Geometric Analysis Research Articles

Quadrotor attitude control with a modified fixed‐time synergetic controller: A geometric analysis and experimental validation

AbstractThis article proposes a novel modified fixed‐time synergetic control (MFTSC) approach to address the quadrotor control problem in the presence of external disturbances. In contrast to previous fixed‐time synergetic control (FTSC) methods, the proposed approach employs an aggregate macrovariable expression with independent fractional powers. This expression expands the set of real numbers that the parameters of the fractional power can take, leading to a significantly higher rate of convergence toward optimal control parameters (more than 28‐fold), as demonstrated through geometric analysis. The stability of the proposed control system is established, and numerical simulations and experimental validation are conducted using a quadrotor test bench to corroborate the theoretical results.

Phenotypic diversity in early Australian dingoes revealed by traditional and 3D geometric morphometric analysis

The dingo is a wild dog endemic to Australia with enigmatic origins. Dingoes are one of two remaining unadmixed populations of an early East Asian dog lineage, the other being wild dogs from the New Guinea highlands, but morphological connections between these canid groups have long proved elusive. Here, we investigate this issue through a morphometric study of ancient dingo remains found at Lake Mungo and Lake Milkengay, in western New South Wales. Direct accelerated mass spectrometry (AMS) radiocarbon dates from an ancient Lake Mungo dingo demonstrate that dingoes with a considerably smaller build than the predominant modern morphotype were present in semi-arid southeastern Australia c.3000–3300 calBP. 3D geometric morphometric analysis of a near-complete Mungo cranium finds closest links to East Asian and New Guinean dogs, providing the first morphological evidence of links between early dingoes and their northern relatives. This ancient type is no longer extant within the range of modern dingo variability, but populations from nearby southeastern Australia show a closer resemblance than those to the north and west. Our results reaffirm prior characterisations of regional variability in dingo phenotype as not exclusively derived from recent domestic dog hybridisation but as having an earlier precedent, and suggest further that the dingo’s phenotype has changed over time.

Automated detection and mapping of crystal tilt using thermal diffuse scattering in transmission electron microscopy

Quantitative interpretation of transmission electron microscopy (TEM) data of crystalline specimens often requires the accurate knowledge of the local crystal orientation. A method is presented which exploits momentum-resolved scanning TEM (STEM) data to determine the local mistilt from a major zone axis. It is based on a geometric analysis of Kikuchi bands within a single diffraction pattern, yielding the center of the Laue circle. Whereas the approach is not limited to convergent illumination, it is here developed using unit-cell averaged diffraction patterns corresponding to high-resolution STEM settings. In simulation studies, an accuracy of approximately 0.1 mrad is found. The method is implemented in automated software and applied to crystallographic tilt and in-plane rotation mapping in two experimental cases. In particular, orientation maps of high-Mn steel and an epitaxially grown La0.7Sr0.3MnO3-SrTiO3 interface are presented. The results confirm the estimates of the simulation study and indicate that tilt mapping can be performed consistently over a wide field of view with diameters well above 100 nm at unit cell real space sampling.

Nonconvex Factorization and Manifold Formulations Are Almost Equivalent in Low-Rank Matrix Optimization

In this paper, we consider the geometric landscape connection of the widely studied manifold and factorization formulations in low-rank positive semidefinite (PSD) and general matrix optimization. We establish a sandwich relation on the spectrum of Riemannian and Euclidean Hessians at first-order stationary points (FOSPs). As a result of that, we obtain an equivalence on the set of FOSPs, second-order stationary points, and strict saddles between the manifold and factorization formulations. In addition, we show that the sandwich relation can be used to transfer more quantitative geometric properties from one formulation to another. Similarities and differences in the landscape connection under the PSD case and the general case are discussed. To the best of our knowledge, this is the first geometric landscape connection between the manifold and factorization formulations for handling rank constraints, and it provides a geometric explanation for the similar empirical performance of factorization and manifold approaches in low-rank matrix optimization observed in the literature. In the general low-rank matrix optimization, the landscape connection of two factorization formulations (unregularized and regularized ones) is also provided. By applying these geometric landscape connections (in particular, the sandwich relation), we are able to solve unanswered questions in the literature and establish stronger results in the applications on geometric analysis of phase retrieval, well-conditioned low-rank matrix optimization, and the role of regularization in factorization arising from machine learning and signal processing. Funding: This work was supported by the National Key R&D Program of China [Grants 2020YFA0711900 and 2020YFA0711901], the National Natural Science Foundation of China [Grants 12271107 and 62141407], and the Shanghai Science and Technology Program [Grant 21JC1400600]. Supplemental Material: The online appendix is available at https://doi.org/10.1287/ijoo.2022.0030 .

