Search Results (347)

The disintegration of near-limit flames propagating through the gap of Hele–Shaw cells has recently become a subject of active research. In this paper, the flamelets resulting from the disintegration of the continuous front are interpreted in terms of the Zeldovich flame balls stabilized by volumetric heat losses. A complicated free-boundary problem for 2D self-drifting near circular flamelets is reduced to a quasi-1D model. The quasi-1D formulation is then utilized to obtain the locus of the flamelet velocity, size, heat losses, and Lewis numbers at which the self-drifting flamelets may exist. Full article

This article introduces two numerical methods based on the Theory of Functional Connections (TFC) for solving linear ordinary differential equations that involve step discontinuities in the forcing term. The novelty of the first proposed approach lies in the direct incorporation of discontinuities into the free function of the TFC framework, while the second proposed method resolves discontinuities through piecewise constrained expressions comprising particular weighted support functions systematically chosen to enforce continuity conditions. The accuracy of the proposed methods is validated for both a second-order initial value and boundary value problem. As a final demonstration, the methods are applied to a third-order differential equation with non-constant coefficients and multiple discontinuities, for which an analytical solution is known. The methods achieve error levels approaching machine precision, even in the case of equations involving functions whose Laplace transforms are not available. Full article

Optical remote sensing images are often partially obscured by clouds due to the inability of visible light to penetrate cloud cover, which significantly limits their subsequent applications. Most existing cloud removal methods formulate the problem using low-rank and sparse priors within a discrete representation framework. However, these approaches typically rely on manually designed regularization terms, which fail to accurately capture the complex geostructural patterns in remote sensing imagery. In response to this issue, we develop a continuous blind cloud removal model. Specifically, the cloud-free component is represented using a continuous tensor function that integrates implicit neural representations with low-rank tensor decomposition. This representation enables the model to capture both global correlations and local smoothness. Furthermore, a band-wise sparsity constraint is employed to represent the cloud component. To preserve the information in regions not covered by clouds during reconstruction, a box constraint is incorporated. In this constraint, cloud detection is performed using an adaptive thresholding strategy, and a morphological erosion function is employed to ensure accurate detection of cloud boundaries. To efficiently handle the developed model, we formulate an alternating minimization algorithm that decouples the optimization into three interpretable subproblems: cloud-free reconstruction, cloud component estimation, and cloud detection. Our extensive evaluations on both synthetic and real-world data reveal that the proposed method performs competitively against state-of-the-art cloud removal methods. Full article

This study presents an analytical model to reduce the impact of wave-induced forces on a vertical seawall by introducing a floating elastic plate (EP) located at a specific distance from two bottom-standing porous structures (BSPs). The hydrodynamic interaction with the EP is described using thin plate theory, while the fluid flow through the porous medium is described by the model developed by Sollit and Cross. The resulting boundary value problem is addressed through linear potential theory combined with the eigenfunction expansion method (EEM), and model validation is achieved through consistency checks with recognized results from the literature. A comprehensive parametric analysis is performed to evaluate the influence of key system parameters such as the porosity and frictional coefficient of the BSPs, their height and width, the flexural rigidity of the EP, and the spacing between the EP and BSPs on vital hydrodynamic coefficients, including the wave force on the seawall, free surface elevation, wave reflection coefficient, and energy dissipation coefficient. The results indicate that higher frictional coefficients and higher BSP heights significantly enhance wave energy dissipation and reduce reflection, in accordance with the principle of energy conservation. Oscillatory trends observed with respect to wavenumbers in the reflection and dissipation coefficients highlight resonant interactions between the structures. Moreover, compared with a single BSP, the double BSP arrangement is more effective in minimizing the wave force on the seawall and free surface elevation in the region between the EP and the wall, even when the total volume of porous material remains unchanged. The inter-structural gap is found to play a crucial role in optimizing resonance conditions and supporting the formation of a tranquility zone. Overall, the proposed configuration demonstrates significant potential for coastal protection, offering a practical and effective solution for reducing wave loads on marine infrastructure. Full article

