Regular Planes Research Articles

A Relationship between Fracture Toughness Kc and Energy Release Rate Gc According to Fracture Morphology Analysis

This study investigated the relationship between fracture toughness (Kc) and energy release rate (Gc) through fracture morphology analysis, emphasizing the critical role of fractal dimensions in accurately characterizing fracture surfaces. Traditional linear elastic fracture mechanics (LEFM) models relate Gc to Kc by combining energy principles with the nominal area of the fracture surface. However, real materials often exhibit plasticity, and their fracture surfaces are not regular planes. To address these issues, this research applied fractal theory and introduced the concept of ubiquitiform surface area to refine the calculation of fracture surfaces, leading to more accurate estimates of Gc and Kc. The method was validated through standard compact tensile specimen tests on a nickel-based superalloy at 550 °C. Additionally, the analysis of fractal dimension differences and dispersion in various fracture regions provides a novel perspective for evaluating the fracture toughness of materials.

A study on the growth process for liquid phase epitaxy of GaN crystal using Na–Li–Ca flux

The liquid epitaxial growth process on the HVPE-GaN seed of GaN crystal was investigated using the Na–Li–Ca flux method. The phase structure and morphology of as-grown GaN crystals were characterized by X-ray diffraction (XRD) and the scanning electron microscope (SEM), respectively. Under the growth time of 70h, a large area of dissolution morphology could be observed accompanied by a decrease in the thickness of the HVPE-GaN seed. At the bottom of the crucible, the thinning of the seed crystal thickness was the most obvious. For the growth time of 150h, there were two kinds of appearances along the height direction, presenting gathered ridges in the upper part and cellular organizations in the middle and bottom parts. For 420h, the as-grown crystal presented a typical hexagonal layered morphology and the side face developed outward forming regular hexagonal crystallographic planes. With prolonging time from 150h to 420h, the LPE growth shifted from non-equilibrium growth mode with an unstable cellular growth surface morphology to near-equilibrium growth mode with a typical hexagonal layered growth morphology. The thickness of as-grown crystal showed a decrease trend from the gas-liquid interface to the bottom of crucible. To get near-equilibrium growth mode for the whole crystal plate in Na-flux method, the promotion of N dissolving, GaN growth unit diffusion is the key issue.

Handwriting-Assistant

Pen-based handwriting has become one of the major human-computer interaction methods. Traditional approaches either require writing on the specific supporting device like the touch screen, or limit the way of using the pen to pure rotation or translation. In this paper, we propose Handwriting-Assistant, to capture the free handwriting of ordinary pens on regular planes with mm-level accuracy. By attaching the inertial measurement unit (IMU) to the pen tail, we can infer the handwriting on the notebook, blackboard or other planes. Particularly, we build a generalized writing model to correlate the rotation and translation of IMU with the tip displacement comprehensively, thereby we can infer the tip trace accurately. Further, to display the effective handwriting during the continuous writing process, we leverage the principal component analysis (PCA) based method to detect the candidate writing plane, and then exploit the distance variation of each segment relative to the plane to distinguish on-plane strokes. Moreover, our solution can apply to other rigid bodies, enabling smart devices embedded with IMUs to act as handwriting tools. Experiment results show that our approach can capture the handwriting with high accuracy, e.g., the average tracking error is 1.84mm for letters with the size of about 2cmx1cm, and the average character recognition rate of recovered single letters achieves 98.2% accuracy of the ground-truth recorded by touch screen.

Kinetics of grain-boundary nucleated transformations in rectangular geometries and one paradox relating to Cahn's model

