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Reflective and Electrically Conductive Surface Silvered Polyimide Films and Coatings Prepared via Unusual Single-Stage Self-Metallization Techniques

Highly reflective and/or surface conductive flexible polyimide films can be prepared by the incorporation of positive valent silver compounds into solutions of poly(amic acid)s formed from a variety of dianhydrides and diamines. Thermal curing of selected silver(I)-containing poly(amic acid)s leads to cycloimidization of the polyimide precursor with concomitant silver(I) reduction and surface aggregation of the metal yielding a reflective and/or conductive silver surface similar to that of the native metal. However, not all silver(I) precursors are effective surface metallization agents and not all poly(amic acid)s metallize with equal facility. Ligand/anion and polyimide structural effects on film metallization efficacy and on physical properties on metallized films are reviewed.

Southward, Robin E.↗

Leveraging the Cloud for Robust and Efficient Lunar Image Processing

The Lunar Mapping and Modeling Project (LMMP) is tasked to aggregate lunar data, from the Apollo era to the latest instruments on the LRO spacecraft, into a central repository accessible by scientists and the general public. A critical function of this task is to provide users with the best solution for browsing the vast amounts of imagery available. The image files LMMP manages range from a few gigabytes to hundreds of gigabytes in size with new data arriving every day. Despite this ever-increasing amount of data, LMMP must make the data readily available in a timely manner for users to view and analyze. This is accomplished by tiling large images into smaller images using Hadoop, a distributed computing software platform implementation of the MapReduce framework, running on a small cluster of machines locally. Additionally, the software is implemented to use Amazon's Elastic Compute Cloud (EC2) facility. We also developed a hybrid solution to serve images to users by leveraging cloud storage using Amazon's Simple Storage Service (S3) for public data while keeping private information on our own data servers. By using Cloud Computing, we improve upon our local solution by reducing the need to manage our own hardware and computing infrastructure, thereby reducing costs. Further, by using a hybrid of local and cloud storage, we are able to provide data to our users more efficiently and securely. 12 This paper examines the use of a distributed approach with Hadoop to tile images, an approach that provides significant improvements in image processing time, from hours to minutes. This paper describes the constraints imposed on the solution and the resulting techniques developed for the hybrid solution of a customized Hadoop infrastructure over local and cloud resources in managing this ever-growing data set. It examines the performance trade-offs of using the more plentiful resources of the cloud, such as those provided by S3, against the bandwidth limitations such use encounters with remote resources. As part of this discussion this paper will outline some of the technologies employed, the reasons for their selection, the resulting performance metrics and the direction the project is headed based upon the demonstrated capabilities thus far.

Cloud Computing↗

Information Management Platform for Data Analytics and Aggregation (IMPALA) System Design Document

The System Design document tracks the design activities that are performed to guide the integration, installation, verification, and acceptance testing of the IMPALA Platform. The inputs to the design document are derived from the activities recorded in Tasks 1 through 6 of the Statement of Work (SOW), with the proposed technical solution being the completion of Phase 1-A. With the documentation of the architecture of the IMPALA Platform and the installation steps taken, the SDD will be a living document, capturing the details about capability enhancements and system improvements to the IMPALA Platform to provide users in development of accurate and precise analytical models. The IMPALA Platform infrastructure team, data architecture team, system integration team, security management team, project manager, NASA data scientists and users are the intended audience of this document. The IMPALA Platform is an assembly of commercial-off-the-shelf (COTS) products installed on an Apache-Hadoop platform. User interface details for the COTS products will be sourced from the COTS tools vendor documentation. The SDD is a focused explanation of the inputs, design steps, and projected outcomes of every design activity for the IMPALA Platform through installation and validation.

Carnell, Andrew↗

Cell partition in two phase polymer systems

Aqueous phase-separated polymer solutions can be used as support media for the partition of biological macromolecules, organelles and cells. Cell separations using the technique have proven to be extremely sensitive to cell surface properties but application of the systems are limited to cells or aggregates which do not significantly while the phases are settling. Partition in zero g in principle removes this limitation but an external driving force must be applied to induce the phases to separate since their density difference disappears. We have recently shown that an applied electric field can supply the necessary driving force. We are proposing to utilize the NASA FES to study field-driven phase separation and cell partition on the ground and in zero g to help define the separation/partition process, with the ultimate goal being to develop partition as a zero g cell separation technique.