The motion of viscous compressible magnetohydrodynamics (MHD) is considered in a domain bounded by a free boundary. The motion interacts through the free surface with an electromagnetic field located in a domain that is exterior to the free surface and bounded by a given fixed surface. Some data for the electromagnetic fields are prescribed on this fixed boundary. On the free surface, jumps in magnetic and electric fields are assumed. We prove the local existence of solutions by the method of successive approximations using Sobolev–Slobodetskii spaces. Full article

A common technique used in factories to shape metal panels is shot peen forming, where the panel is sprayed with a high-velocity stream of small steel pellets called “shot.” The impacts between the hard steel shot and the softer metal of the panel cause localized plastic deformation, which is used to improve the fatigue properties of the material’s surface. The residual stress distribution imparted by impacts also results in bending, which suggests that a torque is associated with it. In this paper, we model shot peen forming as the application of spatially varying torques to a Kirchhoff plate, opting to use the language of thermoelasticity in order to introduce these torque distributions. First, we derive the governing equations for the thermoelastic thin plate model and show that only a torque-type resultant of the temperature distribution shows up in the bending equation. Next, to calibrate from the shot peen operation, an empirical “effective torque” parameter used in the thermoelastic model, a simple and non-invasive test is devised. This test relies only on measuring the maximum displacement of a uniformly shot peened plate as opposed to characterizing the residual stress distribution. After discussing how to handle the unconventional fully free boundary conditions germane to shot peened plates, we introduce an approach to solving the inverse problem whereby the peening distribution required to obtain a specified plate contour can be obtained. Given that the relation between shot peen distributions and bending displacements at a finite set of points is non-unique, we explore a regularization of the inverse problem which gives rise to shot peen distributions that match the capabilities of equipment in the factory. In order to validate our proposed model, an experiment with quantified uncertainty is designed and carried out which investigates the agreement between the predictions of the calibrated model and real shot peen-forming operations. Full article

Detecting previously unseen anomalies in sensor data is a challenging problem for artificial intelligence when sensor-specific and deployment-specific characteristics of the time series need to be learned from a short calibration period. From the application point of view, this challenge becomes increasingly important because many applications are gravitating towards utilising low-cost sensors for Internet of Things deployments. While these sensors offer cost-effectiveness and customisation, their data quality does not match that of their high-end counterparts. To improve sensor data quality while addressing the challenges of anomaly detection in Internet of Things applications, we present an anomaly detection framework that learns a normality model of sensor data. The framework models the typical behaviour of individual sensors, which is crucial for the reliable detection of sensor data anomalies, especially when dealing with sensors observing significantly different signal characteristics. Our framework learns sensor-specific normality models from a small set of anomaly-free training data while employing an unsupervised feature engineering approach to select statistically significant features. The selected features are subsequently used to train a Local Outlier Factor anomaly detection model, which adaptively determines the boundary separating normal data from anomalies. The proposed anomaly detection framework is evaluated on three real-world public environmental monitoring datasets with heterogeneous sensor readings. The sensor-specific normality models are learned from extremely short calibration periods (as short as the first 3 days or 10% of the total recorded data) and outperform four other state-of-the-art anomaly detection approaches with respect to F1-score (between 5.4% and 9.3% better) and Matthews correlation coefficient (between 4.0% and 7.6% better). Full article

Seismic responses of Nuclear Island (NI) structures have great significance in the foundation adaptability analysis and the seismic design of equipment. However, with the increasing complexity of nuclear power site conditions, establishing a reasonable and effective soil–pile–structure dynamic interaction model has become the key technical problem that needs to be solved. In this study, a pseudo three-dimensional soil–pile–structure dynamic interaction model considering soil nonlinearity and heterogeneity is developed for seismic response analysis of NI structures. Specifically, the nonlinearity of the near-field soil is described via the equivalent linear method, the radiation damping effect of half space is simulated through viscous boundary, and the displacement/stress conditions at lateral boundaries of the heterogeneous site are derived from free-field response analysis. Meanwhile, an equivalent stiffness–mass principle is established to simplify NI superstructures, while pile group effects are incorporated via a node-coupling scheme within the finite-element framework. Two validation examples are presented to demonstrate the accuracy and efficiency of the proposed model. Finally, seismic response analysis of two typical NI structure of reactor types (CPR1000 and AP1000) based on the actual complex site conditions in China is also presented to study the effect of radiation damping, soil conditions, and pile foundation. Key findings demonstrate the necessity of integrating SSI effects and nonlinear characteristics of non-rock foundations. While the rock-socketed pile exhibits superior performance compared to the CFG pile alternative; this advantage is offset by higher costs and construction complexity. The research findings can serve as a valuable reference for the foundation adaptability analysis and optimizing the design of equipment under the similar complex condition of the soil site. Full article

