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NASA NTRS2012

Using Game Theoretic Models to Predict Pilot Behavior in NextGen Merging and Landing Scenario

In this paper, we present an implementation of the Semi Network-Form Game framework to predict pilot behavior in a merging and landing scenario. In this scenario, two aircraft are approaching to a freeze horizon with approximately equal distance when they become aware of each other via an ADS-B communication link that will be available in NextGen airspace. Both pilots want to gain advantage over the other by entering the freeze horizon earlier and obtain the first place in landing. They re-adjust their speed accordingly. However, they cannot simply increase their speed to the maximum allowable values since they are concerned with safety, separation distance, effort, possibility of being vectored-off from landing and possibility of violating speed constraints. We present how to model these concerns and the rest of the system using semi network-from game framework. Using this framework, based on certain assumptions on pilot utility functions and on system configuration, we provide estimates of pilot behavior and overall system evolution in time. We also discuss the possible employment of this modeling tool for airspace design optimization. To support this discussion, we provide a case where we investigate the effect of increasing the merging point speed limit on the commanded speed distribution and on the percentage of vectored aircraft.

Yildiz, Yildiray↗

NASA NTRS2012

Autonomous Onboard Science Data Analysis for Comet Missions

Coming years will bring several comet rendezvous missions. The Rosetta spacecraft arrives at Comet 67P/Churyumov-Gerasimenko in 2014. Subsequent rendezvous might include a mission such as the proposed Comet Hopper with multiple surface landings, as well as Comet Nucleus Sample Return (CNSR) and Coma Rendezvous and Sample Return (CRSR). These encounters will begin to shed light on a population that, despite several previous flybys, remains mysterious and poorly understood. Scientists still have little direct knowledge of interactions between the nucleus and coma, their variation across different comets or their evolution over time. Activity may change on short timescales so it is challenging to characterize with scripted data acquisition. Here we investigate automatic onboard image analysis that could act faster than round-trip light time to capture unexpected outbursts and plume activity. We describe one edge-based method for detect comet nuclei and plumes, and test the approach on an existing catalog of comet images. Finally, we quantify benefits to specific measurement objectives by simulating a basic plume monitoring campaign.

comets↗

NASA NTRS2012

Observations of the Crab Nebula with the Chandra X-Ray Observatory

The Crab Nebula and its pulsar has been the subject of a number of detailed observations with the Chandra X-ray Observatory. The superb angular resolution of Chandra s high-resolution telescope has made possible numerous remarkable results. Here we describe a number of specific studies of the Crab that I and my colleagues have undertaken. We discuss the geometry of the system, which indicates that the "inner X-ray ring", typically identified with the termination shock of the pulsar s particle wind, is most likely not in the equatorial plane of the pulsar. Other topics are the northern wisps and their evolution with time; the characterization of features in the jet to the southeast; pulse-phase spectroscopy and possible correlations with the features at other wavelengths, particularly the optical polarization; and a search for correlations of the X-ray flux with the recently-discovered gamma -ray flares.

Weisskopf, Martin C.↗

NASA NTRS2013

Tool for Automated Retrieval of Generic Event Tracks (TARGET)

Methods have been developed to identify and track tornado-producing mesoscale convective systems (MCSs) automatically over the continental United States, in order to facilitate systematic studies of these powerful and often destructive events. Several data sources were combined to ensure event identification accuracy. Records of watches and warnings issued by National Weather Service (NWS), and tornado locations and tracks from the Tornado History Project (THP) were used to locate MCSs in high-resolution precipitation observations and GOES infrared (11-micron) Rapid Scan Operation (RSO) imagery. Thresholds are then applied to the latter two data sets to define MCS events and track their developments. MCSs produce a broad range of severe convective weather events that are significantly affecting the living conditions of the populations exposed to them. Understanding how MCSs grow and develop could help scientists improve their weather prediction models, and also provide tools to decision-makers whose goals are to protect populations and their property. Associating storm cells across frames of remotely sensed images poses a difficult problem because storms evolve, split, and merge. Any storm-tracking method should include the following processes: storm identification, storm tracking, and quantification of storm intensity and activity. The spatiotemporal coordinates of the tracks will enable researchers to obtain other coincident observations to conduct more thorough studies of these events. In addition to their tracked locations, their areal extents, precipitation intensities, and accumulations all as functions of their evolutions in time were also obtained and recorded for these events. All parameters so derived can be catalogued into a moving object database (MODB) for custom queries. The purpose of this software is to provide a generalized, cross-platform, pluggable tool for identifying events within a set of scientific data based upon specified criteria with the possibility of storing identified events into a searchable database. The core of the application uses an implementation of the connected component labeling (CCL) algorithm to identify areas of interest, then uses a set of criteria to establish spatial and temporal relationships between identified components. The CCL algorithm is used for identifying objects within images for computer vision. This application applies it to scientific data sets using arbitrary criteria. The most novel concept was applying a generalized CCL implementation to scientific data sets for establishing events both spatially and temporally. The combination of several existing concepts (pluggable components, generalized CCL algorithm, etc.) into one application is also novel. In addition, how the system is designed, i.e., its extensibility with pluggable components, and its configurability with a simple configuration file, is innovative. This allows the system to be applied to new scenarios with ease.