Brooks, D. E.↗

Hydrothermal alteration experiments of olivine with varying Fe contents: An attempt to simulate aqueous alteration of the carbonaceous chondrites

Hydrothermal alteration experiments of olivine powder with several Fe/Mg ratios were carried out under acidic and neutral conditions, and transition electron microscopy (TEM) observations were made on the run products. Well-developed tubular crystals of serpentine (chrysotile) were synthesized from Fo100 under both acidic and neutral conditions, and from Fo92 and Fo80 under acidic condition. Abundance and size of chrysotile apparenlty dependent on the Fe contents of olivine, i.e. with increasing Fe contents, less and smaller chrysotile was formed. Acidity of the solution plays an important role for the formation of chrysotile. Platy and fibrous crystals of phyllosilicate, probably serpentine, were obtained from Fo50 and Fo20 treated under acidic condition, which are most similar to the phyllosilicates in the CI and CM chondrites. Framboidal aggregates of Fe-rich grains (presumably Fe-hydroxide) were formed from Fa100 and Fo20, but no phyllosilicate was formed from Fa100.

Takatori, Koichi↗

Recommendations Emerging from an Analysis of NASA's Deep Space Communications Capacity

During 2016-2017, NASA’s Space Communications and Navigation (SCaN) Office chartered a study of Deep Space Network (DSN) communications capacity relative to projected future-mission demand over the next 30 years. In this paper, we briefly describe the methodology used to analyze capacity vs. demand over such a broad timeframe, summarize key findings emerging from the analysis, and discuss the associated recommendations. Performing the analysis entailed: identifying key factors shaping the anticipated future mission set, identifying several alternative future mission set scenarios consistent with these factors, and then analyzing each mission set scenario in terms of required antenna capacity, downlink and uplink capabilities, and spectrum as a function of time. On the basis of these aggregate requirements, DSN loading simulations were then conducted that examined how well each of the postulated mission sets could load up onto the the DSN’s “in-plan” architecture. To the extent that capacity shortfalls emerged during these baseline simulations, architectural solutions to the shortfalls were then postulated and tested via additional simulations. In general, the trend analyses and baseline loading simulations indicated a significant progression in challenges over the next three decades. In the current decade, the DSN appeared to be operating very close to capacity. The first human exploration mission and its secondary payload launch opportunities for cubesats traveling beyond GEO contributed to this loading. As a consequence, the main challenge appeared to be managing peak assetcontention periods. In the next decade, the DSN continued to operate close to capacity but also began transitioning to more frequent human mission support. Upgrading for, and operating, a human-rated system while continuing to meet robotic mission customer requirements emerged as the key challenge. In the 2030’s and beyond, simulations suggested a need for fundamentally new capability and capacity. The high data rates and long link distances characteristic of human Mars exploration drove requirements far beyond what is currently “in plan.” The key challenge then became determining the most cost-effective combination of RF and optical assets for communicating with the postulated human Mars assets while still providing for the needs of all the other missions across the solar system. Various link budget, visibility, and loading analyses ultimately suggested that the human Mars exploration demands of the 2030’s could best be addressed with two cross-linked RF-optical areostationary relays (or an areostationary relay and deep space habitat) providing a dual “trunk link” to an array of 2-to-3 additional 34m beam waveguide antennas and an ~8.5m optical antenna at each DSN Complex. The dual “trunk link” would enable the same amount of total data return to Earth as a single trunk link at twice the data rate, but with only half the required array size on the ground, assuming use of Multiple Spacecraft Per Antenna (MSPA) techniques. MSPA techniques, including a Multiple Uplink Per Antenna (MUPA) technique currently under investigation, also showed promise for reducing asset contention in the decades prior to human Mars exploration.

