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

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At least 1,729 records · Page 96
All sourcesNASA NTRSDOE OSTI
NASA NTRS2006

Optics Program Modified for Multithreaded Parallel Computing

A powerful high-performance computer program for simulating and analyzing adaptive and controlled optical systems has been developed by modifying the serial version of the Modeling and Analysis for Controlled Optical Systems (MACOS) program to impart capabilities for multithreaded parallel processing on computing systems ranging from supercomputers down to Symmetric Multiprocessing (SMP) personal computers. The modifications included the incorporation of OpenMP, a portable and widely supported application interface software, that can be used to explicitly add multithreaded parallelism to an application program under a shared-memory programming model. OpenMP was applied to parallelize ray-tracing calculations, one of the major computing components in MACOS. Multithreading is also used in the diffraction propagation of light in MACOS based on pthreads [POSIX Thread, (where "POSIX" signifies a portable operating system for UNIX)]. In tests of the parallelized version of MACOS, the speedup in ray-tracing calculations was found to be linear, or proportional to the number of processors, while the speedup in diffraction calculations ranged from 50 to 60 percent, depending on the type and number of processors. The parallelized version of MACOS is portable, and, to the user, its interface is basically the same as that of the original serial version of MACOS.

Lou, John↗
DOE OSTI2021

SISGR: Chemomechanics of Far-From-Equilibrium Interfaces (COFFEI)

Portable, reliable, and deployable devices for energy storage and conversion require fundamental changes in design of solid-state composites comprising ceramics and metals. These materials comprise the electrodes and electrolytes of next-generation solid-oxide fuel cells and all solid-state batteries, forming solid-state functional composites. The advent of solid-state batteries – which replace liquid electrolytes with solid electrolytes capable of lithium ion transport for reliable energy storage in portable batteries – and the increased demand space for all solid-state fuel cells capable of oxygen reduction at intermediate temperatures remain important challenges for improved material stability and decreased system cost. However, little is understood about three fundamental facets of materials that enable such solid-state energy applications. First, how do such materials deform, fracture, or delaminate under operando conditions? Second, how does such mechanical deformation limit or facilitate electronic and ionic transport within and across such material interfaces? Third, how we can predictably design interface-rich composites to engineer both structural and electrochemical stability? This COFFEI Group comprised expertise from Materials Science & Engineering and Nuclear Science & Engineering to integrate unique in situ experiments, simulations, and fabricated interfaces that address these fundamental questions in solid-state interfaces of nanoscale composites that will guide solid-state electrochemistry, transport kinetics, and mechanical deformation for nonstoichiometric materials that enable such applications. In particular, we built on COFFEI’s understanding of chemomechanical coupling among defect concentrations, ionic transport, electron transport, and stored elastic energy that is particularly acute in the far-from-equilibrium conditions typical of energy device applications. By tailoring our focus to solid-state interfaces, we addressed these important issues by (a) developing and applying advanced in situ and ex situ characterization tools to characterize model materials and interfaces synthesized with molecular-level control, under both laboratory-controlled and extreme environments representative of energy device operation; and (b) employing computational modeling and simulation frameworks to predict transport mechanisms, reactivity and stability of these model materials and interfaces under significant chemical strains typical of energy device operation. Recent progress provided insights to additional materials systems and electrochemomechanical fatigue and fracture that were not fully envisioned when the program was initiated. Specifically, in the final three years of COFFEI we pursued two integrated thrusts, with complementary focus. Thrust I focused on failure-resistant electrochemomechanical composites, while Thrust II focused on strain-modulated conductivity and reactivity across interfaces. In contrast to our initial COFFEI focus, these thrusts concentrated wholly on solid-state material interfacial interactions and included greater integration of multiscale visualization including in situ electron microscopy of strained structures/interactions and mesoscale simulations. Successful development of functionally superior and long-lived battery and fuel cell systems and stress adaptable oxides requires a deeper, fundamental understanding of the coupling among the historically important subfields of solid-state electrochemistry, transport kinetics, and mechanical deformation for nonstoichiometric metal oxide electrodes. In this program, the understanding and the application of chemomechanical coupling of defect concentrations, ionic transport, electro-catalytic activity and stored elastic energy, particularly acute in the far-from-equilibrium conditions typical of energy device applications, are being refined and implications for device operation clarified, including for miniaturized solid-state batteries and fuel cells.

