Search Results (1,608)

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

A covariant reconstruction framework for electromagnetic Kantowski–Sachs (KS) geometries in teleparallel $F\left(T\right)$ gravity is developed using the coframe/spin-connection (CSC) formalism and the Coley–Landry invariant approach. In a restricted Maxwell-compatible branch, the electromagnetic conservation laws strongly constrain the anisotropic KS scale factors and lead to the scaling ${\rho }_{\mathrm{em}}\propto A_3^{-4}$. The corresponding symmetric and antisymmetric field equations are derived and used to reconstruct the functional form of $F\left(T\right)$ directly from the KS dynamics. Power-law and exponential ansätze generate distinct invariant reconstruction branches associated with electric, magnetic, and transverse electromagnetic sectors. The exponential branch naturally admits reduced teleparallel de Sitter limits and shifted models of the form $F\left(T\right)=f(T_0-T)$. The reconstructed branches describe anisotropic cosmological sectors together with local BH-interior-like sectors that may reproduce reduced BH-interior-like or RN–dS-type behaviors at the level of the KS dynamics. These branches are organized through the invariant coframe/spin-connection classification and screened using the necessary leading-order viability conditions $F_T>0$ and $F_{TT}>0$. The local and branch-dependent nature of the construction is emphasized throughout. Full article

The integration density of photonic integrated circuits is fundamentally limited by evanescent field overlap and subsequent inter-channel crosstalk. Layered transition metal dichalcogenides (TMDCs) bypass these confinement constraints through intrinsic optical birefringence and high refractive indices. Here, we report the near-infrared optical constants and waveguide dispersion of molybdenum diselenide (MoSe₂). Ellipsometry performed on centimeter-scale crystals yields an in-plane refractive index of 4.1–4.7 over 1000–2000 nm, with an extinction coefficient close to the sensitivity limit of the fit away from strong excitonic resonances. To validate the anisotropic dielectric tensor at the device scale, scattering-type scanning near-field optical microscopy (s-SNOM) was utilized to map the propagation of transverse-magnetic modes in 235 nm thick exfoliated flakes. Spatial Fourier analysis of the edge-scattered near-field interference yields effective mode indices that precisely match the modeled dispersion. Using the verified dielectric tensor, finite-element simulations demonstrate that single-mode MoSe₂ waveguides optically outperform equivalent tungsten disulfide (WS₂) benchmarks. The enhanced evanescent field suppression in the claddings of MoSe₂ waveguide increases the coupling length by a factor of 3.5, reducing the required routing pitch and enabling a 12.5% direct increase in on-chip integration density. The results identify MoSe₂ as a high-index anisotropic platform for compact waveguiding in the near-infrared. 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

Freeze–thaw durability of 3D-printed engineered cementitious composites (3DP-ECC) is strongly affected by print-induced interlayer defects and anisotropy, particularly in cold regions. This study investigated Cast-ECC and Z-direction 3DP-ECC incorporating Yellow River sediment (YRS) as an equal-mass replacement for quartz sand at 0–100%. Compressive, three-point bending, and four-point bending tests, relative dynamic elastic modulus (RDME), XCT, MIP, SEM–EDS, and Weibull damage modeling were used to evaluate degradation up to 150 freshwater freeze–thaw cycles. Moderate YRS replacement (25–50%) improved particle packing, reduced visible defects, and refined the pore structure, thereby enhancing frost resistance. The R50 mixture showed the best residual performance: after 150 cycles, compressive strength decreased from 55 to 46 MPa in Cast-ECC and from 54 to 44 MPa in 3DP-ECC, corresponding to retention rates of 83.6% and 81.5%, respectively. The residual peak load in four-point bending of 3DP-ECC-R50 was 15.4% lower than that of Cast-ECC-R50, confirming the detrimental role of interlayer defects under loading perpendicular to the layers. RDME-based Weibull fitting described the overall damage evolution (R² = 0.876–0.994), while XCT, MIP, and SEM–EDS indicated that interlayer discontinuities, pore-structure evolution, and local microstructural degradation governed anisotropic deterioration. The results support durability-oriented design of YRS-based 3DP-ECC in cold regions. 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

