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NASA NTRS1997

Estimation of Slow Crack Growth Parameters for Constant Stress-Rate Test Data of Advanced Ceramics and Glass by the Individual Data and Arithmetic Mean Methods

The two estimation methods, individual data and arithmetic mean methods, were used to determine the slow crack growth (SCG) parameters (n and D) of advanced ceramics and glass from a large number of room- and elevated-temperature constant stress-rate ('dynamic fatigue') test data. For ceramic materials with Weibull modulus greater than 10, the difference in the SCG parameters between the two estimation methods was negligible; whereas, for glass specimens exhibiting Weibull modulus of about 3, the difference was amplified, resulting in a maximum difference of 16 and 13 %, respectively, in n and D. Of the two SCG parameters, the parameter n was more sensitive to the estimation method than the other. The coefficient of variation in n was found to be somewhat greater in the individual data method than in the arithmetic mean method.

Choi, Sung R.↗

NASA NTRS1997

An Integrated Product Environment

Mechanical Advantage is a mechanical design decision support system. Unlike our CAD/CAM cousins, Mechanical Advantage addresses true engineering processes, not just the form and fit of geometry. If we look at a traditional engineering environment, we see that an engineer starts with two things - performance goals and design rules. The intent is to have a product perform specific functions and accomplish that within a designated environment. Geometry should be a simple byproduct of that engineering process - not the controller of it. Mechanical Advantage is a performance modeler allowing engineers to consider all these criteria in making their decisions by providing such capabilities as critical parameter analysis, tolerance and sensitivity analysis, math driven Geometry, and automated design optimizations. If you should desire an industry standard solid model, we would produce an ACIS-based solid model. If you should desire an ANSI/ISO standard drawing, we would produce this as well with a virtual push of the button. For more information on this and other Advantage Series products, please contact the author.

Higgins, Chuck↗

NASA NTRS1999

Two-Channel Satellite Retrievals of Aerosol Properties: An Overview

In order to reduce current uncertainties in the evaluation of the direct and indirect effects of tropospheric aerosols on climate on the global scale, it has been suggested to apply multi-channel retrieval algorithms to the full period of existing satellite data. This talk will outline the methodology of interpreting two-channel satellite radiance data over the ocean and describe a detailed analysis of the sensitivity of retrieved aerosol parameters to the assumptions made in different retrieval algorithms. We will specifically address the calibration and cloud screening issues, consider the suitability of existing satellite data sets to detecting short- and long-term regional and global changes, compare preliminary results obtained by several research groups, and discuss the prospects of creating an advanced retroactive climatology of aerosol optical thickness and size over the oceans.

Mishchenko, Michael I.↗

NASA NTRS2000

Interactive Soil Dust Aerosol Model in the GISS GCM: Sensitivity of the Soil Dust Cycle to Radiative Properties of Soil Dust Aerosols - Part 1

The sensitivity of the soil dust aerosol cycle to the radiative forcing by soil dust aerosols is studied. Four experiments with the NASA/GISS atmospheric general circulation model, which includes a soil dust aerosol model, are compared, all using a prescribed climatological sea surface temperature as lower boundary condition. In one experiment, dust is included as dynamic tracer only (without interacting with radiation), whereas dust interacts with radiation in the other simulations. Although the single scattering albedo of dust particles is prescribed to be globally uniform in the experiments with radiatively active dust, a different single scattering albedo is used in those experiments to estimate whether regional variations in dust optical properties, corresponding to variations in mineralogical composition among different source regions, are important for the soil dust cycle and the climate state. On a global scale, the radiative forcing by dust generally causes a reduction in the atmospheric dust load corresponding to a decreased dust source flux. That is, there is a negative feedback in the climate system due to the radiative effect of dust. The dust source flux and its changes were analyzed in more detail for the main dust source regions. This analysis shows that the reduction varies both with the season and with the single scattering albedo of the dust particles. By examining the correlation with the surface wind, it was found that the dust emission from the Saharan/Sahelian source region and from the Arabian peninsula, along with the sensitivity of the emission to the single scattering albedo of dust particles, are related to large scale circulation patterns, in particular to the trade winds during Northern Hemisphere winter and to the Indian monsoon circulation during summer. In the other regions, such relations to the large scale circulation were not found. There, the dependence of dust deflation to radiative forcing by dust particles is probably dominated by physical processes with short time scales. The experiments show that dust radiative forcing can lead to significant changes both in the soil dust cycle and in the climate state. To estimate dust concentration and radiative forcing by dust more accurately, dust size distributions and dust single scattering albedo in the model should be a function of the source region, because dust concentration and climate response to dust radiative forcing are sensitive to dust radiative parameters.