36 MATERIALS SCIENCE↗
NASA NTRS1987

A high speed buffer for LV data acquisition

The laser velocimeter (autocovariance) buffer interface is a data acquisition subsystem designed specifically for the acquisition of data from a laser velocimeter. The subsystem acquires data from up to six laser velocimeter components in parallel, measures the times between successive data points for each of the components, establishes and maintains a coincident condition between any two or three components, and acquires data from other instrumentation systems simultaneously with the laser velocimeter data points. The subsystem is designed to control the entire data acquisition process based on initial setup parameters obtained from a host computer and to be independent of the computer during the acquisition. On completion of the acquisition cycle, the interface transfers the contents of its memory to the host under direction of the host via a single 16-bit parallel DMA channel.

Cavone, Angelo A.↗
NASA NTRS1973

Design of a modular digital computer system DRL 4 and 5

Design and development efforts for a spaceborne modular computer system are reported. An initial baseline description is followed by an interface design that includes definition of the overall system response to all classes of failure. Final versions for the register level designs for all module types were completed. Packaging, support and control executive software, including memory utilization estimates and design verification plan, were formalized to insure a soundly integrated design of the digital computer system.

Source record↗
NASA NTRS2004

Graphical User Interface Development for Representing Air Flow Patterns

In the Turbine Branch, scientists carry out experimental and computational work to advance the efficiency and diminish the noise production of jet engine turbines. One way to do this is by decreasing the heat that the turbine blades receive. Most of the experimental work is carried out by taking a single turbine blade and analyzing the air flow patterns around it, because this data indicates the sections of the turbine blade that are getting too hot. Since the cost of doing turbine blade air flow experiments is very high, researchers try to do computational work that fits the experimental data. The goal of computational fluid dynamics is for scientists to find a numerical way to predict the complex flow patterns around different turbine blades without physically having to perform tests or costly experiments. When visualizing flow patterns, scientists need a way to represent the flow conditions around a turbine blade. A researcher will assign specific zones that surround the turbine blade. In a two-dimensional view, the zones are usually quadrilaterals. The next step is to assign boundary conditions which define how the flow enters or exits one side of a zone. way of setting up computational zones and grids, visualizing flow patterns, and storing all the flow conditions in a file on the computer for future computation. Such a program is necessary because the only method for creating flow pattern graphs is by hand, which is tedious and time-consuming. By using a computer program to create the zones and grids, the graph would be faster to make and easier to edit. Basically, the user would run a program that is an editable graph. The user could click and drag with the mouse to form various zones and grids, then edit the locations of these grids, add flow and boundary conditions, and finally save the graph for future use and analysis. My goal this summer is to create a graphical user interface (GUI) that incorporates all of these elements. I am writing the program in Java, a language that is portable among platforms, because it can run on different operating systems such as Windows and Unix without having to be rewritten. I had no prior experience of programming in Java at the start of my internship; I am continuously learning as I create the program. I have written the part of the program that enables a user to draw several zones, edit them, and store their locations. The next phase of my project is to allow the user to click on the side of a zone and create a boundary condition for it. A previous intern wrote a program that allows the user to input boundary conditions. I can integrate the two programs to create a larger, more usable program. After that, I will develop a way for the user to save the graph for future reference. Another eventual goal is to make the GUI capable of creating three-dimensional zones as well. Researchers such as my mentor, Dr. David Ashpis, need a quick, user-friendly

Chaudhary, Nilika↗
NASA NTRS2018

Using the cFS Command and Data Dictionary (CCDD) to Automate Software Development on Habulous

