Search Results (252)

Based on the spatial compact finite difference (SCFD) method, an improved high-order temporal accuracy scheme for high-dimensional time-fractional diffusion equations (TFDEs) is presented in this work. Combining the temporal piecewise quadratic interpolation and the high-dimensional SCFD method, the proposed numerical method is described. In order to establish the stability and convergence analysis, we introduce a norm $\left|\right|·{\left|\right|}_{{\tilde{H}}^1}$, which is rigorously proved equivalent to the standard $H^1$-norm. Considering that the coefficients of high-order numerical schemes are not entirely positive, we introduce an appropriate parameter to transform the numerical scheme into an equivalent form with positive coefficients. Based on the equivalent form, we prove that the temporal and spatial convergence orders are $(3-\gamma )$ and 4 by applying the convergence of geometric progression. The proposed scheme ensures that the theoretical convergence accuracy at each time step is of order $(3-\gamma )$ without requiring any additional processing techniques. Ultimately, the convergence of the proposed high-order accurate scheme is verified through numerical experiments involving (non-)linear high-dimensional TFDEs. Full article

Graphene-based micro-ring modulators are promising candidates for next-generation optical interconnects, offering compact footprints, broadband operation, and CMOS compatibility. However, most demonstrations to date have relied on conventional straight bus coupling geometries, which limit design flexibility and require extremely small coupling gaps to reach critical coupling. This work presents a comprehensive comparative analysis of straight, bent, and racetrack bus geometries in graphene-on-silicon nitride (Si₃N₄) micro-ring modulators operating near 1.31 µm. Based on finite-difference time-domain simulation results, a proposed racetrack-based modulator structure demonstrates that extending the coupling region enables critical coupling at larger gaps—up to 300 nm—while preserving high modulation efficiency. With only 6–12% graphene coverage, this geometry achieves extinction ratios of up to 28 dB and supports electrical bandwidths approaching 90 GHz. Findings from this work highlight a new co-design framework for coupling geometry and graphene coverage, offering a pathway to high-speed and high-modulation-depth graphene photonic modulators suitable for scalable integration in next-generation photonic interconnects devices. Full article

We describe the output characteristics of a compact, passively Q-switched, diode-end-pumped (Er/Yb):Glass laser operating in a multi-pulse burst mode. Such operation enables much higher optical efficiency and larger output of total energy than possible with conventional solitary pulse emissions. The laser generated a 15-pulse burst of pulses at 1.5 μm with a combined energy of 5.8 mJ. Measurements of pulse energies, spatial mode characteristics, output beam divergence, and impact of thermal effects in the (Er/Yb):Glass are described. These results are compared to predictions of a numerical simulation using a finite-difference beam propagation method (FD-BPM) that incorporates thermal effects caused by distributed local heating in the glass. We show good agreement between the measured and simulated laser output characteristics. Full article

We propose a high-speed all-optical logic gate design based on silicon racetrack and ring resonators patterned on a silica substrate. The architecture features racetrack resonators at both the input and output, with a central ring resonator enabling the required phase-sensitive interference for logic processing. Logic operations are achieved through the interplay of constructive and destructive interference induced by phase-shifted input beams. Using the finite-difference time-domain (FDTD) method in Lumerical software, we simulate and demonstrate seven fundamental Boolean logic functions, namely XOR, AND, OR, NOT, NOR, NAND, and XNOR, at an operating wavelength of 1.33 µm. The system supports a data rate of 47.94 Gb/s, suitable for ultrafast optical computing. The performance is quantitatively evaluated using the contrast ratio (CR) as the reference metric, with more than acceptable values of 13.09 dB (XOR), 13.84 dB (AND), 13.14 dB (OR), 13.80 dB (NOT), 14.53 dB (NOR), 13.80 dB (NAND), and 14.67 dB (XNOR), confirming strong logic level discrimination. Comparative analysis with existing optical gate designs underscores the advantages of our compact silicon-on-silica structure in terms of speed, CR performance, and integration potential. This study validates the effectiveness of racetrack–ring configurations for next-generation all-optical logic circuits. Full article

