Backward erosion piping (BEP) is a leading internal erosion mechanism for flood protection system failures. A model capable of predicting critical hydraulic conditions for BEP initiation at multiple scales while also incorporating soil variability is a pressing need. This study formulates and validates a novel multiscale probabilistic BEP initiation framework with incorporation of soil variability

Backward erosion piping (BEP) is a significant contributor to failures in global flood protection infrastructure, yet it remains among the least understood geotechnical phenomena, particularly concerning the fundamental mechanisms driving its initiation. This study focuses on the development of a novel stochastic framework for the prediction of critical hydraulic gradients causing BEP initiation. The

This work is concerned with the analysis of a space–time finite element discontinuous Galerkin method on polytopal meshes (XT-PolydG) for the numerical discretization of wave propagation in coupled poroelastic–elastic media. The mathematical model consists of the low-frequency Biot’s equations in the poroelastic medium and the elastodynamics equation for the elastic one. To realize the coupling suitable

The dynamics of the magnetization in ferromagnetic materials is governed by the Landau–Lifshitz–Gilbert equation, which is highly nonlinear with the nonconvex sphere constraint $|{\textbf{m}}|=1$. A crucial issue in designing numerical schemes is to preserve this sphere constraint in the discrete level. A popular numerical method is the normalized tangent plane finite element method (NTP-FEM), which

To study and enhance the obstacle‐crossing performance of the electric shovel, an obstacle‐crossing model that employs a coupling methodology integrating the discrete element method (DEM) and multi‐body dynamics (MBD) is constructed. Secondly, the influence of grouser height (GH), track velocity (TV), slope inclination (SI) and slope height (SH) on obstacle‐crossing performance is investigated through

We study a higher-order surface finite-element penalty-based discretization of the tangential surface Stokes problem. Several discrete formulations are investigated, which are equivalent in the continuous setting. The impact of the choice of discretization of the diffusion term and of the divergence term on numerical accuracy and convergence, as well as on implementation advantages, is discussed. We

In this article, convergence and quasi-optimal rate of convergence of an Adaptive Finite Element Method is shown for the Dirichlet boundary control problem that was proposed by Chowdhury et al. (2017, Error bounds for a Dirichlet boundary control problem based on energy spaces, Math. Comp., 86, 1103–1126). The theoretical results are illustrated by numerical experiments.

Molecular dynamics (MD) and the material point method (MPM) are both particle methods in spatial discretization. Molecular dynamics is a discrete particle method that is widely applied to predict fundamental physical properties and dynamic materials behaviors at nanoscale. The MPM is a continuum‐based particle method that was proposed about three decades ago to simulate large‐deformation problems involving

The dynamic pile‐soil interaction significantly affects the accuracy of pile vibration response analysis. However, currently, there is no well‐established method for simulating pile toe soil under high‐strain dynamic loading (HSDL), which presents a major challenge for pile driving analysis. This paper proposes a fictitious soil pile model to simulate reactions and stress wave propagation in the base

The numerical investigation in this study focuses on the propagation of hydraulically driven fractures in deformable porous media containing two fluid phases. The fully coupled hydro‐mechanical governing equations are discretized and solved using the extended element‐free Galerkin method. The wetting fluid is injected into the initial crack. The pores are filled with both wetting and non‐wetting fluid

A three‐field finite element (FE) model for dynamic porous media considering the de la Cruz and Spanos (dCS) theory is presented. Due to fluid viscous dissipation terms, wave propagation in the dCS theory yields an additional rotational wave compared to Biot (BT) theory. In addition, introducing porosity as a dynamic variable in the dCS model allows solid‐fluid nonreciprocal interactions. Due to the

During the process of treating soft soil foundations with prefabricated drainage drains (PVD), “soil columns” form around the PVD, and a “weak zone” forms outside the range of the “soil columns.” The difference in properties between the two forms a distinct interface, leading to a gradual decrease in drainage efficiency and obstruction of vertical drainage channels, which in turn causes cracks and

SIAM Journal on Numerical Analysis, Volume 62, Issue 6, Page 2784-2787, December 2024. Abstract. This note is the correction of an error in the proof of Theorem 4.1 in [Q. Cheng and J. Shen, SIAM J. Numer. Anal., 60 (2022), pp. 970–998].