Final paper is attached. The NASA developed Core Flight System (cFS) is a reusable software architecture that has been used on multiple spaceflight missions. By using this framework, missions are able to reuse code from other missions, as well as leverage deployment onto similar computer architectures (i.e. not "reinvent the wheel" on each new mission). The success in the cFS concept can be seen in the large number of projects using cFS at FSW-2018. The Habulous project is an Earth-based testbed, used for hardware and software that may one day be used on a future space habitat unit, with many participating groups from various NASA centers and aerospace organizations around the country. The distributed nature of the various teams mean that defining (and following) an interface definition is critical on the project. Additionally, since various groups use various types of computer hardware (32/64-bit, big/little endian, Linux/VxWorks/Windows) many additional complications exist in interfacing all the various components into a final integrated system. cFS is used on the majority the flight software (FSW) in running in Habulous. But some subsystems have elected to not use cFS, and use a software bridge (called SBN_lib) to interact with the other cFS nodes in Habulous. In order to most efficiently develop the FSW, a central database is used to define and store each message sent by cFS. A Command and Data Dictionary (CDD) is something nearly universal on spacecraft, but as a team we worked to develop the CDD before the SW development was complete, and not treat it like "as built" documentation. To manage the CDD, the cFS Command and Data Dictionary (CCDD) tool was chosen (available from NASA as open source software). The CCDD tool has successfully been used to automate/autocode a large amount of software used on Habulous, as we are hoping to use it to define even more items in the future (time-triggered Ethernet (TTE) network maps, CPU scheduling). Additionally, Habulous has been exploring the use of cFS on wildly heterogeneous CPUs, and how to coordinate all those various machines using/extending the software bus – network (SBN) application in cFS, as well as TTE to coordinate message passing between various synchronized machines. The major topics to be covered in the presentation are: (1) Updating to the CCSDS_v2 extended headers (and using CPU# as subsystem ID). (2) Managing all the message identification numbers for each cFS message sent/received on any of the various CPUs. (3) Using the CCDD information to automatically generate the C-header files that define the structure for all software bus (SB) commands/telemetry messages. (4) Using the CCDD to automatically generate XML Telemetry and Command Exchange (XTCE) files, which streams display production/integration/testing in a web based display architecture (5) Extending/customizing SBN to pass messages among computers on multiple networks. (6) Using "Protobetter" inside SBN to manage different endian-ness/architectures. (7) Using SBN_lib to allow non-cFS node to communicate with cFS nodes. (8) Developing TTE network and schedule tables for all the various CPUs to use.

Hirsh, Robert L.↗
NASA NTRS1985

Isoparametric 3-D Finite Element Mesh Generation Using Interactive Computer Graphics

An isoparametric 3-D finite element mesh generator was developed with direct interface to an interactive geometric modeler program called POLYGON. POLYGON defines the model geometry in terms of boundaries and mesh regions for the mesh generator. The mesh generator controls the mesh flow through the 2-dimensional spans of regions by using the topological data and defines the connectivity between regions. The program is menu driven and the user has a control of element density and biasing through the spans and can also apply boundary conditions, loads interactively.

Kayrak, C.↗
NASA NTRS1988

CAMELOT 2: Personnel transport between Earth and Mars

A summary of the second phase of a design study fo a cycling spacecraft for regular and frequency personnel transport between Earth and a Mars base is presented. The first-phase study, called project CAMELOT, was a mission analysis and configuration design and was completed by the Space Systems Design class at the University of Michigan in the winter term, 1987. In the second phase, the configuration and component design has been developed by the Space Systems Design class in the winter term, 1988, beyond the initial configuration study. Analysis has led to numerous design modifications and improvements, as well as providing more detailed system definition. Major components of the second phase study include innovative detailed designs such as an interface between the rotating and non-rotating portions of the spacecraft, an elevator system that changes orientation to eliminate Coriolis forces, an electromagnetic radiation shield that significantly reduces the mass of the spacecraft, and a detailed assembly sequence and cost analysis. In addition, modifications to the propulsion and the power generation subsystems, taxi-docking facilities, and internal layout design have led to a more efficient, more reliable, and more comfortable vehicle. Finite-element stress and dynamic analysis has verified much of the system and indicates the validity of the design. Computer simulation of many moving components, including torus rotation, elevator and interface operations, and attitude control mechanisms further validate and support the various systems.