Lee, Carlyn-Ann↗

Efficient Implementation of the Invariant Imbedding T-Matrix Method and the Separation of Variables Method Applied to Large Nonspherical Inhomogeneous Particles

Three terms, ''Waterman's T-matrix method'', ''extended boundary condition method (EBCM)'', and ''null field method'', have been interchangeable in the literature to indicate a method based on surface integral equations to calculate the T-matrix. Unlike the previous method, the invariant imbedding method (IIM) calculates the T-matrix by the use of a volume integral equation. In addition, the standard separation of variables method (SOV) can be applied to compute the T-matrix of a sphere centered at the origin of the coordinate system and having a maximal radius such that the sphere remains inscribed within a nonspherical particle. This study explores the feasibility of a numerical combination of the IIM and the SOV, hereafter referred to as the IIMþSOV method, for computing the single-scattering properties of nonspherical dielectric particles, which are, in general, inhomogeneous. The IIMþSOV method is shown to be capable of solving light-scattering problems for large nonspherical particles where the standard EBCM fails to converge. The IIMþSOV method is flexible and applicable to inhomogeneous particles and aggregated nonspherical particles (overlapped circumscribed spheres) representing a challenge to the standard superposition T-matrix method. The IIMþSOV computational program, developed in this study, is validated against EBCM simulated spheroid and cylinder cases with excellent numerical agreement (up to four decimal places). In addition, solutions for cylinders with large aspect ratios, inhomogeneous particles, and two-particle systems are compared with results from discrete dipole approximation (DDA) computations, and comparisons with the improved geometric-optics method (IGOM) are found to be quite encouraging.

Invariant imbedding method↗

Characterization of Evidence for Human System Risk Assessment

Understanding the kinds of evidence available and using the best evidence to answer a question is critical to evidenced-based decision-making, and it requires synthesis of evidence from a variety of sources. Categorization of human system risks in spaceflight, in particular, focuses on how well the integration and interpretation of all available evidence informs the risk statement that describes the relationship between spaceflight hazards and an outcome of interest. A mature understanding and categorization of these risks requires: 1) sufficient characterization of risk, 2) sufficient knowledge to determine an acceptable level of risk (i.e., a standard), 3) development of mitigations to meet the acceptable level of risk, and 4) identification of factors affecting generalizability of the evidence to different design reference missions. In the medical research community, evidence is often ranked by increasing confidence in findings gleaned from observational and experimental research (e.g., "levels of evidence"). However, an approach based solely on aspects of experimental design is problematic in assessing human system risks for spaceflight. For spaceflight, the unique challenges and opportunities include: (1) The independent variables in most evidence are the hazards of spaceflight, such as space radiation or low gravity, which cannot be entirely duplicated in terrestrial (Earth-based) analogs, (2) Evidence is drawn from multiple sources including medical and mission operations, Lifetime Surveillance of Astronaut Health (LSAH), spaceflight research (LSDA), and relevant environmental & terrestrial databases, (3) Risk metrics based primarily on LSAH data are typically derived from available prevalence or incidence data, which may limit rigorous interpretation, (4) The timeframe for obtaining adequate spaceflight sample size (n) is very long, given the small population, (5) Randomized controlled trials are unattainable in spaceflight, (6) Collection of personal and environmental data on the astronaut population may create opportunities for advanced analytics and human-environment modeling that goes beyond that achieved in isolated experimental designs; and (7) Translation of relevant research to operations is a complex, transdisciplinary enterprise in which the approach must apply across the physical, biological, behavioral, and social sciences. The approach to synthesizing evidence must address both source and fidelity of data, and reflect the most general attributes of quality of evidence in science and engineering: reliability and validity. The authors are developing a two-factor approach which includes the various kinds of evidence required to understand risks and for the integrated interpretation of all evidence that is essential to develop standards and countermeasures. A unified framework for aggregating and assessing different kinds of evidence provides a consistent, traceable, evidence-based decision-making process to translate research to operations in an environment where engineers, scientists, physicians, and managers all engage in analyzing the trade space of vehicle design, standards, requirements and solutions for spaceflight.

