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At least 1,009 records · Page 56

Development of Semi-Empirical Damping Equation for Baffled Tank with Oblate Spheroidal Dome

Propellant slosh is a potential source of disturbance that can significantly impact the stability of space vehicles. The slosh dynamics are typically represented by a mechanical model of a spring-mass-damper. This mechanical model is then included in the equation of motion of the entire vehicle for Guidance, Navigation and Control analysis. The typical parameters required by the mechanical model include natural frequency of the slosh, slosh mass, slosh mass center location, and the critical damping ratio. A fundamental study has been undertaken at NASA MSFC to understand the fluid damping physics from a ring baffle in the barrel section of a propellant tank. An asymptotic damping equation and CFD blended equation have been derived by NASA MSFC team to complement the popularly used Miles equation at different flow regimes. The new development has found success in providing a nonlinear damping model for the Space Launch System. The purpose of this study is to further extend the semi-empirical damping equations into the oblate spheroidal dome section of the propellant tanks. First, previous experimental data from the spherical baffled tank are collected and analyzed. Several methods of taking the dome curvature effect, including a generalized Miles equation, area projection method, and equalized fill height method, are assessed. CFD simulation is used to shed light on the interaction of vorticity around the baffle with the locally curved wall and liquid-gas interface. The final damping equation will be validated by a recent subscale test with an oblate spheroidal dome conducted at NASA MSFC.

Yang, H. Q.↗

Mineralization of collagen may occur on fibril surfaces: evidence from conventional and high-voltage electron microscopy and three-dimensional imaging

The interaction between collagen and mineral crystals in the normally calcifying leg tendons from the domestic turkey, Meleagris gallopavo, has been investigated at an ultrastructural level with conventional and high-voltage electron microscopy, computed tomography, and three-dimensional image reconstruction methods. Specimens treated by either aqueous or anhydrous techniques and resin-embedded were appropriately sectioned and regions of early tendon mineralization were photographed. On the basis of individual photomicrographs, stereoscopic pairs of images, and tomographic three-dimensional image reconstructions, platelet-shaped crystals may be demonstrated for the first time in association with the surface of collagen fibrils. Mineral is also observed in closely parallel arrays within collagen hole and overlap zones. The mineral deposition at these spatially distinct locations in the tendon provides insight into possible means by which calcification is mediated by collagen as a fundamental event in skeletal and dental formation among vertebrates.

NASA Discipline Musculoskeletal↗

Physical, Chemical, and Petrological Characteristics of Chondritic Materials and Their Relationships to Small Solar System Bodies: Chapter - 2

Chondrite materials with varying abundances of volatile-bearing phases are expected at the destinations for the asteroid sample-return missions Hayabusa2 and OSIRIS-REx. The targets of the missions are 162173 (1999 JU3) Ryugu and 101955 (1999 RQ36) Bennu. Spectroscopic analyses of these asteroids suggest that their surface materials are related to types 1 and 2 carbonaceous chondrites. Some studies suggest that the parent bodies of these chondrites may have also experienced some thermal and/or shock metamorphism. The physical properties of boulders at asteroid surfaces and fine particles in asteroid regoliths are consequences of the diverse processes that fragmented them, mobilized them, and redeposited them in unique accumulations. Sample-return missions are likely to encounter a broad range of carbonaceous chondrite (CC)-like materials, to which aqueous alteration, thermal, and shock metamorphism imparted changes affecting their sub-micron- to meter-scale physical properties. Consequently, implementation of scale-dependent analytical techniques to the study of the chemical, physical, and geotechnical characteristics of these CC-like materials is fundamental to safe mission operations, sample selection, and return. However, most of the available knowledge for informing and formulating expectations about regolith processes, products, and properties on carbonaceous small bodies comes from missions that studied anhydrous (e.g., Itokawa studied by Hayabusa) and/or much larger asteroids (e.g., Vesta studied by Dawn). No previous mission is likely directly relevant to small ice-free carbonaceous NEOs 162173 Ryugu or 101955 Bennu, although the Rosetta Spaceraft performed a flyby of the large asteroid Lutetia which has variously been classified as M and C type (Pätzold et al., 2011). Carbonaceous chondrites carry the best record of the history, distribution, and activity of water in the early solar system. Ordinary and Enstatite chondrites carry only partial records, but these are still critical to understanding the full story. We will describe the records of water-rock interactions on asteroids, as recorded in these meteorites, with particular emphasis on the timing, nature, settings, and fluid compositions. An integral part of this story is the rare, but fortunate, preservation of actual early solar system water as aqueous fluid inclusions.

