DETERMINING THE COEFFICIENT OF FRICTION OF WOOD-BASED MATERALS FOR FURNITURE PANELS IN THE ASPECT OF MODELLING THEIR SHREDDING PROCESS

In order to improve the power selection of the drive unit for the shredding machines,theauthors determine the values of friction coefficients used in the cutting force models. These values consider the friction between steel and such wood-based materials as chipboard, MDF and OSB. The tests concern laminated and non-laminated external surfaces and surfaces subjected to cutting processes. The value of the coefficient of friction for the tested materials is in the range: for the static coefficient of friction 0.77-0.33, and for the kinetic coefficient of friction 0.68-0.25. The highest values of the static and kinematic coefficient of friction were recorded for MDF (non-laminated external surface) and they were equal respectively: 0.77 and 0.68. In turn, thesmallest values of the discussed coefficients were recorded for chipboard (laminated external wood-base surface), which were at the level of 0.33 and 0.25, resp.

Atomic-Scale Friction Studies on Single-Crystal Gallium Arsenide Using Atomic Force Microscope and Molecular Dynamics Simulation

This paper provides a fresh perspective and new insights into nanoscale friction by investigating it through molecular dynamics (MD) simulation and atomic force microscope (AFM) nanoscratch experiments. This work considered gallium arsenide, an important III–V direct bandgap semiconductor material residing in the zincblende structure, as a reference sample material due to its growing usage in 5G communication devices. In the simulations, the scratch depth was tested as a variable in the fine range of 0.5–3 nm to understand the behavior of material removal and to gain insights into the nanoscale friction. Scratch force, normal force, and average cutting forces were extracted from the simulation to obtain two scalar quantities, namely, the scratch cutting energy (defined as the work performed to remove a unit volume of material) and the kinetic coefficient of friction (defined as the force ratio). A strong size effect was observed for scratch depths below 2 nm from the MD simulations and about 15 nm from the AFM experiments. A strong quantitative corroboration was obtained between the specific scratch energy determined by the MD simulations and the AFM experiments, and more qualitative corroboration was derived for the pile-up and the kinetic coefficient of friction. This conclusion suggests that the specific scratch energy is insensitive to the tool geometry and the scratch speed used in this investigation. However, the pile-up and kinetic coefficient of friction are dependent on the geometry of the tool tip.

Growth Kinetics of the (110) Faces of Complex Potassium Cobalt–Nickel Sulphate K2CoxNi1−x(SO4)2·6H2O Crystals

The normal growth rate, the steepness of polygonized growth hillocks and the velocity of step movement on the (110) faces of potassium cobalt–nickel sulphate crystals in aqueous solutions with cobalt to nickel ratios of 1:1 and 1:2 were investigated as a function of supersaturation by the geometry of growth hillocks using laser interferometry. It was found that the morphologies of growth hillocks on the (110) faces of the crystals grown from 1:1 and 1:2 solutions are similar and that the growth hillocks are formed by multiple screw dislocation sources. The experimental data on the growth kinetics of the (110) faces of the crystals were analyzed by using the Burton–Cabrera–Frank theory. It was found that (1) there is a critical supersaturation for the growth of the (110) faces, and the value of this supersaturation in the 1:2 solution is higher than that in the 1:1 solution, and (2) the kinetic coefficient of the step movement in the sectors of growth hillocks is highly anisotropic, and the values of this coefficient are larger in 1:2 solution than in 1:1 solution. These results are discussed in the presented work.

MODELING AT ION NITRIDING

The paper analyzes the processes occurring in the saturating medium and the processed material, which makes it possible to explain the reasons for the high growth rate of phases during ion nitriding. It is shown that the kinetic coefficient is the link between the technological parameters and the output results of the process. An algorithm for calculating the output parameters of the ion nitriding process is proposed, which, taking into account the principles of similarity and identification, can be used for any steels and alloys.