Source record↗
DOE OSTI2022

hPIC2: A hardware-accelerated, hybrid particle-in-cell code for dynamic plasma-material interactions

The exascale era of high performance computing promises to bring the field of computational plasma physics ever closer to the goal of accurate multiscale modeling. Such computers will rely on hardware acceleration to offload work to dedicated components, notably general-purpose graphics processing units (GPUs). However, devices from different manufacturers require software to be written with different parallel programming models, greatly increasing the code maintenance burden of applications designed to perform on more than one such device. hPIC2 is a hybrid plasma simulation code developed with the Kokkos performance portability framework to target the architectures that will drive exascale computing for the foreseeable future. As a hybrid simulation code, hPIC2 investigates the simultaneous use of various plasma models on the same domain, at the same time. hPIC2 also optionally couples to RustBCA, which accurately models ion-material interactions using the binary collision approximation (BCA) method. In conclusion, hPIC2 therefore achieves scalable performance on a variety of computing architectures when simulating complex and diverse plasmas, particularly near plasma-material interfaces.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2023

Accurate computational design of three-dimensional protein crystals

Protein crystallization plays a central role in structural biology. Despite this, the process of crystallization remains poorly understood and highly empirical, with crystal contacts, lattice packing arrangements and space group preferences being largely unpredictable. Programming protein crystallization through precisely engineered side-chain-side-chain interactions across protein-protein interfaces is an outstanding challenge. Here, in this study, we develop a general computational approach for designing three-dimensional protein crystals with prespecified lattice architectures at atomic accuracy that hierarchically constrains the overall number of degrees of freedom of the system. We design three pairs of oligomers that can be individually purified, and upon mixing, spontaneously self-assemble into >100 µm three-dimensional crystals. The structures of these crystals are nearly identical to the computational design models, closely corresponding in both overall architecture and the specific protein-protein interactions. The dimensions of the crystal unit cell can be systematically redesigned while retaining the space group symmetry and overall architecture, and the crystals are extremely porous and highly stable. Our approach enables the computational design of protein crystals with high accuracy, and the designed protein crystals, which have both structural and assembly information encoded in their primary sequences, provide a powerful platform for biological materials engineering.

59 BASIC BIOLOGICAL SCIENCES↗
NASA NTRS2000

Information Power Grid: Distributed High-Performance Computing and Large-Scale Data Management for Science and Engineering

We use the term "Grid" to refer to distributed, high performance computing and data handling infrastructure that incorporates geographically and organizationally dispersed, heterogeneous resources that are persistent and supported. This infrastructure includes: (1) Tools for constructing collaborative, application oriented Problem Solving Environments / Frameworks (the primary user interfaces for Grids); (2) Programming environments, tools, and services providing various approaches for building applications that use aggregated computing and storage resources, and federated data sources; (3) Comprehensive and consistent set of location independent tools and services for accessing and managing dynamic collections of widely distributed resources: heterogeneous computing systems, storage systems, real-time data sources and instruments, human collaborators, and communications systems; (4) Operational infrastructure including management tools for distributed systems and distributed resources, user services, accounting and auditing, strong and location independent user authentication and authorization, and overall system security services The vision for NASA's Information Power Grid - a computing and data Grid - is that it will provide significant new capabilities to scientists and engineers by facilitating routine construction of information based problem solving environments / frameworks. Such Grids will knit together widely distributed computing, data, instrument, and human resources into just-in-time systems that can address complex and large-scale computing and data analysis problems. Examples of these problems include: (1) Coupled, multidisciplinary simulations too large for single systems (e.g., multi-component NPSS turbomachine simulation); (2) Use of widely distributed, federated data archives (e.g., simultaneous access to metrological, topological, aircraft performance, and flight path scheduling databases supporting a National Air Space Simulation systems}; (3) Coupling large-scale computing and data systems to scientific and engineering instruments (e.g., realtime interaction with experiments through real-time data analysis and interpretation presented to the experimentalist in ways that allow direct interaction with the experiment (instead of just with instrument control); (5) Highly interactive, augmented reality and virtual reality remote collaborations (e.g., Ames / Boeing Remote Help Desk providing field maintenance use of coupled video and NDI to a remote, on-line airframe structures expert who uses this data to index into detailed design databases, and returns 3D internal aircraft geometry to the field); (5) Single computational problems too large for any single system (e.g. the rotocraft reference calculation). Grids also have the potential to provide pools of resources that could be called on in extraordinary / rapid response situations (such as disaster response) because they can provide common interfaces and access mechanisms, standardized management, and uniform user authentication and authorization, for large collections of distributed resources (whether or not they normally function in concert). IPG development and deployment is addressing requirements obtained by analyzing a number of different application areas, in particular from the NASA Aero-Space Technology Enterprise. This analysis has focussed primarily on two types of users: the scientist / design engineer whose primary interest is problem solving (e.g. determining wing aerodynamic characteristics in many different operating environments), and whose primary interface to IPG will be through various sorts of problem solving frameworks. The second type of user is the tool designer: the computational scientists who convert physics and mathematics into code that can simulate the physical world. These are the two primary users of IPG, and they have rather different requirements. The results of the analysis of the needs of these two types of users provides a broad set of requirements that gives rise to a general set of required capabilities. The IPG project is intended to address all of these requirements. In some cases the required computing technology exists, and in some cases it must be researched and developed. The project is using available technology to provide a prototype set of capabilities in a persistent distributed computing testbed. Beyond this, there are required capabilities that are not immediately available, and whose development spans the range from near-term engineering development (one to two years) to much longer term R&D (three to six years). Additional information is contained in the original.