SIAM Journal on Numerical Analysis, Volume 62, Issue 6, Page 2782-2783, December 2024. Abstract. We correct a mistake in the paper [P. Manns and C. Kirches, SIAM J. Numer. Anal., 58 (2020), pp. 3427–3447]. The grid refinement strategy in Definition 4.3 needs to ensure that the order of the (sets of) grid cells that are successively refined is preserved over all grid iterations. This was only partially

SIAM Journal on Numerical Analysis, Volume 62, Issue 6, Page 2745-2781, December 2024. Abstract. We introduce a novel method, called swarm-based simulated annealing (SSA), for nonconvex optimization which is at the interface between the swarm-based gradient-descent (SBGD) [J. Lu et al., arXiv:2211.17157; E. Tadmor and A. Zenginoglu, Acta Appl. Math., 190 (2024)] and simulated annealing (SA) [V. Cerny

The Cracking Elements Method (CEM) is a numerical tool for simulation of quasi-brittle fracture. It neither needs remeshing, nor nodal enrichment, or a complicated crack-tracking strategy. The cracking elements used in the CEM can be considered as a special type of Galerkin finite elements. A disadvantage of the CEM is that it uses nonlinear interpolation of the displacement field (e.g. Q8 and T6 elements

A design optimization framework is proposed for process parameters in additive manufacturing. A finite element approximation of the coupled thermomechanical model is used to simulate the fused deposition of heated material and compute the objective function for each analysis. Both gradient-based and gradient-free optimization methods are developed. The gradient-based approach, which results in a balance

Deep geothermal energy, carbon capture and storage, and hydrogen storage hold considerable promise for meeting the energy sector's large‐scale requirements and reducing emissions. However, the injection of fluids into the Earth's crust, essential for these activities, can induce or trigger earthquakes. In this paper, we highlight a new approach based on reinforcement learning (RL) for the control of

Functional linear regression is one of the fundamental and well-studied methods in functional data analysis. In this work, we investigate the functional linear regression model within the context of reproducing kernel Hilbert space by employing general spectral regularization to approximate the slope function with certain smoothness assumptions. We establish optimal convergence rates for estimation

Soil–rock mixture (SRM) slopes consist of soils and rocks and are widely distributed globally. In addition to heterogeneity and discontinuity within SRM slopes, the inherent spatial variability can be observed in soil and rock properties. However, spatial variability in rock and soil properties and layouts has not been well considered in the stability analysis of SRM slopes. Additionally, SRM slopes

SIAM Journal on Numerical Analysis, Volume 62, Issue 6, Page 2719-2744, December 2024. Abstract. A novel family of high-order structure-preserving methods is proposed for the nonlinear Schrödinger equation. The methods are developed by applying the multiple relaxation idea to the exponential Runge–Kutta methods. It is shown that the multiple relaxation exponential Runge–Kutta methods can achieve high-order

The present paper introduces a methodology for formulating two-dimensional structural theories featuring arbitrary kinematic fields. In the proposed approach, each displacement variable can be examined through an independent expansion function, enabling the integration of both classical and higher-order theories within a unified framework. The Carrera Unified Formulation is used to derive the governing

In this paper, we propose a conforming multi-domain spectral method that combines mapping techniques to solve the diffusive-viscous wave equation in the exterior domain of two complex obstacles. First, we confine the exterior domain within a relatively large rectangular computational domain. Then, we decompose the rectangular domain into two sub-domains, each containing one obstacle. By applying coordinate

We study the $L^{p}$ rate of convergence of the Milstein scheme for stochastic differential equations when the drift coefficients possess only Hölder regularity. If the diffusion is elliptic and sufficiently regular, we obtain rates consistent with the additive case. The proof relies on regularization by noise techniques, particularly stochastic sewing, which in turn requires (at least asymptotically)