Additive manufacturing of interlocking glass masonry units

AbstractIn comparison to traditional glass casting, glass additive manufacturing (AM) presents an opportunity to increase design flexibility and reduce tooling costs for the production of highly variable geometries. While the latter has been extensively explored for masonry units, there is minimal research on the former for its viability to produce structural building components. This paper encompasses design, manufacturing, and experimental testing to assess the feasibility of using glass AM to produce interlocking masonry units for the construction industry. The glass 3D printer employed in this study is capable of printing a maximum volume of 32.5 $$\times $$ × 32.5 $$\times $$ × 38 cm–suitable for producing full-size masonry units. As part of this work, we discuss how to adapt design guidelines for glass AM to produce interlocking units. To evaluate fabrication ease and structural performance, three fabrication methods, Fully Hollow, Print-Cast, and Fully Printed, are compared. To compare the accuracy, repeatability, and structural capacity of each masonry unit, geometric analysis, surface roughness, and mechanical testing is conducted. Results varied by fabrication method, with average strength ranging from 3.64$$-$$ - 42.3 MPa for initial fracture and 64.0–118 MPa for ultimate strength. Accuracy in print dimensions was less than 1 mm with a standard deviation of 0.14–1.6 mm. Results demonstrated that Fully Hollow masonry units provide a more immediate path to implementation, while Fully Printed units have the potential to provide an entirely glass, transparent, and circular building component fabrication method.

Visuomotor predictors of interception.

Intercepting moving targets is a fundamental skill in human behavior, influencing various domains such as sports, gaming, and other activities. In these contexts, precise visual processing and motor control are crucial for adapting and navigating effectively. Nevertheless, there are still some gaps in our understanding of how these elements interact while intercepting a moving target. This study explored the dynamic interplay among eye movements, pupil size, and interceptive hand movements, with visual and motion uncertainty factors. We developed a simple visuomotor task in which participants used a joystick to interact with a computer-controlled dot that moved along two-dimensional trajectories. This virtual system provided the flexibility to manipulate the target's speed and directional uncertainty during chase trials. We then conducted a geometric analysis based on optimal angles for each behavior, enabling us to distinguish between simple tracking and predictive trajectories that anticipate future positions of the moving target. Our results revealed the adoption of a strong interception strategy as participants approached the target. Notably, the onset and amount of optimal interception strategy depended on task parameters, such as the target's speed and frequency of directional changes. Furthermore, eye-tracking data showed that participants continually adjusted their gaze speed and position, continuously adapting to the target's movements. Finally, in successful trials, pupillary responses predicted the amount of optimal interception strategy while exhibiting an inverse relationship in trials without collisions. These findings reveal key interactions among visuomotor parameters that are crucial for solving complex interception tasks.

Feeding mode drives mandibular shape in extant Delphinidae

AbstractDelphinidae is the most diverse family within the toothed whale clade, displaying two biosonar modes, different feeding strategies, and diving and habitat adaptations. This work examines the delphinid mandible to determine the association between shape, size and ecological variables in extant species. Geometric morphometric analysis on 95 mandibles belonging to 30 (out of 38) extant species, representatives of all 17 extant genera, was performed in occlusal (or dorsal) and lateral (or labial) view. The results reveal that feeding mode and climate primarily drive mandibular shape in extant species. Biosonar mode is an evolutionary driver in mandibular shape in occlusal view, while diet and maximum prey size play a significant role in size only in both views. By contrast, Diving Ecology, Superficial Temperature and Rostral index do not play a significant role in driving delphinid mandibular shape and size.

