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Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

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At least 19 records

A High-Speed, Event-Driven, Active Pixel Sensor Readout for Photon-Counting Microchannel Plate Detectors

Silicon array readouts for microchannel plate intensifiers offer several attractive features. In this class of detector, the electron cloud output of the MCP intensifier is converted to visible light by a phosphor; that light is then fiber-optically coupled to the silicon array. In photon-counting mode, the resulting light splashes on the silicon array are recognized and centroided to fractional pixel accuracy by off-chip electronics. This process can result in very high (MCP-limited) spatial resolution while operating at a modest MCP gain (desirable for dynamic range and long term stability). The principal limitation of intensified CCD systems of this type is their severely limited local dynamic range, as accurate photon counting is achieved only if there are not overlapping event splashes within the frame time of the device. This problem can be ameliorated somewhat by processing events only in pre-selected windows of interest of by using an addressable charge injection device (CID) for the readout array. We are currently pursuing the development of an intriguing alternative readout concept based on using an event-driven CMOS Active Pixel Sensor. APS technology permits the incorporation of discriminator circuitry within each pixel. When coupled with suitable CMOS logic outside the array area, the discriminator circuitry can be used to trigger the readout of small sub-array windows only when and where an event splash has been detected, completely eliminating the local dynamic range problem, while achieving a high global count rate capability and maintaining high spatial resolution. We elaborate on this concept and present our progress toward implementing an event-driven APS readout.

Kimble, Randy A.↗

A High-Speed, Event-Driven, Active Pixel Sensor Readout for Photon-Counting Microchannel Plate Detectors

Silicon array readouts for microchannel plate intensifiers offer several attractive features. In this class of detector, the electron cloud output of the MCP intensifier is converted to visible light by a phosphor; that light is then fiber-optically coupled to the silicon array. In photon-counting mode, the resulting light splashes on the silicon array are recognized and centroided to fractional pixel accuracy by off-chip electronics. This process can result in very high (MCP-limited) spatial resolution for the readout while operating at a modest MCP gain (desirable for dynamic range and long term stability). The principal limitation of intensified CCD systems of this type is their severely limited local dynamic range, as accurate photon counting is achieved only if there are not overlapping event splashes within the frame time of the device. This problem can be ameliorated somewhat by processing events only in pre-selected windows of interest or by using an addressable charge injection device (CID) for the readout array. We are currently pursuing the development of an intriguing alternative readout concept based on using an event-driven CMOS Active Pixel Sensor. APS technology permits the incorporation of discriminator circuitry within each pixel. When coupled with suitable CMOS logic outside the array area, the discriminator circuitry can be used to trigger the readout of small sub-array windows only when and where an event splash has been detected, completely eliminating the local dynamic range problem, while achieving a high global count rate capability and maintaining high spatial resolution. We elaborate on this concept and present our progress toward implementing an event-driven APS readout.

Kimble, Randy A.↗

Transformation of two and three-dimensional regions by elliptic systems

A reliable linear system is presented for grid generation in 2-D and 3-D. The method is robust in the sense that convergence is guaranteed but is not as reliable as other nonlinear elliptic methods in generating nonfolding grids. The construction of nonfolding grids depends on having reasonable approximations of cell aspect ratios and an appropriate distribution of grid points on the boundary of the region. Some guidelines are included on approximating the aspect ratios, but little help is offered on setting up the boundary grid other than to say that in 2-D the boundary correspondence should be close to that generated by a conformal mapping. It is assumed that the functions which control the grid distribution depend only on the computational variables and not on the physical variables. Whether this is actually the case depends on how the grid is constructed. In a dynamic adaptive procedure where the grid is constructed in the process of solving a fluid flow problem, the grid is usually updated at fixed iteration counts using the current value of the control function. Since the control function is not being updated during the iteration of the grid equations, the grid construction is a linear procedure. However, in the case of a static adaptive procedure where a trial solution is computed and used to construct an adaptive grid, the control functions may be recomputed at every step of the grid iteration.

Mastin, C. Wayne↗

Methods for Computationally Efficient Structured CFD Simulations of Complex Turbomachinery Flows

This research presents more efficient computational methods by which to perform multi-block structured Computational Fluid Dynamics (CFD) simulations of turbomachinery, thus facilitating higher-fidelity solutions of complicated geometries and their associated flows. This computational framework offers flexibility in allocating resources to balance process count and wall-clock computation time, while facilitating research interests of simulating axial compressor stall inception with more complete gridding of the flow passages and rotor tip clearance regions than is typically practiced with structured codes. The paradigm presented herein facilitates CFD simulation of previously impractical geometries and flows. These methods are validated and demonstrate improved computational efficiency when applied to complicated geometries and flows.

