SEARCH · Engineering Papers

Results for “Direct Sequence”

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

SourceResearch connectionFrom yearThrough year

Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.

At least 829 records · Page 46

All sources NASA NTRS DOE OSTI

NASA NTRS1989

Characterization of robotics parallel algorithms and mapping onto a reconfigurable SIMD machine

The kinematics, dynamics, Jacobian, and their corresponding inverse computations are six essential problems in the control of robot manipulators. Efficient parallel algorithms for these computations are discussed and analyzed. Their characteristics are identified and a scheme on the mapping of these algorithms to a reconfigurable parallel architecture is presented. Based on the characteristics including type of parallelism, degree of parallelism, uniformity of the operations, fundamental operations, data dependencies, and communication requirement, it is shown that most of the algorithms for robotic computations possess highly regular properties and some common structures, especially the linear recursive structure. Moreover, they are well-suited to be implemented on a single-instruction-stream multiple-data-stream (SIMD) computer with reconfigurable interconnection network. The model of a reconfigurable dual network SIMD machine with internal direct feedback is introduced. A systematic procedure internal direct feedback is introduced. A systematic procedure to map these computations to the proposed machine is presented. A new scheduling problem for SIMD machines is investigated and a heuristic algorithm, called neighborhood scheduling, that reorders the processing sequence of subtasks to reduce the communication time is described. Mapping results of a benchmark algorithm are illustrated and discussed.

Lee, C. S. G.↗

NASA NTRS1991

Digital Image Velocimetry

Proposed technique for production of velocity maps from sequences of photographic video images of flows seeded with small particles. In digital image velocimetry, image analyzed by digital Fourier tranformation. Process free of noise, more precise, and consumes less time. Eliminates need to process photographs, indicates directions of velocity vectors unambiguously, and offers increased dynamic ranges. Because all processing performed electronically, eventually capable of mapping flow-velocity fields in real time.

Cho, Y. C.↗

NASA NTRS1992

Impact-generated winds on Venus: Causes and effects

The pressure of the dense atmosphere of Venus significantly changes the appearance of ejecta deposits relative to craters on the Moon and Mercury. Conversely, specific styles and sequences of ejecta emplacement can be inferred to represent different intensities of atmospheric response winds acting over different timescales. Three characteristic timescales can be inferred from the geologic record: surface scouring and impactor-controlled (angle and direction) initiation of the long fluidized run-out flows; nonballistic emplacement of inner, radar-bright ejecta facies and radar-dark outer facies; and very late reworking of surface materials. These three timescales roughly correspond to processes observed in laboratory experiments that can be scaled to conditions on Venus (with appropriate assumptions): coupling between the atmosphere and earlytime vapor/melt (target and impactor) that produces an intense shock that subsequently evolves into blast/response winds; less energetic dynamic response of the atmosphere to the outward-moving ballistic ejecta curtain that generates nonthermal turbulent eddies; and late recovery of the atmosphere to impact-generated thermal and pressure gradients expressed as low-energy but long-lived winds. These different timescales and processes can be viewed as the atmosphere equivalent of shock melting, material motion, and far-field seismic response in the target. The three processes (early Processes, Atmospheric Processes, and Late Recovery Winds) are discussed at length.

Schultz, Pater H.↗

NASA NTRS2004

A DMAP Program for the Selection of Accelerometer Locations in MSC/NASTRAN

A new program for selecting sensor locations has been written in the DMAP (Direct Matrix Abstraction Program) language of MSC/NASTRAN. The program implements the method of Effective Independence for selecting sensor locations, and is executed within a single NASTRAN analysis as a "rigid format alter" to the normal modes solution sequence (SOL 103). The user of the program is able to choose among various analysis options using Case Control and Bulk Data entries. Algorithms tailored for the placement of both uni-axial and tri- axial accelerometers are available, as well as several options for including the model s mass distribution into the calculations. Target modes for the Effective Independence analysis are selected from the MSC/NASTRAN ASET modes calculated by the "SOL 103" solution sequence. The initial candidate sensor set is also under user control, and is selected from the ASET degrees of freedom. Analysis results are printed to the MSCINASTRAN output file (*.f06), and may include the current candidate sensors set, and their associated Effective Independence distribution, at user specified iteration intervals. At the conclusion of the analysis, the model is reduced to the final sensor set, and frequencies and orthogonality checks are printed. Example results are given for a pre-test analysis of NASA s five-segment solid rocket booster modal test.