An optical power splitter (OPS) with arbitrary splitting ratios has attracted significant research interest for its broad applications in photonic integrated circuits. A series of OPSs with arbitrary splitting ratios based on silicon nitride (Si₃N₄) platforms are presented. The devices are designed with ultra-compact dimensions using three-dimensional finite-difference time-domain (3D FDTD) analysis and an inverse design algorithm. Within a 50 nm bandwidth (1525 nm to 1575 nm), we demonstrated a 1 × 2 OPS with splitting ratios of 1:1, 1:1.5, and 1:2; a 1 × 3 OPS with ratios of 1:2:1 and 2:1:2; and a 1 × 4 OPS with ratios of 1:1:1:1 and 2:1:2:1. The target splitting ratios are achieved by optimizing pixel distributions in the coupling region. The dimensions of the designed devices are 1.96 × 1.96 µm², 2.8 × 2.8 µm², and 2.8 × 4.2 µm², respectively. The designed devices achieve transmission efficiencies exceeding 90% and exhibit excellent power splitting ratios (PSRs). Full article

An innovative high-order dimensionality reduction approach, which integrates a condensed finite-difference scheme with proper orthogonal decomposition techniques, has been explored for solving diffusion equations. The difference scheme with forth order accurate in both space and time is introduced through the idea of interpolation approximation. The quartic spline function and $(2,2)$ Padé approximation were utilized in space and time discretization, respectively. The stability and convergence were proven. Moreover, the dimensionality reduction formulas were derived using the proper orthogonal decomposition (POD) method, which is based on the matrix representation of the compact finite-difference scheme. The bases of the POD method were established by cumulative contribution rate of the eigenvalues of snapshot matrix that is different from the traditional ways in which the bases were established by the first eigenvalues. The method of cumulative contribution rate can optimize the degree of freedom. The error analysis of the reduced bases high-order POD finite-difference scheme was provided. Numerical experiments are conducted to validate the soundness and dependability of the reduced-order algorithm. The comparisons between the $(2,2)$ finite-difference method, the traditional POD method, and reduced dimensional method with cumulative contribution rate were discussed. Full article

Cryosurgery employs extremely low temperatures to destroy abnormal or cancerous tissue. Conventional systems use cryogenic fluids like liquid nitrogen or argon, which pose challenges in handling, cost, and precise temperature control. This study explores thermoelectric (TE) cooling using the Peltier effect as an efficient alternative. A numerical optimization of multi-stage TE coolers using bismuth telluride (Bi₂Te₃) is performed through finite element analysis in COMSOL Multiphysics. Results show that the optimized multi-stage TE system achieves a minimum temperature of −70 °C, a 90 K temperature difference, and 4.0 W cooling power—outperforming single-stage (SS) systems with a maximum ΔT of 73.27 K. The study also investigates the effects of material properties, current density, and geometry on performance. An optimized multi-stage (MS) configuration improves cooling efficiency by 22.8%, demonstrating the potential of TE devices as compact, energy-efficient, and precise solutions for cryosurgical applications. Future work will explore advanced nanomaterials and hybrid systems to further improve performance in biomedical cooling. Full article

In this paper, we propose a high-order compact difference scheme for a class of time-fractional convection–diffusion–reaction equations (CDREs) with variable coefficients. Using the Lagrange polynomial interpolation formula for the time-fractional derivative and a compact finite difference approximation for the spatial derivative, we establish an unconditionally stable compact difference method. The stability and convergence properties of the method are rigorously analyzed using the Fourier method. The convergence order of our discrete scheme is $\mathcal{O}({\tau }^{4-\alpha }+h^8)$, where $\tau$ and h represent the time step size and space step size, respectively. This work contributes to providing a better understanding of the dependability of the method by thoroughly examining convergence and conducting an error analysis. Numerical examples demonstrate the applicability, accuracy, and efficiency of the suggested technique, supplemented by comparisons with previous research. Full article

