Abstract In this paper, we propose a new preconditioned SOR method for solving the multi-linear systems whose coefficient tensor is an \({\mathcal{M}}\)-tensor. The corresponding comparison for spectral radii of iterative tensors is given. Numerical examples demonstrate the efficiency of the proposed preconditioned methods.

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To solve large deformation geotechnical problems, a novel strain‐smoothed particle finite element method (SPFEM) is proposed that incorporates a simple and effective edge‐based strain smoothing method within the framework of original PFEM. Compared with the original PFEM, the proposed novel SPFEM can solve the volumetric locking problem like previously developed node‐based smoothed PFEM when lower‐order

Most of previous analyses on the active earth pressure were performed in two‐dimensional cases using the Mohr‐Coulomb (M‐C) failure function to describe the soil strength. However, all failures of retained slopes indicate a somewhat three‐dimensional (3D) feature, and the M‐C function is found to overestimate the tensile strength of cohesive soil. In this work, a kinematic limit analysis–based approach

In this work, the elastic buckling of porous solids was investigated using a lattice spring model (LSM). The capability of the LSM to solve elastic buckling problems was comprehensively verified by comparing well‐established numerical and analytical solutions. Following this, the buckling of a porous solid was studied, in which two porous structures were considered, ie, the random porous model and

Discrete element method (DEM) has become a preeminent numerical tool for investigating the mechanical behavior of granular soils. However, traditional DEM uses sphere clusters to approximate realistic particles, which is computationally demanding when simulating many particles. This paper demonstrates the potential of using a physics engine technique to simulate realistic particles. The physics engines

The intergranular strain concept was originally developed to capture the small‐strain behaviour of the soil with hypoplastic models. A change of the deformation direction leads to an increase of the material stiffness. To obtain elastic behaviour for smallstrains, only the elastic part of the material stiffness matrix is used. Two different approaches for an application of this concept to nonhypoplastic

In the small strain domain, asphalt mixes (AM) have a linear viscoelastic (LVE) behavior that is strongly dependent on frequency and temperature. The maximum ratio of modulus values can be up to 1000, and traditional elastic analyses are not pertinent. The possibility to characterize AM from frequency response functions (FRFs) was studied. A new optimization process using the finite element method

Wellbore stability problems and stimulation operations call for models helping in understanding the subsurface behaviour and optimizing engineering performance. We present a fast, iteratively coupled model for the flow and mechanical behaviour that employs a time‐sequential approach. Updates of pore pressure are calculated in a timestepping approach and propagated analytically to updates of the mechanical

A cavity expansion–based solution is proposed in this paper for the interpretation of CPTu data under a partially drained condition. Variations of the normalized cone tip resistance, cone factor, and undrained‐drained resistance ratio are examined with different initial specific volume and overconsolidation ratio, based on the exact solutions of both undrained and drained cavity expansion in CASM,

Embedded stabilizing piles are a significant optimization measure for traditional piles used to reinforce slopes or landslides. The determination of the embedded depth of the pile top is essential for engineering design. On the basis of the potential overtop‐sliding failure mechanism for a piled slope, the corresponding overall slip surface is assumed to consist of the upper part from the original

The stability of vertical unsupported circular excavations in rock media, obeying generalized Hoek‐Brown yield criterion, has been investigated by using the lower bound finite elements limit analysis. An axisymmetric analysis, composed of a planar domain with a mesh of three‐noded triangular elements, has been carried out. The optimization problem is dealt with by using the semidefinite programming

In the recent paper [1] D. Azagra studies the global shape of continuous convex functions defined on a Banach space X. More precisely, when X is separable, it is shown that for every continuous convex function f:X→R there exist a unique closed linear subspace Y of X, a convex function h:X/Y→R with the property that limt→∞⁡h(u+tv)=∞ for all u,v∈X/Y, v≠0, and x⁎∈X⁎ such that f=h∘π+x⁎, where π:X→X/Y is

In this paper, we obtain the large deviation principle for random variables in sublinear expectation spaces taking values in Rd, which do not have to satisfy the independent identical distributed condition. We also give an example, where we construct a sequence of random variables in the framework of sublinear expectations satisfying our assumption.

