Long Range Dependence (LRD) in functional sequences is characterized in the spectral domain under suitable conditions. Particularly, multifractionally integrated functional autoregressive moving averages processes can be introduced in this framework. The convergence to zero in the Hilbert-Schmidt operator norm of the integrated bias of the periodogram operator is proved. Under a Gaussian scenario,

Hard-thresholding-based algorithms have seen various advantages for sparse optimization in controlling the sparsity and allowing for fast computation. Recent research shows that when techniques of the Newton-type methods are integrated, their numerical performance can be improved surprisingly. This paper develops a gradient projection Newton pursuit algorithm that mainly adopts the hard-thresholding

This paper presents analytical solutions for the finite expansion problems of a spherical or cylindrical cavity, using a simple yet novel graphical approach recently proposed by Chen & Abousleiman in 2022, in both original Cam Clay (OCC) and modified Cam Clay (MCC) soils under undrained conditions. It is shown that, for a soil mass subjected to isotropic in situ stress conditions, the stress paths

In this paper, a general interfacial thermal contact model is proposed to investigate the heat conduction characteristics at the interface of bilayered saturated soils. The semianalytical solutions of thermal consolidation of the bilayered saturated soils considering thermo-osmosis effect under ramp-type heating are derived by using the Laplace transform. Then, the expressions of the temperature increment

SIAM Journal on Numerical Analysis, Volume 60, Issue 3, Page 1494-1515, June 2022. The ensemble Kalman filter (EnKF) belongs to the class of iterative particle filtering methods and can be used for solving control-to-observable inverse problems. In this context, the EnKF is known as ensemble Kalman inversion (EKI). In recent years several continuous limits in the number of iterations and particles

SIAM Journal on Numerical Analysis, Volume 60, Issue 3, Page 1472-1493, June 2022. In this paper we propose two exponential integrators of first and second order applied to a class of quasilinear wave-type equations. The analytical framework is an extension of the classical Kato framework and covers quasilinear Maxwell's equations in full space and on a smooth domain as well as a class of quasilinear

In this paper, several Newton-type methods of convergence order 2 or higher were tested on various nonlinear systems of equations and on an advanced material law implemented in a finite-element code. The computational speed, numerical efficiency, and robustness of each method were evaluated for each studied case. The effect of numerical damping was also studied. The results were then compared to put

This paper presents a combined experimental-modeling effort to interpret the coupled thermo-hydro-mechanical behaviors of the freezing soil, where an unconfined, fully saturated clay is frozen due to a temperature gradient. By leveraging the rich experimental data from the microCT images and the measurements taken during the freezing process, we examine not only how the growth of ice induces volumetric

SIAM Journal on Numerical Analysis, Volume 60, Issue 3, Page 1450-1471, June 2022. We consider an elliptic linear-quadratic parameter estimation problem with a finite number of parameters. A novel a priori bound for the parameter error is proved and, based on this bound, an adaptive finite element method driven by an a posteriori error estimator is presented. Unlike prior results in the literature

In this paper we introduce a fractional variant of the characteristic function of a random variable. It exists on the whole real line, and is uniformly continuous. We show that fractional moments can be expressed in terms of Riemann–Liouville integrals and derivatives of the fractional characteristic function. The fractional moments are of interest in particular for distributions whose integer moments

SIAM Journal on Numerical Analysis, Volume 60, Issue 3, Page 1385-1449, June 2022. In this paper, we develop and analyze numerical methods for high-dimensional Fokker--Planck equations by leveraging generative models from deep learning. Our starting point is a formulation of the Fokker--Planck equation as a system of ordinary differential equations (ODEs) on finite-dimensional parameter space with

Abstract not available

Pipe cooling is an important measure for controlling the temperature of mass concrete during the hydration period. In this paper, a new algorithm (partitioned iterative algorithm, PIA) is proposed to address the complicated process of dissecting cooling pipes in mass concrete and the difficulty of balancing the accuracy and efficiency of the simulation. The algorithm is based on the idea of finite

We introduce and study fractional Sobolev spaces of functions taking their values in a Banach space. Our approach is based on Riemann-Liouville derivative. In this regard, paper is a continuation of the paper [D. Idczak, S. Walczak, Fractional Sobolev spaces via Riemann-Liouville derivatives, J. of Function Spaces and Appl. 2013 (2013), Art. ID 128043, 15 pp.], where real-valued functions are investigated

SIAM Journal on Numerical Analysis, Volume 60, Issue 3, Page 1363-1384, June 2022. We study the recovery of multivariate functions from reproducing kernel Hilbert spaces in the uniform norm. Surprisingly, a certain weighted least squares recovery operator which uses random samples from a tailored distribution leads to near-optimal results in several relevant situations. The results are stated in terms

In this paper, we consider a Cauchy problem for fractional evolution equations with Hilfer’s fractional derivative on semi-infinite interval. An elementary fact shows that semi-infinite interval is not compact, the classical Ascoli-Arzelà theorem is not valid. In order to establish the global existence criteria, we first generalize Ascoli-Arzelà theorem into the semi-infinite interval. Next, we introduce

We provide a sufficient condition for sets of mobile sampling in terms of the surface density of the set.

