Search Results (796)

The transfer-matrix method is employed to investigate a spin-1/2 Ising chain under open and periodic boundary conditions. It is demonstrated that finite-size Ising chains with antiferromagnetic coupling may exhibit significantly distinct magnetic behavior under open and periodic boundary conditions. While the open Ising chains display intriguing magnetic features regardless of the system size, mainly due to a specific contribution of boundary spins, the magnetic behavior of closed Ising chains depends basically on the number of spins. The closed Ising chains with an odd number of spins are subject to a geometric spin frustration leading to an additional plateau in the magnetization curve, which is naturally absent in the closed Ising chains with an even number of spins. Despite different microscopic origins, the magnetization curves of open and closed Ising chains with an odd number of spins exhibit an identical intermediate plateau, with only small quantitative differences appearing at moderate temperatures, which means that a geometric spin frustration of odd-membered rings is somewhat similar to the effect of open boundaries. The magnetization curves of the open Ising chains with an even number of spins differ drastically from those of the closed Ising chains due to the presence of an additional intermediate magnetization plateau. Furthermore, the initial susceptibility, inverse initial susceptibility, and susceptibility–temperature product are examined in detail as functions of temperature. These magnetic response functions demonstrate that the Curie constant and Weiss temperature represent fundamental characteristics of the magnetic system that are independent of the choice of boundary conditions. Full article

In this work, plasmonic photoconductive antenna (PCA) structures with different grating-width and gap configurations were numerically investigated to evaluate their influence on transient-current generation and terahertz (THz) emission performance. Two geometrical scaling strategies were considered: a fixed-gap configuration with a constant 100 nm photoconductive gap and a proportional-gap configuration in which the gap size was equal to the grating width. Three-dimensional finite element method (FEM) simulations were performed to analyze transient carrier dynamics, THz pulse electric-field behavior, and frequency-domain spectral response under 800 nm optical excitation. The results demonstrate that reducing the inter-grating gap enhances plasmonic near-field confinement and carrier localization near the metal–semiconductor interface, leading to stronger transient-current responses and enhanced THz characteristics. Spatial field and carrier-distribution analyses further confirmed improved electric-field localization and carrier confinement for the fixed-gap structures. In addition, voltage-dependent investigations showed that increasing the applied bias voltage strengthens carrier acceleration and enhances the simulated THz response within the investigated operating range. The results further demonstrate that the observed enhancement is governed not only by grating periodicity but also by the grating-width/gap-size ratio, highlighting the importance of geometrical fill-factor optimization. Polarization-dependent simulations confirmed the plasmonic origin of the enhanced transient-current generation and THz emission. These findings demonstrate that optimal THz performance arises from a balanced interplay between plasmonic field localization, optical absorption, and carrier-transport dynamics, providing design guidelines for the optimization of plasmonic THz PCAs. Full article