It was found by Jägle and Mittenmeijer [Acta Mater. 59 (2011) 5775-5786] as a result of computer simulation that Cahn's equation underestimates pronouncedly the transformed fraction in reality. To test the hypothesis that a strong correlation in the arrangement of grains in the Cahn model (they are “tied” to planes) can be responsible for this phenomenon, the paradox of packing is described: the structures composed of the same elements (random parallelepipeds) transforming in the same way, but packed differently, give different transformation rates. One of these structures is a special Cahn model – the grain structure of parallelepipeds formed by three sets of random parallel planes orthogonal to each other. An alternative structure consists of the same parallelepipeds, but randomly packed; it looks like a real grain structure. It is shown analytically that the kinetics of transformation in the first structure is considerably slowed down in comparison with that in the second. For the various intermediate structures under consideration, the kinetic curves are between these two, so that the following rule is established: the transformation kinetics is accelerated, when the correlation in the arrangement of the parallelepipeds weakens. Preliminarily, volume-fraction expressions are obtained for the systems of an infinite number of parallel planes arranged both regularly and randomly. As a special case of random arrangement, a non-Poissonian point process (the second-order Erlang process) of the arrangement of planes is considered for the first time. The exact volume-fraction expression obtained for this case shows that it cannot be derived by Cahn's method, i.e. the extended-volume approach is applicable only to Poisson processes. The volume fraction equations for regular planes are used to study cubic grain structures, both regular and random. It is shown that Cahn's equation underestimates the transformation kinetics in both regular and random structures with four different size distributions of cubes; the degree of underestimation depends on the size distribution, being the largest in the regular structure.

Acoustic scattering reduction in elastic materials with Bat optimization algorithm

A scattering-cancelation method is followed in this analysis. The opportunity to reduce the scattering effect in rigid cylinder with elastic cloaking material is investigated in the paper. The rigid cylinder with elastic cloaking and without elastic cloaking is analyzed for regular planes waves to test the scattering effect of the rigid cylinder. The energy due to reflected and travelled waves is presented mathematically. The parameter of the elastic cloaking such as thickness, density and Poisson ratio are optimized using BAT algorithm. Pressure filed of the rigid cylinder and directivity patterns scatter pressures in the cylinder are analyzed. The results revealed that, bat algorithm optimization provide the better results for elastic cloaking in the cylinder to reduce scattering effect.

Kinetics of Grain-Boundary Nucleated Transformations in Rectangular Geometries and One Paradox Relating to Cahn's Model

It was found by Jagle and Mittenmeijer [Acta Mater. 59 (2011) 5775-5786] as a result of computer simulations that Cahn’s equation underestimates pronouncedly the transformed fraction in reality. To test the hypothesis that a strong correlation in the arrangement of grains in the Cahn model (they are “tied” to planes) can be responsible for this phenomenon, the paradox of packing is described: the structures composed of the same elements (random parallelepipeds) transforming in the same way, but packed differently, give different transformation rates. One of these structures is a special Cahn model – the grain structure of parallelepipeds formed by three sets of random parallel planes orthogonal to each other. An alternative structure consists of the same parallelepipeds, but randomly packed; it looks like a real grain structure. It is shown analytically that the kinetics of transformation in the first structure is considerably slowed down in comparison with that in the second. For the various intermediate structures under consideration, the kinetic curves are between these two, so that the following rule is established: the transformation kinetics is accelerated, when the correlation in the arrangement of the parallelepipeds weakens. Preliminarily, volume-fraction expressions are obtained for the systems of an infinite number of parallel planes arranged both regularly and randomly. As a special case of random arrangement, a non-Poissonian point process (the second-order Erlang process) of arrangement of planes is considered for the first time. The exact volume-fraction expression obtained for this case shows that it cannot be derived by Cahn’s method, i.e. the extended-volume approach is applicable only to Poisson processes. The volume fraction equations for regular planes are used to study cubic grain structures, both regular and random. It is shown that Cahn’s equation underestimates the transformation kinetics in both regular and random structures with four different size distributions of cubes; the degree of underestimation depends on the size distribution, being the largest in the regular structure.

Dense Stereo Matching Strategy for Oblique Images That Considers the Plane Directions in Urban Areas

The perspective distortion of oblique images has a substantial impact on dense matching, i.e., it reduces the matching precision. In this article, a strategy of dense matching in which the object plane direction is considered is proposed. According to many regular planes in urban areas, epipolar rectification with minimum distortions relative to the selected reference planes can be generated. The matching results of epipolar images relative to various reference planes are weighted and fused into a single depth map, which is a better matching result. The experimental results demonstrate that the perspective distortion has a substantial influence on the dense matching performance. The root-mean-square error (RMSE) of the flatness for horizontal objects is increased by approximately 30%, and the RMSE of the flatness for facades is increased by approximately 40%. Hence, the proposed matching strategy, in which the object plane is considered, can effectively improve the matching results.