Perlwitz, Jan↗

NASA NTRS2002

Photoevaporation of Clumps in Photodissociation Regions

We present the results of an investigation of the effects of Far Ultraviolet (FUV) radiation (6.0eV < hv < 13.6eV) from hot early type OB stars on clumps in star-forming molecular clouds. Clumps in FUV-illuminated regions (or photodissociation regions or PDRs) undergo external heating and photodissociation as they are exposed to the FUV field, resulting in a loss of cold, molecular lump mass as it is converted to warm atomic gas. The heating, if rapid, creates strong photoevaporative mass flows off the clump surfaces, and drives shocks into the clumps, compressing them to high densities. The clumps lose mass on relatively short timescales. The evolution of an individual clump is found to be sensitive to three dimensionless parameters: Nc0, the ratio of the initial column density of the clump to the column N(0) approx. 10(exp 21) cm(exp -2) of a warm FUV-heated surface region; upsilon, the ratio of the sound speed in the heated surface to that in the cold clump material: and t(FUV)t(c), the ratio of the "turn-on time" t(FUV) of the heating flux on a clump to its initial sound crossing-time t(c). The evolution also depends on whether a confining interclump medium exists, or whether the interclump region has negligible pressure, as is the case for turbulence-generated clumps. In this paper, we use spherical 1-D numerical hydrodynamic models as well as approximate analytical models to study the dependence of clump photoevaporation on the physical parameters of the clump, and to derive the dynamical evolution, mass loss rates and photoevaporative timescales of a clump for a variety of astrophysical situations. Turbulent clumps evolve so that their column densities are equal to a critical value determined by the local FUV field, and typically have short photo evaporation timescales, approx. 10(exp 4-5) years for a 1 M(solar mass) clump in a typical star-forming region (Nc0 = 10, upsilon = 10). Clumps with insufficient magnetic pressure support, and in strong FUV fields may be driven to collapse by the compressional effect of converging shock waves. We also estimate the rocket effect on photoevaporating clumps and find that it is significant only for the smallest clumps, with sizes much less than the extent of the PDR itself. Clumps that are confined by all interclump medium may either get completely photoevaporated, or may preserve a shielded core with a warm, dissociated, protective shell that, absorbs the incident FUV flux. We compare our results with observations of some well studied PDRs: the Orion Bar, M17SW NGC 2023 and the Rosette Nebula. The data are consistent with both interpretations of clump origin. turbulence and pressure confinement, with a slight indication for favouring the turbulent model for clumps over pressure-confined

Gorti, Uma↗

NASA NTRS2002

Evaluation and Characterization Study of Dual Pulse Laser-Induced Spark (DPLIS) For Rocket Engine Ignition System Application

This paper addresses the progress of technology development of a laser ignition system at NASA Marshall Space Flight Center (MSFC). Initial hot-fire tests in a small-scale rocket chamber at MSFC have demonstrated the DPLIS concept having two main advantages over existing laser ignition concepts. First, the DPLIS can be potentially optimized its laser pulse format to maximize the initial plasma volume, the plasma lifetime, as well as the flame kernel growth rate. Characterization studies of the laser pulse format are now underway with experiments of igniting gaseous hydrogen/air in a Hencken burner. Once ignition is achieved, the flame is open to the atmosphere. This open environment allows easy access for diagnostics of the ignition phenomenon. The quick turn-around time of conducting experiments on this burner make it more amenable for conducting a large number of experiments for statistical analysis of the sensitivity of the test parameters. The results from these experiments will help optimize the laser format for future testing in an H2/O2 subscale rocket chamber.