We propose a dual-ring optical filter based on direct binary search inverse design. The proposed device comprises two cascaded rings in an add–drop configuration. A physical model was established using temporal coupled mode theory to derive theoretical spectra and analyze key parameters governing transmission performance. Based on theoretical results, a direct binary search algorithm was implemented. The parameters of the proposed device were calculated using a three-dimensional finite-difference time-domain method for verification. The numerical results demonstrate a free spectral range of 86 nm, with insertion loss and extinction ratios of 0.3 dB and 22 dB, respectively. The proposed device has a narrow spectral linewidth of 0.3 nm within a compact footprint of $24 \mathsf{\mu }\mathrm{m}\times 25.5 \mathsf{\mu }\mathrm{m}$. The device shows significant application potential in laser external cavities and dense wavelength division multiplexing systems. Moreover, this work provides a novel methodology for precision design of photonic devices. Full article

In this paper, a discrete element method (DEM) coupled with a finite element method (FEM) was used to elucidate the impact of packing structures and size ratios on the cold die compaction behavior of pure copper powders. HCP structure, SC structure, and three random packing structures with different particle size ratios (1:2, 1:3, and 1:4) were generated by the DEM, and then simulated by the FEM to analyze the average relative density, von Mises stress, and force chain structures of the compact. The results show that for HCP and SC structures with a regular stacking structure, the average relative densities of the compact were higher than those of random packing structures, which were 0.9823, 0.9693, 0.9456, 0.9502, and 0.9507, respectively. Compared with their initial packing density, it could be improved by up to 21.13%. For the bigger particle in HCP and SC structures, the stress concentration was located between the adjacent layers, while in the small particles, it was located between contacted particles. During the initial compaction phase, smaller particles tend to occupy the voids between larger particles. As the pressure increases, larger particles deform plastically in a notable way to create a stabilizing force chain. This action reduces the axial stress gradient and improves radial symmetry. The transition from a contact-dominated to a body-stress-dominated state is further demonstrated by stress distribution maps and contact force vector analysis, highlighting the interaction between particle rearrangement and plasticity. Full article

High concrete gravity dams, particularly Roller-Compacted Concrete (RCC) types, face long-term safety challenges due to weak interlayer formation and crack propagation. This study presented a comprehensive evaluation of safety monitoring indexes for the Guxian high RCC dam (currently under construction) using both numerical and mathematical models. A finite element method (FEM) is employed with a strength reduction approach to assess dam stability considering weak layers. In parallel, a fracture mechanical model is used to investigate the safety of the Guxian dam based on failure assessment diagrams (FADs) for calculating the safety factor and the residual strength curve for calculating critical crack depth for two different crack locations, single-edge and center-through crack, to investigate the high possible risk associated with crack location on the dam safety. Additionally, the Guxian dam’s resistance to hydraulic fracture is assessed under two fracture mechanic failure modes, Mode I (open type) and Mode II (in-plane shear), by computing the ultimate overload coefficient using a proposed novel derived formula. The results show that weak layers reduce the dam’s safety index by approximately 20%, especially in lower sections with extensive interfaces. Single-edge cracks pose greater risk, decreasing the safety factor by 10% and reducing critical crack depth by 40% compared to center cracks. Mode II demonstrates higher resistance to hydraulic fracture due to greater shear strength and fracture energy, whereas Mode I represents the most critical failure scenario. The findings highlight the urgent need to incorporate weak layer behavior and hydraulic fracture mechanisms into dam safety monitoring, and to design regulations for high RCC gravity dams. Full article

