A concise method has been formulated for identifying a set of forces needed to constrain the behavior of a mechanical system, modeled as a set of particles and rigid bodies, when it is subject to motion constraints described by nonholonomic equations that are inherently nonlinear in velocity. An expression in vector form is obtained for each force; a direction is determined, together with the p...

The so-called renormalization group (RG) method is applied to derive kinetic and transport equations from the respective microscopic equations. The derived equations include Boltzmann equation in classical mechanics, Fokker-Planck equation, a rate equation in a quantum field theoretical model. Utilizing the formulation of the RG method which elucidates the important role played by the choice of...

A thermohydrodynamic (THD) analysis of turbulent flow in journal bearings is presented based on the computational fluid dynamic (CFD) techniques. The bearing has infinite length and operates under incompressible and steady conditions. In this analysis, the numerical solution of Navier-Stokes equations with the equations governing the kinetic energy of turbulence and the dissipation rate, couple...

in this paper, the capabilities of modeling linear viscoelasticty in a finite element method software package (comsol multiphysics) have been investigated. the governing equations of linear viscoelasticity have been developed for 2d cases of plane stress and plane strain. these equations have been verified by solving a related engineering example. since the developed equations are suitable for ...

In this paper, the min-time optimal control problem is mainly investigated in the linear time invariant (LTI) continuous-time control system with a constrained input. A high order dynamical LTI system is firstly considered for this purpose. Then the Pontryagin principle and some necessary optimality conditions have been simultaneously used to solve the optimal control problem. These optimality ...

In this paper, a three dimensional analysis of arbitrary straight-sided quadrilateral nanocomposite plates are investigated. The governing equations are based on three-dimensional elasticity theory which can be used for both thin and thick nanocomposite plates. Although the equations can support all the arbitrary straight-sided quadrilateral plates but as a special case, the numerical results f...

Simulation of turbulence boiling, generation of vapour and predication of its behaviour are still subject to debate in the two-phase flow area and they receive a high level of worldwide attention. In this study, a new arrangement of the three dimensional governing equations for turbulence two-phase flow with heat and mass transfer are derived by using ensemble averaging two-fluid model and ...

the aim of this work is to describe the qualitative behavior of the solution set of a givensystem of fractional differential equations and limiting behavior of the dynamical system or flow defined by the system of fractional differential equations. in order to achieve this goal, it is first necessary to develop the local theory for fractional nonlinear systems. this is done by the extension of ...