Carrier dynamics and recombination mechanisms in InP twinning superlattice nanowires.

Nominal dopant-free zinc blende twinning superlattice InP nanowires have been grown with high crystal-quality and taper-free morphology. Here, we demonstrate its superior optical performance and clarify the different carrier recombination mechanisms at different temperatures using a time resolved photoluminescence study. The existence of regular twin planes and lateral overgrowth do not significantly increase the defect density. At room temperature, the as-grown InP nanowires have a strong emission at 1.348 eV and long minority carrier lifetime (∼3 ns). The carrier recombination dynamics is mainly dominated by nonradiative recombination due to surface trapping states; a wet chemical etch to reduce the surface trapping density thus boosts the emission intensity and increases the carrier lifetime to 7.1 ns. This nonradiative recombination mechanism dominates for temperatures above 155 K, and the carrier lifetime decreases with increasing temperature. However, radiative recombination dominates the carrier dynamics at temperature below ∼75 K, and a strong donor-bound exciton emission with a narrow emission linewidth of 4.5 meV is observed. Consequently, carrier lifetime increases with temperature. By revealing carrier recombination mechanisms over the temperature range 10-300 K, we demonstrate the attraction of using InP nanostructure for photonics and optoelectronic applications.

Molecular Dynamics Simulation to Investigate the Rake Angle Effects on Nanometric Cutting of Single Crystal Ni3Al

Molecular dynamics, an effective method to gain an insight into nanometric behaviour of materials, was employed to study the nano-cutting behaviour of single crystal Ni3Al in nanometric scale. In this paper, comparisons were made for compressive/tensile stress, subsurface damage and surface roughness with three rake angles of a diamond tool. Subsurface damage was partitioned by region and studied with work hardening in detail. A model for precise characterization of surface roughness was established with consideration of local surface fluctuation. Simulation results showed that the chip thickness increased as rake angle changed from negative to positive, and the boundary formed between tensile and compressive stress was in consistent with the glide direction of stacking fault. Subsurface damage decreased as the increase of rake angle, and regular glide planes of stacking faults were found in front of the cutting tool. Further, the pinned dissociated 1/2 superpartial dislocation with anti-phase boundary was demonstrated. The model was tested and characterized by implanted pits on perfect surface. Results showed that surface roughness can be well characterized, and an evident discrepancy was observed among three rake angles, especially for 30° rake angle, which showed an distinct smooth surface compared with the others.

A study of the crystallographic pitting behavior of Al-0.54Mg-0.66Si aluminum alloy in acidic chloride solutions

Some specific corrosion environments require Al-Mg-Si aluminum alloy extrusions to have superior corrosion resistance. In order to clarify its corrosion mechanism and enhance its corrosion resistance, the corrosion occurrence, propagation path and corrosion morphology of the alloy was characterized by scanning electron microscope (SEM), electron backscatter diffraction (EBSD) and transmission electron microscopy (TEM). It was found that the corrosion of the alloy first occurred at the grain boundary. Then the grain boundary becomes the origin of the crystallographic pitting after being attacked, and Mg in the Mg5Si6 phase inside the grain is preferentially corroded by precipitate free zone (PFZ), so that the corrosion propagates into the interior of the grain. The morphology of crystallographic pitting presents a regular step-like planes and is always propagated parallel to the direction of {100}Al in the grain. Further, the corroded Mg5Si6 precipitates becomes cathodes in the local area at a later stage, leading to the regular step-like planes has been transformed into dimple-like appearances.