Steinberg, S. L.↗

A heuristic approach to worst-case carrier-to-interference ratio maximization in satellite system synthesis

Consideration is given to the problem of allotting GEO locations to communication satellites so as to maximize the smallest aggregate carrier-to-interference (C/I) ratio calculated at any test point (assumed earth station). The location allotted to each satellite must be within the satellite's service arc, and angular separation constraints are enforced for each pair of satellites to control single-entry EMI. Solutions to this satellite system synthesis problem (SSSP) are found by embedding two heuristic procedures for the satellite location problem (SLP), in a binary search routine to find an estimate of the largest increment to the angular separation values that permits a feasible solution to SLP and SSSP. Numerical results for a 183-satellite, 208-beam example problem are presented.

Reilly, Charles H.↗

High Performance Access to Archival Data Stored in HDF4 and HDF5 on Cloud Object Stores Without Reformatting the Files

Cloud computing offers numerous advantages for users of extensive Earth science data collections. These benefits encompass direct online access to data files and granules from any location, scalable access supporting parallel computing workflows, and flexible computing tools enabling innovative experimentation with processing techniques. However, older archival file formats designed for distinct computing systems hinder efficient access to decade-long time-series data when compared to data stored in modern cloud-optimized formats like Web Object Stores (WOS), exemplified by Amazon Web Services’ Simple Storage Service (S3). We describe DMR++ (Dataset Metadata Response plus plus), a technology facilitating efficient access to HDF5 (Hierarchical Data Format, version 5) and HDF4 files stored on WOS systems without requiring data reformatting. DMR++ achieves performance comparable to technologies like Zarr while preserving the original file structure, a substantial benefit considering the vast quantity of archival files held by organizations such as NASA. Moreover, DMR++ typically outperforms cloud-optimized versions of HDF5. Essentially an XML (Extensible Markup Language) document usually stored alongside the described data, DMR++ can also be generated on-the-fly but is generally created during data staging to the WOS. Archival files that use HDF4/5 often store large arrays of numerical data. The data in these files is often compressed, typically reducing their size by a factor of four or more. To achieve efficient access to portions of those arrays, they are 'chunked' into smaller sub-arrays, each individually compressed. The chunk size is a compromise, where spinning disks can efficiently access data in smaller chunks while S3 favors larger chunks. A simple optimization of aggregating smaller chunks that are stored adjacently, transferring them in a single access and then individually decompressing them will improve performance. NASA data pose an additional challenge: special Application Programmer Interface (API) libraries are often needed to compute some variables. These libraries are incompatible with WOS environments. Our solution involves storing computed values in the DMR++ document or a companion file, making them accessible like other variables and eliminating the need for specialized APIs. We outline specific optimizations for both satellite grid and swath data stored in HDF4-EOS2 (Earth Observing System).

James Gallagher↗

The Spatial Vision Tree: A Generic Pattern Recognition Engine- Scientific Foundations, Design Principles, and Preliminary Tree Design

New foundational ideas are used to define a novel approach to generic visual pattern recognition. These ideas proceed from the starting point of the intrinsic equivalence of noise reduction and pattern recognition when noise reduction is taken to its theoretical limit of explicit matched filtering. This led us to think of the logical extension of sparse coding using basis function transforms for both de-noising and pattern recognition to the full pattern specificity of a lexicon of matched filter pattern templates. A key hypothesis is that such a lexicon can be constructed and is, in fact, a generic visual alphabet of spatial vision. Hence it provides a tractable solution for the design of a generic pattern recognition engine. Here we present the key scientific ideas, the basic design principles which emerge from these ideas, and a preliminary design of the Spatial Vision Tree (SVT). The latter is based upon a cryptographic approach whereby we measure a large aggregate estimate of the frequency of occurrence (FOO) for each pattern. These distributions are employed together with Hamming distance criteria to design a two-tier tree. Then using information theory, these same FOO distributions are used to define a precise method for pattern representation. Finally the experimental performance of the preliminary SVT on computer generated test images and complex natural images is assessed.

Rahman, Zia-ur↗

A multi-level solution algorithm for steady-state Markov chains

A new iterative algorithm, the multi-level algorithm, for the numerical solution of steady state Markov chains is presented. The method utilizes a set of recursively coarsened representations of the original system to achieve accelerated convergence. It is motivated by multigrid methods, which are widely used for fast solution of partial differential equations. Initial results of numerical experiments are reported, showing significant reductions in computation time, often an order of magnitude or more, relative to the Gauss-Seidel and optimal SOR algorithms for a variety of test problems. The multi-level method is compared and contrasted with the iterative aggregation-disaggregation algorithm of Takahashi.

