Geometric Criteria Research Articles

The influence of aspect ratio on the determination of tearing energy in mode I fracture tests

The energy for tearing is a classical measure of fracture toughness for elastic materials at finite strains. The prominent approach to quantify the tearing energy utilizes a tensile test on edge-cut thin rectangular specimens with low height-to-width ratio to determine the critical stretch at which a crack propagates from the tip of the cut. The analysis of the experiment, proposed by Rivlin and Thomas (1953), relies on the assumption that a large portion of the test piece is in a state of plane strain, and that the change of the total elastic energy is equal to the energy release due to the formation of new crack surfaces. While these assumptions are well justified for test pieces with sufficiently low height-to-width ratio, limitations in the availability and homogeneity of various sample materials have enforced the use of specimens with higher height-to-width ratios. In order to analyse the applicability of the classical theory and the corresponding errors, we investigate in the present work the influence of the sample’s height-to-width ratio on the estimation of the tearing energy in mode I fracture tests. Exemplified with experiments and simulations for the elastomer Ecoflex 1:1, we show that reliable measurements can be obtained even for a quadratic sample geometry. For tough materials, however, significant overestimation of the tearing energy is expected already for a height-to-width ratio larger than 1/2. Surprisingly, in very brittle materials the tearing energy is vice-versa prone to be underestimated by up to 10% for ratios up to 1. The error also depends on the non-linear stress–strain characteristics, as illustrated by the use of different constitutive models. While a generally valid geometrical criterion cannot be defined based on the present results, our results suggest that the error hardly exceeds 10% for height-to-width ratios of up to 1/2.

Does Serial Femtosecond Crystallography Depict State-Specific Catalytic Intermediates of the Oxygen-Evolving Complex?

Recent advances in serial femtosecond crystallography (SFX) of photosystem II (PSII), enabled by X-ray free electron lasers (XFEL), provided the first geometric models of distinct intermediates in the catalytic S-state cycle of the oxygen-evolving complex (OEC). These models are obtained by flash-advancing the OEC from the dark-stable state (S1) to more oxidized intermediates (S2 and S3), eventually cycling back to the most reduced S0. However, the interpretation of these models is controversial because geometric parameters within the Mn4CaO5 cluster of the OEC do not exactly match those expected from coordination chemistry for the spectroscopically verified manganese oxidation states of the distinct S-state intermediates. Here we focus on the first catalytic transition, S1 → S2, which represents a one-electron oxidation of the OEC. Combining geometric and electronic structure criteria, including a novel effective oxidation state approach, we analyze existing 1-flash (1F) SFX-XFEL crystallographic models that should depict the S2 state of the OEC. We show that the 1F/S2 equivalence is not obvious, because the Mn oxidation states and total unpaired electron counts encoded in these models are not fully consistent with those of a pure S2 state and with the nature of the S1 → S2 transition. Furthermore, the oxidation state definition in two-flashed (2F) structural models is practically impossible to elucidate. Our results advise caution in the extraction of electronic structure information solely from the literal interpretation of crystallographic models and call for re-evaluation of structural and mechanistic interpretations that presume exact correspondence of such models to specific catalytic intermediates of the OEC.

Extremal area of polygons sliding along curves

In this paper we study the area function of polygons, where the vertices are sliding along curves. We give geometric criteria for the critical points and determine also the Hesse matrix at those points. This is the starting point for a Morse-theoretic approach, which includes the relation with the topology of the configuration spaces. Moreover the condition for extremal area gives rise to a new type of billiard: the inner area billiard.

A particle finite element method based on Level–Set functions

Since the seminal work of Idelsohn, Oñate and Del-Pin (2004), the Particle Finite Element Method (PFEM) has relied on a Delaunay triangulation and the Alpha–Shape (AS) algorithm in the remeshing process. This approach guarantees a good quality of the Lagrangian mesh, but introduces a list of shortcomings that demand geometrical treatments tailored to each problem. In order to improve the remeshing process in PFEM, this work proposes the use of a Level–Set (LS) function instead of the Alpha–Shape algorithm. Since the Level–Set considers the boundary of the fluid and its interior, and not only a geometric criterion as does the Alpha–Shape, the proposed strategy (PFEM–LS) shows more robustness than the classical approach (PFEM–AS) owing to three main improvements. First, the LS function allows for a better control over the elements that are created during the fluid/fluid contact, which helps to reduce mass creation. Second, it helps to preserve the smoothness of the free surface and to reduce mass loss. Third, it allows the meshing of solitary particles that are detached from the free surface, which improves the representation of drops in PFEM. The methodology is presented and validated using free surface flow problems in 2D.

