Search NASA⌕ Search

SEARCH · Search NASA

Results for “voids”

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.

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

At least 253 records · Page 14

Alpha-Quartz Plastic Strength Investigation Via Diffraction Experiments on Novaculite Using A D-Dia and Elastic Plastic Self- Consistent Interpretation [Thesis}

X-Ray Tomography. Porosity is commonly measured using mercury injection (MI) or water immersion porosimeter (WIP). Both MI and WIP utilize pressure to fill open voids with mercury or water respectively. A measure of the volume change of the sample is then used to estimate the percentage of open voids. However, for the purpose of rheological study it is important to get an accurate measure of open and closed voids. X-ray tomography has been selected as it offers a three-dimensional view into the sample that can quantify all pores limited only by the voxel size which is in the micron range for this study. Radiographs for tomography were collected at the Material Science and Technology Division at Los Alamos National Lab using the Carl Zeiss Xradio 520 instrument and Scout-and-Scan version 16.1 operating software. Two samples were imaged, the starting material and the deformed sample SiO2_65. 3001 radiographs were taken of the starting material with a 6 second exposure time using a 4x objective lens. The x-ray beam was set to 60 kilovoltage peak (kVp) and 5 watts. 1901 radiographs were taken of SiO2_65 with a 25 second exposure time using a 10x objective lens. The x-ray beam was set to 80 kVp and 7 watts. Radiograph files were analyzed by Brian Patterson using Avizo. Void and inclusion volumes were output by voxel sized (1.03 μm) slices, used to calculate a total percentage volume for the starting material.

36 MATERIALS SCIENCE↗

Influence of soft inclusions on the strength of wrought materials

The three dimensional soft particles (such as sulfides, silicates and voids) present in most materials are modelled by circular voids in sheet metal. Relationships are sought between the shape and orientation of a hole after rolling and testing in tension. Then, the effect of hole shape and size on mechanical properties is considered experimentally. The presence of voids has a negligible influence on the ultimate tensile stress of ductile materials based on the unperforated area because plastic flow neutralizes the stress intensification present in the elastic region. However, the shape and orientation of the defects are found to play an important role relative to strain at fracture. In certain engineering applications the strain at fracture is more important than the stress at fracture and in this sense the presence of voids are considered to influence the strength of a ductile material.

Pai, D. M.↗

Development of an impact- and solvent-resistant thermoplastic composite matrix, phase 3

The polyimide from BTDA 1,6-hexanediamine and m-phenylenediamine was selected from a prior study for the present study. Methods to prepare prepreg which would provide low void composites at low molding pressures from the thermoplastic polyimide were studied. Cresol solutions of the polyimide were applied to a balanced weave carbon fabric and the cresol removed prior to composite molding. Low void composites were prepared from smoothed prepregs at high pressures (34.5 MPa) and temperatures as low as 260 C. Lower molding pressures lead to higher void composites. Need for a lower melt viscosity in the neat resin is suggested as a requirement to achieve low void composites at low pressures. Some mechanical properties are included.

Delano, C. B.↗

Nondestructive evaluation of structural ceramics

Research on nondestructive evaluation (NDE) of structural ceramics for heat engine applications is reviewed. Microfocus radiography and scanning laser acoustic microscopy are the NDE techniques highlighted. The techniques were applied to research samples of sintered silicon nitride and silicon carbide in the form of modulus-of-rupture (MOR) bars. The strength and limitations of the aforementioned techniques are given in terms of probablility of detection for voids in green and sintered MOR bars. Voids for this purpose were introduced by seeding green ceramic bars and characterizing each void in terms of its size, shape, location, and nature before and after sintering. The effects of material density, microstructure, surface finish, thickness, void depth, and size characteristics on detectability are summarized.