Horton, Graham↗

Chaotic, subduction-like downflows in a spherical model of convection in the earth's mantle

Model calculations are described for a compressible fluid in a three-dimensional spherical shell with 80 percent of the surface heat flow generated within the model mantle. The numerical solutions are strongly chaotic, with surface planforms dominated by long curvilinear downflows reminiscent of the descending slabs in the earth's mantle. The results suggest that descending slabs play an important part in driving mantle convection, and that their chaotic evolution may influence the spatial and temporal behavior of plates and thus the dispersal and aggregation of continents.

Glatzmaier, Gary A.↗

Models for the interaction of rarefied gas with a surface

Various theoretical models are discussed for the interaction of gaseous atoms with solids at energies of approximately 10 eV. The surface is modeled by a one- and three-dimensional aggregate of atoms with different initial conditions and lattice parameters. In calculating the accommodation coefficients, the direct integration of the equations of motion of gaseous molecules and atoms in the crystal lattice of the solid is used. An analysis of the advantages and the drawbacks of the models, as well as the possibilities of the analytical solutions in a one-dimensional case, is given. The dependence of the energy and the normal and the tangential momenta accommodation coefficients on the collision parameters is obtained.

Pyarnpuu, A. A.↗

Formation of Ordered Arrays of Proteins on Surfaces

Van der Waals (dispersion) forces contribute to interactions of proteins with other molecules or with surfaces, but because of the structural complexity of protein molecules, the magnitude of these effects is usually estimated based on idealized models of the molecular geometry, e.g., spheres or spheroids. The calculations reported here seek to account for both the geometric irregularity of protein molecules and the material properties of the interacting media. While the latter are found to fall in the generally accepted range, the molecular shape is shown to cause the magnitudes of the interactions to differ significantly from those calculated using idealized models, with important consequences. First, the roughness of the molecular surface leads to much lower average interaction energies for both protein-protein and protein-surface cases relative to calculations in which the protein molecule is approximated as a sphere. These results indicate that a form of steric stabilization may be an important effect in protein solutions. Underlying this behavior is appreciable orientational dependence, one reflection of which is that molecules of complementary shape are found to exhibit very strong attractive dispersion interactions. Although this has been widely discussed previously in the context of molecular recognition processes, the broader implications of these phenomena may also be important at larger molecular separations, e.g., in the dynamics of aggregation, precipitation and crystal growth.

Lenhoff, A. M.↗

Van der Waals Interactions Involving Proteins

Van der Waals (dispersion) forces contribute to interactions of proteins with other molecules or with surfaces, but because of the structural complexity of protein molecules, the magnitude of these effects is usually estimated based on idealized models of the molecular geometry, e.g., spheres or spheroids. The calculations reported here seek to account for both the geometric irregularity of protein molecules and the material properties of the interacting media. Whereas the latter are found to fall in the generally accepted range, the molecular shape is shown to cause the magnitudes of the interactions to differ significantly from those calculated using idealized models. with important consequences. First, the roughness of the molecular surface leads to much lower average interaction energies for both protein-protein and protein-surface cases relative to calculations in which the protein molecule is approximated as a sphere. These results indicate that a form of steric stabilization may be an important effect in protein solutions. Underlying this behavior is appreciable orientational dependence, one reflection of which is that molecules of complementary shape are found to exhibit very strong attractive dispersion interactions. Although this has been widely discussed previously in the context of molecular recognition processes, the broader implications of these phenomena may also be important at larger molecular separations, e.g., in the dynamics of aggregation, precipitation, and crystal growth.