It is shown that the kernel of a Toeplitz operator with 2×2 symbol G can be described exactly in terms of any given function in a very wide class, its image under multiplication by G, and their left inverses, if the latter exist. As a consequence, under many circumstances the kernel of a block Toeplitz operator may be described as the product of a space of scalar complex-valued functions by a fixed

There are few examples of non-autonomous vector fields exhibiting complex dynamics that may be proven analytically. We analyse a family of periodic perturbations of a weakly attracting robust heteroclinic network defined on the two-sphere. We derive the first return map near the heteroclinic cycle for small amplitude of the perturbing term, and we reduce the analysis of the non-autonomous system to

A FORTRAN program, consistent with the commercially available finite element (FE) code ABAQUS, is developed based on a three‐dimensional (3D) linear elastic brittle damage constitutive model with two damage criteria. To consider the heterogeneity of rock, the developed FORTRAN program is used to set the stiffness and strength properties of each element of the FE model following a Weibull distribution

This paper focuses on selection mechanisms of the minimal speed of traveling waves to the Lotka-Volterra reaction-diffusion model. We first establish general conditions for the linear and nonlinear selection by way of an upper and lower solution method. Then some explicit criteria are derived by subtly constructing formulas of upper and lower solutions. The obtained conditions substantially improve

We prove that Bernstein operators preserve log-concavity of functions. We give a proof, which bases solely on elementary properties of the binomial coefficients. We prove that the Berntein semigroup (T(t))t≥0 also has the log-concavity preserving property. We also solve two problems presented recently by I. Raşa.

This work considers a chemotaxis system with signal-dependent motility in a smooth bounded domain Ω⊂Rn. If λ∈R,μ>0 andl>max⁡{n+24,1} are constants, then the system{ut=Δ(γ(v)u)+λu−μul,x∈Ω,t>0,vt=Δv−v+w,x∈Ω,t>0,wt=Δw−w+u,x∈Ω,t>0, with homogeneous Neumann boundary conditions possesses a global solution. Moreover, the solution satisfies‖u(⋅,t)−(λ+μ)1l−1‖L∞+‖v(⋅,t)−(λ+μ)1l−1‖L∞+‖w(⋅,t)−(λ+μ)1l−1‖L∞→0 as

We consider the scalar delay differential equationx˙(t)=−x(t)+fK(x(t−1)) with a nondecreasing feedback function fK depending on a parameter K, and we verify that a saddle-node bifurcation of periodic orbits takes place as K varies. The nonlinearity fK is chosen so that it has two unstable fixed points (hence the dynamical system has two unstable equilibria), and these fixed points remain bounded away

The periodically forced light-limited Droop model represents microalgae growth under co-limitation by light and a single substrate, accounting for periodic fluctuations of factors such as light and temperature. In this paper, we describe the global dynamics of this model, considering general monotone growth and uptake rate functions. Our main result gives necessary and sufficient conditions for the

In this paper, we consider the linear stability of the elliptic relative equilibria of the restricted 4-body problem where the three primaries form a Lagrangian triangle. By reduction, the linearized Poincaré map is decomposed to the essential part, the Keplerian part and the elliptic Lagrangian part where the last two parts have been studied in literature. The linear stability of the essential part

We introduce a dynamical-systems approach for the study of the Sard problem in sub-Riemannian Carnot groups. We show that singular curves can be obtained by concatenating trajectories of suitable dynamical systems. As an application, we positively answer the Sard problem in some classes of Carnot groups.