Species delimitation in Xanthium sect. Acanthoxanthium (Heliantheae, Asteraceae) and the neglected species Xanthium argenteum

AbstractXanthium is a genus of annual herbaceous plants that stands out within Asteraceae for being wind‐pollinated, diclinous monoecious, and bearing solitary pistillate flowers in peculiar spiny structures (burs). Xanthium sect. Acanthoxanthium is native to South America and characterized by the presence of trifurcate spines at the base of the leaves. Past taxonomic treatments of the section have been contradictory, some recognising up to six species, others reducing all to a single polymorphic species. Altogether, 42 samples of X. sect. Acanthoxanthium were analysed, the vast majority taken from herbarium specimens between 20 and 160 years old. We sampled multiple specimens of X. spinosum from throughout its broad range as well as those taxa with narrower distributions, covering the whole range of morphological variation in the section. When possible, we included types and original material. We used Hyb‐Seq techniques to obtain information from about 1000 single‐copy nuclear genes and complete plastomes. Phylogenomic data were submitted to coalescent‐based species delimitation approaches (SPEEDEMON). Additionally, we performed geometric morphometric analysis of leaf outlines. The results strongly support the identification of four lineages in the section favouring the acceptance of four of the hitherto described species, i.e., X. ambrosioides, X. argenteum, X. catharticum, and X. spinosum. These results were to some extent corroborated by morphometric analyses. While X. ambrosioides was well distinct from X. spinosum based on leaf morphology, such difference was not observed between X. spinosum and X. catharticum. However, X. catharticum differs from X. spinosum in its ecological requirements, being a species rather adapted to high‐mountain environments of the Neotropics. Intriguingly, X. argenteum – a taxon described from a single herbarium collection – was also inferred as a species.

Thermoluminescence (TL) properties of Eu3+ incorporated with CaB4O7 phosphors prepared by solution-combustion process

The solution-combustion approach was used to create CaB4O7:Eu3+phosphors using Ba (NO3)2, Eu (NO3)3·5H2O, H3BO3, NH3(ON)H2, and NH4NO3 as source materials. We investigated the thermoluminescence (TL) characteristics of beta (β)-irradiated CaB4O7:Eu3+. When the TL intensity was evaluated at different dosages of β, it rose with the dose. Changes in peak temperature were observed because of the investigation of the effects of varying heating rates on TL glow curves. Moreover, the positions of the peak temperature and the TL intensity did not change when the same sample was measured again, suggesting that the sample was stable. Additionally, the study calculated several kinetic parameters, including activation energy (E), frequency factor (s), and geometrical factor (μg), for distinct TL glow curves. Through geometric analysis of TL glow peaks, the study determined activation energies and kinetic orders, enabling the calculation of the frequency factor. The findings highlight the suitability of the prepared phosphor for dosimetry and provide insights into trap characteristics crucial for continuous illumination at room temperature. The study also emphasises the importance of optimising trap depth for prolonged afterglow, shedding light on the interplay between trap energies and luminescence characteristics. These findings deepen our comprehension of phosphor behavior and open the door to better dosimetry applications.

Noether symmetries, conservation laws and geometric properties of the Banados-Teitelboim-Zanelli black hole metric

This study provides a comprehensive analysis of the Banados-Teitelboim-Zanelli (BTZ) black hole, a significant solution in three-dimensional gravity. We begin with a detailed exploration of the BTZ black hole metric, highlighting its derivation and physical properties, such as its horizon structure and thermodynamic characteristics. The thermodynamics of BTZ black holes, including temperature, entropy, and free energy, are analyzed to understand their stability and behavior. A central focus of this work is the application of Noether symmetry principles to the BTZ black hole. We systematically compute the Noether symmetries of the BTZ metric and discuss their physical implications, including their role in conservation laws and stability analysis. This includes an examination of perturbations and their impact on the stability of the black hole, as well as a detailed geodesic analysis that leverages Noether symmetries to simplify the study of particle motion in this spacetime. Additionally, we investigate the first integrals associated with the BTZ black hole metric, elucidating their significance for the dynamics and conservation laws within this framework. The geometric analysis is further expanded through the Cartan structure equations, providing insight into the intrinsic geometric properties of the BTZ black hole and associated curvature tensors. Overall, this work integrates thermodynamic, symmetric, and geometric analyses to offer a unified understanding of the BTZ black hole’s structure and behavior, contributing to the broader field of black hole physics in lower-dimensional spacetimes.