Roth, Charles M.↗

The MSP 2001 Mars Environmental Compatibility Assessment (MECA)

The Mars Environmental Compatibility Assessment (MECA) will evaluate the Martian environment for soil and dust-related hazards to human exploration as part of the Mars Surveyor Program 2001 Lander. Sponsored by the Human Exploration and Development of Space (HEDS) enterprise, MECA's goal is to evaluate potential geochemical and environmental hazards that may confront future Martian explorers, and to guide HEDS scientists in the development of high fidelity Mars soil simulants. The integrated MECA payload contains a wet-chemistry laboratory, a microscopy station, an electrometer to characterize the electrostatics of the soil and its environment, and arrays of material patches to study the abrasive and adhesive properties of soil grains. The instrument will acquire soil samples with a robotic arm equipped with a camera. MECA will examine surface and subsurface soil and dust in order to characterize particle size, shape, hardness, and also physical characteristics that may provide clues to mineralogy. MECA will characterize soil/water mixtures with respect to pH, redox potential, total dissolved ions, and trace toxins. MECA will determine the nature of electrostatic charging associated with excavation of soil, and the influence of ionizing radiation on material properties. It will also observe natural dust accumulation on engineering materials. To accomplish these objectives, MECA is allocated a mass of 10 kg within an enclosure of 35 x 25 x 15 cm. The Wet Chemistry Laboratory (WCL) consists of four identical cells that will accept samples from surface and subsurface regions accessible to the Lander's robotic arm, mix them with water, and perform extensive analysis of the solution. Ion-selective electrodes and related sensors will evaluate total dissolved solids, redox potential, pH, and the concentration of many soluble ions and gases in wet Martian soil. These electrodes can detect potentially dangerous heavy-metal ions, emitted pathogenic gases, and the soil's corrosive potential. Experiments will include cyclic voltammetry and anodic stripping voltammetry. Complementary to the Viking experiments, the chemical laboratory will characterize the water-soil solution rather than emitted gases. Nonetheless, through analysis of dissolved gases it will be able to replicate many of the Viking observations related to oxidants. MECA's microscopy station combines optical and atomic-force microscopy (AFM) in an actively focused, controlled illumination environment to image particles from millimeters to nanometers in size. Careful selection of substrates allows controlled experiments in adhesion, abrasion, hardness, aggregation, magnetic and other properties. Special tools allow primitive manipulation (brushing and scraping) of samples. Soil particle properties including size, shape, color, hardness, adhesive potential (electrostatic and magnetic), will be determined using an array of sample receptacles and collection substrates. The simple, rugged atomic-force microscope will image in the submicron size range and has the capability of performing a particle-by-particle analysis of the dust and soil. On Earth, the earliest forms of life are preserved as microfossils. The atomic-force microscope will have the required resolution to image down to the scale of terrestrial microfossils and beyond. Mounted on the end of the robot arm, MECA's electrometer actually consists of four types of sensors: an electric field meter, several triboelectricity monitors, an ion gauge, and a thermometer. Tempered only by ultraviolet-light-induced ions and a low-voltage breakdown threshold, the dry, cold, dusty martian environment presents an imposing electrostatic hazard to both robots and humans. The field meter will measure the ambient field on nearby objects while the triboelectric sensors, using identical circuitry, will measure the charge accumulated on test substances as they are dragged through the soil by the arm. The ion chamber, open to the environment, will sense both charged dust and free ions in the air. Over and above the potential threat to electronics, the electrostatic environment holds one of the keys to transport of dust and, consequently, Martian meteorology. Viewed with the robot arm camera, the abrasion and adhesion plates are strategically placed to allow direct observation of the interaction between materials and soils on a macroscopic scale. Materials of graded hardness are placed directly under the robot arm scoop to sense wear and soil hardness. A second array, placed on the lander deck, is deployed after the dust plume of landing has settled. It can be manipulated in a primitive fashion by the arm, first having dirt deposited on it from the scoop and subsequently shaken clean. A third array will passively collect dust from the atmosphere. In addition to objectives related to human exploration, the MECA data set will be rich in information relevant to basic geology, paleoclimate, and exobiology issues. To understand both contemporaneous and ancient processes on Mars, the mineralogy, petrology, and reactivity of Martian surface materials should be constrained. The MECA experiment will shed light on these quantities through its combination of chemistry and microscopy. MECA will be capable of measuring the composition of ancient surface water environments, observing microscopic evidence of geological (and biological?) processes, inferring soil and dust transport, comminution and weathering mechanisms, and characterizing soil horizons that might be encountered during excavation.