Herrick, Gregory P.↗

Measuring track densities in lunar grains using image analysis

We have used digitized scanning electron micrographs and computer image analysis programs to measure track densities in lunar soil grains. Tracks were formed by highly ionizing solar energetic particles and cosmic rays. Back-scattered electron images produced suitable high contrast images for analysis. We used computer counting and measurement of area to obtain track densities. We found an excellent correlation with manual measurements for track densities below 1x10(exp 8) cm(exp -2). For track densities between 1x10(exp 8) to 1x10(exp 9) cm(exp -2) we found that a regression formula using the percentage area covered by tracks gave good agreement with manual measurements. Measurement of tract densities in lunar samples has been a very rewarding technique for measuring exposure ages and soil maturation processes. We have shown that we can reliably measure track densities in lunar grains using image analysis techniques. Automating track counting may allow application of this technique to important problems in regolith dynamics including the ratio of radiation exposure to reworking in various surface and core samples and in regolith breccias.

Blanford, G. E.↗

Particulate Emission and Optical Measurements in n-Heptane Low-Swirl Non-Premixed Flames at Elevated Pressures

A series of ground combustion tests conducted at elevated pressures demonstrates in-chamber optical measurements of soot emissions, combined with conventional gaseous and particle emissions sampling techniques. Utilizing a micro-radial-entry counter-swirl (MRX) burner, we successfully stabilized an n-heptane low-swirl, non-premixed spray flame across a wide range of equivalence ratios at pressures reaching 250 psia. Our optical diagnostics feature a temporally gated diffused-backlight illumination extinction imaging (DBI-EI) system, equipped with a 470-nm strobe high-intensity LED array as the illumination source, along with a line-of-sight telecentric camera. By accessing the flame tube, the pulsed DBI-EI provides illuminating optical extinction images, enabling experimental estimation of soot volume fractions within the reaction zone. This imaging technique will allow for real-time observation of soot formation dynamics occurring above the air-blast fuel injector. To further enhance our analysis, we employed simultaneous gaseous and particulate extractive diagnostics, interpreting in-flame particulate information through CO2 sampling, exhaust particle sizing, and particle counting. The processed dataset reveals a promising application of DBI-EI for propulsion emission analysis in high-pressure environments, where optical beam-steering effects can significantly impact results. This report is essential to bridging the divide between in-flame optical diagnostics and exhaust extractive measurements. By achieving an understanding of non-premixed combustion emission characteristics, we attempt to provide invaluable data for computer code validation, advancing the field of combustion research and supporting the development of cleaner, more efficient engines.

high-pressure flame↗

Particulate Emission and Optical Measurements in n-Heptane Low-Swirl Non-Premixed Flames at Elevated Pressures

A series of ground combustion tests conducted at elevated pressures demonstrates in-chamber optical measurements of soot emissions, combined with conventional gaseous and particle emissions sampling techniques. Utilizing a micro-radial-entry counter-swirl (MRX) burner, we successfully stabilized an n-heptane low-swirl, non-premixed spray flame across a wide range of equivalence ratios at pressures reaching 250 psia. Our optical diagnostics feature a temporally gated diffused-backlight illumination extinction imaging (DBI-EI) system, equipped with a 470-nm strobe high-intensity LED array as the illumination source, along with a line-of-sight telecentric camera. By accessing the flame tube, the pulsed DBI-EI provides illuminating optical extinction images, enabling experimental estimation of soot volume fractions within the reaction zone. This imaging technique will allow for real-time observation of soot formation dynamics occurring above the air-blast fuel injector. To further enhance our analysis, we employed simultaneous gaseous and particulate extractive diagnostics, interpreting in-flame particulate information through CO2 sampling, exhaust particle sizing, and particle counting. The processed dataset reveals a promising application of DBI-EI for propulsion emission analysis in high-pressure environments, where optical beam-steering effects can significantly impact results. This report is essential to bridging the divide between in-flame optical diagnostics and exhaust extractive measurements. By achieving an understanding of non-premixed combustion emission characteristics, we attempt to provide invaluable data for computer code validation, advancing the field of combustion research and supporting the development of cleaner, more efficient engines.

