Search Results (2,647)

Research into auxetic foams—materials with a negative Poisson’s ratio— is expanding, yet their integration into orthotics for diverse neuropathic conditions remains largely unexplored. This pilot study evaluates the feasibility of fabricating custom auxetic foam insoles and characterizing vertical ground reaction force (vGRF) trends across a heterogeneous cohort. In collaboration with the NASA/Marshall Space Flight Center, six participants, including five representing varied neuropathic etiologies and one healthy control, performed randomized walking trials under three conditions: barefoot, over-the-counter (OTC) insoles, and custom auxetic prototypes. The healthy control was retained in the cohort-level analysis to preserve methodological symmetry across experimental conditions. To maintain physical rigor, vGRF data were mass-normalized (N/kg). A Friedman test (n = 6) evaluated global differences, supplemented by a dual-bootstrap analysis (1000 resamples) to quantify effect magnitudes (r) and numerical uncertainty. Although the Friedman test revealed no statistically significant global differences (Q = 0.333, df = 2, p = 0.846), a descriptively large effect size (r = 0.58) was observed for the auxetic material versus barefoot walking. However, wide 95% bootstrap confidence intervals prevent population-level inference, reinforcing the exploratory nature of these findings. Subject-specific observations showed descriptive differences in vGRF in three participants (0.17 to 1.18 N/kg), while increases in others occurred alongside confounding factors such as self-selected walking velocity. This work demonstrates the mechanical application of auxetic insole prototypes, providing a foundational rationale for future trials utilizing standardized walking velocity to isolate material performance. Full article

This paper investigates the dynamic behavior of non-Darcy seepage systems in post-failure rock. A one-dimensional non-Darcy seepage evolution equation is established, and a 6-dimensional nonlinear ordinary differential system is derived via the spectral truncation method. Eigenvalue analysis is adopted to determine the instability and bifurcation conditions, with the bifurcation diagram plotted. The fourth-order Runge–Kutta method is used to obtain phase trajectory patterns under different initial values. The results confirm the existence of transcritical bifurcations and fold bifurcations. The dynamic response of the system is discontinuous with control parameters, and phase trajectory symmetry breaking occurs with the increase in nonlinear terms. The reduced-order model shows diverse phase trajectories including equilibrium, periodic, chaotic attractors and unstable states. The system is sensitive to initial values, which significantly affect phase trajectory behaviors. The system may lose stability and trigger water inrush hazards under critical conditions. The bifurcation diagram and critical parameters obtained can provide a theoretical basis for the early warning, risk assessment and prevention of coal mine water inrush hazards. Full article

In two-phase systems with heat transfer, developing tools that allow the analysis of interphase phenomena is crucial. In molten salt nuclear reactors, the fuel salt and helium in the core form a two-phase liquid–gas system. Understanding the heat transfer behavior between phases allows us to assess the impact of temperature changes in each phase as well as the feedback of neutron processes in the reactor. This work proposes using an upscaled heat transfer model to analyze the two-phase system, highlighting the importance of solving boundary value problems to obtain the closure variables in a unit cell with symmetry and periodicity. The closure variables are crucial for determining the heat transfer coefficients that exhibit the MSR’s scaled behavior. The coefficients are validated against the literature, and the results of the numerical experiments show that the cross-heat transfer coefficients exhibit symmetric properties. Full article