Vary, Alex↗

Flight experiment of thermal energy storage

Thermal energy storage (TES) enables a solar dynamic system to deliver constant electric power through periods of sun and shade. Brayton and Stirling power systems under current considerations for missions in the near future require working fluid temperatures in the 1100 to 1300+ K range. TES materials that meet these requirements fall into the fluoride family of salts. These salts store energy as a heat of fusion, thereby transferring heat to the fluid at constant temperature during shade. The principal feature of fluorides that must be taken into account is the change in volume that occurs with melting and freezing. Salts shrink as they solidify, a change reaching 30 percent for some salts. The location of voids that form as result of the shrinkage is critical when the solar dynamic system reemerges into the sun. Hot spots can develop in the TES container or the container can become distorted if the melting salt cannot expand elsewhere. Analysis of the transient, two-phase phenomenon is being incorporated into a three-dimensional computer code. The code is capable of analysis under microgravity as well as 1 g. The objective of the flight program is to verify the predictions of the code, particularly of the void location and its effect on containment temperature. The four experimental packages comprising the program will be the first tests of melting and freezing conducted under microgravity. Each test package will be installed in a Getaway Special container to be carried by the shuttle. The package will be self-contained and independent of shuttle operations other than the initial opening of the container lid and the final closing of the lid. Upon the return of the test package from flight, the TES container will be radiographed and finally partitioned to examine the exact location and shape of the void. Visual inspection of the void and the temperature data during flight will constitute the bases for code verification.

Namkoong, David↗

Regenerator performance in a Vuilleumier refrigerator compared with a third-order numerical model

A three-stage Vuilleumier refrigerator was used to measure the performance of various third stage regenerators. The refrigerator operates between 2.5 and 5.0 Hz and, depending on the material used in the third stage regenerator, achieves temperatures of 8 to 20 K at the cold end of the third stage. This paper presents a comparison of regenerator performance for four regenerator materials: 229 micron diameter spheres of Pb(+)5 pct Sb, 229 micron diameter spheres of brass, 216 micron irregularly-shaped GdRh powder, and a mixture of 229 microns and 762 microns diameter spheres of Pb(+5) pct Sb. The experimental results are compared with a first-order model that neglects the void volume within the regenerator and with a third-order model that considers the effect of pressure oscillations in the regenerator void volume. Experimental results indicate that regenerator losses are dominated by the pressure oscillation in the void volume rather than the mass flow through the temperature gradient in the regenerator. These results are consistent with the third-order numerical model. This model shows that the heat capacity of the gas in the void space as well as the heat capacity of the matrix influences the regenerator performance.

Bradley, P. E.↗

Experimental and Computational Investigations of Phase Change Thermal Energy Storage Canisters

Two sets of experimental data are examined in this paper, ground and space experiments, for cylindrical canisters with thermal energy storage applications. A 2-D computational model was developed for unsteady heat transfer (conduction and radiation) with phase-change. The radiation heat transfer employed a finite volume method. The following was found in this study: (1) Ground Experiments: the convection heat transfer is equally important to that of the radiation heat transfer; radiation heat transfer in the liquid is found to be more significant than that in the void; including the radiation heat transfer in the liquid resulted in lower temperatures (about 15 K) and increased the melting time (about 10 min.); generally, most of the heat flow takes place in the radial direction. (2) Space Experiments: radiation heat transfer in the void is found to be more significant than that in the liquid (exactly the opposite to the Ground Experiments); accordingly, the location and size of the void affects the performance considerably; including the radiation heat transfer in the void resulted in lower temperatures (about 40 K).

Ibrahim, Mounir↗

Sulfur Impurities and the Microstructure of Alumina Scales

The relationship between the microstructure of alumina scales, adhesion, and sulfur content was examined through a series of nickel alloys oxidized in 1100 to 1200 deg. C cyclic or isothermal exposures in air. In cyclic tests of undoped NiCrAl, adhesion was produced when the sulfur content was reduced, without any change in scale microstructure. Although interfacial voids were not observed in cyclic tests of NiCrAl, they were promoted by long-term isothermal exposures, by sulfur doping, and in most exposures of NiAl. Two single crystal superalloys, PWA 1480 and Rene' N5, were also tested, either in the as-received condition or after the sulfur content had been reduced to less than 1 ppmw by hydrogen annealing. The unannealed alloys always exhibited spalling to bare metal, but interfacial voids were not observed consistently. Desulfurized PWA 1480 and Rene' N5 exhibited remarkable adhesion and no voidage for either isothermal or cyclic exposures. The most consistent microstructural feature was that, for the cases where voids did form, the scale undersides exhibited corresponding areas with ridged oxide grain boundaries. Voids were not required for spallation nor were other microstructural features essential for adhesion. These observations are consistent with the model whereby scale spallation is controlled primarily by interfacial sulfur segregation and the consequent degradation of oxide-metal bonding.