Trinh, Huu P.↗

NASA NTRS2004

DSMC Simulations of Hypersonic Flows With Shock Interactions and Validation With Experiments

The capabilities of a relatively new direct simulation Monte Carlo (DSMC) code are examined for the problem of hypersonic laminar shock/shock and shock/boundary layer interactions, where boundary layer separation is an important feature of the flow. Flow about two model configurations is considered, where both configurations (a biconic and a hollow cylinder-flare) have recent published experimental measurements. The computations are made by using the DS2V code of Bird, a general two-dimensional/axisymmetric time accurate code that incorporates many of the advances in DSMC over the past decade. The current focus is on flows produced in ground-based facilities at Mach 12 and 16 test conditions with nitrogen as the test gas and the test models at zero incidence. Results presented highlight the sensitivity of the calculations to grid resolution, sensitivity to physical modeling parameters, and comparison with experimental measurements. Information is provided concerning the flow structure and surface results for the extent of separation, heating, pressure, and skin friction.

Moss, James N.↗

NASA NTRS2004

DSMC Simulations of Hypersonic Flows With Shock Interactions and Validation With Experiments

The capabilities of a relatively new direct simulation Monte Carlo (DSMC) code are examined for the problem of hypersonic laminar shock/shock and shock/boundary layer interactions, where boundary layer separation is an important feature of the flow. Flow about two model configurations is considered, where both configurations (a biconic and a hollow cylinder-flare) have recent published experimental measurements. The computations are made by using the DS2V code of Bird, a general two-dimensional/axisymmetric time accurate code that incorporates many of the advances in DSMC over the past decade. The current focus is on flows produced in ground-based facilities at Mach 12 and 16 test conditions with nitrogen as the test gas and the test models at zero incidence. Results presented highlight the sensitivity of the calculations to grid resolutions, sensitivity to physical modeling parameters, and comparison with experimental measurements. Information is provided concerning the flow structure and surface results for the extent of separation, heating, pressure, and skin friction.

Moss, James N.↗

NASA NTRS2003

Aeroelastic System Development Using Proper Orthogonal Decomposition and Volterra Theory

This research combines Volterra theory and proper orthogonal decomposition (POD) into a hybrid methodology for reduced-order modeling of aeroelastic systems. The out-come of the method is a set of linear ordinary differential equations (ODEs) describing the modal amplitudes associated with both the structural modes and the POD basis functions for the uid. For this research, the structural modes are sine waves of varying frequency, and the Volterra-POD approach is applied to the fluid dynamics equations. The structural modes are treated as forcing terms which are impulsed as part of the uid model realization. Using this approach, structural and uid operators are coupled into a single aeroelastic operator. This coupling converts a free boundary uid problem into an initial value problem, while preserving the parameter (or parameters) of interest for sensitivity analysis. The approach is applied to an elastic panel in supersonic cross ow. The hybrid Volterra-POD approach provides a low-order uid model in state-space form. The linear uid model is tightly coupled with a nonlinear panel model using an implicit integration scheme. The resulting aeroelastic model provides correct limit-cycle oscillation prediction over a wide range of panel dynamic pressure values. Time integration of the reduced-order aeroelastic model is four orders of magnitude faster than the high-order solution procedure developed for this research using traditional uid and structural solvers.

Lucia, David J.↗

NASA NTRS2002

Phylogeny and systematic position of Opiliones: a combined analysis of chelicerate relationships using morphological and molecular data

The ordinal level phylogeny of the Arachnida and the suprafamilial level phylogeny of the Opiliones were studied on the basis of a combined analysis of 253 morphological characters, the complete sequence of the 18S rRNA gene, and the D3 region of the 28S rRNA gene. Molecular data were collected for 63 terminal taxa. Morphological data were collected for 35 exemplar taxa of Opiliones, but groundplans were applied to some of the remaining chelicerate groups. Six extinct terminals, including Paleozoic scorpions, are scored for morphological characters. The data were analyzed using strict parsimony for the morphological data matrix and via direct optimization for the molecular and combined data matrices. A sensitivity analysis of 15 parameter sets was undertaken, and character congruence was used as the optimality criterion to choose among competing hypotheses. The results obtained are unstable for the high-level chelicerate relationships (except for Tetrapulmonata, Pedipalpi, and Camarostomata), and the sister group of the Opiliones is not clearly established, although the monophyly of Dromopoda is supported under many parameter sets. However, the internal phylogeny of the Opiliones is robust to parameter choice and allows the discarding of previous hypotheses of opilionid phylogeny such as the "Cyphopalpatores" or "Palpatores." The topology obtained is congruent with the previous hypothesis of "Palpatores" paraphyly as follows: (Cyphophthalmi (Eupnoi (Dyspnoi + Laniatores))). Resolution within the Eupnoi, Dyspnoi, and Laniatores (the latter two united as Dyspnolaniatores nov.) is also stable to the superfamily level, permitting a new classification system for the Opiliones. c2002 The Willi Hennig Society.

