Time-domain numerical modeling of wave propagation in poroelastic media with rational approximation of the fractional attenuation

n this work, we investigate the poroelastic waves by solving the time-domain Biot-JKD equation with an efficient numerical method. The viscous dissipation occurring in the pores depends on the square root of the frequency and is described by the Johnson-Koplik-Dashen (JKD) dynamic tortuosity/permeability model. The temporal convolutions of order 1/2 shifted fractional derivatives are involved in the time-domain Biot-JKD model, causing the problem to be stiff and challenging to be implemented numerically. Based on the best relative approximation of the square-root function, we design an efficient algorithm to approximate and localize the convolution kernel by introducing a finite number of auxiliary variables that satisfy a local system of ordinary differential equations. The imperfect hydraulic contact condition is used to describe the interface boundary conditions and the Runge-Kutta discontinuous Galerkin (RKDG) method together with the splitting method is applied to compute the numerical solutions. Several numerical examples are presented to show the accuracy and efficiency of our approach.

Analysis of the spectral symbol associated to discretization schemes of linear self-adjoint differential operators

Given a linear self-adjoint differential operator $$\mathscr {L}$$ L along with a discretization scheme (like Finite Differences, Finite Elements, Galerkin Isogeometric Analysis, etc.), in many numerical applications it is crucial to understand how good the (relative) approximation of the whole spectrum of the discretized operator $$\mathscr {L}\,^{(n)}$$ L ( n ) is, compared to the spectrum of the continuous operator $$\mathscr {L}$$ L . The theory of Generalized Locally Toeplitz sequences allows to compute the spectral symbol function $$\omega $$ ω associated to the discrete matrix $$\mathscr {L}\,^{(n)}$$ L ( n ) . Inspired by a recent work by T. J. R. Hughes and coauthors, we prove that the symbol $$\omega $$ ω can measure, asymptotically, the maximum spectral relative error $$\mathscr {E}\ge 0$$ E ≥ 0 . It measures how the scheme is far from a good relative approximation of the whole spectrum of $$\mathscr {L}$$ L , and it suggests a suitable (possibly non-uniform) grid such that, if coupled to an increasing refinement of the order of accuracy of the scheme, guarantees $$\mathscr {E}=0$$ E = 0 .

MERACLE: Constructive Layer-Wise Conversion of a Tensor Train into a MERA

In this article, two new algorithms are presented that convert a given data tensor train into either a Tucker decomposition with orthogonal matrix factors or a multi-scale entanglement renormalization ansatz (MERA). The Tucker core tensor is never explicitly computed but stored as a tensor train instead, resulting in both computationally and storage efficient algorithms. Both the multilinear Tucker-ranks as well as the MERA-ranks are automatically determined by the algorithm for a given upper bound on the relative approximation error. In addition, an iterative algorithm with low computational complexity based on solving an orthogonal Procrustes problem is proposed for the first time to retrieve optimal rank-lowering disentangler tensors, which are a crucial component in the construction of a low-rank MERA. Numerical experiments demonstrate the effectiveness of the proposed algorithms together with the potential storage benefit of a low-rank MERA over a tensor train.

Young’s modulus and Poisson’s ratio of the deformable cement adhesives

The article outlines the methods, which has designated Young’s Modulus and Poisson’s Ratio of deformable cement adhesives. These indicators are necessary for the strength calculation of the lightweight floor systems (LFS), that do not require screeds with and without heating, using the finite element method. It was noticed that the diagrams of the dependence the stress on deformation in deformable cement adhesives are similar to the model of the ‘Madrid parabola’ used in testing concrete and cement mortar. In order to determine that the theory of ‘Madrid parabola’ is correct, calculations were performed using the least amount of squares approximation method. The data of the experimental studies combined with the formula calculations, allowed the study to achieve a reliable result, together to determine whether the theory of relative approximation is correct or not. All these actions have allowed determining the smallest deformations εc2 in deformable cement adhesives type C2S1 and C2S2 and their compressive strength. Thanks, these two methods (experimental and calculation) the functions describing deformable cement adhesives are defined. They were named S1 and S2 Evola and can be used by designers and producers of floor systems that do not require screeds.

On exact values of relative approximations of classes of periodic functions by splines

We obtain the conditions under which the exact values of the best relative approximation of classes of periodic functions by splines coincide with the exact values of the best approximations of these classes by splines without constraints.

Complexity issues for the symmetric interval eigenvalue problem

We study the problem of computing the maximal and minimal possible eigenvalues of a symmetric matrix when the matrix entries vary within compact intervals. In particular, we focus on computational complexity of determining these extremal eigenvalues with some approximation error. Besides the classical absolute and relative approximation errors, which turn out not to be suitable for this problem, we adapt a less known one related to the relative error, and also propose a novel approximation error. We show in which error factors the problem is polynomially solvable and in which factors it becomes NP-hard.

Research on the Evaluation and Selection of Third-Party Logistics Providers in B2C E-Commerce Mode

For B2C e-commerce enterprises, it is of great importance to select the third-party logistics (3PL) providers. The paper, focused on the concept of “logistics capability”, took full account of the characteristics of B2C e-commerce and its logistics service and referred to the research findings of scholars. As a result, on six dimensions, the evaluation indexes of 3PL providers' logistics capability in the mode of B2C e-commerce were identified. Besides, Case studies were conducted with multi-index decision and evaluation methods based on Relative Approximation, showing that the final results are reliable.