high-pressure flame↗

Non-Equilibrium Properties from Equilibrium Free Energy Calculations

Calculating free energy in computer simulations is of central importance in statistical mechanics of condensed media and its applications to chemistry and biology not only because it is the most comprehensive and informative quantity that characterizes the eqUilibrium state, but also because it often provides an efficient route to access dynamic and kinetic properties of a system. Most of applications of equilibrium free energy calculations to non-equilibrium processes rely on a description in which a molecule or an ion diffuses in the potential of mean force. In general case this description is a simplification, but it might be satisfactorily accurate in many instances of practical interest. This hypothesis has been tested in the example of the electrodiffusion equation . Conductance of model ion channels has been calculated directly through counting the number of ion crossing events observed during long molecular dynamics simulations and has been compared with the conductance obtained from solving the generalized Nernst-Plank equation. It has been shown that under relatively modest conditions the agreement between these two approaches is excellent, thus demonstrating the assumptions underlying the diffusion equation are fulfilled. Under these conditions the electrodiffusion equation provides an efficient approach to calculating the full voltage-current dependence routinely measured in electrophysiological experiments.

Pohorille, Andrew↗

Beagle 2: The Next Exobiology Mission to Mars

Beagle 2 is a 60 kg probe (with a 30 kg lander) developed in the United Kingdom for inclusion on the European Space Agency's 2003 Mars Express. Beagle 2 will deliver to the Martian surface a payload which consists of a high percentage of science instruments to landed spacecraft mass. Beagle 2 will be launched in June, 2003 with Mars Express on a Soyuz-Fregat rocket from the Baikonur Cosmodrome in Kazakhstan. Beagle 2 will land on Mars on December 26, 2003 in the Isidis Planitia basin (approximately 10 degrees N and 275 degrees W), a large sedimentary basin that overlies the boundary between ancient highlands and northern plains. Isidis Planitia, the third largest basin on Mars, which is possibly filled with sediment deposited at the bottom of long-standing lakes or seas, offers an ideal environment for preserving traces of life. Beagle 2 was developed to search for organic material and other volatiles on and below the surface of Mars in addition to the study of the inorganic chemistry and mineralogy. Beagle 2 will utilize a mechanical mole and grinder to obtain samples from below the surface, under rocks and inside rocks. A pair of stereo cameras will image the landing site along with a microscope for examination of surface and rock samples. Analyses will include both rock and soil samples at various wavelengths, X-ray spectrometer and Mossbauer spectrometer as well as a search for organics and other light element species (e.g. carbonates and water) and measurement of their isotopic compositions. Beagle 2 has as its focus the goal of establishing whether evidence for life existed in the past on Mars at the Isidis Planitia site or at least establishing if the conditions were ever suitable. Carbonates and organic components were first recognized as existing on Mars when they were found in the Martian meteorite Nakhla. Romanek et al showed the carbonates in ALH84001 were formed at low temperatures. McKay et al noted possible evidence of early life on Mars within the ALH84001 meteorite. Thomas-Keprta et al showed the magnetite biomarkers in ALH84001's carbonates are indistinguishable from those formed by magnetotactic bacteria found on Earth. Gibson et al showed there was significant evidence for liquid water and biogenic products present on Mars across a 3.9 billion year period. A mechanical arm (PAW) operates from the lander and is used for science operations along with sample acquisition. Instruments attached to the PAW include: stereo cameras, Mossbauer instrument, X-ray fluorescence instrument, microscope, environmental sensors, rock corer/grinder, a spoon, mirror, brushes, a mole attachment for acquisition of subsurface to depths of 1 to 2 meters and an illumination device. Each camera has 14 filters which have been optimized for mineralogy composition, dust and water vapor detection. The microscope's camera is designed for viewing the size and shape of dust particles, rock surfaces, microfossils, and characteristics of the samples prior to introduction into the gas analysis package (GAP). The camera has a resolution of 4 microns/pixel, features four color capability (red, green, blue and UV (ultraviolet) fluoresence), a depth of focus of 40 micrometers and translation stage of +3 millimeters. The heart of the Beagle 2's life detection package is the gas analysis package (GAP), which consists of a mass spectrometer with collectors at fixed masses for precise isotopic ratio measurements and voltage scanning for spectral analysis. Primary aim of the GAP is to search for the presence of bulk constituents, individual species, and isotopic fractionations for both extinct and extent life along with studying the low-temperature geochemistry of the hydrogen, carbon, nitrogen and oxygen components on Mars from both the surface and atmosphere. GAP is a magnetic sector mass spectrometer with the range of 1 to 140 amu which can be operated in both the static and dynamic modes. A triple Faraday collector array will be used for C, N and O ratios along with a double Faraday array for H/D. Pulse counting electron multiplier will be utilized for noble gases and selected organics. Anticipated detection limits are at the picomole level for operation in the static mode of operation and high precision isotopic measurements will be made in the dynamic mode. Sample processing and preparation system consists of reaction vessels along with references. Sample ovens capable of being heated are attached to the manifold for sample combustion. Surface, subsurface materials and interior rock specimens will be combusted in pure oxygen gas at various temperature intervals to release organic matter and volatiles. Combustion process will permit detection of all forms and all atoms of carbon present in the samples. A chemical processing system is capable of a variety of conversion reactions. Gases are manipulated either by cryogenic or chemical reactions and passed through the gas handling portion of the vacuum system. There are two modes of operation: quantitative analysis and precise isotopic measurements. Additional information is contained in the original extended abstract.

