the retrieval algorithm and the calibration system of UV instruments but also make the interpretation of data difficult because the upper stratospheric ozone has systematic and complex diurnal variabilities that are comparable to the anthropogenic signal one wants to extract. We will highlight our recent efforts in untangling this knot. Finally, we will discuss the results from the OMPS limb scattering instrument, a recent addition to this constellation, that has been operating on the Suomi NPP satellite since October 2011. It is helping us capture how the ozone layer in the lower stratosphere and troposphere is evolving in response to the climate change and rising chemical pollutants in some parts of the world, while the upper stratosphere slowly recovers due to phaseout of the chemicals that initiated the decline of the ozone layer in the late 70s.

P Bhartia↗

NASA NTRS1994

Accurate interlaminar stress recovery from finite element analysis

The accuracy and robustness of a two-dimensional smoothing methodology is examined for the problem of recovering accurate interlaminar shear stress distributions in laminated composite and sandwich plates. The smoothing methodology is based on a variational formulation which combines discrete least-squares and penalty-constraint functionals in a single variational form. The smoothing analysis utilizes optimal strains computed at discrete locations in a finite element analysis. These discrete strain data are smoothed with a smoothing element discretization, producing superior accuracy strains and their first gradients. The approach enables the resulting smooth strain field to be practically C1-continuous throughout the domain of smoothing, exhibiting superconvergent properties of the smoothed quantity. The continuous strain gradients are also obtained directly from the solution. The recovered strain gradients are subsequently employed in the integration o equilibrium equations to obtain accurate interlaminar shear stresses. The problem is a simply-supported rectangular plate under a doubly sinusoidal load. The problem has an exact analytic solution which serves as a measure of goodness of the recovered interlaminar shear stresses. The method has the versatility of being applicable to the analysis of rather general and complex structures built of distinct components and materials, such as found in aircraft design. For these types of structures, the smoothing is achieved with 'patches', each patch covering the domain in which the smoothed quantity is physically continuous.

Tessler, Alexander↗

NASA NTRS2017

Properties, Propagation, and Excitation of EMIC Waves Properties, Propagation, and Excitation of EMIC Waves

Electromagnetic ion cyclotron (EMIC) waves (0.1-5 Hz) play an important role in particle dynamics in the Earth's magnetosphere. EMIC waves are preferentially excited in regions where hot anisotropic ions and cold dense plasma populations spatially overlap. While the generation region of EMIC waves is usually on or near the magnetic equatorial plane in the inner magnetosphere, EMIC waves have both equatorial and off-equator source regions on the dayside in the compressed outer magnetosphere. Using field and plasma measurements from the Magnetospheric Multiscale (MMS) mission, we perform a case study of EMIC waves and associated local plasma conditions observed on 19 October 2015. From 0315 to 0810 UT, before crossing the magnetopause into the magnetosheath, all four MMS spacecraft detected long-lasting He(exp +)-band EMIC wave emissions around local noon (MLT = 12.7 - 14.0) at high L-shells (L = 8.8 - 15.2) and low magnetic latitudes (MLAT = -21.8deg - -30.3deg). Energetic (greater than 1 keV) and anisotropic ions were present throughout this event that was in the recovery phase of a weak geomagnetic storm (min. Dst = -48 nT at 1000 UT on 18 October 2015). The testing of linear theory suggests that the EMIC waves were excited locally. Although the wave event is dominated by small normal angles, its polarization is mixed with right- and left-handedness and its propagation is bi-directional with regard to the background magnetic field. The short inter-spacecraft distances (as low as ~15 km) of the MMS mission make it possible to accurately determine the k vector of the waves using the phase difference technique. Preliminary analysis finds that the k vector magnitude, phase speed, and wavelength of the 0.3-Hz wave packet at 0453:55 UT are 0.005 km(exp -1), 372.9 km/s, and 1242.9 km, respectively.

Zhang, Jichun↗

NASA NTRS2019

Refinement of Vortex Generators in a Streamline-Traced, External-Compression Supersonic Inlet

Computational simulations of the flow within a streamline-traced, external-compression supersonic inlet for Mach 1.664 without and with vortex generators were performed to refine the characterization of the inlet performance as measured by the total pressure recovery and the radial and circumferential total pressure distortion indices at the engine face. The refinement of the simulations concerned two aspects: 1) refinement of the grid for the simulations to evaluate and reduce uncertainty, and 2) refinement of the modeling and design of the vortex generators. The vortex generators studied were rectangular vane-type vortex generators arranged in co-rotating arrays within the subsonic diffuser. The vortex generator geometric factors of interest included the height, circumferential spacing, and angle-of-incidence. The flow through the inlet was simulated numerically through the solution of the steady-state, Reynolds-averaged Navier-Stokes equations on multi-block, structured grids using the Wind-US flow solver. The vortex generators were simulated using either a vortex generator model or with grids generated about each vortex generator. Statistical methods were used to compute confidence intervals and grid convergence indices to establish the uncertainties of the analyses with respect to grid refinement. Design-of-experiments methods were applied to quantify the effects of the geometric factors of the vortex generators. The analyses of the computed results illustrate the complexities of quantifying the uncertainties of the inlet performance and the implications of the uncertainties for the design of a vortex generator array for the STEX inlet.