We use a generalized Riemann-Liouville type derivative of an abstract function of one variable and existence of a weak solution to an abstract fractional parabolic problem on [0, T] containing Riemann-Liouville derivative of a function of one variable and spectral fractional powers of a weak Dirichlet-Laplace operator to study existence of a strong solution to this problem. Our goal in this regard

In this paper, a three-dimensional arbitrary Lagrangian-Eulerian (ALE) formulation based on the consistent corotational method for flexible structures' large deformation problems is proposed. In contrast with the Lagrangian formulations, the proposed formulation can accurately describe moving boundary and load problems using moving nodes. The ALE formulation for flexible structures with an arbitrarily

Static liquefaction‐induced failure in tailings dams can result in extensive economic and environmental damage. In practice, the use of constitutive models capable of capturing this phenomenon and assessing structures susceptible to liquefaction is increasing. Numerous constitutive models exist and have been applied to model static liquefaction of tailings materials, but the extent of the influence

In this work we study the asymptotic consistency of the weak-form sparse identification of nonlinear dynamics algorithm (WSINDy) in the identification of differential equations from noisy samples of solutions. We prove that the WSINDy estimator is unconditionally asymptotically consistent for a wide class of models that includes the Navier–Stokes, Kuramoto–Sivashinsky and Sine–Gordon equations. We

Permeable pipe pile, a novel pile foundation integrating drainage and bearing functions, improves the bearing capacity of the pile foundation by accelerating the consolidation of the soil around the pile. In this study, a mathematical model is established to simulate the consolidation of surrounding clayey soils and the pile–soil interaction, where the rheological properties of the soils are described

The behavior of soft soils distributed in coastal areas usually exhibits obvious time‐dependent behavior after loading. To reasonably describe the stress‐strain relationship of soft soils, this paper establishes a viscoelastic‐viscoplastic small‐strain constitutive model based on the component model and the hardening soil model with small‐strain stiffness (HSS model). First, the Perzyna's viscoplastic

We propose an alternative definition of a mixed partial derivative in the Caputo sense for functions of two variables defined on the rectangle \(P=[0,a]\times [0,b]\) (\(a>0, b>0\)). We give an integral representation of functions possessing such a derivative. Moreover, we study the existence and uniqueness of a solution, as well as the Ulam–Hyers type stability of a fractional counterpart of a nonlinear

Prefabricated horizontal drains combined with vacuum preloading (PHDs‐VP) have addressed the shortcomings of prefabricated vertical drains combined with vacuum preloading (PVDs‐VP), beginning to emerge as a popular method for dredged slurry treatment. However, theoretical research on PHDs‐VP consolidation is relatively scarce. This study proposes a novel analytical model for predicting the consolidation

With the continuous urban development, tunnels are increasingly designed with curved alignments to avoid existing structures and to make better use of the underground space. However, these tunnels are usually subjected to complex forces, and current research on the curved tunnels face stability remains incomplete. This paper presents a detailed face stability analysis of curved tunnels, both analytically

The p‐y curve method provides a relatively simple and efficient means for analyzing the cyclic response of horizontally loaded piles. This study proposes a p‐y spring element based on a bounding surface p‐y model, which can be readily implemented in Abaqus software using the user‐defined element (UEL) interface. The performance of these p‐y spring elements is validated by simulating field tests of

In order to reveal the influence of double arc‐shaped fissure dip angles on the macro‐micro failure and energy evolution laws of rock masses, a numerical model of red sandstone was firstly established using the PFC2D. Moreover, mesoscopic parameters of the numerical model were calibrated based on the uniaxial compression tests on intact and single straight fissure red sandstone specimens. Then, particle

Based on the discrete element method and the centrifugal similarity theory, Particle Flow Code PFC2D was employed to establish numerical models of soil for compressed shallow foundations. The particle size effect and boundary effect of soil‐bearing capacity for compressed shallow foundations, as well as the microscopic characteristics and failure mechanisms of soil, were studied. The results show that

Let G be a finite abelian group. Let f:G→C be a signal (i.e. function). The classical uncertainty principle asserts that the product of the size of the support of f and its Fourier transform fˆ, supp(f) and supp(fˆ) respectively, must satisfy the condition:|supp(f)|⋅|supp(fˆ)|≥|G|.