In this paper, we present a compact finite difference method for solving the cubic–quintic Schrödinger equation with an additional anti-cubic nonlinearity. By applying a special treatment to the nonlinear terms, the proposed method preserves both mass and energy through provable conservation properties. Under suitable assumptions on the exact solution, we establish upper and lower bounds for the numerical solution in the infinity norm, and further prove that the errors are fourth-order accurate in space and second-order in time in both the 2-norm and infinity norm. A detailed description of the nonlinear system solver at each time step is provided. We validate the proposed method through numerical experiments that demonstrate its efficiency, including fourth-order convergence (when sufficiently small time steps are used) and machine-level accuracy in the relative errors of mass and energy. Full article

In this paper, the analysis method which coupled discrete element method (DEM) and finite element method (FEM) is used to simulate the double compaction of random packing of Cu and Al composite powders with multiple particle sizes. Cu and Al composite powders with varying particle size ratios from 1:2 to 1:5 were generated by DEM and then imported to MSC. Marc software (MSC.MARC2015 version) to construct FEM analysis. The effects of metal ratios, compaction pressure and size ratios on the relative density and von Mises stress of the compact were studied. The results show that the average relative density of the compact increases with the Al content, and the stress decreases. The stress in the Cu particle is particularly higher than that in the Al particle, mainly because the contact normal force of the Cu particle is nearly parallel at each contact surface. Therefore, the phenomenon of stress concentration is easier to occur within copper particles. When Al content is 30wt.%, the particle size difference enhances densification efficiency by up to 12.3%, as evidenced by an initial relative density increase from 0.7915 to 0.8047, primarily due to smaller Cu particles effectively filling interparticle voids. When the compaction pressure is fixed, the average relative density of the compact with the particle size ratio 1:5 is higher than the others, and the contact forces inside the particles significantly decrease. Full article

Atrial leadless pacemakers (ALPMs) offer a minimally invasive solution for patients requiring atrial pacing, but current designs face significant challenges related to fixation stability, perforation risk, and retrievability. This study presents a novel self-expanding nitinol fixation system designed for deployment within the left atrial appendage (LAA), incorporating a flexible adapter for secure pacemaker engagement and retrieval. Finite-element simulations were conducted to assess gravitational displacement across different anatomical orientations, and fixture-expansion behavior was analyzed under various mesh configurations. The pacemaker drop analysis results demonstrated minimal displacement in neutral and upward-tilted LAA models, with increased instability observed in downward-tilted orientations. The fixture-expansion study showed that the 0.2 mm mesh design provided adequate mechanical strength and strain tolerance while maintaining a compact profile. This novel fixation system improves current ALPM limitations by providing stable, retrievable anchoring and favorable biomechanical performance. It may also serve as a dual-function platform for atrial pacing and stroke prevention when integrated with a left atrial appendage (LAA) occluder. These findings support further preclinical validation for clinical translation. Full article

This paper focuses on improvement effects on soil foundations under dynamic compaction (DC). Firstly, a confocal ellipsoidal densification model (CEDM) composed of a heavy compacted zone (HCZ) and a weak compacted zone (WCZ) was proposed to describe the subarea characteristic of an improvement range. Next, based on a confocal assumption of HCZ and WCZ ellipses, a mass balance equation considering changes in soil dry density in different compacted zones was established for solving the ellipsoidal parameters. Then, a designed laboratory test was conducted and a two-dimensional (2D) finite element model (FEM) established. The simulated crater depth and dynamic stress agreed well with testing results, confirming that the established FEM could be used for investigating the DC process. Finally, the applicability of the solution procedure for the proposed CEDM was verified. The predicted HCZ and WCZ were in close agreement with the simulated results, indicating that the proposed CEDM could be used for estimating the soil improvement range. With increases in tamping times, the HCZ ellipse moved down in the vertical direction without volumetric expansion, while the WCZ ellipse expanded along the depth and lateral directions. These findings may offer some guidelines for research into improvement effects on soil foundation under DC. Full article