Clune, Thomas↗

NASA NTRS2013

Azimuthal Spoke Propagation in Hall Effect Thrusters

Spokes are azimuthally propagating perturbations in the plasma discharge of Hall Effect Thrusters (HETs) that travel in the E x B direction and have been observed in many different systems. The propagation of azimuthal spokes are investigated in a 6 kW HET known as the H6 using ultra-fast imaging and azimuthally spaced probes. A spoke surface is a 2-D plot of azimuthal light intensity evolution over time calculated from 87,500 frames/s videos. The spoke velocity has been determined using three methods with similar results: manual fitting of diagonal lines on the spoke surface, linear cross-correlation between azimuthal locations and an approximated dispersion relation. The spoke velocity for three discharge voltages (300, 400 and 450 V) and three anode mass flow rates (14.7, 19.5 and 25.2 mg/s) yielded spoke velocities between 1500 and 2200 m/s across a range of normalized magnetic field settings. The spoke velocity was inversely dependent on magnetic field strength for low B-field settings and asymptoted at B-field higher values. The velocities and frequencies are compared to standard drifts and plasma waves such as E x B drift, electrostatic ion cyclotron, magnetosonic and various drift waves. The empirically approximated dispersion relation yielded a characteristic velocity that matched the ion acoustic speed for 5 eV electrons that exist in the near-anode and near-field plume regions of the discharge channel based on internal measurements. Thruster performance has been linked to operating mode where thrust-to-power is maximized when azimuthal spokes are present so investigating the underlying mechanism of spokes will benefit thruster operation.

Cylindrical Hall Thruster (CHT)↗

NASA NTRS2014

NuSTAR Observations of X-Ray Bursts from the Magnetar 1E 1048.1-5937

We report the detection of eight bright X-ray bursts from the 6.5 s magnetar 1E 1048.1−5937, during a 2013 July observation campaign with the Nuclear Spectroscopic Telescope Array. We study the morphological and spectral properties of these bursts and their evolution with time. The bursts resulted in count rate increases by orders of magnitude, sometimes limited by the detector dead time, and showed blackbody spectra with kT is approx. 6-8 keV in the T90 duration of 1-4 s, similar to earlier bursts detected from the source. We find that the spectra during the tail of the bursts can be modeled with an absorbed blackbody with temperature decreasing with flux. The burst flux decays followed a power law of index 0.8-0.9. In the burst tail spectra, we detect a is approx. 13 keV emission feature, similar to those reported in previous bursts from this source as well as from other magnetars observed with the Rossi X-ray Timing Explorer.We explore possible origins of the spectral feature such as proton cyclotron emission, which implies a magnetic field strength of B is approx. 2×10(exp15) G in the emission region. However, the consistency of the energy of the feature in different objects requires further explanation.