We study the inverse problem of unique recovery of a complex-valued scalar function V:M×C→C, defined over a smooth compact Riemannian manifold (M,g) with smooth boundary, given the Dirichlet-to-Neumann map, in a suitable sense, for the elliptic semi-linear equation −Δgu+V(x,u)=0. We show that uniqueness holds for a large class of non-linearities when the manifold is conformally transversally anisotropic

We consider the initial boundary value problem of pseudo-parabolic equation with singular potential. We obtain global existence, asymptotic behavior and blowup of solutions with initial energy J(u0)≤d. Moreover, we estimate the upper bound of the blowup time for J(u0)<0 and 0

The study of damping rates for distributed and boundary feedback control systems is important in the design of control mechanisms for distributed parameter systems. Despite the fact that many papers have been published regarding the determination of spectra and also possibly the sharpest systemwide uniform rates of energy decay, many problems remain open. In this paper, we first mention a few examples

We study first order evolutive Mean Field Games where the Hamiltonian are non-coercive. This situation occurs, for instance, when some directions are “forbidden” to the generic player at some points. We establish the existence of a weak solution of the system via a vanishing viscosity method and, mainly, we prove that the evolution of the population's density is the push-forward of the initial density

We consider the one-dimensional Swift-Hohenberg equation coupled to a conservation law. As a parameter increases the system undergoes a Turing bifurcation. We study the dynamics near this bifurcation. First, we show that stationary, periodic solutions bifurcate from a homogeneous ground state. Second, we construct modulating traveling fronts which model an invasion of the unstable ground state by the

A smoothed particle hydrodynamics (SPH) framework for three‐dimensional dynamic soil‐multibody interaction modeling is presented, where both soils and rigid bodies are discretized using SPH particles. In the framework, soils are modeled using the Drucker‐Prager model, while rigid bodies are considered with a multibody dynamics solver. A hybrid contact method suitable for three‐dimensional simulations

In this paper, we study the following critical Dirac-Klein-Gordon system in R3:{iε∑k=13αk∂ku−aβu+V(x)u−λϕβu=P(x)f(|u|)u+Q(x)|u|u,−ε2Δϕ+Mϕ=4πλ(βu)⋅u, where ε>0 is a small parameter, a>0 is a constant. We prove the existence and concentration of solutions under suitable assumptions on the potential V(x),P(x) and Q(x). We also show the semiclassical solutions ωε with maximum points xε concentrating at

A conjecture posed by MacDonald and Rosenthal states the composition operator Cφ acting on the Newton space N2(P) induced by φ(z)=mz+m−12 is bounded, where m∈(0,1). Our first result is proving that the aforementioned conjecture holds. We investigate complex symmetry of composition operators acting on the Newton space, which is different from that on the Hardy space. In addition, normality and co-isometry

A logarithmic model type chemotaxis equation is introduced with porous medium diffusion and a population dependent consumption rate. The classical assumption that individual bacterium can sense the chemical gradient is not taken. Instead, the chemotactic term appears by assuming that the migration distance is inversely proportional to the amount of food if food is the reason for migration. The existence

This paper gives the pointwise Hölder (or multifractal) spectrum of continuous functions on the interval [0,1] whose graph is the attractor of an iterated function system consisting of r≥2 affine maps on R2. These functions satisfy a functional equation of the form ϕ(akx+bk)=ckx+dkϕ(x)+ek, for k=1,2,…,r and x∈[0,1]. They include the Takagi function, the Riesz-Nagy singular functions, Okamoto's functions

The Spin-Boson model describes a two-level quantum system that interacts with a second-quantized boson scalar field. Recently the relation between the integral kernel of the scattering matrix and the resonance in this model has been established in [18] for the case of massless bosons. In the present work, we treat the massive case. On the one hand, one might rightfully expect that the massive case

In this paper, we consider surfaces in 4–dimensional pseudo–Riemannian space–forms with index 2. First, we obtain some of geometrical properties of such surfaces considering their relative null space. Then, we get classifications of quasi–minimal surfaces with positive relative nullity.

