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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 127 records · Page 7
All sourcesNASA NTRSDOE OSTI
DOE OSTI2022

Control of deviatoric stress in the diamond anvil cell through thermal expansion mismatch stress in thin films

Elastic and plastic properties of materials and phase transitions at extreme conditions vary with both hydrostatic pressure and deviatoric stress. To generate and measure controlled deviatoric stress at pressures beyond those accessible with large volume differential and rotational presses and optical access for spectroscopy, experiments tested the combination of diamond anvil cell and thin film technology. Thin films of polycrystalline Cr-doped Al 2 O 3 ruby were prepared using pulsed laser deposition on single-crystal substrates of either Al 2 O 3 sapphire or yttria-stabilized cubic zirconia for contrasting initial film stress, and loaded in diamond anvil cells for confining stress. The piezospectroscopic response of the ruby films demonstrates consistently higher deviatoric stress in the film on zirconia relative to the film on the control sapphire, and an increase in deviatoric stress with applied load. Complementary synchrotron X-ray diffraction of the zirconia substrate confirmed that no pressure-induced phase transitions impacted the stress state of the ruby film, but differences in compressibility of film and substrate result in changes in film stress analogous to thermal expansion mismatch. Furthermore, this technique may be applied to evaluate elastic and plastic response of thin films of a variety of materials under extreme stress.

36 MATERIALS SCIENCE↗
DOE OSTI2022

High-pressure Cr 3+ R-line luminescence of zoisite and kyanite: a probe of octahedral site distortion

Here, the Cr 3+ luminescence spectra of zoisite and kyanite, two geologically important minerals, were studied up to 40 and 20 GPa, respectively, in various pressure media. Cr 3+ substitutes into the octahedral aluminum sites in both minerals and the R-line luminescence is a particularly sensitive site-specific probe of the octahedral Al site. Unlike many previous studies where Cr 3+ luminescence was utilized, both these minerals have multiple highly distorted octahedral sites resulting in very large splitting of their R-lines, ~ 300 cm -1 in zoisite and ~ 360 cm -1 in kyanite (for reference, ruby is 29 cm -1 ). For zoisite, the R-line splitting increases as pressure increases and more than triples from its ambient value by 40 GPa, while the R-line splitting in kyanite from the M1 and M2 sites does not change when compressed in a Ne pressure medium up to 20 GPa. We do not observe evidence of any phase transitions in either zoisite or kyanite across the pressure range of these new luminescence measurements. Furthermore, we present some high-pressure luminescence results where kyanite was known to be bridged between the diamond anvils and show how these spectra illustrate the different effect of uniaxial relative to hydrostatic stress on luminescence spectra.

36 MATERIALS SCIENCE↗
DOE OSTI2022

CO 2 supplementation eliminates sugar-rich media requirement for plant propagation using a simple inexpensive temporary immersion photobioreactor

In vitro plant propagation systems such as temporary immersion bioreactors (TIBs) are valuable tools that enable production of disease-free plants with improved traits. However, TIB systems can be expensive, difficult to implement, and prone to contamination due to sugar rich propagation media. Using rapidly growing chicory root cultures to expedite design-build-test cycles, we report here an improved, low-cost version of a previously reported Hydrostatically-driven TIB (Hy-TIB) that facilitates economical use of gas mixtures. Bioreactor improvements include decreased material costs, expanded modes of operation, and a horizontal orientation of a plastic film plant growth chambers that increase propagule light exposure. To take advantage of these improvements, we describe here experiments that evaluate the impacts of elevated CO 2 on propagation of cacao (Theobroma cacao) secondary embryos and nodal cultures of yam (Dioscorea spp.) during both phototrophic and photomixotrophic growth. Our experiments show that elevated CO 2 during plant propagation significantly improved both cacao and yam propagule development and eliminated the need for supplemental sugars in tissue culture growth media. Thus, our improved Hy-TIB shows potential as a simple, low-cost, and scalable propagation platform with cost-effective gas composition control and reduced risk of contamination overgrowth. We provide detailed instructions for assembly of this Hy-TIB design and discuss the implications of its adoption in food-insecure regions of the world.