NASA Discipline Evolutionary Biology↗

NASA NTRS1990

A dynamic growth model of vegetative soya bean plants: model structure and behaviour under varying root temperature and nitrogen concentration

A differential equation model of vegetative growth of the soya bean plant (Glycine max (L.) Merrill cv. Ransom') was developed to account for plant growth in a phytotron system under variation of root temperature and nitrogen concentration in nutrient solution. The model was tested by comparing model outputs with data from four different experiments. Model predictions agreed fairly well with measured plant performance over a wide range of root temperatures and over a range of nitrogen concentrations in nutrient solution between 0.5 and 10.0 mmol NO3- in the phytotron environment. Sensitivity analyses revealed that the model was most sensitive to changes in parameters relating to carbohydrate concentration in the plant and nitrogen uptake rate.

Non-NASA Center↗

NASA NTRS2007

Transient Numerical Modeling of Catalytic Channels

This paper presents a transient model of catalytic combustion suitable for isolated channels and monolith reactors. The model is a lumped two-phase (gas and solid) model where the gas phase is quasi-steady relative to the transient solid. Axial diffusion is neglected in the gas phase; lateral diffusion, however, is accounted for using transfer coefficients. The solid phase includes axial heat conduction and external heat loss due to convection and radiation. The combustion process utilizes detailed gas and surface reaction models. The gas-phase model becomes a system of stiff ordinary differential equations while the solid phase reduces, after discretization, into a system of stiff ordinary differential-algebraic equations. The time evolution of the system came from alternating integrations of the quasi-steady gas and transient solid. This work outlines the numerical model and presents some sensitivity studies on important parameters including internal transfer coefficients, catalytic surface site density, and external heat-loss (if applicable). The model is compared to two experiments using CO fuel: (1) steady-state conversion through an isothermal platinum (Pt) tube and (2) transient propagation of a catalytic reaction inside a small Pt tube. The model requires internal mass-transfer resistance to match the experiments at lower residence times. Under mass-transport limited conditions, the model reasonably predicted exit conversion using global mass-transfer coefficients. Near light-off, the model results did not match the experiment precisely even after adjustment of mass-transfer coefficients. Agreement improved for the first case after adjusting the surface kinetics such that the net rate of CO adsorption increased compared to O2. The CO / O2 surface mechanism came from a sub-set of reactions in a popular CH4 / O2 mechanism. For the second case, predictions improved for lean conditions with increased external heat loss or adjustment of the kinetics as in the first case. Finally, the results show that different initial surface-species distribution leads to different steady-states under certain conditions. These results demonstrate the utility of a lumped two-phase model of a transient catalytic combustor with detailed chemistry.

Struk, Peter M.↗

NASA NTRS2004

Error Modeling of Multi-baseline Optical Truss: Application to SIM Metrology Truss Field Dependent Error - Part II

The current design of the Space Interferometry Mission (SIM) employs a 19 laser-metrology-beam system (also called L19 external metrology truss) to monitor changes of distances between the fiducials of the flight system's multiple baselines. The function of the external metrology truss is to aid in the determination of the time-variations of the interferometer baseline. The largest contributor to truss error occurs in SIM wide-angle observations when the articulation of the siderostat mirrors (in order to gather starlight from different sky coordinates) brings to light systematic errors due to offsets at levels of instrument components (which include comer cube retro-reflectors, etc.). This error is labeled external metrology wide-angle field-dependent error. Physics-based model of field-dependent error at single metrology gauge level is developed and linearly propagated to errors in interferometer delay. In this manner delay error sensitivity to various error parameters or their combination can be studied using eigenvalue/eigenvector analysis. Also validation of physics-based field-dependent model on SIM testbed lends support to the present approach. As a first example, dihedral error model is developed for the comer cubes (CC) attached to the siderostat mirrors. Then the delay errors due to this effect can be characterized using the eigenvectors of composite CC dihedral error. The essence of the linear error model is contained in an error-mapping matrix. A corresponding Zernike component matrix approach is developed in parallel, first for convenience of describing the RMS of errors across the field-of-regard (FOR), and second for convenience of combining with additional models. Average and worst case residual errors are computed when various orders of field-dependent terms are removed from the delay error. Results of the residual errors are important in arriving at external metrology system component requirements. Double CCs with ideally co-incident vertices reside with the siderostat. The non-common vertex error (NCVE) is treated as a second example. Finally combination of models, and various other errors are discussed.

comer cube retro-reflector↗

NASA NTRS2009

The Use of Meteorlogical Data to Improve Contrail Detection in Thermal Imagery over Ireland.