A new framework for the assessment of model probabilities of the different crystal plasticity models for lamellar grains in Titanium alloys

This paper presents a novel framework for assessing the relative accuracy of the different slip transfer criterion in modeling the constitutive response of the lamellar morphology grains in Titanium alloys. The main steps involved in the proposed framework include: (i) rigorous statistical evaluation of the salient morphological characteristics of the lamellar grains using image processing techniques, (ii) modeling the effects of dislocation slip transfer as additive penalties to the critical resolved shear strengths of the different slip systems in each phase, (iii) consideration of multiple geometric slip transfer criteria for the numerical evaluation of the different penalty terms, and (iv) the Bayesian calibration of the material parameters in the constitutive descriptions using spherical nanoindentation experimental data on a polycrystalline Ti-6Al-4V sample. Step (iv) described above involves the construction and refinement of a Gaussian process (GP) surrogate model for the indentation measurements, which is trained on crystal plasticity finite element simulations incorporating the constitutive descriptions selected in Steps (ii) and (iii). The GP surrogates are then combined with Markov Chain Monte Carlo sampling techniques to calibrate the parameters in the various constitutive models studied in this work. Additionally, we have computed the posterior model probabilities for all the constitutive models considered and identified the most plausible slip transfer criterion. This specific constitutive model is then utilized to present a homogenized crystal plasticity model for the lamellar morphology. The proposed framework presents a robust scale-bridging protocol for incorporating the uncertain information obtained from lower scales.

Synthesis, non-covalent interactions and chemical reactivity of 1-pentyl-3-phenylquinoxalin-2(1H)-one — Structural and computational studies

This contribution presents the synthesis of a new quinoxaline derivative, 1-pentyl-3-phenylquinoxalin-2(1H)-one with formula C19H20N2O, through an alkylation reaction, followed by a thorough structural characterization. X-ray crystallography revealed that π-stacking and unconventional CH…O/π hydrogen bonding play a significant role in the supramolecular solid-state framework. These interactions are further assisted by infrequent CO…π interactions and CH…HC dispersive contacts. These non-covalent interactions (NCIs) are analyzed in terms of geometrical criteria, and Hirshfeld surface analysis is used to demonstrate their individual contributions. The nature and strength of prevalent NCIs are thoroughly discussed via computational tools NCI, NBO, and QTAIM. Moreover, the application of Density Functional Theory (DFT) at the wB97X-D/cc-pVTZ level yields valuable insights into both the global and local chemical reactivity of studied compound, thereby enhancing our understanding of the chemistry involved in the synthesis of quinoxaline and its derivatives.

Hydrogen bonded configurations in liquid water and their correlations with local tetrahedral structures

Hydrogen-bonded structures in liquid water lies at the root of its many anomalous properties. The ability of water to form hydrogen bonds is perceived to be the reason for the formation of locally favored tetrahedral structures (LFTS) in liquid water. These tetrahedral environments also lay the foundation for the two-state theories of water. In molecular dynamics simulations, hydrogen bonds are often assigned between molecules if they satisfy certain geometric or energetic criteria, or a combination of both. Potential of Mean Force landscapes may be used to identify the geometric criteria for identifying hydrogen bonds, and distinguishing ‘ice-like’ hydrogen bonds. In this work, we report the statistical information of hydrogen-bonded structures in liquid water from molecular simulations of the iAMOEBA water model. The fraction of different hydrogen-bonded structures is also compared with the fraction of LFTS molecules to gain insights into the hydrogen-bonded configuration of LFTS molecules. The structure of different hydrogen-bonded configurations, using various structural descriptors is also reported. We find that tetrahedral environments in liquid water (as modeled by the iAMOEBA force-field) are largely, but not exclusively constituted by the molecules that donate and accept two hydrogens each when ‘ice-like’ hydrogen bonds are considered.