59 BASIC BIOLOGICAL SCIENCES↗
DOE OSTI2021

Predicting Fluid Flow Regime, Permeability, and Diffusivity in Mudrocks from Multiscale Pore Characterisation

In geoenergy applications, mudrocks prevent fluids to leak from temporary (H 2 , CH 4 ) or permanent (CO 2 , radioactive waste) storage/disposal sites and serve as a source and reservoir for unconventional oil and gas. Understanding transport properties integrated with dominant fluid flow mechanisms in mudrocks is essential to better predict the performance of mudrocks within these applications. In this study, small-angle neutron scattering (SANS) experiments were conducted on 71 samples from 13 different sets of mudrocks across the globe to capture the pore structure of nearly the full pore size spectrum (2 nm–5 μm). We develop fractal models to predict transport properties (permeability and diffusivity) based on the SANS-derived pore size distributions. The results indicate that transport phenomena in mudrocks are intrinsically pore size-dependent. Depending on hydrostatic pore pressures, transition flow develops in micropores, slip flow in meso- and macropores, and continuum flow in larger macropores. Fluid flow regimes progress towards larger pore sizes during reservoir depletion or smaller pore sizes during fluid storage, so when pressure is decreased or increased, respectively. Capturing the heterogeneity of mudrocks by considering fractal dimension and tortuosity fractal dimension for defined pore size ranges, fractal models integrate apparent permeability with slip flow, Darcy permeability with continuum flow, and gas diffusivity with diffusion flow in the matrix. This new model of pore size-dependent transport and integrated transport properties using fractal models yields a systematic approach that can also inform multiscale multi-physics models to better understand fluid flow and transport phenomena in mudrocks on the reservoir and basin scale.

36 MATERIALS SCIENCE↗
DOE OSTI2025

Rules for the crystallite size and dislocation density evolution in phases during α-ω transformation in Zr under high-pressure and severe plastic flow

The first in-situ X-ray diffraction (XRD) study of the evolution of the crystallite size and dislocation density in phases during plastic strain-induced phase transformation (PT) is performed utilizing α-ω PT in strongly pre-deformed commercially pure Zr as an important example. Rough diamond anvils (rough-DA) are introduced to intensify all occurring processes during heterogeneous compression of Zr in a diamond anvil cell (DAC). The main rule is found that during α-ω PT the crystallite size and dislocation density in ω-Zr depend solely on the volume fraction of ω-Zr and are independent of pressure, plastic strain tensor, its path, and initial nanostructure. Crystallite size in ω-Zr increases from 10 to 60 nm during the PT, while dislocation density reduces from 1.83×10 15 /m 2 to 0.6×10 15 /m 2 . Rough-DA produce a steady nanostructure in α-Zr before PT with smaller crystallite size and larger dislocation density than smooth-DA, leading to a reduction of the minimum pressure for α-ω PT to a record value 0.67 GPa, 9 times smaller than under hydrostatic loading and 5.1 times lower than the phase equilibrium pressure. In addition to strain, the kinetics of strain-induced PT unexpectedly depends on time. Also, strain-controlled part of kinetics is zero order, in contrast to the first-order kinetics with smooth-DA. The obtained results open a new window for understanding the mutual effects of nanostructure evolution and PT during severe plastic flow in various technological and natural processes. In conclusion, they may bring up economic strategies of producing nanocomposites and single-phase nanostructured materials with optimal properties.

Crystalline size↗
DOE OSTI2022

Multiscale mechanical design of the lightweight, stiff, and damage-tolerant cuttlebone: A computational study

Cuttlebone, the endoskeleton of cuttlefish, offers an intriguing biological structural model for designing low-density cellular ceramics with high stiffness and damage tolerance. Cuttlebone is highly porous (porosity ~93%) and lightweight (density less than 20% of seawater), constructed mainly by brittle aragonite (95 wt%), but capable of sustaining hydrostatic water pressures over 20 atmospheres and exhibits energy absorption capability under compression comparable to many metallic foams (~4.4 kJ/kg). Here, in this work, we computationally investigate how such remarkable mechanical efficiency is enabled by the multiscale structure of cuttlebone. Using the common cuttlefish, Sepia Officinalis, as a model system, we first conducted high-resolution synchrotron micro-computed tomography (µ-CT) and quantified the cuttlebone's multiscale geometry, including the 3D asymmetric shape of individual walls, the wall assembly patterns, and the long-range structural gradient of walls across the entire cuttlebone (ca. 38 chambers). The acquired 3D structural information enables systematic finite-element simulations, which further reveal the multiscale mechanical design of cuttlebone: at the wall level, wall asymmetry provides optimized energy absorption while maintaining high structural stiffness; at the chamber level, variation of walls (number, pattern, and waviness amplitude) contributes to progressive damage; at the entire skeletal level, the gradient of chamber heights tailors the local mechanical anisotropy of the cuttlebone for reduced stress concentration. Our results provide integrated insights into understanding the cuttlebone's multiscale mechanical design and provide useful knowledge for the designs of lightweight cellular ceramics.