Peck, Jeff↗

NASA NTRS2011

Variability in Surface BRDF at Different Spatial Scales (30 m-500 m) Over a Mixed Agricultural Landscape as Retrieved from Airborne and Satellite Spectral Measurements

Over the past decade, the role of multiangle remote sensing has been central to the development of algorithms for the retrieval of global land surface properties including models of the bidirectional reflectance distribution function (BRDF), albedo, land cover/dynamics, burned area extent, as well as other key surface biophysical quantities represented by the anisotropic reflectance characteristics of vegetation. In this study, a new retrieval strategy for fine-to-moderate resolution multiangle observations was developed, based on the operational sequence used to retrieve the Moderate Resolution Imaging Spectroradiometer (MODIS) Collection 5 reflectance and BRDF/albedo products. The algorithm makes use of a semiempirical kernel-driven bidirectional reflectance model to provide estimates of intrinsic albedo (i.e., directional-hemispherical reflectance and bihemispherical reflectance), model parameters describing the BRDF, and extensive quality assurance information. The new retrieval strategy was applied to NASA's Cloud Absorption Radiometer (CAR) data acquired during the 2007 Cloud and Land Surface Interaction Campaign (CLASIC) over the well-instrumented Atmospheric Radiation Measurement Program (ARM) Southern Great Plains (SGP) Cloud and Radiation Testbed (CART) site in Oklahoma, USA. For the case analyzed, we obtained approx.1.6 million individual surface bidirectional reflectance factor (BRF) retrievals, from nadir to 75 off-nadir, and at spatial resolutions ranging from 3 m - 500 m. This unique dataset was used to examine the interaction of the spatial and angular characteristics of a mixed agricultural landscape; and provided the basis for detailed assessments of: (1) the use of a priori knowledge in kernel-driven BRDF model inversions; (2) the interaction between surface reflectance anisotropy and instrument spatial resolution; and (3) the uncertain ties that arise when sub-pixel differences in the BRDF are aggregated to a moderate resolution satellite pixel. Results offer empirical evidence concerning the influence of scale and spatial heterogeneity in kernel-driven BRDF models; providing potential new insights into the behavior and characteristics of different surface radiative properties related to land/use cover change and vegetation structure.

Roman, Miguel O.↗

NASA NTRS2012

Variability in Surface BRDF at Different Spatial Scales (30m-500m) Over a Mixed Agricultural Landscape as Retrieved from Airborne and Satellite Spectral Measurements

Over the past decade, the role of multiangle 1 remote sensing has been central to the development of algorithms for the retrieval of global land surface properties including models of the bidirectional reflectance distribution function (BRDF), albedo, land cover/dynamics, burned area extent, as well as other key surface biophysical quantities represented by the anisotropic reflectance characteristics of vegetation. In this study, a new retrieval strategy for fine-to-moderate resolution multiangle observations was developed, based on the operational sequence used to retrieve the Moderate Resolution Imaging Spectroradiometer (MODIS) Collection 5 reflectance and BRDF/albedo products. The algorithm makes use of a semiempirical kernel-driven bidirectional reflectance model to provide estimates of intrinsic albedo (i.e., directional-hemispherical reflectance and bihemispherical reflectance), model parameters describing the BRDF, and extensive quality assurance information. The new retrieval strategy was applied to NASA's Cloud Absorption Radiometer (CAR) data acquired during the 2007 Cloud and Land Surface Interaction Campaign (CLASIC) over the well-instrumented Atmospheric Radiation Measurement Program (ARM) Southern Great Plains (SGP) Cloud and Radiation Testbed (CART) site in Oklahoma, USA. For the case analyzed, we obtained approx.1.6 million individual surface bidirectional reflectance factor (BRF) retrievals, from nadir to 75deg off-nadir, and at spatial resolutions ranging from 3 m - 500 m. This unique dataset was used to examine the interaction of the spatial and angular 18 characteristics of a mixed agricultural landscape; and provided the basis for detailed assessments of: (1) the use of a priori knowledge in kernel-driven BRDF model inversions; (2) the interaction between surface reflectance anisotropy and instrument spatial resolution; and (3) the uncertainties that arise when sub-pixel differences in the BRDF are aggregated to a moderate resolution satellite pixel. Results offer empirical evidence concerning the influence of scale and spatial heterogeneity in kernel-driven BRDF models; providing potential new insights into the behavior and characteristics of different surface radiative properties related to land/use cover change and vegetation structure.