MAGNETAR 1E 1048.1-5937↗

NASA NTRS2016

Tangle-Free Mesh Motion for Ablation Simulations

Problems involving mesh motion-which should not be mistakenly associated with moving mesh methods, a class of adaptive mesh redistribution techniques-are of critical importance in numerical simulations of the thermal response of melting and ablative materials. Ablation is the process by which material vaporizes or otherwise erodes due to strong heating. Accurate modeling of such materials is of the utmost importance in design of passive thermal protection systems ("heatshields") for spacecraft, the layer of the vehicle that ensures survival of crew and craft during re-entry. In an explicit mesh motion approach, a complete thermal solve is first performed. Afterwards, the thermal response is used to determine surface recession rates. These values are then used to generate boundary conditions for an a posteriori correction designed to update the location of the mesh nodes. Most often, linear elastic or biharmonic equations are used to model this material response, traditionally in a finite element framework so that complex geometries can be simulated. A simple scheme for moving the boundary nodes involves receding along the surface normals. However, for all but the simplest problem geometries, evolution in time following such a scheme will eventually bring the mesh to intersect and "tangle" with itself, inducing failure. This presentation demonstrates a comprehensive and sophisticated scheme that analyzes the local geometry of each node with help from user-provided clues to eliminate the tangle and enable simulations on a wide-class of difficult problem geometries. The method developed is demonstrated for linear elastic equations but is general enough that it may be adapted to other modeling equations. The presentation will explicate the inner workings of the tangle-free mesh motion algorithm for both two and three-dimensional meshes. It will show abstract examples of the method's success, including a verification problem that demonstrates its accuracy and correctness. The focus of the presentation will be on the algorithm; specifics on how the techniques may be used in spacecraft design will be not discussed.

Droba, Justin↗

NASA NTRS2016

Design of Superconducting Gravity Gradiometer Cryogenic System for Mars Mission

Measurement of a planet's gravity field provides fundamental information about the planet's mass properties. The static gravity field reveals information about the internal structure of the planet, including crustal density variations that provide information on the planet's geological history and evolution. The time variations of gravity result from the movement of mass inside the planet, on the surface, and in the atmosphere. NASA is interested in a Superconducting Gravity Gradiometer (SGG) with which to measure the gravity field of a planet from orbit. An SGG instrument is under development with the NASA PICASSO program, which will be able to resolve the Mars static gravity field to degree 200 in spherical harmonics, and the time-varying field on a monthly basis to degree 20 from a 255 x 320 km orbit. The SGG has a precision two orders of magnitude better than the electrostatic gravity gradiometer that was used on the ESA's GOCE mission. The SGG operates at the superconducting temperature lower than 6 K. This study developed a cryogenic thermal system to maintain the SGG at the design temperature in Mars orbit. The system includes fixed radiation shields, a low thermal conductivity support structure and a two-stage cryocooler. The fixed radiation shields use double aluminized polyimide to emit heat from the warm spacecraft into the deep space. The support structure uses carbon fiber reinforced plastic, which has low thermal conductivity at cryogenic temperature and very high stress. The low vibration cryocooler has two stages, of which the high temperature stage operates at 65 K and the low temperature stage works at 6 K, and the heat rejection radiator works at 300 K. The study also designed a second option with a 4-K adiabatic demagnetization refrigerator (ADR) and two-stage 10-K turbo-Brayton cooler.

Gradiometer↗

NASA NTRS2016

Design of Superconducting Gravity Gradiometer Cryogenic System for Mars Mission

Measurement of a planets gravity field provides fundamental information about the planets mass properties. The static gravity field reveals information about the internal structure of the planet, including crustal density variations that provide information on the planets geological history and evolution. The time variations of gravity result from the movement of mass inside the planet, on the surface, and in the atmosphere. NASA is interested in a Superconducting Gravity Gradiometer (SGG) with which to measure the gravity field of a planet from orbit. An SGG instrument is under development with the NASA PICASSO program, which will be able to resolve the Mars static gravity field to degree 200 in spherical harmonics, and the time-varying field on a monthly basis to degree 20 from a 255 x 320 km orbit. The SGG has a precision two orders of magnitude better than the electrostatic gravity gradiometer that was used on the ESAs GOCE mission. The SGG operates at the superconducting temperature lower than 6 K. This study developed a cryogenic thermal system to maintain the SGG at the design temperature in Mars orbit. The system includes fixed radiation shields, a low thermal conductivity support structure and a two-stage cryocooler. The fixed radiation shields use double aluminized polyimide to emit heat from the warm spacecraft into the deep space. The support structure uses carbon fiber reinforced plastic, which has low thermal conductivity at cryogenic temperature and very high stress. The low vibration cryocooler has two stages, of which the high temperature stage operates at 65 K and the low temperature stage works at 6 K, and the heat rejection radiator works at 300 K. The study also designed a second option with a 4-K adiabatic demagnetization refrigerator (ADR) and two-stage 10-K turbo-Brayton cooler.