36 MATERIALS SCIENCE↗
DOE OSTI2020

Exploring the role of electronic structure on photo-catalytic behavior of carbon-nitride polymorphs

A fully self-consistent density-functional theory (DFT) with improved functionals is used herein to provide a comprehensive account of structural, electronic, and optical properties of C 3 N 4 polymorphs. Using our recently developed van Leeuwen-Baerends (vLB) corrected local-density approximation (LDA), we implemented LDA + vLB within full-potential N th -order muffin-tin orbital (FP-NMTO) method and show that it improves structural properties and band gaps compared to semi-local functionals (LDA/GGA). We demonstrate that the LDA + vLB predicts band-structure and work-function for well-studied 2D-graphene and bulk-Si in very good agreement with experiments, and more exact hybrid functional (HSE) calculations as implemented in the Quantum-Espresso (QE) package. The structural and electronic-structure (band gap) properties of C 3 N 4 polymorphs calculated using FP-NMTO-LDA + vLB is compared with more sophisticated hybrid-functional calculations. We also perform detailed investigation of photocatalytic behavior using QE-HSE method of C 3 N 4 polymorphs through work-function, band (valence and conduction) position with respect to water reduction and oxidation potential. Our results show $γ$-C 3 N 4 as the best candidate for photocatalysis among all the C 3 N 4 polymorphs but it is dynamically unstable at ‘zero’ pressure. We show that $γ$-C 3 N 4 can be stabilized under hydrostatic-pressure, which improves its photocatalytic behavior relative to water reduction and oxidation potentials.

36 MATERIALS SCIENCE↗
DOE OSTI2020

Hard, transparent, sp3-containing 2D phase formed from few-layer graphene under compression

Despite several theoretically proposed two-dimensional (2D) diamond structures, experimental efforts to obtain such structures are in initial stage. Recent high-pressure experiments provided significant advancements in the field, however, expected properties of a 2D-like diamond such as sp 3 content, transparency and hardness, have not been observed together in a compressed graphene system. Here, we compress few-layer graphene samples on SiO 2 /Si substrate in water and provide experimental evidence for the formation of a quenchable hard, transparent, sp 3 -containing 2D phase. Our Raman spectroscopy data indicates phase transition and a surprisingly similar critical pressure for two-, five-layer graphene and graphite in the 4e6 GPa range, as evidenced by changes in several Raman features, combined with a lack of evidence of significant pressure gradients or local non-hydrostatic stress components of the pressure medium up to ≈ 8 GPa. The new phase is transparent and hard, as evidenced from indentation marks on the SiO 2 substrate, a material considerably harder than graphene systems. Furthermore, we report the lowest critical pressure (≈ 4 GPa) in graphite, which we attribute to the role of water in facilitating the phase transition. Overall, theoretical calculations and experimental data indicate a novel, surface to- bulk phase transition mechanism that gives hint of diamondene formation.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2024

The intrinsic mechanical properties of hydromagnesite, Mg 5 (CO 3 ) 4 (OH) 2 ·4H 2 O, a key phase of reactive MgO carbonate cement

To potentially enable CO 2 sequestration, reactive MgO carbonate cement is emerging as an alternative binder to Portland cement. Understanding the mechanical properties of its binding phase is critical for understanding the strength development and performing materials design for reactive MgO cement systems; however, the intrinsic mechanical properties of hydromagnesite (Mg 5 (CO 3 ) 4 (OH) 2 ·4H 2 O), a key binding phase, remain unexplored. Here the present study utilized synchrotron-based high-pressure X-ray diffraction to determine the unit cell-scale, intrinsic mechanical properties of hydromagnesite for the first time. Up to hydrostatic loading of 7.7 GPa, the bulk modulus of hydromagnesite was determined as 59 GPa or 71 GPa fitted using the second-order or third-order Birch-Murnaghan equation of state, which we contextualize with binding phases in various cement systems. The experiment results are applicable in materials design of low-carbon concrete and valuable for the validation and calibration of atomistic models.