The morphological and structural state of rough solid electrodes usually has a complex effect on the kinetics of an electrochemical process. In order to correctly distinguish the influence of different factors on the rate of an electrode reaction, it is necessary to first separate a purely geometric current rise caused by the surface area increase. At the same time, it is necessary to take into account that surface roughness itself often not only leads to a geometric rise in the electrode area, but also contributes to a change in the kinetic parameters of the electrochemical process. As a consequence, the conclusion regarding an electrocatalytic effect will be reasonable only if the roughness effect is correctly taken into account. The most difficult problem is to establish the role of roughness when experimental electrochemical data are obtained under mixed diffusion–kinetic control of the electrode process. However, the use of appropriate theoretical approaches is required to correctly determine the kinetic characteristics of the electrochemical stage, i.e., of the charge transfer stage. This paper establishes the influence of the morphology and structure of electrodeposited copper coatings on the kinetics of the cathodic reduction of nitrate ion, which occurs in a mixed diffusion–kinetic mode, using the theoretical model of chronoamperometry of an electrochemical process on a rough electrode developed earlier by the authors. Several Cu-electrodes with roughness and structure, the parameters of which vary widely enough, were obtained by cathodic deposition from sulfate solutions of different compositions. The integral (roughness factor) and local (average roughness) characteristics of the surface morphology were determined by methods of underpotential deposition and atomic force microscopy, respectively. Structural investigation of the electrodeposited coatings was carried out by X-ray diffraction to determine their crystallographic structure and average crystallite size. The methods of voltammetry and a rotating disk electrode revealed the mixed kinetics of the electroreduction of ${\mathrm{NO}}_3^{-}$ ions. The kinetic parameters of the charge transfer stage on the copper coatings with a roughness factor of f_r ≤ 3.5 are determined for the first time in this paper by treatment of the experimental current decay curves with the non-linear theoretical equation obtained by the authors for the chronoamperogram of the process on rough electrodes. It was found that the rate constant of the charge transfer stage and the exchange current density of the nitrate ion electroreduction increase by about 50%, with an increase in the average surface roughness from 25 to 120 nm. Considering that this effect is not caused by a purely geometric increase in the true surface area of the electrode, and that the average crystallite size is approximately the same (25 ± 2 nm) for all investigated coatings, it can be concluded that the electrocatalytic activity of copper increases in the reaction of the cathodic reduction of nitrate ions during the transition to copper electrodes with the higher average surface roughness. Taking into account XRD data, the role of the structural and morphological state in the kinetics of the electroreduction of nitrate ions has been established. The smoothest polycrystalline coating was found to be the least electrocatalytically active in this reaction. On the contrary, the roughest coatings with the most prominent plane (220) show the highest activity, which increases with increasing average roughness, possibly due to the growth of defects and excess energy of such curved surfaces. Full article

Robotic belt grinding is an effective and widely adopted finishing method for superalloys, offering notable advantages such as high material removal capability, low heat input, and reduced workpiece damage. In addition, robots can readily integrate multiple sensors—such as infrared radiation cameras, force sensors, and high-speed cameras—which facilitate real-time monitoring of the grinding process and thereby enhance grinding quality control. With the establishment and continuous advancement of large-scale artificial intelligence (AI) data models, new breakthroughs have emerged in the optimization of robotic grinding processes. Owing to its dexterous workspace and advantages in high flexibility and cost-effectiveness, robotic belt grinding has become a critical process for the precision forming of complex curved components such as aero-engine blades and blisks. However, factors such as the limited absolute accuracy of industrial robots, time-varying grinding contact states, and significant transient boundary effects make it difficult for the current constant-parameter open-loop machining mode to simultaneously meet the demands for high material removal efficiency and high surface integrity on complex profiles. This paper systematically reviews the technologies for precision control and process optimization of robotic belt grinding aimed at pointwise precise material removal. First, the structural composition of the robotic belt grinding system and the material removal mechanism are analyzed. Then, centered on the compensation concept, a hierarchical progressive technical framework is outlined, covering geometric calibration compensation, force/position hybrid online compensation, transient entry boundary compensation, and system-level comprehensive compensation of multi-source errors, with a comparison of the applicable scenarios and the effects on shape and property control at each level. Furthermore, under the support of effective compensation, the collaborative optimization methods of material removal modeling, multi-objective optimization of process parameters, force-constrained trajectory planning, and intelligent adaptive processes are elaborated. Finally, current technical bottlenecks are summarized, and future trends in next-generation adaptive grinding technology driven by digital twins and embodied intelligence are envisioned. This review aims to provide a systematic theoretical reference for the high-precision and intelligent upgrading of robotic precision grinding systems. Full article

The aim of this paper is to characterize a relativistic bulk viscous fluid string spacetime whose energy–momentum tensor satisfying certain geometric symmetries. At first, it is shown that a relativistic bulk viscous fluid string spacetime is a generalized quasi-Einstein manifold. Then, we characterize such a spacetime, satisfying Codazzi type of energy–momentum tensor (denoted by ${\mathcal{T}}^{\oslash }$), covariant constant ${\mathcal{T}}^{\oslash }$, recurrent and generalized recurrent ${\mathcal{T}}^{\oslash }$, and almost pseudo-symmetric and weakly symmetric ${\mathcal{T}}^{\oslash }$, respectively. Next, we consider quadratic Killing ${\mathcal{T}}^{\oslash }$ in such a spacetime. Finally, we provide a concrete example using partial differential equations. Full article