Zolensky, Michael E.↗

Performance and stability of telemanipulators using bilateral impedance control

A new method of control for telemanipulators called bilateral impedance control is investigated. This new method differs from previous approaches in that interaction forces are used as the communication signals between the master and slave robots. The new control architecture has several advantages: (1) It allows the master robot and the slave robot to be stabilized independently without becoming involved in the overall system dynamics; (2) It permits the system designers to arbitrarily specify desired performance characteristics such as the force and position ratios between the master and slave; (3) The impedance at both ends of the telerobotic system can be modulated to suit the requirements of the task. The main goals of the research are to characterize the performance and stability of the new control architecture. The dynamics of the telerobotic system are described by a bond graph model that illustrates how energy is transformed, stored, and dissipated. Performance can be completely described by a set of three independent parameters. These parameters are fundamentally related to the structure of the H matrix that regulates the communication of force signals within the system. Stability is analyzed with two mathematical techniques: the Small Gain Theorem and the Multivariable Nyquist Criterion. The theoretical predictions for performance and stability are experimentally verified by implementing the new control architecture on a multidegree of freedom telemanipulator.

Moore, Christopher Lane↗

Space Radiation Effects on Human Cells: Modeling DNA Breakage, DNA Damage Foci Distribution, Chromosomal Aberrations and Tissue Effects

Future long-tem space travel will face challenges from radiation concerns as the space environment poses health risk to humans in space from radiations with high biological efficiency and adverse post-flight long-term effects. Solar particles events may dramatically affect the crew performance, while Galactic Cosmic Rays will induce a chronic exposure to high-linear-energy-transfer (LET) particles. These types of radiation, not present on the ground level, can increase the probability of a fatal cancer later in astronaut life. No feasible shielding is possible from radiation in space, especially for the heavy ion component, as suggested solutions will require a dramatic increase in the mass of the mission. Our research group focuses on fundamental research and strategic analysis leading to better shielding design and to better understanding of the biological mechanisms of radiation damage. We present our recent effort to model DNA damage and tissue damage using computational models based on the physics of heavy ion radiation, DNA structure and DNA damage and repair in human cells. Our particular area of expertise include the clustered DNA damage from high-LET radiation, the visualization of DSBs (DNA double strand breaks) via DNA damage foci, image analysis and the statistics of the foci for different experimental situations, chromosomal aberration formation through DSB misrepair, the kinetics of DSB repair leading to a model-derived spectrum of chromosomal aberrations, and, finally, the simulation of human tissue and the pattern of apoptotic cell damage. This compendium of theoretical and experimental data sheds light on the complex nature of radiation interacting with human DNA, cells and tissues, which can lead to mutagenesis and carcinogenesis later in human life after the space mission.

Ponomarev, A. L.↗

Intelligent neuroprocessors for in-situ launch vehicle propulsion systems health management

Efficacy of existing on-board propulsion systems health management systems (HMS) are severely impacted by computational limitations (e.g., low sampling rates); paradigmatic limitations (e.g., low-fidelity logic/parameter redlining only, false alarms due to noisy/corrupted sensor signatures, preprogrammed diagnostics only); and telemetry bandwidth limitations on space/ground interactions. Ultra-compact/light, adaptive neural networks with massively parallel, asynchronous, fast reconfigurable and fault-tolerant information processing properties have already demonstrated significant potential for inflight diagnostic analyses and resource allocation with reduced ground dependence. In particular, they can automatically exploit correlation effects across multiple sensor streams (plume analyzer, flow meters, vibration detectors, etc.) so as to detect anomaly signatures that cannot be determined from the exploitation of single sensor. Furthermore, neural networks have already demonstrated the potential for impacting real-time fault recovery in vehicle subsystems by adaptively regulating combustion mixture/power subsystems and optimizing resource utilization under degraded conditions. A class of high-performance neuroprocessors, developed at JPL, that have demonstrated potential for next-generation HMS for a family of space transportation vehicles envisioned for the next few decades, including HLLV, NLS, and space shuttle is presented. Of fundamental interest are intelligent neuroprocessors for real-time plume analysis, optimizing combustion mixture-ratio, and feedback to hydraulic, pneumatic control systems. This class includes concurrently asynchronous reprogrammable, nonvolatile, analog neural processors with high speed, high bandwidth electronic/optical I/O interfaced, with special emphasis on NASA's unique requirements in terms of performance, reliability, ultra-high density ultra-compactness, ultra-light weight devices, radiation hardened devices, power stringency, and long life terms.