Geometric discontinuities in aero-engine turbine blades generate multiple stress concentrations along the airfoil, rendering life prediction exceptionally challenging. While conventional skeletal point method (SPM) offers reasonable accuracy in predicting creep-fatigue-interaction (CFI) life for simple structural specimens, they prove inadequate for geometries with poor symmetry. This study introduces a novel two-dimensional skeletal point method (2D SPM) to analyze stress evolution characteristics, identify representative stresses, and predict CFI life in complex structures. Leveraging the film-cooling hole (FCH) features of a representative turbine blade, three perforated plate specimens were designed, manufactured, and subjected to CFI testing. Failure analysis confirmed crack initiation at hole-edge stress concentration zones, followed by inward propagation. Specimen fracture surfaces exhibited predominantly ductile dimpling features, with multi-origin fatigue characteristics observed only near hole-edges, collectively indicating creep-damage-dominated failure mechanisms. Five life prediction methodologies were comparatively evaluated. The results demonstrate that the 2D-SPM achieved the highest accuracy (all predictions within twofold scatter bands), followed by the conventional SPM (also within twofold scatter bands). The nominal stress method showed moderate accuracy (within fivefold scatter bands), while both hot point method and TCD methods proved unsuitable for creep-fatigue scenarios with significant stress evolution. Full article

Meaningful partitioning of 2D binary shapes remains a challenging problem in shape analysis because many existing methods rely mainly on local geometric rules or skeleton simplification, which often struggle to separate the main body of a shape from its protruding parts in a perceptually meaningful way. This limitation becomes more evident in shapes with thin limbs, branching structures, or irregular extensions, where preserving topology while achieving human-consistent decomposition is difficult. We present a fully automatic framework for the hierarchical partitioning of 2D binary shapes into semantically meaningful core bodies and protruding limbs (tails). The pipeline begins by generating candidate structural lines through multi-directional centroid tracking along horizontal, vertical, and diagonal (±45°) bands. Three direction-specific Sugeno fuzzy controllers first evaluate these lines based on normalized length, angular alignment, and minimum distance to the boundary. A second pair of fuzzy systems then classifies segments as either tails or core parts using thickness statistics derived from the distance transform. For ambiguous merged tail groups, iterative midpoint splitting is applied until stable labeling is achieved. High-curvature boundary corners are then detected via signed turning-angle analysis, and candidate cutting rays are assessed through exact region splitting, tail area measurement, and label purity analysis. An adaptive third-stage fuzzy controller ranks these candidates according to cut length, purity, and area. The highest-scoring non-overlapping cuts are executed iteratively, progressively peeling peripheral parts while preserving the overall topology and symmetry of the shape. The proposed framework is evaluated on a targeted subset of 32 categories from the 2D Shape Structure Dataset Results on this evaluated subset indicate that the method produces coherent and topologically consistent partitions, with competitive agreement with the available human-annotated references. This training-free framework provides an interpretable tool for 2D shape analysis, with potential applications in object recognition, computer animation, and symmetry studies. Full article

The current paper studies the global shell layer of the Finite Ring Continuum framework in the symmetry-complete regime realized here by framed finite fields, ${\mathbb{F}}_{\mathsf{p}}(\mathsf{t};0,1,e_{\mathsf{t}})$, with $\mathsf{p}=4\mathsf{t}+1$. We show that a single symmetry-complete shell carries a unified finite Euclidean datum for which its continuum comparison interpretation reproduces the familiar structural roles of e, $\pi$, and i of a one-phase step with an exponential kernel, a half-period, and a quarter-turn, respectively. In the same shell, the orbital geometry is generated by additive meridian action and multiplicative phase action from that same frame datum. The resulting orbital shell has a canonical spherical completion, combinatorially equivalent to the two-sphere, with labels depending on the chosen frame, but the shell type fixed up to isomorphism. Arbitrary finite-precision approximation on this external spherical comparison object is then obtained within every fixed symmetry-complete shell by the scale-periodic framed-rational refinement generated by the same frame datum. The Fourier formalism is developed strictly as a discrete Fourier transform over the shell ring, with conventional continuum Fourier language becoming a continuum large-$\mathsf{p}$ comparison case of that shell formalism. Full article

