Four-dimensional Integral Model of Dry Friction on the Example of Wheel Movement

A four-dimensional model of dry friction in the interaction of a solid wheel and a horizontal rough surface is investigated. It is assumed that there is no separation between the wheel and the horizontal surface. The movement of the body occurs in conditions of combined dynamics, when in addition to the sliding movement, the body participates in spinning and rolling. The equation of motion of the wheel is compiled using the Appel equation. The resulting model of sliding, spinning, and rolling friction is given for the case where the contact area is a circle. The cumbersome integral expressions were replaced by fractional-linear Pade approximations. Pade approximations accurately describe the behavior of the components of the friction model. A mathematical model is proposed that describes the simultaneous sliding, spinning and rolling of a solid wheel. The dependences of the parallel and perpendicular components of the friction force and the torque of the spinning friction were ploted with respect to the parameter that characterizes the movement of the wheel. Comparisons of the integral friction model and the model based on Pade approximations are presented. The results of the comparison showed a qualitative correspondence of the models. After obtaining the equation of motion, the simulation of motion at a constant control torque of the wheel is carried out. The graphs allow you to match the logical behavior of the wheel movement.

Integral equations of a rectilinear ribbon vibrator near a perfectly conducting infinite screen

The problem of excitation of a rectilinear ribbon vibrator near a perfectly conducting infinite screen is considered. A general equation, a two-dimensional integral equation, and a one-dimensional integral equation with respect to the current density are obtained. The results of numerical calculations are presented.

An Importance Sampling Framework for Time-Variant Reliability Analysis Involving Stochastic Processes

In recent years, methods were proposed so as to efficiently perform time-variant reliability analysis. However, importance sampling (IS) for time-variant reliability analysis is barely studied in the literature. In this paper, an IS framework is proposed. A multi-dimensional integral is first derived to define the time-variant cumulative probability of failure, which has the similar expression to the classical definition of time-invariant failure probability. An IS framework is then developed according to the fact that time-invariant random variables are commonly involved in time-variant reliability analysis. The basic idea of the proposed framework is to simultaneously apply time-invariant IS and crude Monte Carlo simulation on time-invariant random variables and stochastic processes, respectively. Thus, the probability of acquiring failure trajectories of time-variant performance function is increased. Two auxiliary probability density functions are proposed to implement the IS framework. However, auxiliary PDFs available for the framework are not limited to the proposed two. Three examples are studied in order to validate the effectiveness of the proposed IS framework.

The on-axis magnetic well and Mercier's criterion for arbitrary stellarator geometries

A simplified analytical form of the on-axis magnetic well and Mercier's criterion for interchange instabilities for arbitrary three-dimensional magnetic field geometries is derived. For this purpose, a near-axis expansion based on a direct coordinate approach is used by expressing the toroidal magnetic flux in terms of powers of the radial distance to the magnetic axis. For the first time, the magnetic well and Mercier's criterion are then written as a one-dimensional integral with respect to the axis arclength. When compared with the original work of Mercier, the derivation here is presented using modern notation and in a more streamlined manner that highlights essential steps. Finally, these expressions are verified numerically using several quasisymmetric and non-quasisymmetric stellarator configurations including Wendelstein 7-X.

Matrix element regression with deep neural networks — Breaking the CPU barrier

The Matrix Element Method (MEM) is a powerful method to extract information from measured events at collider experiments. Compared to multivariate techniques built on large sets of experimental data, the MEM does not rely on an examples-based learning phase but directly exploits our knowledge of the physics processes. This comes at a price, both in term of complexity and computing time since the required multi-dimensional integral of a rapidly varying function needs to be evaluated for every event and physics process considered. This can be mitigated by optimizing the integration, as is done in the MoMEMta package, but the computing time remains a concern, and often makes the use of the MEM in full-scale analysis unpractical or impossible. We investigate in this paper the use of a Deep Neural Network (DNN) built by regression of the MEM integral as an ansatz for analysis, especially in the search for new physics.