On the Construction of Mathematical Models of the Membrane Theory of Convex Shells

Introduction. The paper considers the issues of constructing mathematical models of the momentless equilibrium stress state of elastic convex shells using methods of the complex analysis. At the same time, shells with a piecewise smooth (ribbed) lateral surface were considered for the first time. The work objective was to find classes of shells for which it is possible to build meaningful mathematical models.Materials and Methods. Using the methods of the theory of the discontinuous Riemann-Hilbert problem for generalized analytic functions, a criterion for the unconditional solvability of the corresponding static problem for the equilibrium equation of a convex shell with a ribbed lateral surface has been obtained. This criterion, combined with the methods of the theory of generalized analytical functions, is a tool for constructing mathematical models of the state of momentless stress equilibrium of elastic convex shells.Results. A method has been developed for constructing mathematical models of the momentless equilibrium stress state of a convex shell under the action of a variable external load and the condition of stress concentration at the corner points of the median surface. The introduction of a vector parameter, as well as the concepts of “order of quasi-correctness” and “quasi-stability”, into the boundary condition provided both quantitative and qualitative comparison of mathematical models. Classes of shells have been found for which the description of mathematical models is given in terms of the geometry of the boundary in the vicinity of the corner points of the median surface. The obtained result, when applied to shallow convex shells, provides a geometric criterion of quasi-stability. It is established that for a shallow shell, which is not quasi-stable, the only adequate mathematical model is a probabilistic one.Discussion and Conclusions. The proposed method for constructing a two-parameter family of problems with a modified boundary condition makes it possible to simulate the momentless equilibrium stress state for fairly wide classes of convex shells with a piecewise-smooth lateral surface under a sleeve connection. At the same time, the developed algorithm for calculating the boundary condition index allowed us to answer the question of the existence of an adequate mathematical model for a shell with a side surface of an arbitrary configuration, and for shells of a special type (specifically, shallow or shells of revolution), to formulate a geometric criterion for the existence of a mathematical model.

Shaking table test of multiple-type isolation control strategies for high-rise structure based on friction pendulum

Given the difficulties associated with deploying isolation technique in high-rise structures, this article conducts a comprehensive comparison of three operating systems: friction pendulum system (FPS) base isolation form: FPS-B, FPS inter-story isolation form: FPS-I, and FPS hybrid isolation form: FPS-H. A 9-layer scaled test model is constructed by using third generation benchmark model, and the accompanying FPS model is created and fabricated using the geometric similarity criterion. Considering four typical ground motions and four peak ground acceleration (PGA), the structural seismic responses of the three control systems were analyzed. The result demonstrates that FPS-H technology greatly decreases the superstructure’ top floor acceleration and even the substructure's acceleration impact in both mild and major earthquakes. The working mechanism of FPS-H technology in terms of vibration reduction is similar to the conjunction of tuned mass damper (TMD) and FPS-B structure. The inertia force of superstructure suppresses the substructure since superstructure has FPS inter-story isolation form, and even the substructure is an FPS-B form that can extend the structural period and segregate earthquake energy. The FPS-H technology, which reduces the acceleration response of the structure's 1st -order mode and restrains the dynamic reaction of the high-order mode by changes the dynamic characteristics of whole structure, is primarily responsible for the long-period structure's effective damping.

The Impact of Fatty Infiltration on MRI Segmentation of Lower Limb Muscles in Neuromuscular Diseases: A Comparative Study of Deep Learning Approaches.