Aircraft induced contrails have been found to have a net warming influence on the climate system, with strong regional dependence. Persistent linear contrails are detectable in 1 Km thermal imagery and, using an automated Contrail Detection Algorithm (CDA), can be identified on the basis of their different properties at the 11 and 12 m w av.el enTgthshe algorithm s ability to distinguish contrails from other linear features depends on the sensitivity of its tuning parameters. In order to keep the number of false identifications low, the algorithm imposes strict limits on contrail size, linearity and intensity. This paper investigates whether including additional information (i.e. meteorological data) within the CDA may allow for these criteria to be less rigorous, thus increasing the contrail-detection rate, without increasing the false alarm rate.

Whelan, Gillian M.↗

NASA NTRS2011

Evaluation of Convective Transport in the GEOS-5 Chemistry and Climate Model

The NASA Goddard Earth Observing System (GEOS-5) Chemistry and Climate Model (CCM) consists of a global atmospheric general circulation model and the combined stratospheric and tropospheric chemistry package from the NASA Global Modeling Initiative (GMI) chemical transport model. The subgrid process of convective tracer transport is represented through the Relaxed Arakawa-Schubert parameterization in the GEOS-5 CCM. However, substantial uncertainty for tracer transport is associated with this parameterization, as is the case with all global and regional models. We have designed a project to comprehensively evaluate this parameterization from the point of view of tracer transport, and determine the most appropriate improvements that can be made to the GEOS-5 convection algorithm, allowing improvement in our understanding of the role of convective processes in determining atmospheric composition. We first simulate tracer transport in individual observed convective events with a cloud-resolving model (WRF). Initial condition tracer profiles (CO, CO2, O3) are constructed from aircraft data collected in undisturbed air, and the simulations are evaluated using aircraft data taken in the convective anvils. A single-column (SCM) version of the GEOS-5 GCM with online tracers is then run for the same convective events. SCM output is evaluated based on averaged tracer fields from the cloud-resolving model. Sensitivity simulations with adjusted parameters will be run in the SCM to determine improvements in the representation of convective transport. The focus of the work to date is on tropical continental convective events from the African Monsoon Multidisciplinary Analyses (AMMA) field mission in August 2006 that were extensively sampled by multiple research aircraft.

Pickering, Kenneth E.↗

NASA NTRS2010

An Assessment of the Surface Longwave Direct Radiative Effect of Airborne Saharan Dust During the NAMMA Field Campaign

In September 2006, NASA Goddard s mobile ground-based laboratories were deployed to Sal Island in Cape Verde (16.73degN, 22.93degW) to support the NASA African Monsoon Multidisciplinary Analysis (NAMMA) field study. The Atmospheric Emitted Radiance Interferometer (AERI), a key instrument for spectrally characterizing the thermal IR, was used to retrieve the dust IR aerosol optical depths (AOTs) in order to examine the diurnal variability of airborne dust with emphasis on three separate dust events. AERI retrievals of dust AOT are compared with those from the coincident/collocated multifilter rotating shadow-band radiometer (MFRSR), micropulse lidar (MPL), and NASA Cloud-Aerosol Lidar and Infrared Pathfinder Satellite Observation (CALIPSO) sensors. The retrieved AOTs are then inputted into the Fu-Liou 1D radiative transfer model to evaluate local instantaneous direct longwave radiative effects (DRE(sub LW)) of dust at the surface in cloud-free atmospheres and its sensitivity to dust microphysical parameters. The top-of-atmosphere DRE(sub LW) and longwave heating rate profiles are also evaluated. Instantaneous surface DRE(sub LW) ranges from 2 to 10 W/sq m and exhibits a strong linear dependence with dust AOT yielding a DRE(sub LW) of 16 W/sq m per unit dust AOT. The DRE(sub LW) is estimated to be approx.42% of the diurnally averaged direct shortwave radiative effect at the surface but of opposite sign, partly compensating for the shortwave losses. Certainly nonnegligible, the authors conclude that DRE(sub LW) can significantly impact the atmospheric energetics, representing an important component in the study of regional climate variation.