We introduce a notion of curvature based on informational holonomy. Let $(M,g)$ be a smooth Riemannian manifold and let $\pi :\mathcal{P}\to M$ be a bundle of state spaces equipped fibrewise with a smooth divergence $D_x$ inducing an information metric $g^{{\mathcal{P}}_x}$. Assuming a connection on $\mathcal{P}$ compatible with this fibrewise information geometry, we measure the deviation of holonomy around small geodesic triangles by transporting a reference state ${\mu }_x$ and comparing it to its image via the induced informational distance $d_x=\sqrt{2D_x}$. Normalizing the resulting distance defect by the geometric area yields a continuous informational holonomy (sectional) curvature$K_{\mathrm{hol}}^{\mathrm{cont}}(x,\mathsf{\Pi })$. We prove that this limit exists for all $(x,\mathsf{\Pi })$ and equals the norm of a vector $W_x(\mathsf{\Pi };{\mu }_x)\in T_{{\mu }_x}{\mathcal{P}}_x$ depending linearly on the curvature of the connection along $\mathsf{\Pi }$. In geometric models induced from the Levi–Civita connection via an isometric representation, $K_{\mathrm{hol}}^{\mathrm{cont}}$ becomes a scalar invariant of $R^g{|}_{\mathsf{\Pi }}$ and, on spaces of constant sectional curvature, reduces to a constant multiple of $|{\sec }_g|$. On the discrete side, we consider quasi-uniform sampling graphs whose edges carry channels approximating parallel transport. Discrete triangle holonomies define a curvature estimator, and under explicit sampling, area-approximation, and channel-consistency assumptions, we establish a discrete-to-continuum convergence theorem with a quantitative error bound controlled by the sampling scale. Full article

Deterministic generation of dissipative Kerr solitons (DKSs) is a key requirement for practical microresonator-based frequency comb sources. Here, we present a design methodology for Si₃N₄ dual-coupled microring resonators (DCMs) that relates device geometry to the intrinsic and interaction parameters governing soliton formation. In particular, the auxiliary-ring geometry controls the avoided mode crossing, enabling targeted control of the interaction strength a and its modal position b through geometric design and refractive-index tuning. The resulting DCM configurations exhibit accessible DKS regions in the $(\Delta ,|S{|}^2)$ parameter space under constant pump power and linear detuning sweeps. These results provide a practical framework for the implementation of robust microresonator frequency comb sources with simplified control. Full article

Disk triboelectric nanogenerator (TENG) design pursues high structural figure of merit (${\mathrm{FOM}}_S$), yet nominal peak designs often sit in regions with steep geometric gradients; under a controlled $\pm 10\%$ symmetric perturbation proxy, worst-case ${\mathrm{FOM}}_S$ retention near the peak frontier falls to 2.7%. We decompose ${\mathrm{FOM}}_S$ into a charge-transfer channel ($Q_{\mathrm{sc},\mathrm{MACRS}}$) and a capacitance channel ($C_{\mathrm{sum}}^{-1}$), and train a multi-output surrogate with a physics consistency constraint on 1944 COMSOL simulations to jointly predict $Q_{\mathrm{sc},\mathrm{MACRS}}$, $C_{\mathrm{sum}}^{-1}$, and ${\mathrm{FOM}}_S$ across electrode-pair number, dielectric-thickness-to-radius ratio ($h/R$), air-gap-to-radius ratio ($d/R$), and dielectric constant. Evaluating 7776 design points reveals that 58.6% of the explored space is charge-dominant, 36.1% mixed, and 5.3% capacitance-dominant; raising dielectric constant shifts the mechanism toward capacitance-limited behavior, while a larger air gap reinforces charge-limited behavior. Mixed-regime windows tolerate the same perturbation proxy far better than peak-${\mathrm{FOM}}_S$ candidates, supplying candidate design windows for pre-fabrication screening within the validated simulation domain. The surrogate reaches pooled out-of-distribution ${\mathrm{FOM}}_S$$R_{{\log }_{10}}^2=0.914$ on 43 unseen structural and dielectric combinations. Delivered through an open-source Streamlit interface, the channel decomposition, mechanism mapping, and tolerance screening let designers identify the limiting mechanism and select candidate designs that are expected to tolerate geometric variation within the validated simulation domain, prior to fabrication. Full article