In this paper, elastodynamic responses of the layered transversely isotropic unsaturated subgrade–pavement system subjected to the moving load are investigated. The unsaturated subgrade soil is described via a triphasic Biot-type model introducing the effect of matric suction, immiscible flows of water and air, and transverse isotropy. The rigid pavement is modeled by the Kirchhoff plate theory, while

In a Hilbert space, we consider a class of nonlinear fractional equations having the Caputo fractional derivative of the time variable t and the space fractional function of the self-adjoint positive unbounded operator. We consider various cases of global Lipschitz and local Lipschitz source with time-singular coefficient. These sources are generalized of the well–known fractional equations such as

Let \(p(\cdot ):\ {\mathbb {R}^n}\rightarrow (0,\infty )\) be a variable exponent function satisfying the globally log-Hölder continuous condition and A a general expansive matrix on \({\mathbb {R}^n}\). In this article, the authors introduce the anisotropic variable Campanato-type spaces and give some applications. Especially, using the known atomic and finite atomic characterizations of anisotropic

The goal of this article is to study the box dimension of the mixed Katugampola fractional integral of two-dimensional continuous functions on \([0,1]\times [0,1]\). We prove that the box dimension of the mixed Katugampola fractional integral having fractional order \((\alpha =(\alpha _1,\alpha _2);~ \alpha _1>0, \alpha _2>0)\) of two-dimensional continuous functions on \([0,1]\times [0,1]\) is still

SIAM Journal on Numerical Analysis, Volume 60, Issue 3, Page 1331-1362, June 2022. A framework to construct time-stable finite-difference schemes that apply boundary conditions strongly (or exactly) is presented for hyperbolic systems. A strong time-stability definition that applies to problems with homogeneous as well as nonhomogeneous boundary data is introduced. Sufficient conditions for strong

SIAM Journal on Numerical Analysis, Volume 60, Issue 3, Page 1307-1330, June 2022. This paper presents the first family of conforming finite element $\ddiv\ddiv$ complexes on tetrahedral grids in three dimensions. In these complexes, finite element spaces of $H(\ddiv\ddiv,\Omega;\Sbb)$ are from a recent article [L. Chen and X. Huang, Math. Comp., 91 (2022), pp. 1107--1142] while finite element spaces

SIAM Journal on Numerical Analysis, Volume 60, Issue 3, Page 1281-1306, June 2022. Adaptive finite element methods (AFEMs) are an increasingly common means of automatically controlling error in numerical simulations. Proofs of convergence and rate of convergence exist for AFEMs; however, these proofs typically rely upon a nested structure for the sequence of meshes. A metric adaptive finite element

SIAM Journal on Numerical Analysis, Volume 60, Issue 3, Page 1251-1280, June 2022. The maximum norm error estimations for virtual element methods are studied. To establish the error estimations, we prove higher local regularity based on delicate analysis of Green's functions and high-order local error estimations for the partition of the virtual element solutions. The maximum norm of the exact gradient

This article presents a multi-phase-field poromechanics model that simulates the growth and thaw of ice lenses and the resultant frozen heave and thaw settlement in multi-constituent frozen soils. The growth of segregated ice inside the freezing-induced fracture is implicitly represented by the evolution of two-phase fields that indicate the locations of segregated ice and the damaged zone, respectively

The torsional low strain integrity test (TLSIT) is now regarded as the most potent alternative to the longitudinal wave test for the existing pile evaluation. However, the lack of the 3D wave theory for the TLSITs greatly hinders the application of this method. This paper establishes a coupled 3D soil-pile model based on the continuum theory. A corresponding analytical solution of the dynamic pile

Convex ℓ1 regularization using an infinite dictionary of neurons has been suggested for constructing neural networks with desired approximation guarantees, but can be affected by an arbitrary amount of over-parametrization. This can lead to a loss of sparsity and result in networks with too many active neurons for the given data, in particular if the number of data samples is large. As a remedy, in