Hansell, R. A.↗

NASA NTRS2011

Test-Anchored Vibration Response Predictions for an Acoustically Energized Curved Orthogrid Panel with Mounted Components

rich body of vibroacoustic test data was recently generated at Marshall Space Flight Center for component-loaded curved orthogrid panels typical of launch vehicle skin structures. The test data were used to anchor computational predictions of a variety of spatially distributed responses including acceleration, strain and component interface force. Transfer functions relating the responses to the input pressure field were generated from finite element based modal solutions and test-derived damping estimates. A diffuse acoustic field model was applied to correlate the measured input sound pressures across the energized panel. This application quantifies the ability to quickly and accurately predict a variety of responses to acoustically energized skin panels with mounted components. Favorable comparisons between the measured and predicted responses were established. The validated models were used to examine vibration response sensitivities to relevant modeling parameters such as pressure patch density, mesh density, weight of the mounted component and model form. Convergence metrics include spectral densities and cumulative root-mean squared (RMS) functions for acceleration, velocity, displacement, strain and interface force. Minimum frequencies for response convergence were established as well as recommendations for modeling techniques, particularly in the early stages of a component design when accurate structural vibration requirements are needed relatively quickly. The results were compared with long-established guidelines for modeling accuracy of component-loaded panels. A theoretical basis for the Response/Pressure Transfer Function (RPTF) approach provides insight into trends observed in the response predictions and confirmed in the test data. The software developed for the RPTF method allows easy replacement of the diffuse acoustic field with other pressure fields such as a turbulent boundary layer (TBL) model suitable for vehicle ascent. Structural responses using a TBL model were demonstrated, and wind tunnel tests have been proposed to anchor the predictions and provide new insight into modeling approaches for this environment. Finally, design load factors were developed from the measured and predicted responses and compared with those derived from traditional techniques such as historical Mass Acceleration Curves and Barrett scaling methods for acreage and component-loaded panels.

Frady, Gregory P.↗

NASA NTRS2011

Test-Anchored Vibration Response Predictions for an Acoustically Energized Curved Orthogrid Panel with Mounted Components

A rich body of vibroacoustic test data was recently generated at Marshall Space Flight Center for a curved orthogrid panel typical of launch vehicle skin structures. Several test article configurations were produced by adding component equipment of differing weights to the flight-like vehicle panel. The test data were used to anchor computational predictions of a variety of spatially distributed responses including acceleration, strain and component interface force. Transfer functions relating the responses to the input pressure field were generated from finite element based modal solutions and test-derived damping estimates. A diffuse acoustic field model was employed to describe the assumed correlation of phased input sound pressures across the energized panel. This application demonstrates the ability to quickly and accurately predict a variety of responses to acoustically energized skin panels with mounted components. Favorable comparisons between the measured and predicted responses were established. The validated models were used to examine vibration response sensitivities to relevant modeling parameters such as pressure patch density, mesh density, weight of the mounted component and model form. Convergence metrics include spectral densities and cumulative root-mean squared (RMS) functions for acceleration, velocity, displacement, strain and interface force. Minimum frequencies for response convergence were established as well as recommendations for modeling techniques, particularly in the early stages of a component design when accurate structural vibration requirements are needed relatively quickly. The results were compared with long-established guidelines for modeling accuracy of component-loaded panels. A theoretical basis for the Response/Pressure Transfer Function (RPTF) approach provides insight into trends observed in the response predictions and confirmed in the test data. The software modules developed for the RPTF method can be easily adapted for quick replacement of the diffuse acoustic field with other pressure field models; for example a turbulent boundary layer (TBL) model suitable for vehicle ascent. Wind tunnel tests have been proposed to anchor the predictions and provide new insight into modeling approaches for this type of environment. Finally, component vibration environments for design were developed from the measured and predicted responses and compared with those derived from traditional techniques such as Barrett scaling methods for unloaded and component-loaded panels.

Frady, Gregory P.↗