Li, X.↗

NASA NTRS2015

Ontology and modeling patterns for state-based behavior representation

This paper provides an approach to capture state-based behavior of elements, that is, the specification of their state evolution in time, and the interactions amongst them. Elements can be components (e.g., sensors, actuators) or environments, and are characterized by state variables that vary with time. The behaviors of these elements, as well as interactions among them are represented through constraints on state variables. This paper discusses the concepts and relationships introduced in this behavior ontology, and the modeling patterns associated with it. Two example cases are provided to illustrate their usage, as well as to demonstrate the flexibility and scalability of the behavior ontology: a simple flashlight electrical model and a more complex spacecraft model involving instruments, power and data behaviors. Finally, an implementation in a SysML profile is provided.

state variable↗

NASA NTRS2016

Linking Remotely Sensed Aerosol Types to Their Chemical Composition

Aerosol types measured during the Ship-Aircraft Bio-Optical Research (SABOR) experiment are related to GEOS-Chem model chemical composition. The application for this procedure to link model chemical components to aerosol type is desirable for understanding aerosol evolution over time. The Mahalanobis distance (DM) statistic is used to cluster model groupings of five chemical components (organic carbon, black carbon, sea salt, dust and sulfate) in a way analogous to the methods used by Burton et al. [2012] and Russell et al. [2014]. First, model-to-measurement evaluation is performed by collocating vertically resolved aerosol extinction from SABOR High Spectral Resolution LiDAR (HSRL) to the GEOS-Chem nested high-resolution data. Comparisons of modeled-to-measured aerosol extinction are shown to be within 35% +/- 14%. Second, the model chemical components are calculation into five variables to calculate the DM and cluster means and covariances for each HSRL-retrieved aerosol type. The layer variables from the model are aerosol optical depth (AOD) ratios of (i) sea salt and (ii) dust to total AOD, mass ratios of (iii) total carbon (i.e. sum of organic and black carbon) to the sum of total carbon and sulfate (iv) organic carbon to black carbon, and (v) the natural log of the aerosol-to-molecular extinction ratio. Third, the layer variables and at most five out of twenty SABOR flights are used to form the pre-specified clusters for calculating DM and to assign an aerosol type. After determining the pre-specified clusters, model aerosol types are produced for the entire vertically resolved GEOS-Chem nested domain over the United States and the model chemical component distributions relating to each type are recorded. Resulting aerosol types are Dust/Dusty Mix, Maritime, Smoke, Urban and Fresh Smoke (separated into 'dark' and 'light' by a threshold of the organic to black carbon ratio). Model-calculated DM not belonging to a specific type (i.e. not meeting a threshold probability) is termed an outlier and those DM values that can belong to multiple types (i.e. showing weak probability of belonging to a specific cluster) are termed as Overlap. MODIS active fires are overlaid on the model domain to qualitatively evaluate the model-predicted Smoke aerosol types.

Aerosol Types↗

NASA NTRS2017

Mapping the Iron Oxidation State in Martian Meteorites

Several types of Martian igneous meteorites have been identified: clinopyroxenites (nakhlites), basaltic shergottites, peridotitic shergottites, dunites (chassignites) and orthopyroxenites [1,2]. In order to constrain the heterogeneity of the Martian mantle and crust, and their evolution through time, numerous studies have been performed on the iron oxidation state of these meteorites [3,4,5,6,7,8,9]. The calculated fO2 values all lie within the FMQ-5 to FMQ+0.5 range (FMQ representing the Fayalite = Magnetite + Quartz buffer); however, discrepancies appear between the various studies, which are either attributed to the choice of the minerals/melts used, or to the precision of the analytical/calculation method. The redox record in volcanic samples is primarily related to the oxidation state in the mantle source(s). However, it is also influenced by several deep processes: melting, crystallization, magma mixing [10], assimilation and degassing [11]. In addition, the oxidation state in Martian meteorites is potentially affected by several surface processes: assimilation of sediment/ crust during lava flowing at Mars' surface, low temperature micro-crystallization [10], weathering at the surface of Mars and low temperature reequilibration, impact processes (i.e. high pressure phase transitions, mechanical mixing, shock degassing and melting), space weathering, and weathering on Earth (at atmospheric conditions different from Mars). Decoding the redox record of Martian meteorites, therefore, requires large-scale quantitative analysis methods, as well as a perfect understanding of oxidation processes.

