混凝土搅拌车搅拌筒磨损数值分析

混凝土运输过程中搅拌筒的磨损一直是一种常见潜在危害,磨损严重时会导致叶片失效,对搅拌的质量和出料匀质性产生影响。通过实验获取搅拌筒内部的磨损费时费力,因此有必要采取一种数值分析方法对搅拌筒的磨损进行预测并提出改进。本文采用摩擦磨损实验的方法来标定颗粒与搅拌筒之间的Archard磨损常数,采用JKR接触模型表征混凝土的流动性能,采用离散元方法(DEM)对搅拌筒筒体及叶片磨损进行预测分析。通过法向接触能量与切向接触能量的对比,证明搅拌筒中的磨损主要为伴有冲击作用的磨粒磨损,搅拌车搅拌筒中搅拌叶片顶部的磨损较为严重。针对磨损比较严重的叶片顶部进行改进,采用T型耐磨结构等改进叶片结构,叶片顶部结构改进后搅拌筒使用寿命能得到明显提升。     

Analysis of the Chemical Composition of Red Pigments and Inks for the Characterization and Differentiation of Contemporary Prints

Prints are one of the most popular artistic forms. They consist of an original matrix that is printed on a paper support. The stamps are part of a series, and each series is composed of a particular number of prints. Many contemporary prints are made using oil inks and synthetic pigments (reds and yellows). Inks are mainly composed of pigments (organic or inorganic) and a binding medium. The analysis of inks has the potential to facilitate and complement the identification of stamps of different origins.

Fourier transform infrared spectroscopy (FTIR) and Scanning Electron Microscopy-Energy Dispersive X-ray (SEM-EDX) are techniques that are typically available in museums and centers related to the study of works of art. Both can be classified as micro-destructive and provide complementary information about the organic and some inorganic compounds (FTIR), and the elemental composition (SEM-EDX). In this article, the two techniques were used to analyze the composition of red ink in prints. As a result of these analyses, it was possible to distinguish among nearly all of the pigments and inks, indicating that the composition of the red ink can be reliably used to differentiate between stamps of different origins in a series of prints.     

Two weight commutators in the Dirichlet and Neumann Laplacian settings

In this paper we establish the characterization of the weighted BMO via two weight commutators in the settings of the Neumann Laplacian ${\mathrm{\Delta }}_{N_{+}}$ on the upper half space ${\mathbb{R}}_{+}^n$ and the reflection Neumann Laplacian ${\mathrm{\Delta }}_N$ on ${\mathbb{R}}^n$ with respect to the weights associated to ${\mathrm{\Delta }}_{N_{+}}$ and ${\mathrm{\Delta }}_N$ respectively. This in turn yields a weak factorization for the corresponding weighted Hardy spaces, where in particular, the weighted class associated to ${\mathrm{\Delta }}_N$ is strictly larger than the Muckenhoupt weighted class and contains non-doubling weights. In our study, we also make contributions to the classical Muckenhoupt–Wheeden weighted Hardy space (BMO space respectively) by showing that it can be characterized via the area function (Carleson measure respectively) involving the semigroup generated by the Laplacian on ${\mathbb{R}}^n$ and that the duality of these weighted Hardy and BMO spaces holds for Muckenhoupt $A^p$ weights with $p\in (1,2]$ while the previously known related results cover only $p\in (1,\frac{n+1}{n}]$. We also point out that this two weight commutator theorem might not be true in the setting of general operators L, and in particular we show that it is not true when L is the Dirichlet Laplacian ${\mathrm{\Delta }}_{D_{+}}$ on ${\mathbb{R}}_{+}^n$.     

On the Motion of Substance in a Channel of a Network: Extended Model and New Classes of Probability Distributions

We discuss the motion of substance in a channel containing nodes of a network. Each node of the channel can exchange substance with: (i) neighboring nodes of the channel, (ii) network nodes which do not belong to the channel, and (iii) environment of the network. The new point in this study is that we assume possibility for exchange of substance among flows of substance between nodes of the channel and: (i) nodes that belong to the network but do not belong to the channel and (ii) environment of the network. This leads to an extension of the model of motion of substance and the extended model contains previous models as particular cases. We use a discrete-time model of motion of substance and consider a stationary regime of motion of substance in a channel containing a finite number of nodes. As results of the study, we obtain a class of probability distributions connected to the amount of substance in nodes of the channel. We prove that the obtained class of distributions contains all truncated discrete probability distributions of discrete random variable ω which can take values 0,1,⋯,N. Theory for the case of a channel containing infinite number of nodes is presented in Appendix A. The continuous version of the discussed discrete probability distributions is described in Appendix B. The discussed extended model and obtained results can be used for the study of phenomena that can be modeled by flows in networks: motion of resources, traffic flows, motion of migrants, etc.     

Simple Equations Method (SEsM): Algorithm,Connection with Hirota Method,Inverse Scattering Transform Method,and Several Other Methods

The goal of this article is to discuss the Simple Equations Method (SEsM) for obtaining exact solutions of nonlinear partial differential equations and to show that several well-known methods for obtaining exact solutions of such equations are connected to SEsM. In more detail, we show that the Hirota method is connected to a particular case of SEsM for a specific form of the function from Step 2 of SEsM and for simple equations of the kinds of differential equations for exponential functions. We illustrate this particular case of SEsM by obtaining the three- soliton solution of the Korteweg-de Vries equation, two-soliton solution of the nonlinear Schrödinger equation, and the soliton solution of the Ishimori equation for the spin dynamics of ferromagnetic materials. Then we show that a particular case of SEsM can be used in order to reproduce the methodology of the inverse scattering transform method for the case of the Burgers equation and Korteweg-de Vries equation. This particular case is connected to use of a specific case of Step 2 of SEsM. This step is connected to: (i) representation of the solution of the solved nonlinear partial differential equation as expansion as power series containing powers of a “small” parameter ϵ; (ii) solving the differential equations arising from this representation by means of Fourier series, and (iii) transition from the obtained solution for small values of ϵ to solution for arbitrary finite values of ϵ. Finally, we show that the much-used homogeneous balance method, extended homogeneous balance method, auxiliary equation method, Jacobi elliptic function expansion method, F-expansion method, modified simple equation method, trial function method and first integral method are connected to particular cases of SEsM.