Search Results (418)

We develop the geometry of events in a deformable cellular spacetime, extending our earlier cellular-spaces framework from cellular complexes to cellular events complexes. The framework operates within the conformal class of Minkowski space; in four dimensions, this is the vanishing-Weyl-tensor sector, which excludes Schwarzschild, Kerr, and gravitational-wave spacetimes. The framework treats integer counts of cell crossings as the primitive geometric data: spatial separation between events is the shortest count of face-adjacent cells; temporal separation is the cell-crossing count of a reference light pulse. Newton’s universal clock is replaced by an operational one: the temporal count distance is the ratio of cell length to the speed of light through a cell, and because both quantities are invariants of the co-deformation, the temporal count is itself an invariant: temporal separation is operationally measured via light-pulse counts rather than posited as an external coordinate. Under the co-deformation principle, a single positive scalar field $\rho$ (cell density) controls both the rod length and the clock period. We prove six results, all expressed in terms of counts on the cellular events complex, with a smooth conformally flat metric $\tilde{g}=e^{2\phi }\eta$ ($\phi =-\frac{1}{3}ln\rho$) appearing only as the comparison/calibration object for convergence statements. First, the scalar curvature of the smooth comparison metric is the closed-form differential operator $\tilde{R}=2\square \rho /{\rho }^{1/3}-(8/3){(\partial \rho )}^2/{\rho }^{4/3}$. Second, the volume of a small Alexandrov interval admits an explicit asymptotic expansion in the interval height T, with leading correction $Q(m,u)T^2$ involving an anisotropic invariant at the midpoint m. Third, Q is irreducible to scalar and Ricci-directional invariants alone; the explicit decomposition $Q=\frac{1}{45}\tilde{R}+\frac{1}{5}{\tilde{R}}_{uu}+\frac{1}{2}\mathcal{J}$ exhibits a third independent invariant $\mathcal{J}(m,u)={(u·\partial )}^2\phi \left(m\right)$ as new structural content of the Lorentzian diagnostic. Fourth, the discrete-to-continuum convergence of counts on the cellular events complex yields a counts-only curvature estimator with rate $O\left(\sqrt{a}\right)$ at the joint scaling $T\asymp \sqrt{a}$. Fifth, the smooth comparison metric itself is reconstructible from counts on the discrete complex at rate $O\left(a\right)$: the conformally flat Lorentzian geometry is uniquely determined, up to background Minkowski calibration, by the cellular events complex. Sixth, a finite collection of Alexandrov-interval volume measurements at a fixed midpoint suffices to recover the full local curvature data $\{\tilde{R}\left(m\right),{\tilde{R}}_{\mu \nu }\left(m\right),\mathcal{J}(m,u)\}$ at rate $O\left(\sqrt{a}\right)$ (curvature spectroscopy); and the temporal light-tick count $\lambda$ is essential in a precise sense—there exist conformally flat Lorentzian geometries indistinguishable on every spatial slice by the earlier spatial-only diagnostic but distinguished at the origin by the events-space directional invariant. The framework’s scope is the conformal class of Minkowski: flat FLRW in conformal time, leading-order weak-field gravity, and 2D gravity. This paper is a mathematical contribution to discrete-to-continuum geometry on cellular events complexes; it is not a physical theory of gravity. Full article

High-entropy transition-metal diborides represent a promising class of ultra-high temperature ceramics. However, atomic insights into their high-temperature elastic response, anisotropic deformation, and fracture mechanisms remain elusive. Herein, we perform molecular dynamic simulations to study the thermomechanical behaviors of (Hf_0.2Zr_0.2Ta_0.2Ti_0.2Nb_0.2)B₂ from 900 to 3300 K by developing an ab initio accuracy deep-learning potential. The proposed potential accurately reproduces lattice parameters, equations of state, and elastic constants, in excellent agreement with density functional theory calculations and available experiments, and remains transferable under thermally expanded and compressed states. The simulations reveal anisotropic thermal expansion, with the out-of-plane expansion exceeding the in-plane expansion, together with progressive elastic softening while preserving C₁₁ > C₃₃ due to the dominant in-plane B-B bonding network. Furthermore, strain-rate- and temperature-dependent tensile and compressive responses show marked crystallographic anisotropy, tension–compression asymmetry, and severe thermomechanical degradation. Atomic structural evolution demonstrates that tensile fracture is dominated by bond stretching and progressive damage accumulation, whereas compressive failure is attributed to densification- and shear-mediated structural instability. These findings provide an atomistic understanding of the thermomechanical behavior and fracture mechanisms of the prototypical single-phase (Hf_0.2Zr_0.2Ta_0.2Ti_0.2Nb_0.2)B₂ high-entropy diboride, offering valuable insights into the design of ultra-high temperature ceramics under extreme service environments. Full article