Without imposing light-tailed noise assumptions, we prove that Tikhonov regularization for Gaussian Empirical Gain Maximization (EGM) in a reproducing kernel Hilbert space is consistent and further establish its fast exponential type convergence rates. In the literature, Gaussian EGM was proposed in various contexts to tackle robust estimation problems and has been applied extensively in a great variety

In this paper, an approach to model thin composite plates reinforced with curvilinear fibres is presented and applied to analyse modes of vibration. Particular attention is given to plates with non-standard geometries, which are less commonly addressed in studies on this topic. Aiming to achieve accuracy with a small number of degrees-of-freedom, the model is based on Kirchhoff’s plate theory, combined

In this paper, our goal is to study the following class of Hardy–Hénon type problems $$\begin{aligned} \left\{ \begin{array}{rclcl}\displaystyle (-\Delta )^{1/2} u& =& \lambda |x|^{\mu } u+|x|^{\alpha }f(u)& \text{ in }& (-1,1),\\ u& =& 0& \text{ on }& \mathbb {R}\setminus (-1,1), \end{array}\right. \end{aligned}$$ when \(\mu \ge \alpha {>-1}\), and the nonlinearity f has exponential critical growth

In this paper, we investigate the optimal control of a semi-linear fractional PDEs involving the spectral diffusion operator, or the realization of the integral fractional Laplace operator with the zero Dirichlet exterior condition, both of order s with \(s\in (0,1)\). The state equation contains a non-smooth nonlinearity, and the objective functional is convex in the control variable but contains

This paper addresses the questions of well-posedness to fractional m-Laplacian reaction diffusion equation with singular potential term and logarithmic nonlinearity: $$\begin{aligned} \left| x\right| ^{-2s}\partial _t u+(-\varDelta )_{m}^{s} u+ (-\varDelta )^{s} \partial _t u\!=\!u|u|^{-2} R(u), \end{aligned}$$ where \(R(u)=\left| u\right| ^{r}\ln (|u|)\). Guided by the made assumptions, we arrive

Soft soils exhibit significant time‐dependent effects during long‐term deformation. To precisely describe the long‐term behavior of soft soils, it is necessary to employ elastoplastic theory and rheology principles for investigating the stress–strain relationship of the soils. In this paper, a super‐subloading modified Cam‐clay model is initially derived. Subsequently, by introducing the Kelvin model

SIAM Journal on Numerical Analysis, Volume 62, Issue 6, Page 2698-2718, December 2024. Abstract. The computation of global radial basis function (RBF) approximations requires the solution of a linear system which, depending on the choice of RBF parameters, may be ill-conditioned. We study the stability and accuracy of approximation methods using the Gaussian RBF in all scaling regimes of the associated

This study introduces a general solution for assessing the longitudinal response of shield tunnels, incorporating the combined effects of joints and soil shear resistance. The analysis employs the Timoshenko beam spring model atop a Vlasov foundation, subjected to arbitrary loads and various boundary conditions. Governing equations and relevant boundary conditions are derived using a variational formulation

Stepped dumpling of waste is the main operating method used in landfill engineering. For the liners located at the bottom of the landfill, the waste can be considered as a vertical loading due to its heavy weight, causing compressive deformation of the liners and, most importantly, tending to lose the effectiveness of the geomembrane with the differential deformation. However, most experiments or numerical