Rational design of metal–organic cages to increase the number of components via dihedral angle control

The general principles of discrete, large self-assemblies composed of numerous components are not unveiled and the artificial formation of such entities is a challenging topic. In metal–organic cages, design strategies for tuning the coordination directions in multitopic ligands by the bend and twist angles were previously developed to solve this problem. In this study, the importance of remote geometric communications between components is emphasized, realizing several types of metal–organic assemblies based on dihedral angle control in multitopic ligands although they have the same coordination directions. Self-assembly of a tritopic ligand with dihedral angles θ = 36.5° and a cis-protected Pd(II) ion affords M9L6 and M12L8 cages as kinetic and thermodynamic products, respectively, whereas an M12L8 sheet is formed when θ = 90°. Geometric analyses of strains in the subcomponent rings reveals that remote geometric communications among neighboring multitopic ligands through coordination bonds are key for large assemblies.

Molar enamel–dentine junction shape of Pliobates cataloniae and other Iberian pliopithecoids

The phylogenetic relationships of the small-bodied catarrhine Pliobates cataloniae (∼11.6 Ma, NE Iberian Peninsula) have been controversial since its original description. However, the recent report of additional dentognathic remains has supported its crouzeliid pliopithecoid status. Based on the available hypodigm, the molar enamel–dentine junction (EDJ) shape of P. cataloniae is compared with that of other pliopithecoids from the same basin as well as both extinct and extant hominoids to further evaluate its pliopithecoid affinities. We also quantitatively compare the EDJ shape among these taxa by means of landmark-based three-dimensional geometric morphometrics using principal component analysis (PCA), canonical variate analysis, and between-group PCA. Permutation tests are performed to test whether Pliobates variation exceeds that of extant hominoid genera. Results indicate that Pliobates is similar in molar EDJ shape to other pliopithecoids, particularly crouzeliids. The variation displayed by Pliobates upper molars is less marked at the EDJ level than at the outer enamel surface, probably owing to differential enamel wear and intraspecific differences in enamel thickness. Multivariate analyses of EDJ shape show that all pliopithecoids (including Pliobates) cluster together in the PCAs, canonical variate analyses, and between-group PCAs and occupy a different portion of the morphospaces from extinct and extant hominoids. Posterior and typicality probabilities strongly support the classification of Pliobates as a pliopithecoid, wheras permutation tests fail to reject the single-genus hypothesis for the P. cataloniae hypodigm. We conclude that P. cataloniae is a crouzeliid pliopithecoid, as recently supported by cladistic analyses of craniodental characters, and that previous cladistic results that supported a stem hominoid status are attributable to postcranial convergences with crown hominoids. Our results further highlight the potential of three-dimensional geometric morphometrics analyses of the EDJ shape for better informing fossil primate alpha-taxonomy by means of quantitatively testing hypotheses about tooth shape variation.

Volcanic weathered crust reservoir analog: Insights from fault-controlled fracture permeability in the trachytic rocks of the Pernambuco Basin, NE Brazil

Naturally fractured volcanic rocks represent a globally significant potential hydrocarbon reservoirs and can also be used for CO2 storage; however, the study of volcanic reservoirs in Brazil is limited. Although numerous volcanic reservoir types have been classified, relatively few studies are dedicated to the weathering of crust-like reservoirs, i.e., volcanic rocks undergoing subaerially alteration by weathering prior to deep burial. This study aims to characterize a volcanic weathered crust reservoir analog located in the coastal zone of the Pernambuco Basin, NE Brazil. We applied a multiscale approach motivated by the expressive potential of volcanic rocks as reservoirs in this marginal basin and considered their implications for CO2 geological storage projects. The deformational aspects observed in this analog have also been observed in other volcanic rocks that crop out in the coastal zone, thus, the data provided here can guide future characterization of both onshore and offshore reservoirs. We focused on an 80 m wide outcrop and employed geometric and topological analysis of two-dimensional fracture networks to investigate the influence of regional fault zone control on the fracture permeability tensors. The parameters of fracture systems were studied using terrestrial gravimetric data, orthophoto mosaic obtained by an unmanned aerial vehicle (UAV), petrography, and outcrop-based structural data. The investigated outcrop includes porphyritic trachytes with euhedral sanidine crystals and minor quartz phenocrysts, sourced from the Ipojuca Magmatic Suite. The residual Bouguer map indicates the influence of at least two regional rift fault zones, i.e., NW-SE (strike-slip) and NE-SW (normal) trending systems, in the studied rocks. These trachytic rocks exhibited a marked dissolution of sanidine phenocrysts and matrix, columnar disjunctions, and natural fractures, causing the porosity and permeability of the reservoir analog to increase. Geometric and topological analyses showed that the south-central sector of the outcrop exhibits heightened connectivity within the fracture network. Furthermore, the principal fracture permeability is controlled by the primary families of the fracture network and regional fault zones. Our results demonstrate that the fracture network observed in the volcanic reservoir analog was influenced by the post-rift tectonic reactivation of Cretaceous structures within the Pernambuco Basin. The secondary porosity resulting from weathering and subsequent dissolution of the primary constituents and fractures of the rocks studied demonstrates the potential for the exploration of these reservoirs as models for known occurrences of volcanic rocks in the onshore and offshore domains of the Pernambuco Basin.