Deep learning methods have been shown to be useful for segmentation of lower limb muscle MRIs of healthy subjects but, have not been sufficiently evaluated on neuromuscular disease (NDM) patients. Evaluate the influence of fat infiltration on convolutional neural network (CNN) segmentation of MRIs from NMD patients. Retrospective study. Data were collected from a hospital database of 67 patients with NMDs and 14 controls (age: 53 ± 17 years, sex: 48 M, 33 F). Ten individual muscles were segmented from the thigh and six from the calf (20 slices, 200 cm section). A 1.5 T. Sequences: 2D T1 -weighted fast spin echo. Fat fraction (FF): three-point Dixon 3D GRE, magnetization transfer ratio (MTR): 3D MT-prepared GRE, T2: 2D multispin-echo sequence. U-Net 2D, U-Net 3D, TransUNet, and HRNet were trained to segment thigh and leg muscles (101/11 and 95/11 training/validation images, 10-fold cross-validation). Automatic and manual segmentations were compared based on geometric criteria (Dice coefficient [DSC], outlier rate, absence rate) and reliability of measured MRI quantities (FF, MTR, T2, volume). Bland-Altman plots were chosen to describe agreement between manual vs. automatic estimated FF, MTR, T2 and volume. Comparisons were made between muscle populations with an FF greater than 20% (G20+) and lower than 20% (G20-). The CNNs achieved equivalent results, yet only HRNet recognized every muscle in the database, with a DSC of 0.91 ± 0.08, and measurement biases reaching -0.32% ± 0.92% for FF, 0.19 ± 0.77 for MTR, -0.55 ± 1.95 msec for T2, and - 0.38 ± 3.67 cm3 for volume. The performances of HRNet, between G20- and G20+ decreased significantly. HRNet was the most appropriate network, as it did not omit any muscle. The accuracy obtained shows that CNNs could provide fully automated methods for studying NMDs. However, the accuracy of the methods may be degraded on the most infiltrated muscles (>20%). 4. Stage 1.

Phosphole aromaticity enhancement by electron pumping through Schleyer hyperconjugative aromaticity: A comprehensive DFT study

Combination of aromaticity and hyperconjugation as two fundamental concepts in organic chemistry results hyperconjugative aromaticity. Due to trigonal pyramidal P (III) atom in phosphole ring, it is only slightly more aromatic than cyclopentadiene. In the present work, the hyperconjugative aromaticity of phosphole derivatives, bearing an electron donating group, have been studied at the DFT-B3LYP/6–311++G(d, p) level of theory using various aromaticity indices such as geometric, magnetic, electronic and energetic criteria. Our DFT calculations reveal that an electropositive substituent can enhance phosphole aromaticity through Schleyer hyperconjugative aromaticity. This hyperconjugative electron donation by the substituents results in a partially anionic phosphole ring. Among the electropositive groups, silyl and germanium substituents have the best performance. The excellent correlations are observed between all aromaticity indices. Our findings could help chemists to design novel hyperconjugative aromatic phospholes.

Holographic Characterisation of Locally Anti-de Sitter Spacetimes

It is shown that an (n+1)-dimensional asymptotically anti-de Sitter solution of the Einstein-vacuum equations is locally isometric to pure anti-de Sitter spacetime near a region of the conformal boundary if and only if the boundary metric is conformally flat and (for n ne 4) the boundary stress–energy tensor vanishes, subject to (i) sufficient (finite) regularity in the metric and (ii) the satisfaction of a conformally invariant geometric criterion on the boundary region. A key tool in the proof is the Carleman estimate of Chatzikaleas and Shao (Commun Math Phys, 2022)—a generalisation of previous work by the author with McGill and Shao in (Class Quant Gravity 38(5), 2020)—which is applied to prove a unique continuation result for the Weyl curvature at the conformal boundary given vanishing to sufficiently high order over the boundary region.

Vizaj-A free online interactive software for visualizing spatial networks.

In many fields of science and technology we are confronted with complex networks. Making sense of these networks often require the ability to visualize and explore their intermingled structure consisting of nodes and links. To facilitate the identification of significant connectivity patterns, many methods have been developed based on the rearrangement of the nodes so as to avoid link criss-cross. However, real networks are often embedded in a geometrical space and the nodes code for an intrinsic physical feature of the system that one might want to preserve. For these spatial networks, it is therefore crucial to find alternative strategies operating on the links and not on the nodes. Here, we introduce Vizaj a javascript web application to render spatial networks based on optimized geometrical criteria that reshape the link profiles. While optimized for 3D networks, Vizaj can also be used for 2D networks and offers the possibility to interactively customize the visualization via several controlling parameters, including network filtering and the effect of internode distance on the link trajectories. Vizaj is further equipped with additional options allowing to improve the final aesthetics, such as the color/size of both nodes and links, zooming/rotating/translating, and superimposing external objects. Vizaj is an open-source software which can be freely downloaded and updated via a github repository. Here, we provide a detailed description of its main features and algorithms together with a guide on how to use it. Finally, we validate its potential on several synthetic and real spatial networks from infrastructural to biological systems. We hope that Vizaj will help scientists and practitioners to make sense of complex networks and provide aesthetic while informative visualizations.