An inverse source problem in degenerate parabolic equations is considered, where the diffusion coefficient are zero on the whole boundary. Based on the strong maximum principle for degenerate parabolic equations established in the paper, the uniqueness of the solution is proved.

Given l>2ν>2d≥4, we prove the persistence of a Cantor–family of KAM tori of measure O(ε1/2−ν/l) for any non–degenerate nearly integrable Hamiltonian system of class Cl(D×Td), where ν−1 is the Diophantine power of the frequencies of the persistent KAM tori and D⊂Rd is a bounded domain, provided that the size ε of the perturbation is sufficiently small. This extends a result by D. Salamon in [25] according

In this paper, we present some controllability results for linear and nonlinear phase-field systems of Caginalp type considered in a bounded interval of R when the scalar control force acts on the temperature equation of the system by means of the Dirichlet condition on one of the endpoints of the interval. In order to prove the linear result we use the moment method providing an estimate of the cost

In this paper, we prove an orbital stability result for the Degasperis-Procesi peakon with respect to perturbations having a momentum density that is first negative and then positive. This leads to the orbital stability of the antipeakon-peakon profile with respect to such perturbations.

This paper is mainly concerned with the generalised principal eigenvalue for time-periodic nonlocal dispersal operators. We first establish the equivalence between two different characterisations of the generalised principal eigenvalue. We further investigate the dependence of the generalised principal eigenvalue on the frequency of the periodic oscillation, the dispersal rate and the dispersal spread

We show global well-posedness and exponential stability of equilibria for a general class of nonlinear dissipative bulk-interface systems. They correspond to thermodynamically consistent gradient structure models of bulk-interface interaction. The setting includes nonlinear slow and fast diffusion in the bulk and nonlinear coupled diffusion on the interface. Additional driving mechanisms can be included

We study the following Neumann problem in one-dimension space arising from population genetics:{ut=duxx+h(x)u2(1−u)in(−1,1)×(0,∞),0≤u≤1in(−1,1)×(0,∞),u′(−1,t)=u′(1,t)=0in(0,∞), where h changes sign in (−1,1) and d is a positive parameter. Lou and Nagylaki (2002) [6] conjectured that if ∫−11h(x)dx≥0, then this problem has at most one nontrivial steady state (i.e., a time-independent solution which is

This paper focuses on the modelling of mixed‐mode fracture using the conventional smoothed particle hydrodynamics (SPH) method and a mixed‐mode cohesive fracture law embedded in the particles. The combination of conventional SPH and a mixed‐mode cohesive model allows capturing fracture and separation under various loading conditions efficiently. The key advantage of this framework is its capability

We show radial symmetry of positive solutions to the Hénon equation −Δu=|x|−ℓuq in RN∖{0}, where ℓ≥0, q>0 and satisfy further technical conditions. A new ingredient is a maximum principle for open subsets of a half space. It allows to apply the Moving Plane Method once a slow decay of the solution at infinity has been established, that is lim|x|→∞⁡|x|γu(x)=L, for some numbers γ∈(0,N−2) and L>0. Moreover

The rotationally symmetric spacelike translating solitons for the MCF in the Minkowski space are considered in this paper. To be specific, the complete classification for such translating solitons according to their rotation axes, which are timelike, spacelike and lightlike, is provided. In particular, the explicit parametrization of the rotationally symmetric spacelike hypersurface of the lightlike

This paper is a contribution to the study of regularity theory for nonlinear elliptic equations. The aim of this paper is to establish some global estimates for non-uniformly elliptic in divergence form as follows−div(|∇u|p−2∇u+a(x)|∇u|q−2∇u)=−div(|F|p−2F+a(x)|F|q−2F), that arises from double phase functional problems. In particular, the main results provide the regularity estimates for the distributional

In several cases of nonlinear dispersive PDEs, the difference between the nonlinear and linear evolutions with the same initial data, i.e. the integral term in Duhamel's formula, exhibits improved regularity. This property is usually called nonlinear smoothing. We employ the method of infinite iterations of normal form reductions to obtain a very general theorem yielding existence of nonlinear smoothing