Aiming at the treatment problem for water inflow in a high geothermal environment, we proposed a grouting simulation method in high‐temperature flowing water: temperature extended‐two‐fluid tracking (txTFT) method. First, a transport model for solving the residence time of slurry was derived. Furthermore, a temperature transport model was established to describe the heat transfer between slurry and

With the acceleration of urbanization, the stability of the foundation is being more crucial to the performance and service of the superstructure. As our understanding of the factors influencing soil's physical and mechanical behavior deepens, it becomes increasingly challenging for traditional limit equilibrium and limit analysis methods to accurately consider the complex factors affecting foundation

Here we introduce a notion of fractional k-dimensional measure, \(0\le k

In this paper, an important property of fractional order operators involving discontinuous functions is discussed, First, a pioneering work of impulsive fractional differential equations is recalled to illuminate the incorrectness of notation \({^C_{t_k}D}^{q}_t\). Second, a class of piecewise-defined equations with Caputo fractional derivative is contrastively investigated, and it is revealed that

SIAM Journal on Numerical Analysis, Volume 62, Issue 6, Page 2667-2697, December 2024. Abstract. We develop a two-stage, second-order, global-in-time energy stable implicit-explicit Runge–Kutta (IMEX RK(2, 2)) scheme for the phase field crystal equation with an [math] time step constraint, and without the global Lipschitz assumption. A linear stabilization term is introduced to the system with Fourier

When can the input of a ReLU neural network be inferred from its output? In other words, when is the network injective? We consider a single layer, x↦ReLU(Wx), with a random Gaussian m×n matrix W, in a high-dimensional setting where n,m→∞. Recent work connects this problem to spherical integral geometry giving rise to a conjectured sharp injectivity threshold for α=m/n by studying the expected Euler

A framework for Chebyshev spectral collocation methods for the numerical solution of functional and delay differential equations (FDEs and DDEs) is described. The framework combines interpolation via the barycentric resampling matrix with a multidomain approach used to resolve isolated discontinuities propagated by nonsmooth initial data. Geometric convergence in the number of degrees of freedom is

Bituminized waste products (BWPs) were produced by conditioning in bitumen the co‐precipitation sludge resulting from the industrial reprocessing of nuclear spent fuel. For some intermediate level long‐lived (ILW‐LL) classified BWPs, a long‐term disposal solution in France is underground geological disposal. One of the challenges for BWPs in geological disposal conditions is their swelling behavior

The regularity of refinable functions has been analysed in an extensive literature and is well-understood in two cases: 1) univariate 2) multivariate with an isotropic dilation matrix. The general (non-isotropic) case offered a great resistance. It was not before 2019 that the non-isotropic case was done by developing the matrix method. In this paper we make the next step and extend the Littlewood-Paley

In this paper, we present a convergence analysis of the Group Projected Subspace Pursuit (GPSP) algorithm proposed by He et al. [26] (Group Projected subspace pursuit for IDENTification of variable coefficient differential equations (GP-IDENT), Journal of Computational Physics, 494, 112526) and extend its application to general tasks of block sparse signal recovery. Given an observation y and sampling

SIAM Journal on Numerical Analysis, Volume 62, Issue 6, Page 2640-2666, December 2024. Abstract. In this article, we show the existence of minimizers in the loss landscape for residual artificial neural networks (ANNs) with a multidimensional input layer and one hidden layer with ReLU activation. Our work contrasts with earlier results in [D. Gallon, A. Jentzen, and F. Lindner, preprint, arXiv:2211

For additive manufacturing of fiber-reinforced composites, integrated structural topology optimization and deposition path planning is critical in capturing the anisotropic material feature for designing dynamic performance-oriented structures. Hence, this paper proposes a concurrent optimization method for simultaneously optimizing the structural topology and the fiber deposition path. The Solid Orthotropic

Predicting the tunnel deformation caused by overlying excavation is a crucial catch in current rail transit construction. Most theoretical studies overlook the effect of dewatering on tunnel response. This study utilized Mindlin's stress solution and an improved incremental method to calculate the additional load resulting from excavation. The load increment due to dewatering was determined based on