Regular black-hole models replace the Schwarzschild singularity with a finite inner core, thereby removing the geometric endpoint at which the classical spacetime description breaks down. This issue is relevant to black-hole quantum information, since a singular interior prevents a regular effective description of interior degrees of freedom and horizon correlations. In this work, the regular black-hole geometry introduced by Dymnikova is used as a compact, single-scale effective background for black-hole quantum information considerations. The aim is not to propose a new regular metric but to clarify how an established finite-core geometry can support a nonsingular description of the Schwarzschild interior at the effective level. The geometry preserves the Schwarzschild asymptotic limit while replacing the divergent central region with a finite de Sitter-like core. The curvature invariants remain finite, and the effective source admits an anisotropic-fluid interpretation whose central limit is isotropic and vacuum-like. This use therefore provides a minimal geometric setting, rather than a newly proposed metric solution, for discussing nonsingular black-hole interiors. It does not establish unitary evaporation, information recovery, dynamical stability, or a microscopic quantum-gravity mechanism. Instead, it identifies a finite-curvature spacetime framework in which questions concerning interior quantum degrees of freedom and horizon entanglement can be formulated without encountering a curvature singularity. Full article

Electrically conductive polymer composites (ECPCs) have attracted growing interest in applications requiring lightweight, processable, and electrically functional materials. Their increasing use has created a strong need for reliable models capable of predicting electrical conductivity from component properties, composite composition, and microstructural features. Although classical percolation theory can describe the sharp increase in conductivity near the percolation threshold, it is often insufficient for predicting conductivity over a wider range of filler concentrations or for distinguishing the underlying conduction mechanisms. This review examines the main modeling approaches used for carbon-filled polymer composites, including percolation-centered, homogenization, network-based, and data-driven models. These approaches are compared in terms of their assumptions, required inputs, strengths, and limitations, with emphasis on how they account for filler morphology, orientation, dispersion, tunneling effects, and conductive-network formation. The review also identifies key challenges and future needs, particularly the development of integrated, orientation-sensitive, and physically informed models for predicting anisotropic electrical conductivity in processed ECPCs. Full article

Reconstructing high-resolution images of anisotropic targets in microwave imaging remains a challenging problem due to the strong directionality of electromagnetic responses and the inherent nonlinearity of the inverse scattering process. To address these issues, we propose a novel Perceptual Generative Adversarial Network (PGAN) enhanced with a Self-Attention mechanism for anisotropic electromagnetic imaging. The perceptual loss encourages the preservation of high-level structural features, while the Self-Attention module enables the model to capture long-range dependencies and directional correlations that are critical in representing anisotropic material distributions. This joint architecture is trained to refine coarse permittivity estimates obtained from conventional Back-Propagation Schemes (BPSs). Numerical simulations and validation using measured experimental data demonstrate that the proposed method achieves improved reconstruction accuracy and structural similarity compared with the PGAN without SA and U-Net. In particular, PGAN with SA reduces the Root Mean Square Error (RMSE) by 15.1% and improves the Structural Similarity Index Measure (SSIM) by 3.8%, confirming its effectiveness in recovering fine-scale details and enhancing reconstruction quality. These results suggest that the proposed framework offers a promising solution for robust and high-resolution electromagnetic imaging in geophysical and remote sensing applications. Full article