Enhanced plasticity due to melt pool flow induced uniform dispersion of reinforcing particles in additively manufactured metallic composites

Additive manufacturing has gained increasing interest to fabricate metal matrix composites. Particle agglomeration remains a critical challenge and can severely compromise the mechanical properties, in particular tensile ductility. Here we investigated and utilized laser powder-bed-fusion (L-PBF) to uniformly disperse particles in metal matrices, taking advantages of particle flow dynamics during melting and remelting. We demonstrate our approach in a TiB2 reinforced aluminum system and produce a high dispersion of fine TiB2 particles (with sizes down to tens of nanometers) in a single print. Both micron- (1-5 μm) and nano-sized (40 nm) TiB2 particles are found to be uniformly dispersed in composites, with a volume fraction of up to 25%. High-fidelity computer modeling indicates that although particles flow with Marangoni vortexes, the melt pool overlapping and subsequent re-melting/re-solidification play an important role for the successful dispersion. The propelling effect of vapor depression and particle filling via the Marangoni vortex flow are the two main mechanisms that lead to the uniform dispersion. A geometric criterion for hatch spacing is derived and verified by experiments for the successful uniform dispersion of reinforcing particles. Compared to composites with nonuniform particle dispersion, L-PBF aluminum 2024 composites show ∼30% higher tensile strength and ∼16% higher Young's modulus, together with a marked improvement of tensile ductility (up to three times higher). The uniform dispersion of reinforcing particles is also achieved in copper materials and thus demonstrates the versatility of our approach to other metals and alloys.

Semantic Segmentation of Mesoscale Eddies in the Arabian Sea: A Deep Learning Approach

Detecting mesoscale ocean eddies provides a better understanding of the oceanic processes that govern the transport of salt, heat, and carbon. Established eddy detection techniques rely on physical or geometric criteria, and they notoriously fail to predict eddies that are neither circular nor elliptical in shape. Recently, deep learning techniques have been applied for semantic segmentation of mesoscale eddies, relying on the outputs of traditional eddy detection algorithms to supervise the training of the neural network. However, this approach limits the network’s predictions because the available annotations are either circular or elliptical. Moreover, current approaches depend on the sea-surface height, temperature, or currents as inputs to the network, and these data may not provide all the information necessary to accurately segment eddies. In the present work, we have trained a neural network for the semantic segmentation of eddies using human-based—and expert-validated—annotations of eddies in the Arabian Sea. Training with human-annotated datasets enables the network predictions to include more complex geometries, which occur commonly in the real ocean. We then examine the impact of different combinations of input surface variables on the segmentation performance of the network. The results indicate that providing additional surface variables as inputs to the network improves the accuracy of the predictions by approximately 5%. We have further fine-tuned another pre-trained neural network to segment eddies and achieved a reduced overall training time and higher accuracy compared to the results from a network trained from scratch.

Topological quantum criticality of the disordered Chern insulator

We consider the two-dimensional topological Chern insulator in the presence of static disorder. Generic quantum states in this system are Anderson localized. However, topology requires the presence of a subset of critical states, with diverging localization length (the Chern insulator analog of the ‘center of the Landau band states’ of the quantum Hall insulator.) We discuss geometric criteria for the identification of these states at weak disorder, and their extension into the regime of strong disorder by analytical methods. In this way, we chart a critical surface embedded in a phase space spanned by energy, topological control parameter, and disorder strength. Our analytical predictions are supplemented by a numerical analysis of the position of the critical states, and their multifractal properties.

A criterion of proper action on some compact extensions of ℝn and applications

Let K be a compact subgroup of [Formula: see text] and [Formula: see text] the semi-direct product group. Let H be a closed subgroup of G and [Formula: see text] a discontinuous group for the homogeneous space [Formula: see text]. We establish a geometrical criterion of the proper action of [Formula: see text] on [Formula: see text], which requires an accurate description of the structure of closed connected subgroups of Euclidean motion groups. As a consequence, we establish a criterion for the existence of a compact Clifford–Klein form [Formula: see text] and study the Calabi–Markus phenomenon.