Gulati, S.↗

Investigating the Feedback Path in a Jet-Surface Resonant Interaction

A resonant interaction between an 8:1 aspect ratio rectangular jet and flat-plates, placed parallel to the jet, is studied experimentally. For certain locations of the plate relative to the jet, the resonance takes place with a loud accompanying tone. The sound pressure level spectra are often marked by multiple peaks. The frequencies of the spectral peaks are studied as a function of the streamwise length of the plate, its relative location to the jet as well as the jet Mach number. It is demonstrated that the tones are not due to a simple feedback between the plate's trailing edge and the nozzle's exit; the leading edge of the plate also comes into play in the frequency selection. With parametric variation, it is found that there is an order in the most energetic spectral peaks; their frequencies cluster in distinct bands. The 'fundamental', i.e., the lowest frequency band is explained by an acoustic feedback involving diffraction at the plate's leading edge.

Resonance↗

CST: A Tool for Optimizing the Efficiency and Effectiveness of Static-Code Analysis Tools

Static Code Analysis (SCA) is a vital component of NASA IV&V’s mission assurance for safety-critical software as it reduces the likelihood of software-induced hazards impacting mission success. Static Code Analysis achieves this by identifying hazards that may not have been otherwise detectable by typical code reviews or other testing. Using SCA tools, however, can be intimidating due to steep learning curves, especially considering tool performance and defect coverage varies greatly. Because of this variation amongst SCA tools, understanding which tools support certain defects and which do not, as well as understanding how to run an analysis based on steps that are unique to each tool, can be difficult to both new and experienced analysts alike. To mitigate this, the SCAWG or the IV&V Static Code Analysis Working Group, created the SCA Checker Taxonomy and Starting Point Profiles. The Checker Selection Tool (CST) incorporates these two SCAWG products into an interactive tool which allows the user to: select organized categories of defects they would like the SCA tools to discover, select default checkers depending on their mission type (e.g. flight), and configure multiple SCA tools at once. C/C++, Java, and Python defect checkers from four common SCA tools were utilized in this iteration of the CST. This iteration also includes the addition of training, SCA tool specific help, and taxonomy guide links, into its design to help users new to Static Code Analysis learn how to perform SCA more efficiently. The CST has been subject to beta testing by experienced static code analysts from the SCAWG to ensure a usable and accurate final product. The implications of the CST in the mission assurance of NASA safety-critical software are profound, as the CST can help identify and reduce false positives and false negatives, fundamentally improving overall SCA efficiency and accuracy.

static code analysis↗

Engineering Lessons Learned and Systems Engineering Applications

Systems Engineering is fundamental to good engineering, which in turn depends on the integration and application of engineering lessons learned. Thus, good Systems Engineering also depends on systems engineering lessons learned from within the aerospace industry being documented and applied. About ten percent of the engineering lessons learned documented in the NASA Lessons Learned Information System are directly related to Systems Engineering. A key issue associated with lessons learned datasets is the communication and incorporation of this information into engineering processes. As part of the NASA Technical Standards Program activities, engineering lessons learned datasets have been identified from a number of sources. These are being searched and screened for those having a relation to Technical Standards. This paper will address some of these Systems Engineering Lessons Learned and how they are being related to Technical Standards within the NASA Technical Standards Program, including linking to the Agency's Interactive Engineering Discipline Training Courses and the life cycle for a flight vehicle development program.