In this article, we focus on the following fractional Choquard equation involving upper critical exponent $$\begin{aligned} \varepsilon ^{2s}(-\varDelta )^su+V(x)u=P(x)f(u)+\varepsilon ^{\mu -N}Q(x)[|x|^{-\mu }*|u|^{2_{\mu ,s}^*}]|u|^{2_{\mu ,s}^*-2}u, \ x \in {\mathbb {R}}^N, \end{aligned}$$ where \(\varepsilon >0\), \(02s\), \(0<\mu

In this paper, we will study optimal feedback control problems derived by a class of Riemann-Liouville fractional evolution equations with history-dependent operators in separable reflexive Banach spaces. We firstly introduce suitable hypotheses to prove the existence and uniqueness of mild solutions for this kind of Riemann-Liouville fractional evolution equations with history-dependent operators

SIAM Journal on Numerical Analysis, Volume 60, Issue 3, Page 1226-1250, June 2022. This paper considers a Monte-Carlo Nystrom method for solving integral equations of the second kind, whereby the values $(z(y_i))_{1\leq i\leq N}$ of the solution $z$ at a set of $N$ random and independent points $(y_i)_{1\leq i\leq N}$ are approximated by the solution $(z_{N,i})_{1\leq i\leq N}$ of a discrete $N$-dimensional

It is known that, in general, an AP-frame is an L2(R)-frame and conversely. Here, in part as a consequence of the Ergodic Theorem, we prove a necessary and sufficient condition for a Gabor system {g(t−k)eil(t−k),l∈L=ω0Z,k∈K=t0Z} to be an L2(R)-Frame in terms of Gaussian stationary random processes. In addition, if X=(X(t))t∈R is a wide sense stationary random process, we study density conditions for

SIAM Journal on Numerical Analysis, Volume 60, Issue 3, Page 1193-1225, June 2022. We investigate a mortar technique for mixed finite element approximations of a class of domain decomposition saddle point problems on nonmatching grids in which the variable associated with the essential boundary condition, referred to as flux, is chosen as the coupling variable. It plays the role of a Lagrange multiplier

This article revisits the formulation of the J-integral in the context of hydraulic fracture mechanics. We demonstrate that the use of the classical J-integral in finite element models overestimates the length of hydraulic fractures in the viscosity-dominated regime of propagation. A finite element analysis shows that the inaccurate numerical solution for fluid pressure is responsible for the loss

A Finite Element (FE) procedure based on a fully implicit backward Euler predictor/corrector scheme for the Cosserat continuum is here presented. The integration algorithm is suitable for yield and plastic potential surfaces with general shape in the deviatoric plane. The key element of the integration scheme is the spectral decomposition of the stress tensor, which is achieved, despite the lack of

An immersed boundary 3D shell element is presented here that is based on Mindlin-Reissner shell theory assumptions and uses quadratic B-spline approximation for the solution. It enables mesh independent analysis wherein the surface representing the shell geometry is defined independently and not by the mesh. The shell geometry is immersed in a uniform background mesh whose elements are 3D B-spline

SIAM Journal on Numerical Analysis, Volume 60, Issue 3, Page 1168-1192, June 2022. We consider the computation of quadrature rules that are exact for a Chebyshev set of linearly independent functions on an interval $[a,b]$. A general theory of Chebyshev sets guarantees the existence of rules with a Gaussian property, in the sense that $2l$ basis functions can be integrated exactly with just $l$ points

SIAM Journal on Numerical Analysis, Volume 60, Issue 3, Page 1136-1167, June 2022. In this paper, we study the propagation speeds of reaction-diffusion-advection fronts in time-periodic cellular and chaotic flows with Kolmogorov--Petrovsky--Piskunov (KPP) nonlinearity. We first apply the variational principle to reduce the computation of KPP front speeds to a principal eigenvalue problem of a linear

Laplace transforms were used in this paper to obtain analytical solutions for the axisymmetric problem under a constant well temperature using the convective heat transfer boundary condition, which included the conduction and convection in the aquifer as well as heat exchange at the boundary. This solution curve intuitively illustrates the temperature distribution within the aquifer. The effects of

The study of greedy approximation in the context of convex optimization is becoming a promising research direction as greedy algorithms are actively being employed to construct sparse minimizers for convex functions with respect to given sets of elements. In this paper we propose a unified way of analyzing a certain kind of greedy-type algorithms for the minimization of convex functions on Banach spaces

This paper gives the mapping properties of the fractional integral operators on Orlicz slice Hardy spaces. We use the extrapolation theory for Hardy type spaces to obtain this result. In particular, our result yields the mapping properties of the fractional integral operators on Hardy slice spaces.