36 MATERIALS SCIENCE↗
DOE OSTI2024

Stress-hybrid virtual element method on six-noded triangular meshes for compressible and nearly-incompressible linear elasticity

In this paper, we present a first-order Stress-Hybrid Virtual Element Method (SH-VEM) on six-noded triangular meshes for linear plane elasticity. Here, we adopt the Hellinger–Reissner variational principle to construct a weak equilibrium condition and a stress based projection operator. In each element, the stress projection operator is expressed in terms of the nodal displacements, which leads to a displacement based formulation. This stress-hybrid approach assumes a globally continuous displacement field while the stress field is discontinuous across each element. The stress field is initially represented by divergence-free tensor polynomials based on Airy stress functions, but we also present a formulation that uses a penalty term to enforce the element equilibrium conditions, referred to as the Penalty Stress-Hybrid Virtual Element Method (PSH-VEM). Numerical results are presented for PSH-VEM and SH-VEM, and we compare their convergence to the composite triangle FEM and B-bar VEM on benchmark problems in linear elasticity. The SH-VEM converges optimally in the L 2 norm of the displacement, energy seminorm, and the L 2 norm of hydrostatic stress. Furthermore, the results reveal that PSH-VEM converges in most cases at a faster rate than the expected optimal rate, but it requires the selection of a suitably chosen penalty parameter.

42 ENGINEERING↗
DOE OSTI2022

Limiting velocities and transonic dislocations in Mg

To accurately predict the mechanical response of materials, especially at high strain rates, it is important to account for dislocation velocities in these regimes. Under these extreme conditions, it has been hypothesized that dislocations can move faster than the speed of sound. However, the presence of such dislocations remains elusive due to challenges associated with measuring these experimentally. In this work, molecular dynamics simulations were used to investigate the dislocation velocities for the basal edge, basal screw, prismatic edge, and prismatic screw dislocations in Mg in the sub-, trans-, and supersonic regimes. Also, our results show that only prismatic edge dislocations achieve supersonic velocities. Furthermore, this work demonstrates that the discrepancy between the theoretical limiting velocity and the MD results for Mg is due to its sensitivity to large hydrostatic stress around the dislocation core, which was not the case for fcc metals such as Cu.

36 MATERIALS SCIENCE↗
DOE OSTI2026

Elastic strain engineering of lattice thermal conductivity of silicon: An ab-initio study

Silicon (Si) is the most essential material in the semiconductor industry. It is important to manage the thermal properties of crystalline Si. Elastic strain engineering (ESE) has proven to be an effective tool in controlling the electrical conductivity of Si in strained-silicon technology; its effects on the thermal conductivity of silicon, therefore, warrants careful investigation. The ESE effect is much more pronounced for nanostructured materials due to the ultralarge elastic strains (on the order of 10%) achievable at the nanoscale. In this work, the lattice thermal conductivity (κ L ) of Si under hydrostatic, biaxial, and uniaxial strain states is studied with ab-initio simulations, and the values of strain-dependent κ L compare well with experimental results and existing molecular dynamics simulations. To understand the mechanisms of strain-modulated κ L , the phonon bands, scattering rate, and Grüneisen parameters of phonon modes are computed. It is shown that strain can significantly change the anharmonicity of the crystal system, thus changing phonon scattering rates and κ L . Our results demonstrate that ESE can reduce silicon κ L by up to approximately 90%. Furthermore, uniaxial and biaxial strains can induce highly anisotropic thermal conductivity in Si, with relative variations up to 58.5% and 14.5%, respectively.