Hecht, M. H.↗

Feeding Ten Billion People Is Possible Within Four Terrestrial Planetary Boundaries

Global agriculture puts heavy pressure on planetary boundaries, posing the challenge to achieve future food security without compromising Earth system resilience. On the basis of process-detailed, spatially explicit representation of four interlinked planetary boundaries (biosphere integrity, land-system change, freshwater use, nitrogen flows) and agricultural systems in an internally consistent model framework, we here show that almost half of current global food production depends on planetary boundary transgressions. Hotspot regions, mainly in Asia, even face simultaneous transgression of multiple underlying local boundaries. If these boundaries were strictly respected, the present food system could provide a balanced diet (2,355 kcal per capita per day) for 3.4 billion people only. However, as we also demonstrate, transformation towards more sustainable production and consumption patterns could support 10.2 billion people within the planetary boundaries analysed. Key prerequisites are spatially redistributed cropland, improved water–nutrient management, food waste reduction and dietary changes. Adoption of the Sustainable Development Goals by all nations in 2015 is the first ever commitment to a world development path that safeguards the stability of the Earth system as a prerequisite for meeting universal human standards1. The longstanding challenge of achieving food security through sustainable agriculture is particularly acute in this context as world agriculture is a leading cause for the current transgressions of multiple planetary boundaries (PBs) globally and regionally2–5. The PB framework is a comprehensive scientific attempt to synoptically define our planet’s biogeophysical limits to anthropogenic interference. It suggests bounds to nine interacting processes that together delineate a Holocene-like Earth system state. The Holocene is chosen as the reference state as it is the only period known to provide a safe operating space for a world population of several billion people, and according to a precautionary principle, the PBs are set in sufficient distance from processes that may critically undermine Earth system resilience and global sustainability. A challenging question, thus, is whether human development goals such as food security can be met while maintaining multiple PBs along with their subglobal manifestations. Further PB transgressions could jeopardize the chances of providing sufficient food for a world population projected to be wealthier and reach >9 billion by 2050. This conundrum portrays a tradeoff between Earth’s biophysical carrying capacity and humankind’s rising food demand, calling in response for radical rethinking of food production and consumption patterns6–9. Yield gap closures, avoidance of excessive input use, shifts towards less resource-demanding diets, food waste reductions and efficient international trade are crucial options for sustainably increasing the food supply10–15. For example, enhancing water-use efficiency on irrigated and rain-fed farms can triple or quadruple crop yields in low-performing systems, suggesting possible global gains of >20% (ref. 16). Even higher gains appear feasible through globally optimized configurations of the land-use pattern17, and cutting food losses by half could generate food for another billion people18. Thus, collective large-scale implementation of such options could sustain food for a further growing world population19. Yet achieving this within a safe operating space as defined by PBs requires not only a halt to but actually a reversal of existing PB transgressions. Previous studies suggest that such a reconciliation might be possible, but these were based on aggregate representations of PBs (not accounting for the spatial patterns of limits, transgressions and interactions) or considered only one boundary in isolation17,20–23. Here, we systematically quantify to what extent current food production depends on local to global transgressions of the PBs for biosphere integrity, land-system change, freshwater use and nitrogen (N) flows, along with the potential of a range of solutions to avoid these transgressions and still increase food supply (Table 1). To this end, we configured an internally consistent process-based model of the terrestrial biosphere including agriculture (LPJmL) with multiple spatially distributed PBs and their interactions. LPJmL is among the longest-established and best-evaluated biosphere models, showing robust performance regarding simulation of, for example, carbon, water and crop yield dynamics (Supplementary Figs. 1 and 2 and Supplementary Table 1; see ref. 24 for a comprehensive benchmarking and Supplementary Methods for more detail on model evaluations). In principle following established definitions4, we refine the computation of some PBs with respect to their regional patterns and interactions (Methods), providing globally gridded precautionary limits to human interference with the Earth system at a level of great detail. In particular, we account for the evidence that many PBs need to be represented spatially explicitly4 to cover their

Gerten, Dieter↗