The entanglement entropy of a random tensor network (RTN) is studied using tools from free probability theory. Random tensor networks are simple toy models that help in understanding the entanglement behavior of a boundary region in the anti-de Sitter/conformal field theory (AdS/CFT) context. These can be regarded as specific probabilistic models for tensors with particular geometry dictated by a graph (or network) structure. First, we introduce a model of RTN obtained by contracting maximally entangled states (corresponding to the edges of the graph) on the tensor product of Gaussian tensors (corresponding to the vertices of the graph). The entanglement spectrum of the resulting random state is analyzed along a given bipartition of the local Hilbert spaces. The limiting eigenvalue distribution of the reduced density operator of the RTN state is provided in the limit of large local dimension. This limiting value is described through a maximum flow optimization problem in a new graph corresponding to the geometry of the RTN and the given bipartition. In the case of series-parallel graphs, an explicit formula for the limiting eigenvalue distribution is provided using classical and free multiplicative convolutions. The physical implications of these results are discussed, allowing the analysis to move beyond the semiclassical regime without any cut assumption, specifically in terms of finite corrections to the average entanglement entropy of the RTN. Full article

An efficient numerical approach utilizing a variational weak form, grounded in 2D elastic theory and variational principles, is proposed for analyzing the in-plane vibrational behavior of rectangular plates resting on elastically restrained boundaries. The differential and integral operators can be discretized into matrix representations employing the differential quadrature method (DQM) and Taylor series expansion techniques. The discretization of dynamics equations stems directly from a weak formulation that circumvents the need for any transformation or discretization of higher-order derivatives encountered in the corresponding strong equations. Utilizing the matrix elementary transformation technique, the displacements of boundary and internal nodes are segregated, subsequently leading to the derivation of the generalized eigenvalue problem pertaining to the free vibration analysis of the Functionally Graded Material (FGM) rectangular plate. Furthermore, the study examines the impact of the gradient parameter, aspect ratio, and elastic constraints on the dimensionless frequency characteristics of the FGM rectangular plate. Ultimately, the modal properties of an in-plane FGM rectangular plate are investigated. Full article

Modern fighter aircraft have an increasing need for at least a moderate level of stealth, and the shape design must bear a part of this constraint. However, the high frequency of close range radar makes high-fidelity radar cross-section computation methods such as the boundary element method too expensive to use in a gradient-free optimization process. On the other hand, asymptotic methods are not able to accurately predict the RCS of complex shapes such as intake cavities. Hence, the need arises for efficient and accurate methods to compute the gradient of high-fidelity radar cross-section computation methods with respect to shape parameters. In this paper, we propose an adjoint formulation for the boundary element method to efficiently compute these gradients. We present a novel approach to calculate the gradient of high-fidelity radar cross-section computations using the boundary element method. Our method employs an adjoint formulation that allows for the efficient computation of these gradients. This is particularly beneficial in shape optimization problems where accurate and efficient methods are crucial to designing modern fighter aircraft with stealth capabilities. By avoiding the need for solving the actual adjoint problem in certain cases, our formulation provides a more streamlined solution while still maintaining high accuracy. We demonstrate the effectiveness of our method by performing shape optimization on various shapes, including simple geometries like spheres and ellipsoids, as well as complex aircraft shapes with multiple variables. Full article