Water–bearing fractures and seepage–prone zones ahead of tunnel faces may evolve rapidly under excavation–induced disturbance, making early identification and process tracking essential for risk mitigation. Cross–hole electrical resistivity tomography (ERT) is sensitive to fluid–controlled conductivity contrasts, but time–series interpretation based on independently inverted snapshots is often unreliable due to ill–posedness, noise, and temporal inconsistency. In this study, we propose an improved time–lapse ERT inversion framework for monitoring evolving water–bearing fractures ahead of tunnels. The method is formulated as a baseline–anchored, Occam–consistent difference inversion that directly estimates resistivity changes relative to an initial state, incorporating error–aware weighting of differenced data and anisotropic regularization adapted to cross–hole sensitivity, so that temporal coherence is enforced during inversion rather than through post hoc differencing. Synthetic verification is conducted using three dynamic scenarios representing horizontal, vertical, and diagonal migration of conductive water–bearing pathways between boreholes. Quantitative comparison against independent inversion across all scenarios and time steps demonstrates that the proposed framework substantially reduces the root mean square error and mean relative error of the recovered resistivity, while significantly improving the spatial correlation coefficient between the recovered and true models, with the largest improvements observed in the diagonal–migration scenario. The reconstructed change maps exhibit more compact anomaly geometry and delineate evolution corridors aligned with the prescribed trajectories, whereas independent inversion produces diffuse and epoch–dependent change patterns. These results indicate that the proposed time–lapse inversion framework provides a more reliable basis for interpreting evolving seepage–related conductive structures in tunnel–ahead investigations. 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

In this study, the stability, electronic, structural, and fracture toughness, and mechanical properties of the Half-Heusler(HH) alloys MnCoSb, MnCoAs, MnCoP, and MnNiSb were comprehensively investigated using first-principles calculations based on density functional theory (DFT). The calculated results reveal that all four alloys exhibit half-metallic characteristics, characterized by the presence of a substantial band gap in the spin-down channel. The phonon spectra and negative formation energies confirm that these alloys possess both dynamic and thermodynamic stability. The Born criteria further validate the structural stability in terms of mechanical properties. Three-dimensional representations of the Young’s modulus, bulk modulus, and shear modulus for the four alloys indicate that MnCoP exhibits the most pronounced anisotropy. The overall fracture toughness of the alloys ranges from 1.58 MPa·m^1/2 to 2.63 MPa·m^1/2, which falls within the typical range for half-metallic materials, albeit at the lower end, attributable to the relatively ductile nature of the four alloys. Although the two methods yield different absolute values, the explicit crack model (Method I) is considered more reliable for anisotropic systems because it directly simulates crack propagation and accounts for local relaxations, while the empirical formula (Method II) provides a useful reference for high-throughput screening. Among the alloys, MnCoSb demonstrates a superior mechanical performance, with K_IC values of 2.63 MPa·m^1/2 and 1.58 MPa·m^1/2 and brittleness indices M of 8.97 and 14.94, indicating excellent damage tolerance compared to the other three alloys. In contrast, MnCoP exhibits higher brittleness and lower mechanical reliability, with K_IC values of 2.00 MPa·m^1/2 and 1.63 MPa·m^1/2 and higher M values of 13.83 and 16.99. This study provides quantitative predictions of fracture toughness and establishes a relationship between microscopic and mechanical properties. These findings offer a theoretical foundation for the application of damage-tolerant HH alloys in fields such as spintronics and magnetism. Full article