Smialek, James L.↗

Bubble and Slug Flow at Microgravity Conditions: State of Knowledge and Open Questions

Based on the experiments carried out over the past decade at microgravity conditions, an overview of our current knowledge of bubbly and slug flows is presented. The transition from bubble to slug flow, the void fraction and the pressure drop are discussed from the data collected in the literature. The transition from bubble to slug flow may be predicted by introducing a critical void fraction that depends on the fluid properties and the pipe diameter; however, the role of coalescence which controls this transition is not clearly understood. The void fraction may be accurately calculated using a drift-flux model. It is shown from local measurements that the drift of the gas with respect to the mixture is due to non-uniform radial distribution of void fraction. The pressure drop happens to be controlled by the liquid flow for bubbly flow whereas for slug flow the experimental results show that pressure drops is larger than expected. From this study, the guidelines for future research in microgravity are given.

Colin, C.↗

Phenylethynyl Containing Polyarylene Ethers/Polyimides Resin Infiltration of Composites

The following tasks were performed at NCA&TSU during the second year in performance of the grant. LaRC-LV-1 13 resin was synthesized at NCA&TSU. In order to perform the synthesis, glassware and needed apparatus were purchased with grant funds along with the appropriate monomers. It was found that the LaRC-LV-1 13 resin was easily synthesized by the NMP solvent/toluene imminization/distilled water precipitation process. However, in use this resin exhibited a bubbling/foaming behavior during cure that was detrimental leading to the production of composite panels having a high void content. Composite panels were fabricated using compression molding and resin transfer molding (RTM) techniques. Initial fiber volume determinations were computed at NCA&TSU along with NASA-Langley measured c-scans on the panels produced. The initial results indicated a unsatisfactory level of approximately 20% by volume of voids. Testing of uniaxial coupons in compression to failure also agreed with these results. The uniaxial coupons delaminated as the major mode of failure indicative of an unacceptably low level of resin and to much void content in the final composites produced. In discussions with Dr. Brian Jensen, it was suggested the void fraction needs to be reduced to at least 2% by volume for a useful composite. The panels produced used both resin synthesized at NASA-Langley and NCA&TSU. In reviewing our progress over the past year, it was noted that the resin as formulated by the current synthesis process bubbled at elevated temperature. This was especially observed in neat resin slugs cured at the recommended one, four and eight hour cure temperatures. Pressurized cures where then performed with pressures up to 200 psi and simultaneously the lowest eight hour cure temperatures. Although this procedure reduced the amount of bubbles to some extent in the neat resin slugs it did not completely eliminate them. The cure reaction appears to be very energetic even at the lowest recommended cure temperature. Currently, the pressurized cure apparatus developed at NCA&TSU is limited to 200 psi.