Martin, A. M.↗

NASA NTRS2017

Dynamic Routing of Aircraft in the Presence of Adverse Weather Using a POMDP Framework

Each year weather-related airline delays result in hundreds of millions of dollars in additional fuel burn, maintenance, and lost revenue, not to mention passenger inconvenience. The current approaches for aircraft route planning in the presence of adverse weather still mainly rely on deterministic methods. In contrast, this work aims to deal with the problem using a Partially Observable Markov Decision Processes (POMDPs) framework, which allows for reasoning over uncertainty (including uncertainty in weather evolution over time) and results in solutions that are more robust to disruptions. The POMDP-based decision support system is demonstrated on several scenarios involving convective weather cells and is benchmarked against a deterministic planning system with functionality similar to those currently in use or under development.

Decision making↗

NASA NTRS2017

The Don Edwards San Francisco Bay National Wildlife Refuge: A Natural Laboratory for Federal Agencies and Partners

The Don Edwards San Francisco Bay National Wildlife Refuge encompasses a rich mosaic of habitats and is a fecund and convenient field site for Earth science research, comprised of tidal salt marsh, open ponds, shallow water, mudflat habitat and encompassing a variety of tide, salinity, elevation, slope, and other conditions. Proximity to the NASA Ames Research Center and overlap with the center's UAS (unmanned aircraft systems) test area presents the opportunity to create a unique natural laboratory that can incubate and support a variety of research and benefit the Refuge in monitoring wildlife changes and habitat evolution over time.

Unmanned Airborne Vehicle↗

NASA NTRS2018

A Fast Monte Carlo Method for Model-Based Prognostics Based on Stochastic Calculus

This work proposes a fast Monte Carlo method to solve differential equations utilized in model-based prognostics. The methodology is derived from the theory of stochastic calculus, and the goal of such a method is to speed up the estimation of the probability density functions describing the independent variable evolution over time. In the prognostic scenarios presented in this paper, the stochastic differential equations describe variables directly or indirectly related to the degradation of a monitored system. The method allows the estimation of the probability density functions by solving the deterministic equation and approximating the stochastic integrals using samples of the model noise. By so doing, the prognostic problem is solved without the Monte Carlo simulation based on Euler's forward method, which is typically the most time consuming task of the prediction stage. Three different prognostic scenarios are presented as proof of concept: (i) life prediction of electrolytic capacitors, (ii) remaining time to discharge of Lithium-ion batteries, and (iii) prognostic of cracked structures under fatigue loading. The paper shows how the method produces probability density functions that are statistically indistinguishable from the distributions estimated with Euler's forward Monte Carlo simulation. However, the proposed solution is orders of magnitude faster when computing the time-to-failure distribution of the monitored system. The approach may enable complex real-time prognostics and health management solutions with limited computing power.

Corbetta, M.↗

NASA NTRS2019

A Fast Monte Carlo Method for Model-Based Prognostics Based on Stochastic Calculus

stochastic calculus↗

NASA NTRS2018

Observations of Fast-Moving Features in the Debris Disk of AU Mic on a Three-Year Timescale: Confirmation and New Discoveries

Context. The nearby and young M star AU Mic is surrounded by a debris disk in which we previously identified a series of large-scale arch-like structures that have never been seen before in any other debris disk and that move outward at high velocities. Aims. We initiated a monitoring program with the following objectives: (1) track the location of the structures and better constrain their projected speeds, (2) search for new features emerging closer in, and ultimately (3) understand the mechanism responsible for the motion and production of the disk features. Methods. AU Mic was observed at 11 different epochs between August 2014 and October 2017 with the IR camera and spectrograph of SPHERE. These high-contrast imaging data were processed with a variety of angular, spectral, and polarimetric differential imaging techniques to reveal the faintest structures in the disk. We measured the projected separations of the features in a systematic way for all epochs. We also applied the very same measurements to older observations from the Hubble Space Telescope (HST) with the visible cameras STIS and ACS. Results. The main outcomes of this work are (1) the recovery of the five southeastern broad arch-like structures we identified in our first study, and confirmation of their fast motion (projected speed in the range 4–12 km/s); (2) the confirmation that the very first structures observed in 2004 with ACS are indeed connected to those observed later with STIS and now SPHERE; (3) the discovery of two new very compact structures at the northwest side of the disk (at 0.40′′ and 0.55′′ in May 2015) that move to the southeast at low speed; and (4) the identification of a new arch-like structure that might be emerging at the southeast side at about 0.4′′ from the star (as of May 2016). Conclusions. Although the exquisite sensitivity of SPHERE allows one to follow the evolution not only of the projected separation, but also of the specific morphology of each individual feature, it remains difficult to distinguish between possible dynamical scenarios that may explain the observations. Understanding the exact origin of these features, the way they are generated, and their evolution over time is certainly a significant challenge in the context of planetary system formation around M stars.