Crystal Structure Variations of Sn Nanoparticles upon Heating

Structural changes in Sn nanoparticles during heating below the melting point have been investigated using differential scanning calorimetry (DSC), x-ray diffraction (XRD) analysis, electron diffraction (ED), and high-resolution transmission electron microscopy (HRTEM). DSC revealed that the heat required to melt the nanoparticles (28.43 J/g) was about half compared with Sn metal (52.80 J/g), which was attributed to the large surface energy contribution for the nanoparticles. ED and XRD analyses of the Sn nanoparticles revealed increased intensity for crystal planes having large interplaner distances compared with regular crystal planes with increasing heat treatment temperature (HTT). HRTEM revealed an increase in interlayer spacing at the surface and near joints between nanoparticles with the HTT, leading to an amorphous structure of nanoparticles at the surface at 220°C. These results highlight the changes that occur in the morphology and crystal structure of Sn nanoparticles at the surface and in the interior with increase of the heat treatment temperature.

On a class of partial planes related to biplanes

In this note we consider partial planes in which for each element x (point or line) there exists a unique opposite element or antipode x* which cannot be joined to x or has no intersection with x. We also require the existence of a triangle. Such partial planes will be called antipodal planes. We are mainly interested in the subclass of regular antipodal planes satisfying: p I L implies p* I L* for all points p and lines L. We shall provide a free construction of infinite regular antipodal planes. The objects thus constructed are not free objects in the usual sense since between antipodal planes there do not exist proper homomorphisms. On the other hand, regular antipodal planes do have a canonical homomorphic image which is a biplane (cf. Payne, J Comb Theory A 12:268–282, 1972). Regular antipodal planes can be coordinatized by certain algebraic systems in a similar way as projective planes are coordinatized by ternary rings. Again by a free construction, we shall provide examples satisfying a configuration theorem comparable to the Fano condition with fixed line at infinity.

EBSD characterization of the growth mechanism of SiC synthesized via direct microwave heating

Well-crystallized 3C-silicon carbide (SiC) grains/nanowires have been synthesized rapidly and conveniently via direct microwave heating, simply using silicon dioxide powders and artificial graphite as raw materials. The comprehensive characterizations have been employed to investigate the micro-structure of the obtained 3C-SiC products. Results indicated that, different from the classic screw dislocation growth mechanism, the 3C-SiC grains/nanowires synthesized via high-energy vacuum microwave irradiation were achieved through the two-dimension nucleation and laminar growth mechanism. Especially, the electron backscattered diffraction (EBSD) was employed to characterize the crystal planes of the as-grown SiC products. The calculated Euler angles suggested that the fastest-growing crystal planes {211} were overlapped gradually. Through the formation of the {421} transformation plane, {211} finally evolved to {220} which existed as the side face of SiC grains. The most stable crystal planes {111} became the regular hexagonal planes in the end, which could be explained by the Bravais rule. The characterization results of EBSD provided important experimental information for the evolution of crystal planes.

The Arabidopsis mitogen-activated protein kinase 6 is associated with γ-tubulin on microtubules, phosphorylates EB1c and maintains spindle orientation under nitrosative stress.

Stress-activated plant mitogen-activated protein (MAP) kinase pathways play roles in growth adaptation to the environment by modulating cell division through cytoskeletal regulation, but the mechanisms are poorly understood. We performed protein interaction and phosphorylation experiments with cytoskeletal proteins, mass spectrometric identification of MPK6 complexes and immunofluorescence analyses of the microtubular cytoskeleton of mitotic cells using wild-type, mpk6-2 mutant and plants overexpressing the MAP kinase-inactivating phosphatase, AP2C3. We showed that MPK6 interacted with γ-tubulin and co-sedimented with plant microtubules polymerized in vitro. It was the active form of MAP kinase that was enriched with microtubules and followed similar dynamics to γ-tubulin, moving from poles to midzone during the anaphase-to-telophase transition. We found a novel substrate for MPK6, the microtubule plus end protein, EB1c. The mpk6-2 mutant was sensitive to 3-nitro-l-tyrosine (NO2 -Tyr) treatment with respect to mitotic abnormalities, and root cells overexpressing AP2C3 showed defects in chromosome segregation and spindle orientation. Our data suggest that the active form of MAP kinase interacts with γ-tubulin on specific subsets of mitotic microtubules during late mitosis. MPK6 phosphorylates EB1c, but not EB1a, and has a role in maintaining regular planes of cell division under stress conditions.