Mold copper plates (Cr–Zr–Cu alloy) frequently fail due to severe wear under high-temperature conditions during continuous casting. To solve this problem, Inconel 718 coatings were prepared on the plate surface via laser cladding to enhance its high-temperature wear resistance. The results demonstrate that the coatings exhibit a defect-free structure with metallurgical bonding to the substrate. The coating primarily consists of a γ-(Fe, Ni, Cr) solid solution and carbides (M₂₃C₆ and M₆C). Notably, elongated columnar Laves phases and coarse Cr–Mo compounds were distributed along grain boundaries, significantly enhancing the coating’s microhardness and high-temperature stability. The coating exhibited an average microhardness of 491.7 HV_0.5, which is approximately 6.8 times higher than that of the copper plate. At 400 °C, the wear rate of the coating was 4.7 × 10⁻⁴ mm³·N⁻¹·min⁻¹, significantly lower than the substrate’s wear rate of 8.86 × 10⁻⁴ mm³·N⁻¹·min⁻¹, which represents only 53% of the substrate’s wear rate. The dominant wear mechanisms were adhesive wear, abrasive wear, and oxidative wear. The Inconel 718 coating demonstrates superior hardness and excellent high-temperature wear resistance, effectively improving both the surface properties and service life of mold copper plates. Full article

We consider the melting of a one-dimensional domain ($x\ge 0$), initially at the melting temperature $u=0$, by fixing the boundary temperature to a value $u(0,t)=U_0>0$—the so called Stefan melting problem. The governing transient heat-conduction equation involves a time derivative and the spatial derivative of the temperature gradient. In the general case the order of the time derivative and the gradient can take values in the range $(0,1]$. In these problems it is known that the advance of the melt front $s\left(t\right)$ can be uniquely determined by a specified prefactor multiplying a power of time related to the order of the fractional derivatives in the governing equation. For given fractional orders the value of the prefactor is the unique solution to a transcendental equation formed in terms of special functions. Here, our main purpose is to provide efficient numerical schemes with low computational complexity to compute these prefactors. The values of the prefactors are obtained through a dimensionalization that allows the recovery of the solution for the quasi-stationary case when the Stefan number approaches zero. The mathematical analysis of this convergence is given and provides consistency to the numerical results obtained. Full article

In this paper, we study perpetual American put options with a generalized standard put payoff and establish sufficient conditions for the existence and uniqueness of the solution to the associated pricing problem. As a key tool, we express the Black–Scholes operator in terms of elasticity. This formulation enables us to demonstrate that the considered pricing problem admits a unique solution when the payoff function exhibits strictly decreasing elasticity with respect to the underlying asset. Furthermore, this approach allows us to derive closed-form solutions for option pricing. Full article

This research introduces an innovative probabilistic method for examining torsional stress behavior in spherical shell structures through Monte Carlo simulation techniques. The spherical geometry of these components creates distinctive computational difficulties for conventional analytical and deterministic numerical approaches when solving torsion-related problems. The authors develop a comprehensive mesh-free Monte Carlo framework built upon the Feynman–Kac formula, which maintains the geometric symmetry of the domain while offering a probabilistic solution representation via stochastic processes on spherical surfaces. The technique models Brownian motion paths on spherical surfaces using the Euler–Maruyama numerical scheme, converting the Saint-Venant torsion equation into a problem of stochastic integration. The computational implementation utilizes the Fibonacci sphere technique for achieving uniform point placement, employs adaptive time-stepping strategies to address pole singularities, and incorporates efficient algorithms for boundary identification. This symmetry-maintaining approach circumvents the mesh generation complications inherent in finite element and finite difference techniques, which typically compromise the problem’s natural symmetry, while delivering comparable precision. Performance evaluations reveal nearly linear parallel computational scaling across up to eight processing cores with efficiency rates above 70%, making the method well-suited for multi-core computational platforms. The approach demonstrates particular effectiveness in analyzing torsional stress patterns in thin-walled spherical components under both symmetric and asymmetric boundary scenarios, where traditional grid-based methods encounter discretization and convergence difficulties. The findings offer valuable practical recommendations for material specification and structural design enhancement, especially relevant for pressure vessel and dome structure applications experiencing torsional loads. However, the probabilistic characteristics of the method create statistical uncertainty that requires cautious result interpretation, and computational expenses may surpass those of deterministic approaches for less complex geometries. Engineering analysis of the outcomes provides actionable recommendations for optimizing material utilization and maintaining structural reliability under torsional loading conditions. Full article