Dunn, DeRome O.↗

Laser Brazing of High Temperature Braze Alloy

The Space Shuttle Main Engine (SSME) consists of 1080 conical tubes, which are furnace brazed themselves, manifolds, and surrounding structural jacket making almost four miles of braze joints. Subsequent furnace braze cycles are performed due to localized braze voids between the coolant tubes. SSME nozzle experiences extremely high heat flux (180 mW/sq m) during hot fire. Braze voids between coolant tubes may result in hot combustion gas escape causing jacket bulges. The nozzle can be disqualified for flight or result in mission failure if the braze voids exceed the limits. Localized braze processes were considered to eliminate braze voids, however, damage to the parent materials often prohibited use of such process. Being the only manned flight reusable rocket engine, it has stringent requirement on the braze process. Poor braze quality or damage to the parent materials limits the nozzle service life. The objective of this study was to develop a laser brazing process to provide quality, localized braze joints without adverse affect on the parent materials. Gold (Au-Cu-Ni-Pd-Mn) based high temperature braze alloys were used in both powder and wire form. Thin section iron base superalloy A286 tube was used as substrate materials. Different Laser Systems including CO2 (10.6 micrometers, 1kW), ND:YAG (1.06 micrometers, 4kW). and direct diode laser (808nm. 150W) were investigated for brazing process. The laser process variables including wavelength. laser power, travel speed and angle of inclination were optimized according to bead geometry and braze alloy wetting at minimum heat input level, The properties of laser brazing were compared to that of furnace brazing. Microhardness profiles were used for braze joint property comparison between laser and furnace brazing. The cooling rate of laser brazing was compared to furnace brazing based on secondary dendritic arm spacing, Both optical and Scanning Electron Microscope (SEM) were used to evaluate the microstructures of the braze materials and tube substrate. Metallography of the laser braze joint was compared to the furnace braze. SEM Energy Disperse X-Ray Spectra (EDX) and back scattered imaging were used to analyze braze alloy segregation. Although all of the laser systems, CO2, ND:YAG, and direct diode laser produced good braze joint, the direct diode laser was selected for its system simplicity, compactness and portability. Excellent laser and braze alloy coupling is observed with powder alloy compared to braze alloy wire. Good wetting is found with different gold based braze alloys. The laser brazing process can be optimized so that the adverse affect on the parent materials can be eliminated. Metallography of the laser braze joint has shown that quality braze joint was produced with laser brazing process. Penetration of the laser braze to the substrate is at neglectable level. Zero penetration is observed. Microstructure examinations shown that no observable changes of the microstructure (grain structure and precipitation) in the HAZ area between laser braze and furnace braze. Wide gaps can be laser brazed with single pass for up to 0.024 inches. Finer dendritic structure is observed in laser brazing compared with equiaxial and coarser grain of the furnace brazing microstructure. Greater segregation is also found in the furnace braze. Higher hardness of the laser braze joint comparing to furnace braze is observed due to the fast cooling rate and Finer microstructure in the laser brazing. Laser braze joint properties meet or exceed the furnace joint properties. Direct diode laser for thin section tube brazing with high temperature braze alloys have been successfully demonstrated. The laser's high energy density and precise control has shown significant advantages in reducing process heat input to the substrates and provide high quality braze joints comparing to other localized braze process such as torch, TIG, and MPTA processes. Significant cost savings can be realized particularly with localized braze comparing to a full furnace braze cycle.

Gao, Y. P.↗

The Relationship Between Constraint and Ductile Fracture Initiation as Defined by Micromechanical Analyses

The use of small laboratory specimens to predict the integrity of large, complex structures relies on the validity of single parameter fracture mechanics. Unfortunately, the constraint loss associated with large scale yielding, whether in a laboratory specimen because of its small size or in a structure because it contains shallow flaws loaded in tension, can cause the breakdown of classical fracture mechanics and the loss of transferability of critical, global fracture parameters. Although the issue of constraint loss can be eliminated by testing actual structural configurations, such an approach can be prohibitively costly. Hence, a methodology that can correct global fracture parameters for constraint effects is desirable. This research uses micromechanical analyses to define the relationship between global, ductile fracture initiation parameters and constraint in two specimen geometries (SECT and SECB with varying a/w ratios) and one structural geometry (circumferentially cracked pipe). Two local fracture criteria corresponding to ductile fracture micromechanisms are evaluated: a constraint-modified, critical strain criterion for void coalescence proposed by Hancock and Cowling and a critical void ratio criterion for void growth based on the Rice and Tracey model. Crack initiation is assumed to occur when the critical value in each case is reached over some critical length. The primary material of interest is A516-70, a high-hardening pressure vessel steel sensitive to constraint; however, a low-hardening structural steel that is less sensitive to constraint is also being studied. Critical values of local fracture parameters are obtained by numerical analysis and experimental testing of circumferentially notched tensile specimens of varying constraint (e.g., notch radius). These parameters are then used in conjunction with large strain, large deformation, two- and three-dimensional finite element analyses of the geometries listed above to predict crack initiation loads and to calculate the associated (critical) global fracture parameters. The loads are verified experimentally, and microscopy is used to measure pre-crack length, crack tip opening displacement (CTOD), and the amount of stable crack growth. Results for A516-70 steel indicate that the constraint-modified, critical strain criterion with a critical length approximately equal to the grain size (0.0025 inch) provides accurate predictions of crack initiation. The critical void growth criterion is shown to considerably underpredict crack initiation loads with the same critical length. The relationship between the critical value of the J-integral for ductile crack initiation and crack depth for SECT and SECB specimens has been determined using the constraint-modified, critical strain criterion, demonstrating that this micromechanical model can be used to correct in-plane constraint effects due to crack depth and bending vs. tension loading. Finally, the relationship developed for the SECT specimens is used to predict the behavior of circumferentially cracked pipe specimens.