SIAM Journal on Numerical Analysis, Volume 60, Issue 3, Page 1111-1135, June 2022. Minimum residual methods such as the least-squares finite element method (FEM) or the discontinuous Petrov--Galerkin (DPG) method with optimal test functions usually exclude singular data, e.g., non-square-integrable loads. We consider a DPG method and a least-squares FEM for the Poisson problem. For both methods we

SIAM Journal on Numerical Analysis, Volume 60, Issue 3, Page 1083-1110, June 2022. This paper proposes and examines a finite element method (FEM) for a Maxwell obstacle problem in electric shielding. The model is given by a coupled system comprising the Faraday equation and an evolutionary variational inequality (VI) of Ampère--Maxwell-type. Based on the leapfrog (Yee) time-stepping and the Nédélec

The Elastoplastic Hysteretic Small Strain (EPHYSS) model is an advanced elastoplastic model as a result from the combination of the Hysteretic Quasi-Hypoelastic model (HQH) model that considers strain-induced anisotropy and can reproduce the nonlinear reversible, hysteretic and dependent on recent history soil behavior, and the Cap-Cone Hardening Soil Modified (HSMOD) model that can reproduce soil

This paper is devoted to investigate the existence and multiplicity of the normalized solutions for the following fractional Schrödinger equation: (P) ( − Δ ) s u + λ u = μ ∣ u ∣ p − 2 u + ∣ u ∣ 2 s ∗ − 2 u , x ∈ R N , u > 0 , ∫ R N ∣ u ∣ 2 d x = a 2 , \left\{\begin{array}{l}{\left(-\Delta )}^{s}u+\lambda u=\mu | u{| }^{p-2}u+| u{| }^{{2}_{s}^{\ast }-2}u,\hspace{1em}x\in {{\mathbb{R}}}^{N},\hspace{1

Problems with moving sources and moving inner boundaries in transient regime are of high interest in many research fields and engineering applications. One approach to properly tackle such problems is based on the Chimera method for non-matching grids, where each moving object is defined on a fine mesh that moves across the fixed coarse background. In this way, the high gradients around moving sources

Currently, inconclusive evidence characterizes the thermally induced deformation of sands. In this context, the role of the transient nature of heat diffusion on the thermally induced deformation of sands has remained largely disregarded. This paper presents a theoretical and computational investigation of the transient dynamics characterizing the thermally induced deformation of sands under oedometric

To better understand the microstructure parameters controlling grain crushing and how the microstructure evolution influences the crushing characteristics of rockfill particles, the emphasis of the present study focuses on the size effects on the crushing strength of rockfill particles, with special attention to internal flaws. Single-particle crushing tests are performed on rockfill particles with

Let n ≥ 2 n\ge 2 and Ω ⊂ R n \Omega \subset {{\mathbb{R}}}^{n} be a bounded nontangentially accessible domain. In this article, the authors investigate (weighted) global gradient estimates for Dirichlet boundary value problems of second-order elliptic equations of divergence form with an elliptic symmetric part and a BMO antisymmetric part in Ω \Omega . More precisely, for any given p ∈ ( 2 , ∞ ) p\in

In this paper, we consider fully nonlinear parabolic problems involving the fractional Laplacian. Hopf type lemmas for both on bounded domain \(\varOmega \) with smooth boundary and half space are obtained. When \(\varOmega \) is a ball or the whole space, we obtain the radial symmetry results of positive solutions. Our results are an extension of Li-Nirenberg [19], Li-Chen [18] and Wang-Chen [24]

A new mixed-dimension coupling method is formulated for members with (bi-symmetric) wide flange cross sections based on the idea of least squares transformations between two sets of point clouds. This coupling method imposes the minimum number of constraint equations required to link the displacement, rotation, and torsion-warping degrees-of-freedom of the dependent node. At the heart of the formulation

In this article, we consider nondiffusive variational problems with mixed boundary conditions and (distributional and weak) gradient constraints. The upper bound in the constraint is either a function or a Borel measure, leading to the state space being a Sobolev one or the space of functions of bounded variation. We address existence and uniqueness of the model under low regularity assumptions, and

A three-invariant continuum cap plasticity model with viscoplastic features is developed for modeling the large deformation of soil. Multiple failure mechanisms including combined shear and compaction yielding and loss of strength under tension can be captured by this model. The shear yield surface of the model is formulated to be nonlinear and pressure-dependent. The model also features a cap surface