Experimental study of strong imbibition in microcapillaries representing pore/throat characteristics of tight rocks

Imbibition pervasively exists in many industrial processes and is fundamental in developing unconventional resources in tight formations. Micromodels have been widely used as powerful tools for real-time observations of imbibition dynamics to support numerical modeling developments and understanding of macroscopic patterns. However, the inherent limitation of 2D micromodels in presenting 3D features in the pores/throats of tight rocks may reduce the reliability of the microfluidic results. Here, we quantitively investigate imbibition dynamics in single pore geometries that consider 2D pore-scale characteristics of tight rocks with an etching depth higher than the critical geometric criteria for including 3D features. We discuss the experimental data based on varying parameters, such as five pore shapes, a wide range of pore-throat aspect ratios (6.25 to 100), two typical throat widths (3 and 8 μm), and local capillary numbers (10-6 to 10-4). The results show that the wetting phase saturations increase linearly with the increasing inlet flow rate, consistent with previous findings in cores and 2.5D micromodels, but only in macropores. Snap-offs are found when the moved meniscus front pressure is higher than the critical capillary pressure of snap-off. An etching depth higher than the critical geometric criteria is necessary but insufficient to mimic imbibition dynamics in tight rocks by 2D micromodels with a pattern that the most pore-throat aspect ratios are less than 30 at a strong imbibition condition.

Synthetic CT in Carbon Ion Radiotherapy of the Abdominal Site.

The generation of synthetic CT for carbon ion radiotherapy (CIRT) applications is challenging, since high accuracy is required in treatment planning and delivery, especially in an anatomical site as complex as the abdomen. Thirty-nine abdominal MRI-CT volume pairs were collected and a three-channel cGAN (accounting for air, bones, soft tissues) was used to generate sCTs. The network was tested on five held-out MRI volumes for two scenarios: (i) a CT-based segmentation of the MRI channels, to assess the quality of sCTs and (ii) an MRI manual segmentation, to simulate an MRI-only treatment scenario. The sCTs were evaluated by means of similarity metrics (e.g., mean absolute error, MAE) and geometrical criteria (e.g., dice coefficient). Recalculated CIRT plans were evaluated through dose volume histogram, gamma analysis and range shift analysis. The CT-based test set presented optimal MAE on bones (86.03 ± 10.76 HU), soft tissues (55.39 ± 3.41 HU) and air (54.42 ± 11.48 HU). Higher values were obtained from the MRI-only test set (MAEBONE = 154.87 ± 22.90 HU). The global gamma pass rate reached 94.88 ± 4.9% with 3%/3 mm, while the range shift reached a median (IQR) of 0.98 (3.64) mm. The three-channel cGAN can generate acceptable abdominal sCTs and allow for CIRT dose recalculations comparable to the clinical plans.

Contribution to Railway Track Maintenance Planning from the Analysis of Dynamic Movements of Trains

Dynamic movements of trains in relation to the track have a significant impact on the displacement stability of rail vehicles, having effects inclusive of operational safety. Although there are numerous approaches to track maintenance planning, most of them are based solely on long-term geometric degradation assessments without taking into account any dynamic parameters in assessing operational safety or establishing means to predict future rolling stock accelerations relative to the track in order to develop safer maintenance plans. This paper introduces a method of track maintenance planning based on geometric degradation modeling and prediction of rolling stock vertical and horizontal acceleration. The goal is to establish how frequent geometric maintenance is necessary to ensure operational safety under geometric and dynamic criteria. This approach is based on regression models defined from geometric and dynamic inspection data. The method was applied in a passenger railway and obtained expressive results that corroborated the need of considering dynamic aspects on maintenance planning, as sections of the analyzed railway were identified with operation becoming unsafe, under the dynamic criterion, before the geometric safety tolerances are reached. This work is intended not only to propose a planning method but also to present to the scientific and technical communities a novel approach to be explored and developed in future research. The obtained results, therefore, do more than confirm quantitatively the relevance of this analysis; they also demonstrate qualitatively how promising the development of this thematic field is. In this regard, this work also presents in its conclusions some research opportunities to be explored for the development of this theme. Doi: 10.28991/CEJ-2023-09-02-02 Full Text: PDF