Panontin, Tina L.↗

A Model for the Breakup of Comet Linear (C/1999 S4)

We propose a mechanism based on the rubble-pile hypothesis of the cometary nucleus (Weissman 1986) to explain the catastrophic breakup of comet LINEAR (C/1999 S4) observed during July-August 2000. We suggest that a solid nucleus made up of 10-100 m "cometesimals" (Weidenschilling 1997) contains a network of inter-connected voids in the inter-cometesimal regions. The production of super-volatile (i.e., species more volatile than water) gases into these voids occurs due to the thermal wave propagating through the nucleus and associated phase transitions of water ice. The network of voids provides an efficient pathway for rapid propagation of these gases within the nucleus resulting in gas pressure caused stresses over a wide regime of the nucleus. This provides a mechanism for catastrophic breakups of small cometary nuclei such as comet LINEAR (C/1999 S4) as well as for some observed cometary outbursts including those that occur at large heliocentric distances (e.g., West et al. 1991). We emphasize the importance of techniques such as radar reflection tomography and radiowave transmission tomography (e.g., Kofman et al. 1998) aboard cometary missions to determine the three dimensional structure of the nucleus in particular the extent of large scale voids.

Samarasinha, Nalin H.↗

High Temperature VARTM of Phenylethynyl Terminated Imides

Fabrication of composite structures using vacuum assisted resin transfer molding (VARTM) is generally more affordable than conventional autoclave techniques. Recent efforts have focused on adapting VARTM for the fabrication of high temperature composites. Due to their low melt viscosity and long melt stability, certain phenylethynyl terminated imides (PETI) can be processed into composites using high temperature VARTM (HT-VARTM). However, one of the disadvantages of the current HT-VARTM resin systems has been the high porosity of the resultant composites. For aerospace applications, the desired void fraction of less than 2% has not yet been achieved. In the current study, two PETI resins, LaRC PETI-330 and LaRC PETI-8 have been used to make test specimens using HT-VARTM. The resins were infused into ten layers of IM7-6K carbon fiber 5-harness satin fabric at 260 C or 280 C and cured at 371 C. Initial runs yielded composites with high void content, typically greater than 7% by weight. A thermogravimetric-mass spectroscopic study was conducted to determine the source of volatiles leading to high porosity. It was determined that under the thermal cycle used for laminate fabrication, the phenylethynyl endcap was undergoing degradation leading to volatile evolution. By modifying the thermal cycle used in laminate fabrication, the void content was reduced significantly (typically approximately 3%). Densities of the composites were determined using a density gradient column and the glass transition temperatures of the cured composites were measured by dynamic mechanical analysis. Photomicrographs of the panels were taken and void contents were determined by acid digestion. The results of this work are presented herein.

Cano, Roberto J.↗

Advanced Signal Processing Techniques Applied to Terahertz Inspections on Aerospace Foams

The space shuttle's external fuel tank is thermally insulated by the closed cell foams. However, natural voids composed of air and trapped gas are found as by-products when the foams are cured. Detection of foam voids and foam de-bonding is a formidable task owing to the small index of refraction contrast between foam and air (1.04:1). In the presence of a denser binding matrix agent that bonds two different foam materials, time-differentiation of filtered terahertz signals can be employed to magnify information prior to the main substrate reflections. In the absence of a matrix binder, de-convolution of the filtered time differential terahertz signals is performed to reduce the masking effects of antenna ringing. The goal is simply to increase probability of void detection through image enhancement and to determine the depth of the void.