Johnston, William E.↗
DOE OSTI2020

Promoting the cleavage of C-O bonds at the interface between a metal oxide cluster and a Co(0001) support

As a first step toward the rational design of Co-based catalysts with a higher activity and selectivity, we determine how one can activate a C-O bond at the interface between a metal oxide cluster and a Co(0001) support. The hypothesis here is that the metal ions in metal oxide clusters on a Co(0001) support enhance the adsorption of CO and weaken the C-O bond strength, which can then facilitate the dissociation of the CO reactant. To test this hypothesis, we developed three computational models of Ti4O8/Co(0001), Zr4O8/Co(0001), and Mn8O8/Co(0001). We quantify the CO adsorption behavior at the interface sites between an oxide cluster and the Co(0001) support as well as the corresponding IR spectra. We correlate the computed CO stretch frequencies with their CO adsorption energies, as well as the CO stretch frequency with the C-O bond length, and related these findings to the changes in the chemical bonding in the bound CO. The interface is the most favorable site for CO adsorption. Adsorption results in an increase of the C-O bond length and a decrease in its vibrational frequency. From a chemical bonding analysis, the bond order in CO at this site drops from 3 (in the gas phase) to 1. This decrease in bond order is a necessary precursor stage for CO dissociation. The experimental measurements of the corresponding FTIR spectra support this point. The favorability of CO adsorption at the interface sites is due to an electron transfer from the metal ion in the metal oxide cluster to the O atom in CO. We establish a linear relationship between C-O bond length and CO frequency and this relationship is found to be independent of the support, type of metal oxide cluster, or the adsorption site.

Fischer-Tropsch Synthesis, Heterogeneous Catalysis↗
DOE OSTI2022

Improving the Accuracy of Atomistic Simulations of the Electrochemical Interface

Atomistic simulation of the electrochemical double layer is an ambitious undertaking, requiring quantum mechanical description of electrons, phase space sampling of liquid electrolytes, and equilibration of electrolytes over nanosecond time scales. All models of electrochemistry make different trade-offs in the approximation of electrons and atomic configurations, from the extremes of classical molecular dynamics of a complete interface with point-charge atoms to correlated electronic structure methods of a single electrode configuration with no dynamics or electrolyte. Here, we review the spectrum of simulation techniques suitable for electrochemistry, focusing on the key approximations and accuracy considerations for each technique. Additionally, we discuss promising approaches, such as enhanced sampling techniques for atomic configurations and computationally efficient beyond density functional theory (DFT) electronic methods, that will push electrochemical simulations beyond the present frontier.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2025

The Elastic Analysis Facility's (EAF's) Contribution to the Future of Analysis at Multi-Experiment Institutions and Future Colliders

The Elastic Analysis Facility (EAF) hosted at Fermi National Accelerator Laboratory (Fermilab) is a platform being developed with the goal of providing a fast and efficient facility for physics analysis. As high-energy physics moves towards collecting larger datasets, such as those from the High-Luminosity LHC, the EAF strives to provide a powerful and adaptable framework for future colliders and multi-experiment institutions. Currently, the EAF supports several experiments including CMS, NOvA, and DUNE as well as serving accelerator physicists and beam line operations through integrated software and secure connections to Fermilab's computing resources. In addition, the EAF was designed with a user-friendly interface, intended to be more intuitive for emerging generations of physicists, that is still accessible for established styles of analysis. The EAF can also achieve better analysis efficiency due to the modernization of software and tools that can better utilize Fermilab's computing power. Furthermore, its design incorporates industry standards whenever possible, enhancing its sustainability and making it a possible template for other national or international laboratories and research facilities. Overall, the EAF is a forward-looking solution that will meet the evolving needs of particle physics, ensuring readiness for future colliders and multi-experiment research institutions.