Anisotropy in Thermal Conductivity↗
DOE OSTI2020

Transport of coexisting Ni-Cu sulfide liquid and silicate melt in partially molten peridotite

Transport of coexisting sulfide and silicate melts in partially molten peridotite contributes to the redistribution of chalcophile elements within the upper mantle as well as the genesis of magmatic Ni-Cu sulfide deposits, but has not been investigated systematically. Using laboratory experiments, theoretical calculations, and X-ray synchrotron microtomography, this study documents the topology and considers controls on the extraction of two immiscible liquids during partial melting of mantle peridotite. Under hydrostatic conditions, the measured dihedral angle at silicate melt-mineral-mineral junctions is 13.7–21.3°. Silicate melt is distributed along grain edges forming incompletely interconnected melt channels that disconnected by some dead ends at melt fractions ~7–9 vol%. Application of theoretically predicted permeability (k ~10 -14 -10 -16 m 2 ) permits estimation of the extraction velocity of silicate melt of 0.7-11.1 μm/day within a single interconnected melt channel. In the absence of silicate melt, isolated sulfide droplets (3.77 vol%) show a sulfide-olivine-olivine dihedral angle of 91.5–101.3°. However, in the presence of silicate melt, sulfide droplets (average size ~2.53±2.14μm, 1σ) are partially surrounded by silicate melt and stranded in triple junctions or melt pockets due to the limitation of the smallest dimension (0.3μm) of melt channels. Thus, the extraction of sulfide liquid is highly restricted by these dead ends and the smallest dimension of melt channels during porous flow of silicate melt. In contrast, during large-strain shear deformation (strain ~1.6–2.5), initially stranded sulfide droplets were elongated and extracted with silicate melt into liquid-rich sheets with a length of several hundred microns, constantly oriented at 14.3±4.5°to the shear plane and antithetic to the shear direction. The angle is lower than that (18-30°) of those sheets containing sulfide liquid only, indicating that silicate melt dominates liquid-rich sheets. Driven by stress, silicate melt-dominated liquid-rich sheets open the appropriately oriented grain boundaries between silicate minerals, thus providing an efficient pathway for the extraction of sulfide liquid during deformation. When such sheet-like channels remain open, sulfide droplets (> millimeter-scale) can be potentially mobile through high strain domains of the upper mantle, contributing to the addition of chalcophile elements and the fertilization of the lithospheric mantle.

high P-T experiment↗
DOE OSTI2026

Thermal loading effects on chalk hydromechanical behavior for nuclear waste disposal

Safe disposal of heat-generating nuclear waste depends on host rock stability under thermal, hydrological, and mechanical stresses. This study investigates the effect of thermal loading on mechanical behavior of the shallowly buried Ghareb formation chalk through triaxial and hydrostatic constant strain rate and creep tests at temperatures up to 100 ˚C and effective pressures up to 20.7 MPa. Experimental results show that thermal loading reduces the elastic moduli of chalk by 50–75%, and a transition occurs above 60 ˚C where creep rates increase rapidly. Water saturation nearly doubles the thermally induced strain compared to dry conditions and strongly decreases material rigidity. Thermal loading also leads to significant pore pressure increases under undrained conditions and leads to reductions in the apparent permeability during drained conditions. Laboratory experimental data were used to parameterize and develop a preliminary constitutive model for predicting future deformation during repository operations in the Ghareb. The strongly coupled effects – mechanical weakening, fluid pressure fluctuations, and permeability modification – demonstrate that elevated repository temperatures will have a pronounced effect on the near field Ghareb behavior during waste disposal operations. The findings indicate that the coupled interactions must be considered in predictive models and repository design to ensure long-term nuclear waste isolation and safety.

12 MANAGEMENT OF RADIOACTIVE AND NON-RADIOACTIVE W↗
DOE OSTI2021

Elucidating the structural properties and reversible regional texture effect of GdB 6 under high pressure

As hard and refractory materials with high chemical resistance and mechanical strength, lanthanide hexaborides (LnB 6 ) have attracted much attention. Among the family of LnB 6 , gadolinium hexaboride (GdB 6 ) occupies a special position due to the half-filled 4f shell of Gd. Here, using in situ synchrotron radiation angle-dispersive X-ray diffraction in a diamond anvil cell at room temperature, the structural stability and compression behavior of GdB 6 are investigated extensively, GdB 6 is observed to be structurally stable up to 73 GPa, and the bulk modulus of 177 GPa is obtained under hydrostatic compression. In this paper, an interesting observation of pressure-induced spotty diffraction rings of GdB6 is reported, its formation mechanism can be well described by the reversible regional texture effect, which highlights the rearrangement of crystal grains under high pressure. The rearrangement mechanism has been well explained by investigating the pressure dependence of full width at half maximum, macro-differential stress and grain size. Collective grain rotation behavior motivated by stress difference is critical for the rearrangement process, the strong isotropy and strong stability of GdB 6 structure also provide necessary conditions for high-pressure grain rotation behavior. These results will help to promote the understanding of high-pressure structural properties of GdB 6 , and provide novel insights on the high-pressure grain behavior in hard materials with strong isotropy and three-dimensional skeleton constituted of strong covalent bonds.