Gibson, Everett K., Jr.↗

Composition and physiological profiling of sprout-associated microbial communities

The native microfloras of various types of sprouts (alfalfa, clover, sunflower, mung bean, and broccoli sprouts) were examined to assess the relative effects of sprout type and inoculum factors (i.e., sprout-growing facility, seed lot, and inoculation with sprout-derived inocula) on the microbial community structure of sprouts. Sprouts were sonicated for 7 min or hand shaken with glass beads for 2 min to recover native microfloras from the surface, and the resulting suspensions were diluted and plated. The culturable fraction was characterized by the density (log CFU/g), richness (e.g., number of types of bacteria), and diversity (e.g., microbial richness and evenness) of colonies on tryptic soy agar plates incubated for 48 h at 30 degrees C. The relative similarity between sprout-associated microbial communities was assessed with the use of community-level physiological profiles (CLPPs) based on patterns of utilization of 95 separate carbon sources. Aerobic plate counts of 7.96 +/- 0.91 log CFU/g of sprout tissue (fresh weight) were observed, with no statistically significant differences in microbial cell density, richness, or diversity due to sprout type, sprout-growing facility, or seed lot. CLPP analyses revealed that the microbial communities associated with alfalfa and clover sprouts are more similar than those associated with the other sprout types tested. Variability among sprout types was more extensive than any differences between microbial communities associated with alfalfa and clover sprouts from different sprout-growing facilities and seed lots. These results indicate that the subsequent testing of biocontrol agents should focus on similar organisms for alfalfa and clover, but alternative types may be most suitable for the other sprout types tested. The inoculation of alfalfa sprouts with communities derived from various sprout types had a significant, source-independent effect on microbial community structure, indicating that the process of inoculation alters the dynamics of community development regardless of the types of organisms involved.