Graphite foil is widely used as a sealing material in flange joints in the form of gaskets or gasket components. Predicting gasket permeability during stress relaxation remains challenging because both the compression state and the gas pressure affect leakage. No unified semi-empirical model based on the Darcy–Klinkenberg framework with compression pressure as a direct input has been available for use in flange-joint numerical simulations. Graphite foil gaskets with a density of about 1.0 g/cm³ and a thickness of ~1.5 mm were tested under compression pressures from 5 to 100 MPa. Helium leakage was measured at helium pressures from 0.5 to 8 MPa. Leakage and deformation during loading and unloading were recorded using EN 13555-based procedures. The results were analyzed using a Darcy–Klinkenberg formulation and equivalent slit- and capillary-based representations of the leakage channels. The second-order model reproduced the pressure-dependent leakage more accurately than the first-order Darcy approximation (R² ≥ 0.9985 vs. 0.916–0.992), particularly where slip-flow effects were significant. Exponential dependences of the intrinsic permeability and the Klinkenberg coefficient on deformation and power-law relations with compression pressure are proposed to model leakage during unloading. The proposed semi-empirical model allows estimation of graphite-foil permeability under stress relaxation with the use of EN 13555 test procedures and its subsequent implementation in numerical simulations of flange joints. Limits of the model’s applicability, including loading regime, ranges of compression pressure, gas pressure and anisotropic nature of permeability, are discussed. Full article

To address the challenge of high false alarm rates caused by dynamic viewpoint noise in mobile chemical inspections, this study established a highly robust adaptive dynamic risk inference model. This research proposes an inference framework integrating spatio-temporal semantic constraints. Spatially, this study constructed a heterogeneous dynamic scene graph and introduced a kinematic-aware anisotropic dynamic field. This field transforms geometric hard boundaries into continuous risk gradients that deform dynamically with target intentions to suppress observation ambiguity. Temporally, the work designed an uncertainty-aware adaptive hysteresis filter, whose state machine thresholds adjust dynamically according to real-time sensor noise levels. Comparative tests on a real-world chemical dataset show that the model achieves a peak F1-Score of 93.1%, reduces the false alarm rate to 1.3 times/h, and requires a single-frame processing time of only 24.8 ms. The method theoretically achieves spatio-temporal dynamic noise reduction, significantly mitigates topological mutations and alarm chattering under complex visual noise conditions, meets edge computing deployment requirements, and provides a high-confidence sensing decision hub for industrial process safety monitoring. Full article

Heterogeneous hydrogels capable of complex, programmable deformation are highly desirable for soft actuators, yet general strategies that simultaneously impart structural anisotropy, rapid responsiveness, and mechanical robustness remain limited. Here, a gradient anisotropic natural rubber-poly(N-isopropylacrylamide) (NR-PNIPAM) composite hydrogel is developed through a simple one-pot polymerization strategy by coupling pH-regulated colloidal stability with gravity-directed redistribution of natural rubber latex particles. Under an optimized pH window, NR nanoparticles gradually migrate during gelation and are fixed as a continuous gradient within the PNIPAM network, generating built-in structural asymmetry for nonuniform deformation. Meanwhile, NR nanoparticles act as soft reinforcing domains to improve mechanical strength, while water-soluble graphene nanosheets provide efficient photothermal conversion for remotely-controlled near-infrared (NIR)-responsive actuation. Benefiting from this synergistic design, the hydrogel exhibits programmable bending and localized folding with high actuation rates of 129° s⁻¹ and 46° s⁻¹, respectively, along with a tensile strength of 0.32 MPa and an active lifting capability exceeding 70 times its own weight. The material further enables biomimetic gripping and lifting under NIR stimulation. This work establishes a general route to robust gradient hydrogels by integrating colloidal regulation, structural anisotropy, and photothermal actuation, offering a versatile platform for high-performance soft intelligent systems. Full article