An obstacle to sub-AdS holography for SYK-like models

We argue that “stringy” effects in a putative gravity-dual picture for SYK-like models are related to the branching time, a kinetic coefficient defined in terms of the retarded kernel. A bound on the branching time is established assuming that the leading diagrams are ladders with thin rungs. Thus, such models are unlikely candidates for sub-AdS holography. In the weak coupling limit, we derive a relation between the branching time, the Lyapunov exponent, and the quasiparticle lifetime using two different approximations.

The specifics of mathematical modeling complex multicomponent chemical processes

A critical analysis of the problem of identifying raw materials for hydrotreating diesel fuel by organosulphuric components and quantifying the value of the rate constant of the hydrodesulphurization reaction is presented. It is proposed to describe the raw material as a set of narrow fractions, in each of which the content of various organosulphuric components is considered as a single pseudo-component. The prospects of separate hydrotreatment of diesel fuel pre - fractionated into wide easily and hardly hydrogenated fractions are confirmed, which allows reducing the loading of the catalyst into the reaction unit of the plant by 1.4-1.7 times compared to the traditional process scheme.. It is proposed to use the concept of kinetic coefficient for mathematical modeling of the hydrotreating process instead of the incorrect reaction rate constant in this case. The dependence of the gross conversion rate constant of the raw material on the time of fixing the depth of its hydrodesulfurization is proved by the example of modeling the hydrotreatment of diesel fuel for a number of raw material variants.

Tensor decompositions for solving the equations of mathematical models of aggregation with multiple collisions of particles

Предложены эффективные методы численного решения задачи Коши для системы кинетических уравнений агрегации типа уравнений Смолуховского, допускающих множественные столкновения частиц. Разработанные методы основываются на представлении массивов кинетических коэффициентов в виде тензорных разложений. Выполнено сравнение канонического тензорного разложения, разложения Таккера и тензорного поезда (TT). Для каждого из рассматриваемых тензорных представлений получены оценки сложности выполнения шага разностной схемы Рунге-Кутты второго порядка. Для канонического и ТТ-разложений проведены численные эксперименты, демонстрирующие эффективность предложенных методов для систем, допускающих одновременные столкновения вплоть до пяти частиц. Efficient methods for the numerical solving of a Cauchy problem for systems of Smoluchowski-type kinetic equations of aggregation with multiple collisions of particles are proposed. The developed methods are based on the tensor representations of kinetic coefficient arrays. The canonical, Tucker, and tensor train (TT) decompositions are compared. The computational complexity of these tensor representations is estimated for a second-order Runge-Kutta. The efficiency of the proposed methods for the systems with collisions of up to five particles is shown in a series of numerical experiments for the canonical and TT-decompositions.

An efficient finite-difference method for solving Smoluchowski-type kinetic equations of aggregation with three-body collisions

Рассмотрена модель агрегационных процессов для класса уравнений типа уравнений Смолуховского, допускающих тройные взаимодействия агрегатов. Предложен численный метод быстрого решения задачи Коши для указанной системы уравнений, позволяющий снизить алгоритмическую сложность $O \l(N^{3}\r)$ шага выполнения разностной схемы предиктор-корректор до $O (RN\log N)$ без потери точности, где $N$ задает количество используемых уравнений, а $R$ определяет ранг массивов кинетических коэффициентов. Эффективность и точность нового численного метода продемонстрированы для модельных задач агрегационной кинетики. We consider a model of aggregation processes for the Smoluchowski-type kinetic equations with three-body collisions of particles. We propose a numerical method for the fast solving of Cauchy problems for the corresponding systems of equations. The proposed method allows one to reduce the step complexity $O \l(N^{3}\r)$ of the finite-difference predictor-corrector scheme to $O (RN\log N)$ without loss of accuracy. Here the parameter $N$ specifies the number of considered equations and $R$ is the rank of kinetic coefficient arrays. The efficiency and accuracy of the proposed numerical method are demonstrated for model problems of aggregation kinetics.