Roman, Miguel O.↗

NASA NTRS1998

Expression of extracellular calcium (Ca2+o)-sensing receptor in human peripheral blood monocytes

The calcium-sensing receptor (CaR) is a G protein-coupled receptor playing key roles in extracellular calcium ion (Ca2+o) homeostasis in parathyroid gland and kidney. Macrophage-like mononuclear cells appear at sites of osteoclastic bone resorption during bone turnover and may play a role in the "reversal" phase of skeletal remodeling that follows osteoclastic resorption and precedes osteoblastic bone formation. Bone resorption produces substantial local increases in Ca2+o that could provide a signal for such mononuclear cells present locally within the bone marrow microenvironment. Indeed, previous studies by other investigators have shown that raising Ca2+o either in vivo or in vitro stimulated the release of interleukin-6 (IL-6) from human peripheral blood monocytes, suggesting that these cells express a Ca2+o-sensing mechanism. In these earlier studies, however, the use of reverse transcription-polymerase chain reaction (RT-PCR) failed to detect transcripts for the CaR previously cloned from parathyroid and kidney in peripheral blood monocytes. Since we recently found that non-specific esterase-positive, putative monocytes isolated from murine bone marrow express the CaR, we reevaluated the expression of this receptor in human peripheral blood monocytes. Immunocytochemistry, flow cytometry, and Western blot analysis, performed using a polyclonal antiserum specific for the CaR, detected CaR protein in human monocytes. In addition, the use of RT-PCR with CaR-specific primers, followed by nucleotide sequencing of the amplified products, identified CaR transcripts in the cells. Therefore, taken together, our data show that human peripheral blood monocytes possess both CaR protein and mRNA very similar if not identical to those expressed in parathyroid and kidney that could mediate the previously described, direct effects of Ca2+o on these cells. Furthermore, since mononuclear cells isolated from bone marrow also express the CaR, the latter might play some role in the "reversal" phase of bone remodeling, sensing local changes in Ca2+o resulting from osteoclastic bone resorption and secreting osteotropic cytokines or performing other Ca2+o-regulated functions that contribute to the control of bone turnover.

NASA Discipline Musculoskeletal↗

DOE OSTI2024

Hybrid additive manufacturing of AISI 316L via asynchronous powder and hot-wire laser directed energy deposition

Hybrid Additive Manufacturing (AM) offers a way to leverage the advantages of different AM technologies, enabling the efficient production of sizeable parts without compromising material properties or geometric complexity capabilities. This study presents an asynchronous hybrid Directed Energy Deposition (DED) strategy employing laser powder DED and laser hot-wire DED. AISI 316L parts comprising multiple powder and wire segments were fabricated with optional machining on AISI 316L substrates to investigate how quality is impacted by (i) alternative process sequences (laser powder DED followed by laser hot-wire DED and vice versa), (ii) machined vs. as-printed interfacial conditions, and (iii) material deposition on top vs. alongside previously built segments. Optical microscopy, X-ray computed tomography, and Vickers hardness were used to characterize the morphology and microstructure of the parts, localized porosity and lack of fusion defects, bulk density, and mechanical properties. Interfacial machining was necessary for dimensional control but promoted lack of fusion voids, resulting in a 99.71 ± 0.01% dense part. As-printed interfaces resulted in a denser part (99.82 ± 0.02%) at the expense of dimensional accuracy. The hardness of the parts with as-printed and machined interfaces was 196 ± 0.37 HV and 192 ± 0.40 HV, respectively, compared to 156 ± 1.4 HV for the substrate. Depositing powder alongside or on top of wire sections resulted in interfaces with a hardness of 217 ± 2.2 HV, compared to 185 ± 3.4 HV for the wire-powder interfaces.