Trinh, Long Buu↗

Ice-Penetrating Robot for Scientific Exploration

The cryo-hydro integrated robotic penetrator system (CHIRPS) is a partially developed instrumentation system that includes a probe designed to deeply penetrate the European ice sheet in a search for signs of life. The CHIRPS could also be used on Earth for similar exploration of the polar ice caps especially at Lake Vostok in Antarctica. The CHIRPS probe advances downward by a combination of simple melting of ice (typically for upper, non-compacted layers of an ice sheet) or by a combination of melting of ice and pumping of meltwater (typically, for deeper, compacted layers). The heat and electric power for melting, pumping, and operating all of the onboard instrumentation and electronic circuitry are supplied by radioisotope power sources (RPSs) and thermoelectric converters energized by the RPSs. The instrumentation and electronic circuitry includes miniature guidance and control sensors and an advanced autonomous control system that has fault-management capabilities. The CHIRPS probe is about 1 m long and 15 cm in diameter. The RPSs generate a total thermal power of 1.8 kW. Initially, as this power melts the surrounding ice, a meltwater jacket about 1 mm thick forms around the probe. The center of gravity of the probe is well forward (down), so that the probe is vertically stabilized like a pendulum. Heat is circulated to the nose by means of miniature pumps and heat pipes. The probe melts ice to advance in a step-wise manner: Heat is applied to the nose to open up a melt void, then heat is applied to the side to allow the probe to slip down into the melt void. The melt void behind the probe is allowed to re-freeze. Four quadrant heaters on the nose and another four quadrant heaters on the rear (upper) surface of the probe are individually controllable for steering: Turning on two adjacent nose heaters on the nose and two adjacent heaters on the opposite side at the rear causes melt voids to form on opposing sides, such that the probe descends at an angle from vertical. This steering capability can be used to avoid debris trapped in the ice or to maneuver closer to a trapped object of scientific interest.

Zimmerman, Wayne↗

High Temperature VARTM of Phenylethynyl Terminated Imides (PETI) Resins

Fabrication of composite structures using vacuum assisted resin transfer molding (VARTM) is generally more affordable than conventional autoclave techniques. Recent efforts have focused on adapting VARTM for the fabrication of high temperature composites. Due to their low melt viscosity and long melt stability, certain phenylethynyl terminated imides (PETI) can be processed into composites using high temperature VARTM (HT-VARTM). However, one of the disadvantages of the current HT-VARTM resin systems has been the high porosity of the resultant composites. For aerospace applications a void fraction of less than 2% is desired. In the current study, two PETI resins, LARCTM PETI-330 and LARCTM PETI-8 have been used to fabricate test specimens using HT-VARTM. The resins were infused into carbon fiber preforms at 260 C and cured between 316 C and 371 C. Modifications to the thermal cycle used in the laminate fabrication have reduced the void content significantly (typically < 3%) for carbon fiber biaxially woven fabric. Photomicrographs of the panels were taken and void contents were determined by acid digestion. For carbon fiber uniaxial fabric, void contents of less than 2% have been obtained using both PETI-8 and PETI-330. Mechanical properties of the panels were determined at both room and elevated temperatures. These include short beam shear and flexure tests. The results of this work are presented herein.

Ghose, Sayata↗

Infusion Processing of Phenylethynyl Terminated Imides by High Temperature RTM and VARTM

Fabrication of composite structures using infusion processes such as resin transfer molding (RTM) and vacuum assisted resin transfer molding (VARTM) is generally more affordable than conventional autoclave techniques. Recent efforts have focused on adapting both technologies for the fabrication of high temperature (HT) resistant composites. Due to their low melt viscosity and long melt stability, certain phenylethynyl terminated imides (PETI) can be processed into composites using these high temperature out-of-autoclave processes. In the current study, two PETI resins, LARC(TradeMark) PETI-330 and LARC(TradeMark) PETI-8 have been used to make test specimens using both RTM and VARTM. For aerospace applications, a void fraction of less than 2% is desired. Traditionally, RTM has had the advantage over VARTM for generating composites with low void content. However, the process is limited in terms of size. Work at NASA LaRC has incorporated modifications to the thermal cycle used in laminate fabrication that have reduced the void content significantly (typically 1-3%) using the current HT-VARTM process. For composite fabrication by both RTM and VARTM, the resins were infused into three carbon fiber preforms (T650-35-3k 5HS, IM7-6k 5HS, and IM7-6k Uniweave) at 316 C and 260 C respectively and cured up to 371 C. The details of the RTM processing carried out at the University of Akron are discussed in this work along with a brief description of the HT-VARTM processing carried out at NASA-LaRC. Photomicrographs of the panels were taken and void contents were determined by acid digestion. Mechanical properties (short beam shear, SBS) of the panels fabricated by both infusion processes were determined at room temperature as well as at various elevated temperatures. The results of this work are presented herein.

Ghose, Sayata↗