Q420 high-strength steel exhibits pronounced anisotropy due to its rolling process, and conventional uniaxial tensile testing is incapable of acquiring strain field evolution information during the local necking stage. In this study, quasi-static uniaxial tensile tests were conducted on Q420 cold-rolled high-strength steel sheets at six orientations (0°, 15°, 30°, 45°, 60°, and 90°) using Digital Image Correlation (DIC) technology. The evolution of the strain field and the corresponding stress–strain responses at different orientations were systematically investigated. The results show that the DIC technique effectively captured the full-field strain evolution of the specimens from uniform deformation to local necking and final fracture in all directions. Taking the 0° direction as an example, the local maximum engineering strain prior to fracture reached 35.866%, whereas the average fracture strain within the gauge section was only approximately 22.5%, corresponding to a ratio of approximately 1.6 and clearly demonstrating the severe strain concentration within the necking zone. The stress–strain curves corresponding to different rolling directions exhibited pronounced anisotropy. The tensile strength was highest in the 90° direction and lowest in the 0° direction; however, the 0° direction exhibited the best ductility, whereas the 45° direction showed the poorest ductility. Among the six orientations, the midpoint transverse engineering strain exhibited the largest absolute value in the 45° direction, further indicating that this orientation is the most susceptible to plastic instability. In this work, DIC-based full-field measurement was combined with multi-directional tensile testing to quantitatively characterize the relationship between local strain concentration and anisotropy. The findings provide high-precision experimental data for the calibration of anisotropic constitutive models and the optimization of forming processes. Full article

This paper develops a unified superelliptic quaternionic framework for the generation and differential geometric analysis of curves and surfaces in affine three-space. Classical quaternionic methods provide an effective algebraic representation of rotations; however, they do not directly incorporate the radial deformation and anisotropic geometric behavior arising from superelliptic structures. To overcome this limitation, we combine quaternion multiplication with the superelliptic metric induced by the Gielis superformula and introduce a systematic construction of space curves and surfaces through superelliptic quaternion-valued functions. The proposed approach represents direction and radius curves as superelliptic quaternions and generates geometric objects by quaternionic rotation followed by projective normalization. This construction extends classical quaternion-based curve and surface generation by allowing rotational motion and superelliptic deformation to be handled within the same algebraic setting. Beyond geometric construction, the framework also provides explicit tools for differential geometric analysis. In particular, we derive the superelliptic Frenet frame associated with a curve and obtain formulations for curvature and torsion in terms of superelliptic quaternion functions. The theory is further extended to parametrized surfaces, where Gaussian curvature and mean curvature are expressed through the corresponding superelliptic quaternionic representation. The results demonstrate that superelliptic quaternions offer a flexible and mathematically coherent structure for linking rotation, deformation, geometric generation, and invariant computation. Therefore, the proposed framework contributes to differential geometry and geometric modeling by providing a unified method for constructing and analyzing a broad class of superelliptic curves and surfaces. Full article

The permeability of coal seams plays a critical role in the efficiency of coalbed methane extraction and gas disaster prevention. Traditional permeability models often overlook the anisotropic and dynamic evolution characteristics of coal under varying stress and gas adsorption conditions. This paper proposes a novel permeability evolution model that integrates the effects of effective stress variation and gas sorption-induced deformation on coal permeability. Starting from the concept of face porosity and utilizing a representative voxel approach, the model incorporates the anisotropy of mechanical parameters and adsorption expansion strain to derive the evolution of permeability in three dimensions. The model is validated against experimental permeability data from two distinct coal samples (Sulcis and Sydney), demonstrating its ability to accurately capture permeability changes under different boundary conditions. Furthermore, the concept of “internal expansion strain coefficient” is introduced to quantify the impact of adsorption-induced matrix deformation on permeability. The model provides a theoretical foundation for predicting gas flow behavior in coal seams under complex in-situ conditions and offers significant insights into the optimization of gas extraction strategies. Full article

Rockfall from slope unstable rock masses is a typical geological hazard induced by brittle failure, with abrupt occurrence, limited macroscopic deformation before failure, and a short warning lead time. Conventional static analysis methods are useful for design-stage stability checks, but they cannot continuously capture structural-plane damage or update the stability state in real time. Dynamic evaluation based on structural dynamics links measurable parameters such as natural frequency, damping ratio, mode shape, vibration trajectory, wave velocity, and energy dissipation to the degradation of structural planes. This review synthesizes the dynamic behavior mechanism, parameter system, theoretical models, sensing technologies, and engineering applications for slope unstable rock masses. Different from previous reviews that mainly summarize rockfall monitoring or conventional slope stability analysis, this paper organizes the literature by failure mode, monitoring scale, model assumptions, field validation, uncertainty sources, and engineering applicability. The single-degree-of-freedom models for sliding-, toppling-, and falling-type rock masses, multi-block chain-collapse models, and data-physics dual-driven surrogate models are compared critically. Contact monitoring based on MEMS sensors, non-contact LDV monitoring, acoustic emission, microseismic monitoring, coda wave interferometry, and cloud-edge early-warning architectures are further reviewed. Key challenges include field-scale validation under heterogeneous and anisotropic geological conditions, environmental compensation, robust threshold calibration, and probabilistic linkage between dynamic indicators and failure probability. The review provides guidance for selecting dynamic evaluation models, designing field monitoring systems, and developing full-life-cycle digital-twin platforms for rockfall risk mitigation. Full article