36 MATERIALS SCIENCE↗

DOE OSTI2024

Evidence for autotrophic growth of purple sulfur bacteria using pyrite as electron and sulfur source

ABSTRACT Purple sulfur bacteria (PSB) are capable of anoxygenic photosynthesis via oxidizing reduced sulfur compounds and are considered key drivers of the sulfur cycle in a range of anoxic environments. In this study, we show that Allochromatium vinosum (a PSB species) is capable of autotrophic growth using pyrite as the electron and sulfur source. Comparative growth profile, substrate characterization, and transcriptomic sequencing data provided valuable insight into the molecular mechanisms underlying the bacterial utilization of pyrite and autotrophic growth. Specifically, the pyrite-supported cell cultures (“py”’) demonstrated robust but much slower growth rates and distinct patterns from their sodium sulfide-amended positive controls. Up to ~200-fold upregulation of genes encoding various c - and b -type cytochromes was observed in “py,” pointing to the high relevance of these molecules in scavenging and relaying electrons from pyrite to cytoplasmic metabolisms. Conversely, extensive downregulation of genes related to LH and RC complex components indicates that the electron source may have direct control over the bacterial cells’ photosynthetic activity. In terms of sulfur metabolism, genes encoding periplasmic or membrane-bound proteins (e.g., FccAB and SoxYZ) were largely upregulated, whereas those encoding cytoplasmic proteins (e.g., Dsr and Apr groups) are extensively suppressed. Other notable differentially expressed genes are related to flagella/fimbriae/pilin(+), metal efflux(+), ferrienterochelin(−), and [NiFe] hydrogenases(+). Characterization of the biologically reacted pyrite indicates the presence of polymeric sulfur. These results have, for the first time, put the interplay of PSB and transition metal sulfide chemistry under the spotlight, with the potential to advance multiple fields, including metal and sulfur biogeochemistry, bacterial extracellular electron transfer, and artificial photosynthesis. IMPORTANCE Microbial utilization of solid-phase substrates constitutes a critical area of focus in environmental microbiology, offering valuable insights into microbial metabolic processes and adaptability. Recent advancements in this field have profoundly deepened our knowledge of microbial physiology pertinent to these scenarios and spurred innovations in biosynthesis and energy production. Furthermore, research into interactions between microbes and solid-phase substrates has directly linked microbial activities to the surrounding mineralogical environments, thereby enhancing our understanding of the relevant biogeochemical cycles. Our study represents a significant step forward in this field by demonstrating, for the first time, the autotrophic growth of purple sulfur bacteria using insoluble pyrite (FeS2) as both the electron and sulfur source. The presented comparative growth profiles, substrate characterizations, and transcriptomic sequencing data shed light on the relationships between electron donor types, photosynthetic reaction center activities, and potential extracellular electron transfer in these organisms capable of anoxygenic photosynthesis. Furthermore, the findings of our study may provide new insights into early-Earth biogeochemical evolutions, offering valuable constraints for understanding the environmental conditions and microbial processes that shaped our planet’s history.

59 BASIC BIOLOGICAL SCIENCES↗

NASA NTRS2014

Combustion Stability Characteristics of the Project Morpheus Liquid Oxygen/Liquid Methane Main Engine

The Project Morpheus liquid oxygen (LOX) / liquid methane rocket engines demonstrated acousticcoupled combustion instabilities during sea‐level ground‐based testing at the NASA Johnson Space Center (JSC) and Stennis Space Center (SSC). High‐amplitude, 1T, 1R, 1T1R (and higher order) modes appear to be triggered by injector conditions. The instability occurred during the Morpheus‐specific engine ignition/start sequence, and did demonstrate the capability to propagate into mainstage. However, the instability was never observed to initiate during mainstage, even at low power levels. The Morpheus main engine is a JSC‐designed ~5,000 lbf‐thrust, 4:1 throttling, pressure‐fed cryogenic engine using an impinging element injector design. Two different engine designs, named HD4 and HD5, and two different builds of the HD4 engine all demonstrated similar instability characteristics. Through the analysis of more than 200 hot fire tests on the Morpheus vehicle and SSC test stand, a relationship between ignition stability and injector/chamber pressure was developed. The instability has the distinct characteristic of initiating at high relative injection pressure drop (dP) at low chamber pressure (Pc); i.e., instabilities initiated at high dP/Pc at low Pc during the start sequence. The high dP/Pc during start results during the injector /chamber chill‐in, and is enhanced by hydraulic flip in the injector orifice elements. Because of the fixed mixture ratio of the existing engine design (the main valves share a common actuator), it is not currently possible to determine if LOX or methane injector dP/Pc were individual contributors (i.e., LOX and methane dP/Pc typically trend in the same direction within a given test). The instability demonstrated initiation characteristic of starting at or shortly after methane injector chillin. Colder methane (e.g., sub‐cooled) at the injector inlet prior to engine start was much more likely to result in an instability. A secondary effect of LOX sub‐cooling was also possibly observed; greater LOX sub‐ cooling improved stability. Some tests demonstrated a low‐amplitude 1L‐1T instability prior to LOX injector chill‐in. The Morpheus main engine also demonstrated chug instabilities during some engine shutdown sequences on the flight vehicle and SSC test stand. The chug instability was also infrequently observed during the startup sequence. The chug instabilities predictably initiated at low dP/Pc at low Pc. The chug instabilities were always self‐limiting; startup chug instabilities terminated during throttle‐up and shutdown chug instabilities decayed by shutdown termination.