Deep stormwater drainage tunnels are increasingly being used to mitigate urban flooding, but in-tunnel sediment deposition reduces their discharge capacity and complicates their maintenance. With direct field observation constrained, numerical simulation is essential, and river-based total sediment load formulas require reassessment for use in deep tunnels. The three-phase (air–water–sediment) CFD solver SedInterFoam is first validated against a benchmark open-channel suspended sediment experiment, and is then applied to a horseshoe tunnel under a fixed design discharge for multiple inlet sediment concentrations spanning urban stormwater conditions. Four classical formulas (Yang, Shen–Hung, Ackers–White, Engelund–Hansen) are evaluated at the CFD-resolved hydraulic state; Toffaleti is omitted because its zone-based formulation is incompatible with the partially filled horseshoe geometry. The CFD consistently shows persistent retention of a substantial fraction of the inlet sediment load, whereas the transport capacity-limited interpretation of the classical formulas predicts near-complete sediment throughput—indicating structural inadequacy for the dilute, supply-limited regime typical of urban stormwater. A Universal Soil Loss Equation (USLE)-style dimensionless deposition formula is therefore proposed, with inlet sediment loading as the explicit independent variable and a tunnel correction factor $K_{tunnel}$ absorbing the geometric, hydraulic, and sediment variations. Its regression yields an almost linear scaling and a nearly constant deposition ratio, while analysis of the internal flow and concentration fields shows that the retained sediment is strongly concentrated near the bed and that near-bed turbulent mixing weakens moderately with a rising inlet concentration. While calibrated for a single non-cohesive settleable sand fraction, the framework provides a transferable basis for inlet-loading-dependent deposition prediction in deep stormwater drainage tunnels, and subsequent extension of $K_{tunnel}$ to broader sediment conditions with field-based validation is expected to enable maintenance planning, dredging volume estimation, and sediment retention risk assessment. Full article

To address the time-consuming and labor-intensive procedures associated with traditional approaches for evaluating the integrated burning rate of wire-embedded propellants in solid rocket motors (SRMs), this study proposes an efficient and reliable prediction method. This new method is based on an improved burning-rate–initial-temperature correlation, achieved through Abaqus-Python secondary development that enables fully automated geometric modeling, transient heat-transfer analysis, and temperature-field extraction for wire-embedded propellants. The relative error between the present method and the experimental results is less than 5%. The accuracy and engineering applicability of the present method are verified. The effects of the material parameters and wire diameters on the integrated burning rate is investigated. The results indicate that wires of different materials exhibit substantial variations in burning-rate enhancement efficiency, with smaller diameters and higher thermal diffusivity producing stronger enhancement effects. When the specific heat capacity and density are held constant, the integrated burning rate increases monotonically with the wire’s thermal conductivity, though the growth trend gradually approaches saturation. In contrast, the influences of the wire’s specific heat capacity and density are comparatively weak. The integrated burning rate prediction framework developed in this study demonstrates strong versatility and scalability. It enables rapid performance evaluation of propellants embedded with wires of various sizes and thermophysical properties, providing valuable theoretical guidance and practical tools for the design and optimization of wire-embedded solid rocket motors. Full article