This paper investigates the solution theory of a class of prescribed positive Q-curvature equations with power-law singularity at the origin and polynomial growth at infinity in the four-dimensional Euclidean space. We focus on the equation involving the biharmonic operator and an exponential nonlinearity, with the prescribed curvature function combining a singular term and a growth term, where a parameter characterizes the strength of the conical singularity at the origin and another parameter describes the growth rate at infinity. Under the finite total curvature constraint, we systematically analyze the asymptotic behavior of normal solutions, establish the necessary condition for existence, prove the existence and uniqueness of radially symmetric normal solutions, and give a complete characterization of the optimal admissible range of the total curvature. Our main results are as follows: (i) We derive the sharp asymptotic behavior of normal solutions both near the singular origin and at infinity, and establish the Pohozaev identity for the singular Q-curvature equation, which yields a universal necessary condition for the existence of normal solutions. (ii) We prove the existence of radially symmetric normal solutions via the Leray–Schauder fixed point theorem combined with a regularization technique, and establish the uniqueness of radial solutions with respect to the initial value at the origin by the strong maximum principle and monotonicity analysis. (iii) We prove the continuity of the total curvature with respect to the initial value via blow-up analysis and energy quantization, and determine the optimal range of the total curvature: for small growth rates, the necessary and sufficient condition for existence is that the total curvature lies between two critical values; for large growth rates, we give a sharp necessary condition and an explicit sufficient condition for the existence of radial solutions. Full article

Recursive constructions derived from finite projective geometries generate scalable families of resolvable block designs exhibiting strong algebraic regularity and intrinsic symmetry. In this work, we investigate the structural optimization of recursion depth in such constructions and demonstrate that the combinatorial growth of recursive chains is governed by a quadratic scaling law originating from the asymptotic expansion of Gaussian binomial coefficients. We show that the resulting exponent is strictly concave, which guarantees the existence and uniqueness of an optimal recursion depth. This optimum occurs at the midpoint of the projective dimension and reflects the dual symmetry of the lattice of projective subspaces. To analyze this behavior, we introduce a normalized objective function that compares recursion depths and reveals a unique maximum corresponding to the midpoint of the projective dimension. Theoretical analysis is supported by exact enumeration and asymptotic validation, confirming that the optimal depth is robust to lower-order perturbations and remains invariant under the natural duality of projective geometry. The proposed framework establishes a direct connection between symmetry properties of discrete geometric structures and optimality in nonlinear discrete systems. These results provide a unified perspective on recursive design constructions, revealing that symmetry not only governs combinatorial structure but also induces a mathematically inevitable optimal configuration. The approach opens new directions for studying symmetry-induced optimality in combinatorial geometry, discrete optimization, and related nonlinear mathematical models. Full article

Traditional analyses of transport phenomena rely on prescribed geometric boundaries, yet natural flow systems dynamically evolve their architecture to maximize access to currents. To address this disparity, we propose a field-theoretic framework for the constructal law that treats physical geometry as a dynamic state variable, represented by a time-dependent conductivity tensor. Using a variational approach grounded in non-equilibrium thermodynamics, we derive a general tensor evolution equation. Within this framework, macroscopic flow architecture emerges deterministically from the continuous competition between non-linear flux-induced accretion, linear entropic relaxation, and spatial smoothing. Scaling analysis reduces this dynamic to a tri-parameter dimensionless phase space: a morphogenic number driving structural growth, a structural diffusion number governing spatial coherence, and a stochastic intensity number providing the microscopic seeds for symmetry breaking. Our principal result is the analytical prediction of a critical bifurcation. When the local morphogenic number strictly exceeds unity, the system escapes its stable, isotropic configuration and branches into highly conductive, anisotropic architectures. We demonstrate the predictive validity and trans-scalar applicability of this continuum theory by mapping it to highly diverse phase transitions, successfully capturing phenomena ranging from microscopic aerosol agglomeration and microbial resistance, to macroscopic coral plasticity and crystal growth instabilities, and finally to the astrophysical launching of relativistic jets from black holes. Full article