Melcher, J. C.↗

NASA NTRS1988

Infrared observations of planetary atmospheres

The goal of this research in to obtain infrared data on planetary atmospheres which provide information on several aspects of structure and composition. Observations include direct mission real-time support as well as baseline monitoring preceding mission encounters. Besides providing a broader information context for spacecraft experiment data analysis, observations will provide the quantitative data base required for designing optimum remote sensing sequences and evaluating competing science priorities. In the past year, thermal images of Jupiter and Saturn were made near their oppositions in order to monitor long-term changes in their atmospheres. Infrared images of the Jovian polar stratospheric hot spots were made with IUE observations of auroral emissions. An exploratory 5-micrometer spectrum of Uranus was reduced and accepted for publication. An analysis of time-variability of temperature and cloud properties of the Jovian atomsphere was made. Development of geometric reduction programs for imaging data was initiated for the sun workstation. Near-infrared imaging observations of Jupiter were reduced and a preliminary analysis of cloud properties made. The first images of the full disk of Jupiter with a near-infrared array camera were acquired. Narrow-band (10/cm) images of Jupiter and Saturn were obtained with acousto-optical filters.

Orton, Glenn S.↗

NASA NTRS2017

The Role of KREEP in the Production of Mg-Suite Magmas and Its Influence on the Extent of Mg-Suite Magmatism in the Lunar Crust

The lunar magnesian-suite, or Mg-suite, is a series of ancient plutonic rocks from the lunar crust. They have received a considerable amount of attention from lunar scientists since their discovery for three primary reasons: 1) their ages and geochemistry indicate they represent pristine magmatic samples that crystallized very soon after the formation of the Moon; 2) their ages often overlap with ages of the ferroan anorthosite (FAN) crust; and 3) planetary-scale processes are needed in formation models to account for their unique geochemical features. Taken as a whole, the Mg-suite samples, as magmatic cumulate rocks, approximate a fractional crystallization sequence in the low-pressure forsterite-anorthite-silica system, and thus these samples are generally thought to be derived from layered mafic intrusions which crystallized very slowly from magmas that intruded the anorthositic crust. However, no direct linkages have been established between different Mg-suite samples based either on field relationships or geochemistry.The model for the origin of the Mg-suite, which best fits the limited available data, is one where Mg-suite magmas form from melting of a hybrid cumulate package consisting of deep mantle dunite, crustal anorthosite, and KREEP (potassium-rare earth elements-phosphorus) at the base of the crust under the Procellarum KREEP Terrane (PKT). In this model, these three LMO (Lunar Magma Ocean) cumulate components are brought into close proximity by the cumulate overturn process. Deep mantle dunitic cumulates with an Mg number of approximately 90 rise to the base of the anorthositic crust due to their buoyancy relative to colder, more dense Fe- and Ti-rich cumulates. This hybridized source rock melts to form Mg-suite magmas, saturated in Mg-rich olivine and anorthitic plagioclase, that have a substantial KREEP component.