36 MATERIALS SCIENCE↗
DOE OSTI2022

Pressure dependent magnetic properties on bulk CrBr 3 single crystals

The van der Waals class of materials offer an approach to two-dimensional magnetism as their spin fluctuations can be tuned upon exfoliation of layers. Moreover, it has recently been shown that spin-lattice coupling and long-range magnetic ordering can be modified with pressure in van der Waals materials. In this work, the magnetic properties of quasi two-dimensional CrBr 3 are reported applying hydrostatic pressure. The application of pressure up to 0.844 GPa shows a 1.77% decrease in saturation magnetization with a decrease in the Curie temperature from 33.05 to 30.41 K. Density functional theory calculations with pressure up to 1 GPa show a reduction in volume and interplanar distance as pressure increases. To further understand the magnetic properties with applied pressure, the magnetocrystalline anisotropy energy (MAE) and exchange coupling parameter (J) are calculated. There is small decrease in MAE and the first nearest neighbor interaction (J 1 ) (U = 2.7 eV and J = 0.7 eV) is increasing with respect to increasing pressure. Overall, CrBr 3 displays ferromagnetic interlayer coupling and the calculated exchange coupling and MAE parameters match well with the observations from the experimental work.

36 MATERIALS SCIENCE↗
DOE OSTI2021

Surrogate approximation of the Grad–Shafranov free boundary problem via stochastic collocation on sparse grids

In magnetic confinement fusion devices, the equilibrium configuration of a plasma is determined by the balance between the hydrostatic pressure in the fluid and the magnetic forces generated by an array of external coils and the plasma itself. The location of the plasma is not known a priori and must be obtained as the solution to a free boundary problem. The partial differential equation that determines the behavior of the combined magnetic field depends on a set of physical parameters (location of the coils, intensity of the electric currents going through them, magnetic permeability, etc.) that are subject to uncertainty and variability. The confinement region is in turn a function of these stochastic parameters as well. In this work, we consider variations on the current intensities running through the external coils as the dominant source of uncertainty. This leads to a parameter space of dimension equal to the number of coils in the reactor. With the aid of a surrogate function built on a sparse grid in parameter space, a Monte Carlo strategy is used to explore the effect that stochasticity in the parameters has on important features of the plasma boundary such as the location of the x-point, the strike points, and shaping attributes such as triangularity and elongation. Furthermore, the use of the surrogate function reduces the time required for the Monte Carlo simulations by factors that range between 7 and over 30.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2024

A weighted shifted boundary method for immersed moving boundary simulations of Stokes' flow

The Shifted Boundary Method (SBM) belongs to the class of unfitted (or immersed, or embedded) finite element methods, and relies on reformulating the original boundary value problem over a surrogate (approximate) computational domain. The surrogate domain is constructed so as to avoid cut cells and the associated problematic implementation and numerical integration issues. Accuracy is maintained by modifying the original boundary conditions using Taylor expansions: hence the name of the method, that shifts the location and values of the boundary conditions. Here, in this article, we extend the SBM to the simulation of incompressible Stokes flow, by appropriately weighting its variational form with the elemental volume fraction of active fluid. This approach allows to drastically reduce spurious pressure oscillations in time, which are produced if the total volume of active fluid were to change abruptly over a time step. The proposed Weighted SBM (W-SBM) exactly preserves states of hydrostatic equilibrium, and induces small mass and momentum conservation errors, which converge as the grid is refined. This is in analogy to cutFEMs and related unfitted approaches, which rely on an affine representation of cut boundaries. We demonstrate the robustness and accuracy of the proposed method with an extensive suite of two-dimensional tests.

97 MATHEMATICS AND COMPUTING↗