The minimal geometric deformation method is applied on Einstein–Maxwell field equations in this study to obtain two novel exact anisotropic solutions for polytropic configurations. A static spherically symmetric seed structure penetrated by the anisotropic fluid distribution is taken into consideration in order to accomplish this goal. The gravitational interaction of the new Lagrangian density is then coupled with the initial fluid configuration, representing an additional matter source. We obtain the field equations that correspond to the associated charged fluid sources. Two separate decoupled systems are developed when the field equations are subjected to a radial transformation. By applying the distinct constraints, each system’s solution is determined individually. The entire fluid configuration is then generated by combining these solutions via a certain linear combination. The constraints needed to determine the integration constants in the internal solutions are provided by junction conditions at the interface between the interior and exterior geometry. The suggested models are then verified by comparing them graphically under the observational data from the $CenX-3$ candidate star. In conclusion, for certain values of the decoupling parameter, our derived relativistic solutions satisfy established physical acceptability requirements. Full article

Liquid crystal physical gels (LCPGs) combine the anisotropic properties of liquid crystals with the structural stability of soft solids. In this work, MBBA-based LCPGs were prepared using chiral oxalamide gelators 1,6-bis((O-leucylmethanol)-N-yloxalamido)hexane (6-O-Me) and 1,9-bis((O-leucylmethanol)-N-yloxalamido)nonane (9-O-Me) and thoroughly characterized for their thermal, rheological, and electrorheological behaviours. Techniques included differential scanning calorimetry, oscillatory rheology, electrorheological testing, and advanced microscopy analysis. A custom microfluidic device was developed for in situ application of an electric field and optical assessment of its influence on microstructure formation. Both gels exhibited distinct gel-like behavior, with storage moduli consistently exceeding loss moduli and sustained network stability under both short- and long-term deformations. The gelators had minimal effect on the isotropic–nematic transition of MBBA but efficiently delayed crystallization, extending the stability window by −8 °C for 9-O-Me and −14 °C for 6-O-Me. When subjected to electric fields, the gel network weakened in the nematic phase, and the fiber assembly during cooling was altered, resulting in the formation of thicker, anisotropic fibers, consistent with microscopic observations. These results illustrate how the properties of LCPGs can be tuned through molecular design and external stimuli, expanding their potential for stimuli-responsive soft matter applications. Full article

This study evaluates the mechanical behavior of bone-implant assemblies used in treating complex proximal humerus fractures, a clinical challenge due to the anisotropic nature of bone and variability in patient-specific conditions. The aim of this study was to compare the stability and stress distribution of three fixation methods: polyaxial locking plates, monoaxial locking plates, and intramedullary nails. Using 4th-generation composite humerus models, a four-part fracture (Neer IV) was simulated. The assemblies underwent axial compression testing using a universal testing machine, complemented by finite element analysis (FEA) and stereomicroscopy. The results indicate that while both plate types exhibited similar mechanical behavior—with stiffness values around 113–115 N/mm and failure initiated by plastic deformation of the implant—the intramedullary nail configuration demonstrated higher stiffness values under the tested experimental conditions (1084 N/mm), approximately 9.5 times higher than that of the plates. However, the nail assembly failed through brittle fracture of the bone rather than implant deformation. We conclude that while the intramedullary nail configuration demonstrated higher stiffness under the tested experimental conditions, its performance is heavily dependent on bone quality. In contrast, locking plates may provide a more gradual load-transfer behavior by transferring a greater proportion of the mechanical load to the implant, potentially making them more suitable for osteoporotic bone conditions, where reducing excessive stress concentration within the bone tissue may be beneficial. Full article