NASA Center KSC↗

Collisional and dynamical history of Gaspra

Interpretation of the impact record on Gaspra requires understanding of the effects of collisions on a target body of Gaspra's size and shape, recognition of impact features that may have different morphologies from craters on larger planets, and models of the geological processes that erase and modify impact features. Crater counts on the 140 sq km of Gaspra imaged at highest resolution by the Galileo spacecraft show a steep size-frequency distribution (cumulative power-law index near -3.5) from the smallest resolvable size (150 m diameter) up through the large feature (1.5 km diameter crater) of familiar crater-like morphology. In addition, there appear to be as many as eight roughly circular concavities with diameters greater than 3 km visible on the asteroid. If we restrict our crater counts to features with traditionally recognized crater morphologies, these concavities would not be included. However, if we define craters to include any concave structures that may represent local or regional damage at an impact size, then the larger features on Gaspra are candidates for consideration. Acceptance of the multi-km features as craters has been cautious for several reasons. First, scaling laws (the physically plausible algorithms for extrapolating from experimental data) indicate that Gaspra could not have sustained such large-crater-forming impacts without being disrupted; second, aside from concavity, the larger structures have no other features (e.g. rims) that can be identified with known impact craters; and third, extrapolation of the power-law size distribution for smaller craters predicts no craters larger than 3 km over the entire surface. On the other hand, recent hydrocode modeling of impacts shows that for given impact (albeit into a sphere), the crater size is much larger than given by scaling laws. Gaspra-size bodies can sustain formation of up to 8-km craters without disruption. Besides allowing larger impact craters, this result doubles the lifetime since the last catastrophic fragmentation event up to one billion years. Events that create multi-km craters also globally damage the material structure, such that regolith is produced, whether or not Gaspra 'initially' had a regolith, contrary to other models in which initial regolith is required in order to allow current regolith. Because the globally destructive shock wave precedes basin formation, crater size is closer to the large size extrapolated from gravity-scaling rather than the strength-scaling that had earlier been assumed for such small bodies. This mechanism may also help explain the existence of Stickney on Phobos. Moreover, rejection of the large concavities as craters based on unfamiliar morphology would be premature, because (aside from Stickney) we have no other data on such large impact structures on such a small, irregular body. The eight candidate concavities cover an area greater than that counted for smaller craters, because they are most apparent where small craters cannot be seen: on low resolution images and at the limb on high resolution images. We estimate that there are at least two with diameter greater than 4 km per 140 sq km, which would have to be accounted for in any model that claims these are impact craters.

Greenberg, R.↗

Fuel Line Based Acoustic Flame-Out Detection System

An acoustic flame-out detection system that renders a large high pressure combustor safe in the event of a flame-out and possible explosive reignition. A dynamic pressure transducer is placed in the fuel and detects the stabilizing fuel pressure oscillations, caused by the combustion process. An electric circuit converts the signal from the combustion vortices, and transmitted to the fuel flow to a series of pulses. A missing pulse detector counts the pulses and continuously resets itself. If three consecutive pulses are missing, the circuit closes the fuel valve. With fuel denied the combustor is shut down or restarted under controlled conditions.

Puster, Richard L.↗

A High Dynamic-Range Photon-Counting Receiver for Deep Space Optical Communication

The Deep Space Optical Communication (DSOC) project will demonstrate free-space optical communication at almost 3 AU, or 3 orders of magnitude further than any previous attempt. DSOC will utilize the 5m Palomar Hale Telescope to receive the downlink signal, which will couple the downlink light onto an optical table and into a superconducting nanowire single photon detector (SNSPD). The output of the SNSPD is digitized by the Ground Laser Receiver Signal Processing Assembly (GSPA) using a high throughput streaming time to digital converter (TDC). The GSPA is a scalable FPGA-based receiver which demodulates and decodes the DSOC downlink signal through novel signal processing algorithms implemented on Xilinx UltraScale+ FPGAs, as well as Python-based software monitor and control routines. Exploiting the unique TDC-based architecture, the GSPA supports over four orders of magnitude of downlink data rates across multiple orders of magnitude of signal and background powers. In this paper we present an overview of the hardware, firmware and software architectures to implement this system, as well as performance analysis for links ranging from near-Earth to 2.8 AU.

Srinivasan, Meera↗

Design, development and manufacture of a breadboard radio frequency mass gauging system

The feasibility of the RF gauging mode, counting technique was demonstrated for gauging liquid hydrogen and liquid oxygen under all attitude conditions. With LH2, it was also demonstrated under dynamic fluid conditions, in which the fluid assumes ever changing positions within the tank, that the RF gauging technique on the average provides a very good indication of mass. It is significant that the distribution of the mode count data at each fill level during dynamic LH2 and LOX orientation testing does approach a statistical normal distribution. Multiple space-diversity probes provide better coupling to the resonant modes than utilization of a single probe element. The variable sweep rate generator technique provides a more uniform mode versus time distribution for processing.