We develop an analytical framework to describe the impact of in-plane strain on the electronic and transport properties of graphene. Starting from a strain-modified nearest-neighbor tight-binding model, we derive the energy spectrum and group velocities, explicitly incorporating bond-dependent hopping renormalization. A dimensionless anisotropy parameter, derived from velocity fluctuations, is introduced to quantify directional transport imbalance. We show that this parameter admits a closed-form expression entirely determined by the strain tensor, linking lattice deformation directly to measurable transport quantities. In the small-strain regime, a compact expression is obtained, $\eta \approx ϵ\left(1+\nu \right)\cos \left(2\theta \right)$, revealing an angular dependence controlled solely by the orientation of the applied deformation. This establishes that strain acts as a purely geometric control parameter, separating magnitude and orientation effects. Within the semiclassical Boltzmann framework, the same parameter fully determines the conductivity tensor, leading to simple expressions for the longitudinal components ${\sigma }_{x,y}={\sigma }_0\left(1\mp \eta \right)$ and a clear identification of the preferred transport direction. Importantly, the total conductivity remains constant, while strain redistributes transport between orthogonal directions. These results provide a transparent and predictive description of strain-induced transport anisotropy, demonstrating that the directional electronic response can be tuned without modifying the material composition, offering a practical route to control electronic response in graphene through purely mechanical means. Full article

Punching is a fundamental and extensively employed process in the field of cold forming, prized for its operational simplicity, high performance, and ability to produce components of superior quality. However, the process is inherently complex, as the selection of optimal punching parameters remains a challenging endeavor. Achieving a high-quality punched product is critically dependent on the precise and validated choice of these parameters, which directly influence the mechanical and geometrical integrity of the final component. In this study, the shear zone height, a key indicator of punched part quality, is systematically investigated. The finite element method (FEM), integrated with the Johnson-Cook material model, is employed to simulate and analyze the influence of various punching parameters on the shear zone height, with particular emphasis on the effect of different punch shaft shapes. The Johnson-Cook model, renowned for its accuracy in capturing material behavior under high strain rates and temperatures, enables a robust and reliable simulation framework. The results of this investigation reveal that punch tools featuring a pointed shaft shape exhibit an almost constant distribution of shear zone height across a range of punching parameters. This consistency suggests that such designs are less sensitive to parameter variations, thereby offering a more stable and predictable performance. Consequently, the pointed punch shape is identified as the optimal configuration for achieving superior punched part quality, minimizing defects, and enhancing process reliability. This work contributes to the advancement of cold forming technology by providing insights into the relationship between punch geometry and shear zone characteristics, ultimately facilitating the selection of punching parameters for improved product quality and process efficiency. 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

When a symplectic integrator is applied to an integrable Hamiltonian system, the step transition map can be viewed as a nearly integrable symplectic map with a step-size-dependent perturbation. In this paper, we establish a Nekhoroshev-type theorem for such maps, providing explicit exponential stability estimates that apply directly to small-twist cases. We explicitly emphasize that our analysis treats a small but strictly positive twist ($m>0$) with quantified m-dependence, rather than a uniform degenerate-twist result; accordingly, the admissible perturbation threshold explicitly deteriorates as the twist constant m approaches zero. Consequently, we prove that symplectic integrators exhibit exponential stability over exponentially long time scales. Our results, derived via resonant normal form construction and the geometric covering of the action space, furnish rigorous and computable bounds for the long-term preservation of action variables, thereby offering new insights into the nonlinear dynamical behavior of geometric discretizations. Full article

Clamp band separation mechanisms are widely used in spacecraft interfaces, and the clamp band preload is a key factor governing both connection reliability and separation performance. The conventional torque-control method is susceptible to friction-induced preload non-uniformity in clamp band separation mechanisms. To overcome this limitation, thermal preloading has been proposed as an alternative installation method. In this paper, a thermo-mechanical analytical model is established for clamp band separation mechanisms during thermal preloading based on curved-beam and thin-shell theories. Theoretical analysis shows that the preload distribution can be divided into three characteristic zones: a stick zone, a slip zone, and a separation zone. In the stick zone, the preload remains constant and is mainly governed by thermal stress and structural relative stiffness. In the slip zone, friction dominates the load transfer, leading to a non-uniform preload distribution. In the separation zone, local disengagement occurs near the clamp band joint end due to the eccentricity-induced bending moment. The proposed model is validated by finite element simulations, and parametric studies are conducted to reveal the effects of friction coefficient and structural geometric parameters on preload distribution. Based on the theoretical model, a zoned-heating method is proposed to improve preload uniformity, providing a useful reference for optimizing the thermal preloading method. Full article