Gill, Paul S.↗

Detailed Multidimensional Simulations of the Structure and Dynamics of Flames

Numerical simulations in which the various physical and chemical processes can be independently controlled can significantly advance our understanding of the structure, stability, dynamics and extinction of flames. Therefore, our approach has been to use detailed time-dependent, multidimensional, multispecies numerical models to perform carefully designed computational experiments of flames on Earth and in microgravity environments. Some of these computational experiments are complementary to physical experiments performed under the Microgravity Program while others provide a fundamental understanding that cannot be obtained from physical experiments alone. In this report, we provide a brief summary of our recent research highlighting the contributions since the previous microgravity combustion workshop. There are a number of mechanisms that can cause flame instabilities and result in the formation of dynamic multidimensional structures. In the past, we have used numerical simulations to show that it is the thermo-diffusive instability rather than an instability due to preferential diffusion that is the dominant mechanism for the formation of cellular flames in lean hydrogen-air mixtures. Other studies have explored the role of gravity on flame dynamics and extinguishment, multi-step kinetics and radiative losses on flame instabilities in rich hydrogen-air flames, and heat losses on burner-stabilized flames in microgravity. The recent emphasis of our work has been on exploring flame-vortex interactions and further investigating the structure and dynamics of lean hydrogen-air flames in microgravity. These topics are briefly discussed after a brief discussion of our computational approach for solving these problems.

Patnaik, G.↗

Arctic and Antarctic Analogs for Planetary Surface Traverses

The proposed paper summarizes the workshop presentations and discusses several of the key findings or lessons including: (1) A recognition that NASA s current approach for long duration planetary surface operations has fundamental differences from any of the operational approaches described by the invited speakers. These approaches drive the crew size and skill mix to accomplish basic objectives and, in turn, drive the logistical pyramid needed to support these operations. NASA will review the operational approaches of the organizations represented to understand the differentiating factors. NASA will then decide if it should alter its current approach to surface exploration. (2) There are potential parallels between key characteristics of the systems used for exploration in these environments, such as heated volume as an analog for pressurized volume or energy usage for various activities. NASA will look at these characteristics to identify which could help with preliminary planning and gather raw data from the presenters to model these characteristics. (3) New technologies are being applied and design approaches are being tailored to take advantage of these technologies on both side. Interactions between these two communities has begun or is expanding to understand how these new technologies are being leveraged: NASA habitation designers are exchanging ideas and approaches with the Antarctic station designers; Antarctic support

Hoffman, Stephen J.↗

All-Sky Medium-Energy Gamma-Ray Observatory (AMEGO)

The gamma-ray energy range from a few hundred keV (kiloelectronvolts) to a few hundred MeV (megaelectronvolts) has remained largely unexplored since the pioneering but limited observations by COMPTEL (The Imaging Compton Telescope) on the CGRO (Compton Gamma Ray Observatory) (1991-2000). Fundamental astrophysics questions can be addressed by a mission in the MeV range, from astrophysical jets and extreme physics of compact objects to a large population of unidentified objects. Such a mission will also provide critical inputs for multimessenger astrophysics by identifying and exploring the astrophysical objects that produce gravitational waves and neutrinos. To address these questions, we are developing AMEGO: All-sky Medium Energy Gamma-ray Observatory, as a NASA probe-class mission, to investigate the energy range from 200 keV to greater than10 GeV with good energy (ranging from less than 1 percent at the low end to approximately 10 percent at the high end) and angular resolution (from 2 to 6 degrees depending on energy) and with sensitivity a factor of 20-50 better than previous instruments. Measurements at these energies are challenging, mainly due to the fact that two photon interaction processes, Compton scattering and pair production, compete. These interaction processes require different approaches in both detection and data analysis, and consequently in the instrument concept. AMEGO will be capable of measuring both Compton-scattering events at lower energies and pair-production events at higher energies. AMEGO will also have sensitivity to linear polarization of detected radiation at a level of 20 percent minimum detectable polarization from a source 1 percent of the Crab intensity, observed for 106 seconds. AMEGO will be operating mainly in scanning (discovery) mode with a field-of-view of 2.5 sr (Special Relativity) (20 percent of the sky observation any time), with the capability to be pointed to particular regions of interest..