Chavez, Elise [Wisconsin U., Madison]↗
DOE OSTI2025

Mantaray: A Rust Package for Ray Tracing Ocean Surface Gravity Waves

Ocean surface gravity waves are an important component of air-sea interaction, influencing energy, momentum, and gas exchanges across the ocean-atmosphere interface. In specific applications such as refraction by ocean currents or bathymetry, ray tracing provides a computationally efficient way to gain insight into wave propagation. In this paper, we introduce Mantaray, an open-source software package implemented in Rust, with a Python interface, that solves the ray equations for ocean surface gravity waves. Mantaray is designed for performance, robustness, and ease of use. The package is modular to facilitate further development and can currently be applied to both idealized and realistic wave propagation problems (Fig. 1).

16 TIDAL AND WAVE POWER↗
NASA NTRS1979

Computer program to calculate three-dimensional boundary layer flows over wings with wall mass transfer

A system of computer programs for calculating three dimensional transonic flow over wings, including details of the three dimensional viscous boundary layer flow, was developed. The flow is calculated in two overlapping regions: an outer potential flow region, and a boundary layer region in which the first order, three dimensional boundary layer equations are numerically solved. A consistent matching of the two solutions is achieved iteratively, thus taking into account viscous-inviscid interaction. For the inviscid outer flow calculations, the Jameson-Caughey transonic wing program FLO 27 is used, and the boundary layer calculations are performed by a finite difference boundary layer prediction program. Interface programs provide communication between the two basic flow analysis programs. Computed results are presented for the NASA F8 research wing, both with and without distributed surface suction.

Mclean, J. D.↗
NASA NTRSDate not supplied

Development of Physics-Based Transition Models for Unstructured-Mesh CFD Codes Using Deep Learning Models

Predicting transition locations over a vehicle surface is of fundamental importance for many engineering applications. With the transition information, the Reynolds-averaged Navier-Stokes (RANS) computations can turn on the turbulence model at the right locations so that drag, lift and other aerodynamic quantities can be accurately predicted. In contrast to the popularity of RANS-based transition modeling in which transition onset is governed by the turbulence equations, physics-based transition models that account for instability waves within the boundary layer, thus more compliant to flow physics, only gained more attention in recent years. This paper describes the development of a new physics-based transition model based on either the linear stability theory (LST) or parabolized stability equations (PSE). The model is designed to communicate with a structured or unstructured-mesh RANS solver back and forth in order to more accurately compute transition fronts over a three-dimensional body. In the developed model, the Python suite of interface codes in conjunction with the LASTRAC software can be executed autonomously to produce transition onset locations for a given laminar or RANS-computed transitional state. In addition, as a proof of concept, the tool set consists of a deep learning neural network model that has been designed and trained to predict instability wave evolutions inside the boundary layer for various instability wave mechanisms across a selected speed range. A machine-learned intelligent profile interpolation model has also been devised to enable reliable instability-wave spectra predictions with just a few points in the mean flow profiles.

Transition Modeling↗
NASA NTRS1978

Computer-aided analysis and design of the shape rolling process for producing turbine engine airfoils

Mild steel (AISI 1018) was selected as model cold rolling material and Ti-6A1-4V and Inconel 718 were selected as typical hot rolling and cold rolling alloys, respectively. The flow stress and workability of these alloys were characterized and friction factor at the roll/workpiece interface was determined at their respective working conditions by conducting ring tests. Computer-aided mathematical models for predicting metal flow and stresses, and for simulating the shape rolling process were developed. These models utilized the upper bound and the slab methods of analysis, and were capable of predicting the lateral spread, roll separating force, roll torque, and local stresses, strains and strain rates. This computer-aided design system was also capable of simulating the actual rolling process, and thereby designing the roll pass schedule in rolling of an airfoil or a similar shape.

Lahoti, G. D.↗