Growth Process of SiC Grains Prepared by High-energy Microwave Irradiation

High-energy vacuum microwave irradiation was directly applied to synthesize silicon carbide (SiC). Results indicated that the well-crystallized β-SiC grains can be obtained rapidly and conveniently via microwave approach, even simply constituents covering silica dioxide powders and artificial graphite were employed as raw materials. Based on the comprehensive micro-structural characterizations, the formation of β-SiC, under high-energy vacuum microwave irradiation, could be properly explained by the mechanism of two-dimension nucleation and growth. Be- sides, the technology of electron backscattered diffraction (EBSD) was particularly used to characterize the crystal plane of the observed SiC grains. The corresponding calculation of Euler angles suggested that the fastest-growing crystal planes {211} should be overlapped gradually, and the evolution from {211} to {220} crystal planes should be realized through the formation of {421} transformation plane. The most stable crystal planes of {111} became the regular hexagonal planes in the end, which can be explained by the Bravis rule. Correspondingly, the {220} crystal planes were finally existed as the side-planes of SiC grains. The detailed EBSD investigation provided the experimen- tal evidences for the evolution of crystal planes in the growth process.

An axiomatic look at a windmill

We present the problem stated in intuitive language as problem 2 at the 52nd International Mathematical Olympiad as a formal statement, and prove that it is valid in ordered regular incidence planes, the weakest ordered geometry whose models can be embedded in projective ordered planes.

Surfactant-free synthesis of highly methanol-tolerant, polyhedral Pd–Pt nanocrystallines for oxygen reduction reaction

Carbon supported polyhedral Pd–Pt nanocrystallines (Pd–Pt/C) are synthesized using a facile surfactant-free process. The morphology of nanocrystallines is tailored by ammonia complexation and Pd/Pt ratios of the metallic precursors. The as-prepared Pd–Pt/C catalysts with low Pt content exhibit oxygen reduction reaction (ORR) activity comparable to that of the commercial Pt/C catalyst, while having much higher methanol tolerance. Compared with the spherical Pd6Pt/C catalyst, the polyhedral Pd6Pt/C catalyst shows 1.56-fold higher mass specific activity for ORR, while its electrochemical surface area (ECSA) is only half of the former. The superior ORR activity may be attributed to the more exposed regular (111) planes, the higher ratio of metallic form and the surface enrichment of Pt atoms.

Spin-liquid ground state in the frustrated kagome antiferromagnet MgCu3(OH)6Cl2

We report muSR experiments on Mg{x}Cu{4-x}(OH)6Cl2 with x \sim 1, a new material isostructural to Herbertsmithite exhibiting regular kagome planes of spin 1/2 (Cu^{2+}), and therefore a candidate for a spin liquid ground state. We evidence the absence of any magnetic ordering down to 20 mK (\sim J/10^4). We investigate in detail the spin dynamics on well characterized samples in zero and applied longitudinal fields and propose a low T defect based interpretation to explain the unconventional dynamics observed in the quantum spin liquid phase.

Morphology and qualitative analysis of mechanism of microcellular PET by compression moulding

This paper presents the morphology and the mechanism of microcellular polyethylene terephthalate (PET) prepared by compression moulding. The microstructures of foamed PET and crystallinity were investigated by optical microscopy, field emission SEM and wide angle X-ray diffraction, and the mechanism of microcellular foaming process was also discussed. The results showed that a peculiar structure was successfully obtained by compression moulding, which looked like oriented elliptical cells aligned along the surface of the sheet due to the biaxial orientations and the restriction by regular crystal planes of PET sheet. A cell nucleation model of PET sheet was formed. The deformed bubble growth (from spherical initial nuclei to ellipsoidal ones) was due to constraint of crystalline planes and competition of bubble growth among neighbouring bubbles. Cooling and decreasing the gas dissolution were found important for bubble shaping in the final phase of bubble growth.

Enumeration of orthogonal Buekenhout unitals

In this paper we develop general techniques for enumerating orthogonal Buekenhout unitals embedded in two-dimensional translation planes. We then apply these techniques in the regular nearfield planes, the odd-order Hall planes, and the odd-order flag-transitive affine planes. Stabilizers of the resulting unitals also are computed.