Bedding fractures strongly influence pore structure and anisotropic flow capacity in laminated shale oil reservoirs, but conventional porosity–permeability relationships cannot adequately explain permeability differences caused by bedding orientation and fracture connectivity. This problem represents an important gap in shale oil reservoir evaluation because cores with similar porosity may exhibit markedly different permeability when bedding-fracture connectivity and flow direction differ. The main question addressed in this study is how bedding-fracture structures in paired horizontal and vertical LGS shale oil cores selected from the same depth intervals influence porosity, permeability, and permeability anisotropy. To answer this question, this study establishes a quantitative framework linking X-ray computed tomography-derived bedding-fracture structure, three-dimensional fractal dimension, and stress-sensitive permeability anisotropy in LGS shale oil cores. Paired horizontal and vertical cores from the same depth intervals were tested under confining pressures of 10–50 MPa. X-ray computed tomography reconstruction was used to extract bedding-fracture volume fraction $V_f,$ fracture number $N_b$, fracture density ${\rho }_b$, connectivity index $C_b$, and three-dimensional box-counting fractal dimension $D_3$. The H-series cores exhibit much higher bedding-parallel permeability than the V-series cores, although their porosity ranges partly overlap. At 10 MPa, the average permeability of the H-series is 0.24402 mD, approximately 21.7 times that of the V-series 0.01127 mD. As confining pressure increases from 10 to 50 MPa, the average permeability decreases by approximately 97.1% for the H-series and 96.5% for the V-series, indicating strong stress sensitivity of bedding-fracture-controlled flow channels. The $D_3$ values range from 2.16 to 2.63 for the H-series and from 2.12 to 2.56 for the V-series. Higher $D_3$, $V_f$, and $C_b$ enhance permeability when bedding fractures are aligned with the flow direction, whereas complex but discontinuous bedding structures may still result in low bedding-normal permeability. A fractal-corrected porosity–permeability model incorporating $\phi$, $V_f$, $C_b$, and $D_3$ is proposed to improve permeability interpretation beyond porosity alone. This study demonstrates that permeability anisotropy in LGS shale oil cores is controlled by the combined effects of pore–fracture volume, directional connectivity, fractal complexity, and stress-induced fracture closure. Full article

In shale reservoirs, where stress heterogeneity and fracture systems commonly coexist, elastic anisotropy is jointly controlled by in situ stress and fractures, resulting in pronounced azimuthal dependence in wide-azimuth AVO/AVAZ responses. This behavior directly affects fracture characterization and hydraulic fracturing design. However, existing studies commonly attribute anisotropy to either fractures or uniaxial stress perturbations in isolation, and a systematic equivalent-medium formulation that unifies stress-driven stiffness evolution with fracture-weakness effects remains insufficient. To address this gap, we derive an acoustoelastic expression under the weak-stress perturbation assumption, combining background stiffness with third-order stress effects. By incorporating linear-slip fracture weakness, we construct a coupled stress–fracture equivalent stiffness matrix. Using Christoffel eigenanalysis and a welded-interface operator, we then compute anisotropic parameters and AVAZ responses under different stress paths. Numerical simulations show that the principal stress difference dominates both the splitting of reflection curves and azimuthal fluctuations, with an approximately linear sensitivity within the weak-stress regime. Unlike conventional descriptions of fracture-induced anisotropy, in which fracture parameters are commonly prescribed, the proposed framework constructs a physically traceable modeling chain from triaxial stress perturbations to stress-dependent fracture weakness, equivalent orthorhombic stiffness, Christoffel-equation-based wave propagation, and AVAZ responses. This provides a forward-modeling foundation for interpreting coupled stress–fracture anisotropy and for designing future inversion constraints under weak-perturbation conditions. Full article

Retinal vessel segmentation remains challenging for thin vessels and low-contrast bifurcations. We evaluate a Swin-UNet-style model family that conditions decoder features with a single-channel local fractal dimension prior refined by a short learnable anisotropic diffusion model and injected through Spatially-Adaptive Normalization (SPADE). On Fundus Image Vessel Segmentations (FIVES), the strongest no-test-time-augmentation result was obtained by OPT-I v2 at 200 epochs, reaching Dice 0.8899, clDice 0.8517, and Area Under the ROC Curve (AUC) 0.9904, compared with 0.8643, 0.8125, and 0.9856 for the matched 200-epoch baseline. In a matched Neural Cellular Automata (NCA)/no-NCA ablation using the same seed, data, 200-epoch budget, and evaluation pipeline, enabling NCA improved the test Dice from 0.8813 to 0.8907 and the test clDice from 0.8325 to 0.8518, with NCA winning on all 80 paired test images for both metrics. The results support PDE (partial differential equation)-SPADE fractal prior conditioning and NCA topology refinement as ablation-grounded improvements over the tested baseline family, while broader matched external validation requires future work. Full article