Elardo, S. M.↗

NASA NTRSDate not supplied

GL4U: Bioinformatics training for students and educators using space omics data

Amanda Marie Saravia-butler↗

NASA NTRSDate not supplied

GL4U: Using Space Omics Data to Provide Bioinformatics Training for Students and Educators

NASA’s GeneLab project provides researchers open access to space-relevant experiment multi-omics data that can be mined to understand the effects of spaceflight on biological systems. To maximize the number of scientists who understand and utilize GeneLab data and data processing pipelines, GeneLab has created GeneLab for Colleges and Universities (GL4U). GL4U provides space biology-relevant training in bioinformatics to the next generation of scientists through direct and indirect approaches. The GeneLab team plans to host two annual data processing bootcamps, one for college-level students (direct) and one for college educators (indirect – training of trainers), in which participants learn to analyze GeneLab’s space-relevant omics data. The GL4U direct training pilot program was conducted in June 2021. During the pilot, students participated in a week-long bootcamp consisting of space biology-specific lectures and hands-on instruction using Jupyter Notebooks to analyze RNA sequence data. This pilot demonstrated the capacity of GL4U for training young scientists and encouraging data re-use. In June 2022, GL4U partnered with Jet Propulsion Laboratory’s (JPL) Planetary Protection Center of Excellence to conduct the indirect training pilot program by training educators at historically black colleges and universities (HBCUs) and minority serving institutions (MSIs). During the educator pilot, participants received materials, training, and will be provided the necessary compute resources to enable them to run the bootcamp at their home institutions or alternatively to adapt the content to implement within existing courses, thereby extending the reach of this initiative. The GL4U training program provides undergraduate students from underrepresented groups the opportunity to learn about NASA and Space Biology, and to enhance their career prospects by gaining hands-on experience analyzing omics data, a skillset that is highly applicable and marketable in the life sciences. Pre- and post-bootcamp surveys were completed by all participants and show the overwhelming success of the bootcamps.

Amanda M. Saravia-Butler↗

NASA NTRSDate not supplied

GL4U: Bioinformatics Training for Students and Educators Using Space Omics Data

Amanda Marie Saravia-butler↗

NASA NTRS1976

Considerations to achieve directionality for gamma ray lasers

A method of alignment of nuclei for a gamma ray laser and a means of achieving preferential emission of radiation along the crystal axis are discussed. The proposed method of preferential emission of radiation along the aligned needles is to have a symmetric field gradient at the nucleus and a sequence of excited levels of spin and parity 2(+) and C(+). The proposed scheme reduces the density of excited states required for lasing and reduces the linewidth due to inhomogeneous broadening. Mossbauer absorption experiments intended to test these ideas are outlined.

Jha, S.↗

NASA NTRS1980

The Mark 3 data base handler

A data base handler which would act to tie Mark 3 system programs together is discussed. The data base handler is written in FORTRAN and is implemented on the Hewlett-Packard 21MX and the IBM 360/91. The system design objectives were to (1) provide for an easily specified method of data interchange among programs, (2) provide for a high level of data integrity, (3) accommodate changing requirments, (4) promote program accountability, (5) provide a single source of program constants, and (6) provide a central point for data archiving. The system consists of two distinct parts: a set of files existing on disk packs and tapes; and a set of utility subroutines which allow users to access the information in these files. Users never directly read or write the files and need not know the details of how the data are formatted in the files. To the users, the storage medium is format free. A user does need to know something about the sequencing of his data in the files but nothing about data in which he has no interest.

Ryan, J. W.↗

NASA NTRS1986

Generation of 'artificial' bursts in a turbulent boundary layer

In an effort to better understand the physics and structure of coherent events in a turbulent boundary layer, an attempt is made to produce 'artificial' bursts. These are generated in a unique turbulent boundary layer, developed on a flat plate towed in an 18-m water channel, and thus with negligible freestream turbulence. The burst-like events are produced by either withdrawing near-water fluid from two minute holes separated in the spanwise direction, or by pitching a miniature delta wing that is flush-mounted to the wall. Either of these two actions generates a hairpin-like vortex and low-speed streak that resemble naturally occurring structures. The resulting sequence of events that occur at a given location can be controlled at will, thus allowing detailed examination via phase-locked measurements and flow visualization. In this paper, the artificial bursts are compared with natural, random bursts, using flow visualization and hot-film signals. Detailed quantitative data on topographical details and dynamical significance of the bursting structure will be addressed in a forthcoming article.

Gad-El-hak, M.↗