We present an updated overview of the symmetry-preserving contact interaction model in hadronic physics, which was developed a little over a decade ago to describe the mass spectrum and internal structure of mesons and diquarks composed of light and heavy quarks. Over the years, the contact interaction model has evolved into a framework capable of treating both ground and excited states, providing a simple yet consistent approach to nonperturbative QCD. In this review, we examine the mass spectrum and elastic form factors of forty mesons with different spins and parities, together with their corresponding diquark partners. Importantly, we update the comparison of contact interaction predictions using recent results from the literature, offering a fresh perspective on the model’s performance, strengths, and limitations. The analysis presented here refines previous conclusions and supports the contact interaction model as a practical tool for hadron structure studies, with potential applications to baryons and multiquark states. We also present comparisons with other theoretical models and approaches, including lattice quantum chromodynamics, and comment on future prospects in view of ongoing and planned experimental programs regarding hadron structure. In particular, forthcoming measurements at FAIR together with future studies at Jefferson Lab and the Electron Ion Collider are expected to provide key insights into hadron structure, with FAIR offering indirect constraints via hadron spectroscopy, hadronic interactions, and in-medium properties; high-precision data on meson structure and form factors from Jefferson Lab and the Electron Ion Collider will provide valuable benchmarks with which to confront predictions based on the contact interaction model. Full article

In robotic grinding of complex curved surfaces, the low stiffness of serial robots causes tool tip deflection and degrades surface quality. The axial symmetry of grinding discs introduces a free rotational parameter at each waypoint, converting a standard 6-DOF robot into a functionally redundant system. However, this redundancy has not been systematically exploited for stiffness optimization along the trajectory. This paper proposes a hierarchical dynamic programming framework to optimize the redundancy angle sequence over the entire grinding trajectory. A kinematic transformation parameterizes the flange target by the redundancy angle, enabling enumeration of feasible candidate configurations over a discretized grid. A composite stiffness index that accounts for the normal, feed, and cross-feed grinding force components is formulated at the contact point. Hierarchical constraint filtering removes configurations that violate posture, singularity, velocity, acceleration, and stiffness constraints. The Viterbi algorithm then recovers the minimum-cost path that balances stiffness performance and joint motion smoothness. Finally, a post-processing step based on a cubic smoothing spline generates $C^2$-continuous joint trajectories. Simulations on a UR5 robot grinding a curved surface evaluate the proposed framework against fixed-angle, greedy, and flange-stiffness baselines. The proposed method improves the mean composite stiffness by 31.7% and 17.9% over the fixed-angle and flange-stiffness baselines, respectively, and reduces the maximum joint jump by two orders of magnitude compared with the greedy strategy. Experimental validation on a UR5 robot confirms that the smoothed trajectory is accurately tracked while the stiffness threshold is preserved. A multi-trajectory analysis further shows that the stiffness threshold is maintained across all grinding trajectories. These results demonstrate the effectiveness of the proposed framework for redundancy optimization in robotic grinding with tool spin symmetry. Full article

Let $U,V\subset \mathbb{H}$ be bounded $C^1$ domains, and let f be quaternion-valued on $U\times V$. We study the mixed Cauchy–Fueter system $D_x^{L}f=0$ and $f{D}_y^R=0$ on product domains by iterating the classical one-variable Borel–Pompeiu formulas in an order consistent with quaternionic multiplication. Under closure regularity on $\overline{U}\times \overline{V}$, we prove an iterated representation formula and show that, in the biregular case, the boundary contribution reduces to the distinguished boundary $\partial U\times \partial V$. This leads to a distinguished boundary transform, ${\mathcal{T}}_{U,V}$, on continuous boundary data. We prove that ${\mathcal{T}}_{U,V}$ maps $C(\partial U\times \partial V;\mathbb{H})$ into $C^{\infty }(U\times V;\mathbb{H})$, establish compact subset estimates for mixed real derivatives, and derive a local approximation theorem within the transform range by finite sums of separated one-variable Cauchy transforms. The analysis is restricted to this representation framework. In particular, the paper does not address a general solvability theory for the mixed inhomogeneous system and does not characterize the full range of ${\mathcal{T}}_{U,V}$. Full article

