The problem of the spreading of a granular mass released at the top of a rough inclined plane was investigated. We experimentally measure the evolution of the avalanche from the initiation up to the deposit using a Moire image processing technique. The results are quantitatively compared with the prediction of an hydrodynamic model based on depth averaged equations. In the model, the interaction between the flowing layer and the rough bottom is described by a non trivial friction force whose expression is derived from measurements on steady uniform flows. We show that the spreading of the mass is quantitatively predicted by the model when the mass is released on a plane free of particles. When an avalanche is triggered on an initially static layer, the model fails in quantitatively predicting the propagation but qualitatively captures the evolution.

Friction law for dense granular flows: application to the motion of a mass down a rough inclined plane

http://www.cs.uvm.edu/~eppstein/personal/JCP03.pdf

Coupled complex adjoint sensitivities for frequency-domain fluorescence tomography: theory and vectorized implementation

This paper describes the theory and implications of a discrete mechanics model for deformable bodies, incorporating behavior such as motion, collision, deformation, etc. The model is fundamentally based on inter-atomic interaction, and recursively reduces resolution by approximating collections of many high-resolution elements with fewer lower-resolution elements. The model can be viewed as an extended mass-spring model. We begin by examining the domain of conceptual design, and find there is a need for physics based simulation, both for interactive shape modeling and analysis. We then proceed with describing a theoretical base for our model, as well as pragmatic additions. Applications in both interactive physics based shape modeling and analysis are presented. The model is aimed at conceptual mechanical design, rapid prototyping, or similar areas where adherence to physical principles, generality and simplicity are more important than metric correctness.

A discrete mechanics model for deformable bodies

The authors analyze the lubricating interfaces of axial piston machines considering thermo-elastohydrodynamic (TEHL) lubrication characteristics. The fluid film geometry in these conditions is strongly influenced by the surface elastic deformation of the solid boundaries. The surface elastic deformations derive from the high dynamic pressures developing in the fluid film, necessary to balance the external oscillating loads. Furthermore, elastic deflections of the fluid film develop from the thermal expansion of the solid bodies, caused by the heat generated due to viscous shear of the fluid film. The accurate determination of the solid boundaries elastic deformation is a key element to predict the fluid film geometry and consequently the lubricating interface performance.When solving for the static elastic deformation of a solid body, constraint conditions must be imposed to avoid rigid body motion. Constraint conditions strongly influence the elastic deformation analysis; therefore their definiti...

https://journals.riverpublishers.com/index.php/IJFP/article/download/216/98

The Impact of Axial Piston Machines Mechanical Parts Constraint Conditions on The Thermo-Elastohydrodynamic Lubrication Analysis of The Fluid Film Interfaces

This paper deals with the modeling and stabilization of nonlinear control systems approximated by fuzzy if-then rules with singleton consequents. The approximated model is found to be piecewise bilinear. First, an optimal method of piecewise bilinear approximation of nonlinear functions is shown. Then, the method of input-output feedback linearization is applied to stabilize piecewise bilinear control systems. An illustrative example is given to show the validity of the proposed methods.

Stabilization of nonlinear systems with piecewise bilinear models derived from fuzzy if-then rules with singletons

The finite element method (FEM) appeared as a need for analysis of complex structural systems, for which there is no simple solution. In the application of the method the structural system is subdivided into elements of finite dimensions, i.e. finite elements. An approximate solution is found for such a small element, and then, by assembling all the elements of the system, a system of algebraic equations is derived. The solution of these equations gives an approximate solution of the complete structural system. In that way a very complex problem is reduced to a solution of simple algebraic equations.

Apostol Poceski

Papers

Fundamentals of the Finite Element Method