We consider nonlinear elliptic equations that are naturally obtained from the elliptic Schrödinger equation −Δu+Vu=0 in the setting of the calculus of variations, and obtain Lq-estimates for the gradient of weak solutions. In particular, we generalize a result of Shen (1995) [39] in the nonlinear setting by using a different approach. This allows us to consider discontinuous coefficients with a small

This paper presents a new viscohypoplastic model for soft clays accounting for their typical features—strength anisotropy and rate dependency. The model is based on the hypoplastic model for clays enhanced by the anisotropic shape of the asymptotic state boundary surface. It has been shown that if the surface is skewed, the model predicts different ultimate strength in compression and in extension

This paper continues the investigation of the relation between the geometry of a circle embedding and the values of its Fourier coefficients. First, we answer a question of Kovalev and Yang concerning the support of the Fourier transform of a starlike embedding. An important special case of circle embeddings are homeomorphisms of the circle onto itself. Under a one-sided bound on the Fourier support

Let H∞(Bc0) be the algebra of all bounded holomorphic functions on the open unit ball of c0 and M(H∞(Bc0)) the spectrum of H∞(Bc0). We prove that for any point z in the closed unit ball of ℓ∞ there exists an analytic injection of the open ball Bℓ∞ into the fiber of z in M(H∞(Bc0)), which is an isometry from the Gleason metric of Bℓ∞ to the Gleason metric of M(H∞(Bc0)). We also show that, for some Banach

This paper presents an improved optimal homotopy analysis algorithm to deal with nonlinear first-order differential equations. We discuss the optimal selection of the auxiliary linear operator in the application of the homotopy analysis method that will accelerate the convergence of series solutions. Then, a powerful algorithm, that employed the optimal auxiliary linear operator, of the homotopy analysis

In this paper we consider sequences of polynomials {Hm(z)}m=0∞ generated by a relation ∑m=0∞Hm(z)tm=1P(t)+ztrQ(t), where P and Q are real polynomials and r∈N, r≥2. In the main result of the paper (cf. Theorem 1) we give a necessary conditions on P and Q (and their zeros) to ensure that for all sufficiently large m, the zeros of the polynomials Hm(z) are real. We also show that the set of all zeros

We propose a new approach to study the long time dynamics of the wave kinetic equation in the statistical description of acoustic turbulence. The approach is based on rewriting the discrete version of the wave kinetic equation in the form of a chemical reaction network, then employing techniques used to study the Global Attractor Conjecture to investigate the long time dynamics of the newly obtained

This paper deals with a class of nonlocal semilinear pseudo-parabolic equation with conical degenerationut−△But−△Bu=|u|p−1u−1|B|∫B|u|p−1udx1x1dx′, on a manifold with conical singularity, where △B is Fuchsian type Laplace operator with totally characteristic degeneracy on the boundary x1=0. By using the modified method of potential well with Galerkin approximation and concavity, the global existence

The theory of basic reproduction ratio R0 is established for a large class of almost periodic and time-delayed compartmental population models. We first present some dynamical properties for linear almost periodic functional differential systems. By using the product space and evolution semigroup approach, we then prove that R0−1 has the same sign as the exponential growth bound of an associated linear

A theory is proposed to evaluate the loosening earth pressure (vertical earth pressure after excavation) acting on a shallow tunnel in unsaturated ground with an arbitrary groundwater level. The theory is developed based on the limit equilibrium theory, combining soil–water characteristic curves, Mohr–Coulomb failure criteria, and effective stress for unsaturated soils. The proposed theory is applied

This work is devoted to the mathematical analysis of Stieltjes Bochner spaces and their applications to the resolution of a parabolic equation with Stieltjes time derivative. This novel formulation allows us to study parabolic equations that present impulses at certain times or lapses where the system does not evolve at all and presents an elliptic behavior. We prove several theoretical results related