Development of improved finite element formulations for pile group behavior analysis under cyclic loading

AbstractThe effect of cyclic loading is an essential factor leading to progressive soil strength degradation. Therefore, a comprehensive analysis of the pile‐soil system behavior under cyclic loading is required to ensure the stability of pile group. There is room for improvement in the inherent constraint of the conventional numerical model in terms of approximating the soil resistance distribution along the pile by point loads at element nodes, necessitating a specific element that integrates considerations of pile group effect and cyclic loading within a unified framework. This study aims to develop a newly specific type of element for efficiently predicting nonlinear behavior within the pile‐soil system, addressing simulations involving nonlinear pile‐soil interaction, pile group effect, and cyclic loading. Modified element formulations based on soil stiffness matrices and soil resistance vectors specifically address pile group effect and consider parameters that influence pile behavior under cyclic lateral loading. The numerical solution procedure with Newton‐Raphson iteration allows the calculation of pile responses in geometric and material nonlinear analyses. The validation of the proposed method includes several examples, comparing it with existing numerical solutions and experimental tests of single piles and pile groups under cyclic loading. These comparisons further support the consistency of the proposed method with measured data and validate its accuracy in considering group effect and cyclic loading. The parametric study illustrates the ability of the proposed method to capture cyclic loading parameters while considering the influence of the number and magnitude of load cycles, the cyclic load direction, and the installation methods.

The upper bound of the buckling stress of axially compressed carbon steel circular cylindrical shells

Abstract The buckling stress of axially compressed circular cylindrical shells (CCSs) is highly sensitive to imperfections. The literature proved that it is hard to generalize the imperfections and the designers are encouraged by the Eurocode EN 1993:1-6 (2007) to conduct geometric and material nonlinear with imperfections analysis (GMNIA) considering different possible forms of imperfections for the shell under design. As GMNIA type of analysis is difficult and requires highly skilled engineers, knowledge of the upper limit of the buckling stress serves as a guide and prevents the overestimation of the shell buckling resistance. It also encourages average skill designers to attempt GMNIA as far as the maximum possible limit is known. Thus, the objective of this study is to provide the upper bound of the buckling stress of carbon steel CCSs. Geometric and material nonlinear analysis (GMNA) of perfect circular cylindrical shells for a wide range of R/t ratio is conducted. It has been found that for cases of small and intermediate R/t values the buckling stress can be predicted by GMNA while the elastic buckling controls those of larger R/t values. The limiting R/t values depend on the steel grade and have been derived for the available standard grades of carbon steel. The obtained results are presented in terms of simplified formulas and a design chart to be used by engineers. Application of the proposed upper bound in simplified design approaches using knock down factor (KDFs) has also been discussed.