Transcriptional and translational inhibition are fundamental regulatory mechanisms in gene networks, governing diverse processes from viral replication to neuroplasticity. Two-component genetic oscillators based on the “activator–repressor” motif serve as ideal models for studying biological rhythms due to their simplicity and rich dynamics. However, systematic theoretical comparisons of distinct inhibitory mechanisms—particularly using inhibition strength as a control variable—remain lacking. Addressing this gap, we present a comprehensive bifurcation analysis of the post-translational repression model, proving the existence and uniqueness of its positive equilibrium, deriving Hopf bifurcation conditions, and identifying critical parameter ranges for sustained oscillations. Using inhibition strength as a key comparator, we systematically contrast transcriptional and post-translational repression, elucidating how different inhibitory mechanisms modulate oscillation initiation and amplitude. We further reveal distinct symmetry–asymmetry patterns in their bifurcation dynamics: transcriptional repression exhibits asymmetric bistable regimes, while post-translational repression manifests narrow, nearly symmetric oscillatory intervals. This unified analytical framework not only advances the theoretical understanding of two-component genetic oscillators but also provides a generalizable paradigm for dissecting complex gene regulatory dynamics. Full article

A discrete Hartley transform (DHT)-based orthogonal frequency division multiplexing (OFDM) scheme is investigated for intensity modulation/direct detection (IM/DD) visible light communication (VLC) systems, where transmitted signals are required to be real-valued and non-negative. To address this constraint, a practical unipolar transmission framework with corresponding bipolar reconstruction is developed. By exploiting the real-valued and self-inverse properties of the DHT, the proposed scheme removes the need for Hermitian symmetry and enables full utilization of available subcarriers. Under equal-bandwidth conditions, this results in an approximately 50% reduction in computational complexity compared with conventional DCO-OFDM and ACO-OFDM schemes. Theoretical analysis and numerical results further show that the proposed approach achieves comparable bit error rate (BER) performance while exhibiting improved spectral confinement, as reflected by reduced out-of-band sidelobes under identical filtering conditions. In addition, it maintains spectral efficiency equivalent to DCO-OFDM under the same bandwidth constraint. These advantages are achieved at the cost of restricting subcarrier modulation to real-valued constellations, which may reduce flexibility in frequency-selective channels. Overall, these findings support DHT-OFDM as a low-complexity, spectrally confined multicarrier waveform for IM/DD VLC systems, particularly in scenarios where efficient spectrum utilization and reduced adjacent-channel interference are required. Full article

The goal of the present paper is to apply a novel biomimetic design strategy for the analysis, emulation, and technical evaluation of design solutions inspired by the morphogenetic logic of the walnut shell microstructure. The shell consists of specialized cells, called sclereids, which develop protrusions and mechanically interlock with neighboring cells, providing exceptional toughness through increased surface contact. To extract and transfer this biological principle, a generative algorithm was developed using the evolutionary solver Galapagos within the Grasshopper visual programming environment. The algorithm generates protrusions on the interfaces of structural blocks and optimizes their contact surface area while maintaining constant block volume. Additional design constraints, including symmetry and manufacturability considerations, were introduced to improve structural performance and computational efficiency. A series of physical specimens with variations in key geometric parameters, such as protrusion number and height, were fabricated using fused filament fabrication (FFF) with PLA material and evaluated through in-plane and out-of-plane three-point bending tests. The results show that increasing the number of protrusions significantly enhances mechanical performance, while increasing their height improves stiffness and interlocking up to a certain threshold, beyond which structural performance decreases due to stress concentration effects. This behavior can be attributed to improved load transfer and stress distribution across the enlarged interfacial area, as well as progressive mechanical engagement between complementary protrusions. The computational model is in good agreement with the experimental results, confirming the validity of the proposed approach. The study demonstrates that biomimetic optimization of interfacial geometry can enhance the mechanical behavior of interlocking systems and provides a framework for translating biological morphogenetic principles into engineering design applications. Full article