Slater, John W.↗

DOE OSTI2021

Geomechanical and flow implications with continued bioconversion of coal to methane: Experiments and modeling

Microbial conversion of coal to methane is a promising technology during transition of coal-based energy from conventional coal mining to natural gas recovery from coal. Significant research advances have been made towards engineering ideal microbial communities and nutrients for bio-stimulation of coal. However, actual field applications require geomechanical and flow behavior characterization of coal during the bioconversion process as well as gas production over the life of the created “biogenic gas reservoirs”. This work presents the results of an experimental investigation to estimate gas/methane production using bioconversion of coal and analyses of variations in bulk modulus, strain and permeability. Bulk modulus of coal demonstrated time-dependent behavior with continued bioconversion of solid coal. The phenomenon was modeled using mass balancing in a closed environment and the logistic equation based biogenic gas production with time. The modeled gas production and changes in modulus of coal showed excellent agreement with the corresponding experimental results. Next, numerical simulation of biogenic conversion of coal in a constant stress in-situ condition, replicating the Huff ‘n Puff method under field conditions, was carried out. The results showed that bioconversion can lead to decrease in effective stress, increase in permeability and decrease in the modulus of coal with time. Repeated recharge of coal with nutrients and recovering the produced gas, that is, sequential cycles of Huff n’ Puff, showed further increase in permeability and decrease in coal strength, potentially leading to coal failure in-situ, further increasing the permeability, thus enhancing the prospect of field application of the technology.

01 COAL, LIGNITE, AND PEAT↗

NASA NTRS1986

Nonlinear system controller design based on domain of attaction: An application to CELSS analysis and control

Nonlinear system controller design based on the domain of attraction is presented. This is particularly suited to investigating Closed Ecological Life Support Systems (CELSS) models. In particular, the dynamic consequences of changes in the waste storage capacity and system mass, and how information is used for control in CELSS models are examined. The models' high dimensionality and nonlinear state equations make them difficult to analyze by any other technique. The domain of attraction is the region in initial conditions that tend toward an attractor and it is delineated by randomly selecting initial conditions from the region of state space being investigated. Error analysis is done by repeating the domain simulations with independent samples. A refinement of this region is the domain of performance which is the region of initial conditions meeting a performance criteria. In nonlinear systems, local stability does not insure stability over a larger region. The domain of attraction marks out this stability region; hence, it can be considered a measure of a nonlinear system's ability to recovery from state perturbations. Considering random perturbations, the minimum radius of the domain is a measure of the magnitude of perturbations for which recovery is guaranteed. Design of both linear and nonlinear controllers are shown. Three CELSS models, with 9 to 30 state variable, are presented. Measures of the domain of attraction are used to show the global behavior of these models under a variety of design and controller scenarios.

Babcock, P. S., IV↗

DOE OSTI2026

Ultrafast x-ray imaging of coherently controlled molecular dynamics in real space and time

Coherent control aims to manipulate chemical processes on the latent length and timescales of atoms and bonds, scales that are intrinsic to molecular dynamics but not directly resolved by most experimental probes. As a result, existing coherent-control experiments, which overwhelmingly rely on spectroscopic observables, leave a crucial blind spot: the direct, real-space recovery of all atomic and molecular rearrangements in response to coherently controlled excitations. Here, we overcome this limitation by integrating a Tannor-Kosloff-Rice pump-control-probe scheme with ultrafast X-ray scattering to capture snapshots of the wavepacket motion in a benchmark molecular system. We demonstrate this by photoexciting diatomic iodine vapor with a visible pump pulse, selectively steering the wavepacket toward ground-state recombination or dissociative pathways with a time-delayed near-IR control pulse, and recording the dynamics with angstrom and femtosecond precision with an ultrashort hard X-ray probe pulse. By comparing these structural observations with numerical solutions of the time-dependent Schrödinger equation, we reveal how coherent control actively reshapes the molecular charge density distribution. Our results pave the way for leveraging structural feedback as a control handle and provide a fundamental microscopic visualization of quantum decoherence and energy redistribution at the atomic level.

Hopper, Thomas R. [SLAC National Accelerator Labor↗

NASA NTRS1997

A Durable Reduction of Cosmic Ray Intensity in the Outer Heliosphere

This paper reports Pioneer 10 (P10) and Pioneer 11 (P11) observations of the intensity J(E(sub p) greater than 80 MeV) of galactic cosmic rays in the heliosphere near the heliographic equator during the 24-year period 1972-1996 and out to a heliocentric radial distance of 65 AU. It updates previous P10/P11 determinations of the time dependence of the radial gradient of intensity and emphasizes the recent 10-year period, especially the consequences of the great Forbush decrease in 1991. A fresh analysis compares P10 and P11 data with comparable data from IMP 8 at 1.0 AU. For this purpose, we have made a critical study of the data from three different instruments on IMP 8 and have developed a new time-dependent reference level of intensity at 1.0 AU for the period 1974-1996. Using this reference, we find that as of late 1996, recovery of intensity following the 1991 Forbush decrease has been markedly less complete in the outer heliosphere than at 1.0 AU. As a consequence, the mean radial gradient between 4 and 65 AU is now only about +0.3% 1/AU. Our findings favor the latitudinal wedge model of the heliosphere (Van Allen and Mihalov, 1990) and suggest that the modulation boundary of the heliosphere is far beyond 65 AU. Generally concordant, but less decisive, evidence of a similar nature has been reported previously by Van Allen (1993), Van Allen (1996), and Webber and Lockwood (1995b).

VanAllen, James A.↗