Cosmological tests of the dark energy models in Finsler-Randers space-time

The Finsler-Randers space-time offers a novel perspective on cosmic dynamics, departing from the constraints of General Relativity. This paper thoroughly investigates two dark energy models resulting from the parametrization of H within this geometric framework. We have conducted some geometrical and physical analysis of the dark energy models in Finslerian geometry. First, we have derived the field equations governing the universe's evolution within the Finsler-Randers formalism, incorporating the presence of dark energy. Through this, we explore its implications on cosmological phenomena, including cosmic expansion, late-time behavior of the universe, cosmological phase transition, and a few more. Also, we employ observational data such as Cosmic Chronometer, Supernovae, Gamma-Ray Bursts, Quasar, and baryon acoustic oscillations to constrain the parameters associated with dark energy in the Finsler-Randers universe. Comparing theoretical predictions with empirical observations, we assess the model viability and discern any deviations from the standard ΛCDM cosmology. Our findings offer intriguing insights into the nature of dark energy within this alternative gravitational framework, providing a deeper understanding of its role in shaping cosmic evolution. The implications of our results extend to fundamental cosmology, hinting at new avenues for research to unravel the mysteries surrounding dark energy and the geometric structure of the universe within non-standard gravitational theories.

Asexuality shapes traits in a hybrid fish

Animal morphology is influenced by several factors, including gonadal development and gametogenesis. Although their effects are well documented in male/female differentiation, much less is known about same-sex effects, such as those caused by their mode of reproduction. Here, using geometric morphometric analyses, we compare two groups of all-female triploid hybrid fish Chrosomus eos × eos-neogaeus, that differ only by their sexual and asexual reproductive strategies. We demonstrate that morphological differences arise from factors inherently associated with their mode of reproduction, with results replicated in two distinct lineages and in natural and common garden environments. Such differences provide additional insight about the costs and benefits of both reproductive strategies, which have mostly been of a demographic, population genetic, or genetic nature. In particular, these findings have important implications for the ecology of asexual organisms and contribute to the study of sex evolution by adding complexity to the paradox of sex theory.

Geometric analysis and design of circular form tools

Abstract Supposing serial or quantity production of cylindrical workpieces having complex geometry the application of circular form tool is applicable. This type of cutting tool has complex geometry as a consequence the geometric and the manufacturing design take a lot of time and cost but it is economical since the cutting process is quite fast. In addition, the tool usage is feasible on conventional or CNC controlled machines and the process is independent from the workers’ facility. The tool profile is the conjugated pair of the workpiece profile. This tool geometry has high resharpening area that is advantageous comparing other form tools. The goal of this study is the manufacturing analysis and the geometric design of those tools. The geometric design process will be determined detailedly in constructional and mathematical way. After them a concrete tool generation process including CAD design will be shown.

Predation scars provide a new method to distinguish native and invasive crab predation on mollusc prey.

Crab species are increasingly important socioeconomic resources that are threatened by human exploitation, climate change, and invasive species, such as European green crabs (Carcinus maenas). However, the continued health of their populations is often uncertain given the limited long-term population data, necessitating alternate approaches to ensure their continued viability. Furthermore, C. maenas are one of the most highly invasive and destructive marine species globally, posing a threat to local ecosystems and species, including socioeconomically important crabs and their mollusc prey. Improved understanding of C. maenas invasions and their impacts on local crab and mollusc resources is therefore vitally important. Here, we present a new method for identifying species-level presence and relative abundances of important crab species, including invasive C. maenas, from the scars they leave on their prey. We conducted controlled manipulative feeding experiments in which individuals of Dungeness crabs (Metacarcinus magister), red rock crabs (Cancer productus), and C. maenas, were allowed to attack snails (Tegula funebralis) and produce sublethal shell damage. Resulting shell damage was photographed and landmarked for geometric morphometric analyses to determine any differences in the shape of shell damage between crab species. There were statistically significant differences between the shape of shell damage created by all three crab species (p < .0001). Shell damage formed a gradient from narrow/deep (C. productus) to shallow/wide (C. maenas) with M. magister as an intermediate form. Our method provides a novel, cost-effective tool for long-term species-specific reconstructions of crab populations and assessing the broader ecological impacts of C. maenas invasions that can inform management and mitigation for these three important crab species.

Two methods for geometric morphometric analysis of trichodinids from killifishes.

In this study, we compared the efficacy of geometric morphometric techniques, including outlines and landmark-based approaches, to support the differentiation of Trichodina bellottii from three co-occurring killifish species. Both methods were able to differentiate trichodinids from different host species. However, discriminat analyses and MANOVA results based on landmarks had greater accuracy possibly because these analyses only provide information on certain points defined by the researcher, while the analyses based on outlines take into account points with less taxonomic information.