Boccaletti, A.↗

NASA NTRSDate not supplied

Flux Comparison of Master-8 and Ordem 3.1 Modelled Space Debris Population

With ESA’s Meteoroid And Space debris Terrestrial Environment Reference (MASTER-8) model and NASA’s Orbital Debris Engineering Model(ORDEM) 3.1, the two premier orbital debris engineering models have been officially released. The two models come with significant enhancements and now represent state-of-the-art orbital debris modelling for their respective agencies. Both models provide the community with estimates of the space debris environment from low Earth orbit (LEO) up to at least geostationary altitude. The MASTER population is an event-based simulation of all known events that generate debris and objects that are part of the U.S. Space Surveillance Network (SSN) catalog, which provides coverage of objects with diameters down to approximately 10cm in LEO and 1 m in geosynchronous Earth orbit (GEO). Different models are used to simulate the artificial objects and their orbit evolution over time. These models are called “sources” since they assign an origin to each individual object and consist of fragments, solid rocket motor (SRM) remainders, sodium-potassium(NaK) droplets, paintflakes, ejecta, and multi-layer insulation (MLI) fragments. The objects from each source are characterized by having individual release mechanisms, as well as orbital distributions, material composition, size, and mass distributions. Dedicated radar and telescope observation data is used to calibrate the model for objects larger than 1 cm in LEO and larger than 10 cm in GEO. For calibrating the small-sized objects, below 1 cm, impact data from returned surfaces are analyzed. Because the >1cm object population is dominated by fragments, the fragmentation event database was updated to include new events, as well as re-evaluate past events. Special attention was drawn to re-evaluating theFengyun-1C anti-satellite test from 2007 and Cosmos-Iridium collision event from 2009 since these events shape the fragment population because of their severity. After 2009, the two largest fragmentations in terms of number of tracked debris are the Briz-M explosion in 2012 and the NOAA-16explosion in 2015. In total, there are 261 confirmed fragmentations in the database up to November 2016.The baseline population for ORDEM 3.1 is based on the U.S. SSN catalog, and observational datasets from radar, in situ, and optical sources provide a foundation from which the model populations are statistically extrapolated to smaller size regions. These regions are not well-covered by the SSN catalog yet may pose the greatest threat to operational spacecraft. The NASA Standard Satellite Breakup Model is used to generate fragments greater than 1mm from collisions and explosions, and these fragment populations are scaled using ground-based radar data. Specific major debris-producing events, including the Fengyun-1C, Iridium 33, and Cosmos2251 debris clouds, and unique populations, such as NaK droplets, were re-examined, modelled, and added to the ORDEM environment separately. Optical measurement data is used to model the GEO population down to 10 cm. The debris environment is propagated using NASA’s LEO-to-GEO Environment Debris model, and future explosions of intact objects and collisions involving objects greater than 10 cm are assessed statistically. The environment from a few millimetres down to 10 𝜇m is modelled using a special degradation model where small particles are generated from intact spacecraft and rocket bodies, then the populations are scaled to fit in situ cratering data from Space Shuttle returned surfaces. Fragments smaller than 10 cm are differentiated based on material density categories, i.e., high-, medium-, and low-density, to better characterize the potential debris risk posed to upper stages and spacecraft. This paper will discuss the MASTER and ORDEM approaches for modelling populations and compare fluxes for specific orbits, including sun-synchronous, ISS-altitude, geosynchronous transfer, and GEO. In the end, a conclusion is drawn towards the importance of having multiple fundamentally different, yet validated, models to estimate the space debris population.

Andre Horstmann↗