Real-time kinematic (RTK) positioning in open-pit mining environments is critically compromised by non-line-of-sight (NLOS) signals and anisotropic multipath effects induced by pit walls, haul roads, and industrial infrastructure. Conventional elevation-dependent stochastic models fail to discriminate between geometrically favorable low-elevation satellites and those subject to directional obstruction, resulting in degraded ambiguity resolution and decimeter-level positioning errors that undermine safety-critical deformation monitoring. This paper presents an adaptive RTK positioning framework utilizing azimuth-integer-based elevation masking to explicitly model site-specific obstruction geometry. The proposed method discretizes the horizontal plane into 360 integer-degree sectors, extracts minimum elevation angles per sector from 24 h line-of-sight (LOS) data, and constructs a smoothed 360°mask profile via moving-window filtering. A virtual elevation-angle transformation is introduced to normalize satellite geometry relative to the local mask, enabling adaptive down-weighting of diffraction-susceptible observations within the stochastic model without requiring multi-day satellite repeat arcs or hardware modifications. The approach was validated using 54 h of BDS data collected at eight monitoring stations within the Wangjialing open-pit mine, China. Implementation of the mask model engendered a selective 8.1% reduction in satellite participation (15.66 to 14.39 satellites) while significantly enhancing observation quality. The ambiguity validation ratio improved by 19.5% (from 9.43 to 11.27 in the experimental project), and the fix success rate increased from 92.4% to 97.2% (exceeding the 95% reliability threshold at all stations). The RMS errors in the east, north, and up directions improved by 34.8% to 65.2%, 28.7% to 77.0%, and 44.8% to 70.8%, respectively, with the most dramatic gains observed at stations subject to severe azimuthal obstruction (e.g., ZDH6 vertical RMS: from 50.7 mm to 14.8 mm). By explicitly modeling anisotropic obstruction geometry through discrete angular sampling, the proposed method achieves sub-centimeter positioning accuracy and robust ambiguity resolution in challenging mining environments without additional hardware or empirical threshold tuning, offering a cost-effective solution for large-scale, real-time deformation monitoring systems. Full article

Acoustoelasticity provides the physical sensing principle for ultrasonic stress measurement. However, most existing formulations are restricted to isotropic media, simple stress conditions, and Cartesian coordinate systems, which limits their applicability in practical sensing scenarios involving curved and anisotropic structures. In this work, a general tensorial formulation of acoustoelasticity is developed based on the theory of incremental deformation. The proposed governing equations describe the motion of incremental displacement with explicit dependence on initial stress or strain, and are applicable to materials with arbitrary symmetry and general initial stress states. Owing to its coordinate-independent tensorial nature, the formulation can be expressed in any curvilinear coordinate system. To facilitate practical ultrasonic sensing applications, the general equations are further expanded in a cylindrical coordinate system for orthotropic materials. This enables the analysis of elastic wave propagation in curved structures such as pipelines, pressure vessels, and boreholes. The formulation establishes a direct relationship between initial stress and effective elastic properties, which determine wave velocities measurable by ultrasonic sensors, such as time-of-flight and phase velocity. The proposed approach provides a rigorous theoretical foundation for ultrasonic stress sensing and nondestructive testing, particularly for curved and anisotropic structures, and supports improved accuracy in sensor-based stress evaluation. Full article

Localized mechanical loading induces complex elastic–plastic interactions in anisotropic crystalline materials. However, quantitative orientation-resolved characterization of residual relative elastic strain heterogeneity remains limited. In this study, high-resolution electron backscatter diffraction was used to map residual in-plane relative elastic strain distributions beneath micro-indents in two annealed body-centered cubic ferritic non-oriented electrical steels, B35AV1900 and 35WW300. Grains oriented near (001), (101), and (111) were analyzed to evaluate the crystallographic effects on residual strain accommodation. Frequency distributions of the in-plane residual relative elastic strain components were constructed, and full width at half maximum values were extracted to quantify strain heterogeneity. The results revealed a pronounced orientation dependence. Near-(001) grains exhibited greater indentation depths and more widely distributed post-indentation deformation features. By contrast, near-(111) grains showed broader residual in-plane relative elastic strain distributions in both alloys. These results indicate that residual strain heterogeneity after unloading is influenced not only by indentation depth but also by crystallographic constraint and orientation-dependent strain redistribution. This study establishes a quantitative orientation-resolved framework for characterizing residual relative elastic strain heterogeneity beneath localized loading. It also provides a basis for linking crystallographic anisotropy, localized deformation, and residual strain redistribution in ferritic electrical steels. Full article