Source record↗

Herschel/PACS Photometry of Transiting-Planet Host Stars with Candidate Warm Debris Disks

Dust in debris disks is produced by colliding or evaporating planetesimals, which are remnants of the planet formation process. Warm dust disks, known by their emission at less than or equal to 24 micrometer, are rare (4% of FGK main sequence stars) and especially interesting because they trace material in the region likely to host terrestrial planets, where the dust has a very short dynamical lifetime. Statistical analyses of the source counts of excesses as found with the mid-IR Wide Field Infrared Survey Explorer (WISE) suggest that warm-dust candidates found for the Kepler transiting-planet host-star candidates can be explained by extragalactic or galactic background emission aligned by chance with the target stars. These statistical analyses do not exclude the possibility that a given WISE excess could be due to a transient dust population associated with the target. Here we report Herschel/PACS 100 and 160 micron follow-up observations of a sample of Kepler and non-Kepler transiting-planet candidates' host stars, with candidate WISE warm debris disks, aimed at detecting a possible cold debris disk in any one of them. No clear detections were found in any one of the objects at either wavelength. Our upper limits confirm that most objects in the sample do not have a massive debris disk like that in beta Pic. We also show that the planet-hosting star WASP-33 does not have a debris disk comparable to the one around eta Crv. Although the data cannot be used to rule out rare warm disks around the Kepler planet-hosting candidates, the lack of detections and the characteristics of neighboring emission found at far-IR wavelengths support an earlier result suggesting that most of the WISE-selected IR excesses around Kepler candidate host stars are likely due to either chance alignment with background IR-bright galaxies and/or to interstellar emission.

Wide Field Infrared Survey Explorer (WISE)↗

Safety Critical Mechanisms

Spaceflight mechanisms have a reputation for being difficult to develop and operate successfully. This reputation is well earned. Many circumstances conspire to make this so: the environments in which the mechanisms are used are extremely severe, there is usually limited or no maintenance opportunity available during operation due to this environment, the environments are difficult to replicate accurately on the ground, the expense of the mechanism development makes it impractical to build and test many units for long periods of time before use, mechanisms tend to be highly specialized and not prone to interchangeability or off-the-shelf use, they can generate and store a lot of energy, and the nature of mechanisms themselves, as a combination of structures, electronics, etc. designed to accomplish specific dynamic performance, makes them very complex and subject to many unpredictable interactions of many types. In addition to their complexities, mechanism are often counted upon to provide critical vehicle functions that can result in catastrophic events should the functions not be performed. It is for this reason that mechanisms are frequently subjected to special scrutiny in safety processes. However, a failure tolerant approach, along with good design and development practices and detailed design reviews, can be developed to allow such notoriously troublesome mechanisms to be utilized confidently in safety-critical applications.

Robertson, Brandan↗

DE 1 RIMS operational characteristics

The Retarding Ion Mass Spectrometer (RIMS) on the Dynamics Explorer 1 spacecraft observes both the thermal and superthermal (50 eV) ions of the ionosphere and inner magnetosphere. It is capable of measuring the detailed species distribution function of these ions in many cases. It was equipped with an integral electrometer to permit in-flight calibration of the detector sensitivities and variations thereof. A guide to understanding the RIMS data set is given. The reduction process from count rates to physical quantities is discussed in some detail. The procedure used to establish in-flight calibration is described, and results of a comparison with densities from plasma wave measurements are provided. Finally, a discussion is provided of various anomalies in the data set, including changes of channeltron efficiency with time, spin modulation of the axial sensor heads, apparent potential differences between the sensor heads, and failures of the radial head retarding potential sweep and of the -Z axial head aperture plane bias. Studies of the RIMS data set should be conducted only with a thorough awareness of the material presented here, or in collaboration with one of the scientists actively involved with RIMS data analysis.

Olsen, R. C.↗

Granular Contact Forces: Proof of "Self-Ergodicity" by Generalizing Boltzmann's Stosszahlansatz and H Theorem

Ergodicity is proved for granular contact forces. To obtain this proof from first principles, this paper generalizes Boltzmann's stosszahlansatz (molecular chaos) so that it maintains the necessary correlations and symmetries of granular packing ensembles. Then it formally counts granular contact force states and thereby defines the proper analog of Boltzmann's H functional. This functional is used to prove that (essentially) all static granular packings must exist at maximum entropy with respect to their contact forces. Therefore, the propagation of granular contact forces through a packing is a truly ergodic process in the Boltzmannian sense, or better, it is self-ergodic. Self-ergodicity refers to the non-dynamic, internal relationships that exist between the layer-by-layer and column-by-column subspaces contained within the phase space locus of any particular granular packing microstate. The generalized H Theorem also produces a recursion equation that may be solved numerically to obtain the density of single particle states and hence the distribution of granular contact forces corresponding to the condition of self-ergodicity. The predictions of the theory are overwhelmingly validated by comparison to empirical data from discrete element modeling.

Metzger, Philip T.↗