Moiseev, Alexander↗

Report of the 1988 2-D Intercomparison Workshop, chapter 3

Several factors contribute to the errors encountered. With the exception of the line-by-line model, all of the models employ simplifying assumptions that place fundamental limits on their accuracy and range of validity. For example, all 2-D modeling groups use the diffusivity factor approximation. This approximation produces little error in tropospheric H2O and CO2 cooling rates, but can produce significant errors in CO2 and O3 cooling rates at the stratopause. All models suffer from fundamental uncertainties in shapes and strengths of spectral lines. Thermal flux algorithms being used in 2-D tracer tranport models produce cooling rates that differ by as much as 40 percent for the same input model atmosphere. Disagreements of this magnitude are important since the thermal cooling rates must be subtracted from the almost-equal solar heating rates to derive the net radiative heating rates and the 2-D model diabatic circulation. For much of the annual cycle, the net radiative heating rates are comparable in magnitude to the cooling rate differences described. Many of the models underestimate the cooling rates in the middle and lower stratosphere. The consequences of these errors for the net heating rates and the diabatic circulation will depend on their meridional structure, which was not tested here. Other models underestimate the cooling near 1 mbar. Suchs errors pose potential problems for future interactive ozone assessment studies, since they could produce artificially-high temperatures and increased O3 destruction at these levels. These concerns suggest that a great deal of work is needed to improve the performance of thermal cooling rate algorithms used in the 2-D tracer transport models.

Jackman, Charles H.↗

Evaluation, Analysis, and Application of Internal Strain-Gage Balance Data

Experimental processes, analytical methods, and numerical algorithms are described that may be used to predict the forces and moments of an internal strain–gage balance during a wind tunnel test. First, the control volume model of a strain–gage balance and the concepts of load state, load space, and output space are introduced. These important abstractions provide a better understanding of fundamental characteristics of different balance load prediction approaches. Then, the description of strain–gage balance data and the definition of the primary bridge sensitivity are discussed. Afterwards, basic elements of the calibration of a typical six–component balance are reviewed. Two fundamentally different balance load prediction methods, the processing of check loads, and related topics are also discussed. Three real–world balance data examples are reviewed in great detail to illustrate typical analysis results for a variety of strain–gage balance designs. Finally, important observations are summarized and recommendations are provided. – Additional information and detailed mathematical derivations can be found in the appendices of the document. They include the following topics: balance terminology, definitions of important statistical metrics, balance axis system conventions, balance load transformations, the combined load diagram, electrical output format options, bi–directional output characteristics, determination of the natural zeros, derivation of two balance load prediction methods, description of two tare load iteration algorithms, modeling of balance temperature effects, basics of three–component moment balances, definition of the percent contribution, detection of linear and near–linear dependencies in balance calibration data, a regression model search algorithm, balance interactions, and other related information.

strain-gage balance↗

Paths and patterns: the biology and physics of swimming bacterial populations

The velocity distribution of swimming micro-organisms depends on directional cues supplied by the environment. Directional swimming within a bounded space results in the accumulation of organisms near one or more surfaces. Gravity, gradients of chemical concentration and illumination affect the motile behaviour of individual swimmers. Concentrated populations of organisms scatter and absorb light or consume molecules, such as oxygen. When supply is one-sided, consumption creates gradients; the presence of the population alters the intensity and the symmetry of the environmental cues. Patterns of cues interact dynamically with patterns of the consumer population. In suspensions, spatial variations in the concentration of organisms are equivalent to variations of mean mass density of the fluid. When organisms accumulate in one region whilst moving away from another region, the force of gravity causes convection that translocates both organisms and dissolved substances. The geometry of the resulting concentration-convection patterns has features that are remarkably reproducible. Of interest for biology are (1) the long-range organisation achieved by organisms that do not communicate, and (2) that the entire system, consisting of fluid, cells, directional supply of consumables, boundaries and gravity, generates a dynamic that improves the organisms' habitat by enhancing transport and mixing. Velocity distributions of the bacterium Bacillus subtilis have been measured within the milieu of the spatially and temporally varying oxygen concentration which they themselves create. These distributions of swimming speed and direction are the fundamental ingredients required for a quantitative mathematical treatment of the patterns. The quantitative measurement of swimming behaviour also contributes to our understanding of aerotaxis of individual cells.

Non-NASA Center↗

Ion Acceleration and Transport in Solar Flares

The purpose of the work proposed for this grant was to develop a promising model for ion acceleration in impulsive solar flares. Solar flares are among the most energetic and interesting phenomena in the solar system, releasing up to 10(exp 32) ergs of energy over timescales ranging from a few tens of seconds to a few tens of minutes. Much of this energy appears as energetic electrons and ions, which produce a wide range of observable radiations. These radiations, in turn, are valuable diagnostics of the acceleration mechanism, the identification of which is the fundamental goal of solar flare research. The specific mechanism we proposed to investigate was based on cascading Alfven waves, the essence of which was as follows: During the primary flare energy release, it is widely believed that magnetic free energy is made available through the large-scale restructuring of the flare magnetic field. Any perturbation of a magnetic field will lead to the formation of MagnetoHydroDynamic (MHD) waves of wavelength comparable to the initial scale of the perturbation. Since the scalesize of a flare energy release region will likely be 10(exp 8)-10(exp 9) cm, the MHD waves will be of very long wavelength. However, it is well known that wave steepening will lead to a cascade of wave energy to smaller wavelengths. Now, MHD waves consist of two specific modes-the Alfven wave and the fast mode wave, and it is the Alfven wave which can interact with the ambient ions and accelerate them via cyclotron resonance. As the Alfven waves cascade to smaller wavenumbers, they can resonate with ions of progressively lower energy, until they eventually (actually, this is less than approx. 1 s) can resonate with ions in the thermal distribution. These ions are then energized out of the thermal background and, since lower-frequency waves are already present as a result of the cascading, to relativistic energies. Hence, cascading Alfven waves naturally accelerate ions from thermal to relativistic energies in one step with one basic mechanism.

Miller, James A.↗

Data-Intensive Science meets Inquiry-Driven Pedagogy: Interactive Big Data Exploration, Threshold Concepts, and Liminality

Threshold concepts in any discipline are the core concepts an individual must understand in order to master a discipline. By their very nature, these concepts are troublesome, irreversible, integrative, bounded, discursive, and reconstitutive. Although grasping threshold concepts can be extremely challenging for each learner as s/he moves through stages of cognitive development relative to a given discipline, the learner's grasp of these concepts determines the extent to which s/he is prepared to work competently and creatively within the field itself. The movement of individuals from a state of ignorance of these core concepts to one of mastery occurs not along a linear path but in iterative cycles of knowledge creation and adjustment in liminal spaces - conceptual spaces through which learners move from the vaguest awareness of concepts to mastery, accompanied by understanding of their relevance, connectivity, and usefulness relative to questions and constructs in a given discipline. For example, challenges in the teaching and learning of atmospheric science can be traced to threshold concepts in fluid dynamics. In particular, Dynamic Meteorology is one of the most challenging courses for graduate students and undergraduates majoring in Atmospheric Science. Dynamic Meteorology introduces threshold concepts - those that prove troublesome for the majority of students but that are essential, associated with fundamental relationships between forces and motion in the atmosphere and requiring the application of basic classical statics, dynamics, and thermodynamic principles to the three dimensionally varying atmospheric structure. With the explosive growth of data available in atmospheric science, driven largely by satellite Earth observations and high-resolution numerical simulations, paradigms such as that of dataintensive science have emerged. These paradigm shifts are based on the growing realization that current infrastructure, tools and processes will not allow us to analyze and fully utilize the complex and voluminous data that is being gathered. In this emerging paradigm, the scientific discovery process is driven by knowledge extracted from large volumes of data. In this presentation, we contend that this paradigm naturally lends to inquiry-driven pedagogy where knowledge is discovered through inductive engagement with large volumes of data rather than reached through traditional, deductive, hypothesis-driven analyses. In particular, data-intensive techniques married with an inductive methodology allow for exploration on a scale that is not possible in the traditional classroom with its typical problem sets and static, limited data samples. In addition, we identify existing gaps and possible solutions for addressing the infrastructure and tools as well as a pedagogical framework through which to implement this inductive approach.

Ramachandran, Rahul↗

Searching for New Physics with Ultrahigh Energy Cosmic Rays

Ultrahigh energy cosmic rays that produce giant extensive showers of charged particles and photons when they interact in the Earth's atmosphere provide a unique tool to search for new physics. Of particular interest is the possibility of detecting a very small violation of Lorentz invariance such as may be related to the structure of space-time near the Planck scale of approximately 10 (exp -35) m. We discuss here the possible signature of Lorentz invariance violation on the spectrum of ultrahigh energy cosmic rays as compared with present observations of giant air showers. We also discuss the possibilities of using more sensitive detection techniques to improve searches for Lorentz invariance violation in the future. Using the latest data from the Pierre Auger Observatory, we derive a best fit to the LIV parameter of 3 .0 + 1.5 - 3:0 x 10 (exp -23) ,corresponding to an upper limit of 4.5 x 10-23 at a proton Lorentz factor of approximately 2 x 10(exp 11) . This result has fundamental implications for quantum gravity models.

Stecker, Floyd W.↗