this research is carried out to design and manufacturing of lathe vibration tool and their tests. firstly, one-dimensional vibration tool is designed and made of the bending vibration mode. one-dimensional vibration tool with half piezoelectric rings is considered to excite the bending mode of tool. structure of vibration tool is designed in abaqus software about 20 khz and then is made with re...

We consider the problem of boundary feedback stabilization of homogeneous equilibria in unstable fluid mixtures that are governed by unstable linear reaction-convection-diffusion equations. We extend boundary feedback control laws designed for the one-dimensional reaction-diffusion equation using the backstepping method to this higher-dimensional case. We show that, under certain mathematical c...

Based on the recently developed Finite Integration Method (FIM) for solving one-dimensional ordinary and partial differential equations, this paper extends the technique to higher dimensional partial differential equations. The main idea is to extend the first order finite integration matrices constructed by using either Ordinary Linear Approach (OLA) (uniform distribution of nodes) or Radial B...

in this paper, we propose a new method for the numerical solution of two-dimensional linear and nonlinear volterra integral equations of the first and second kinds, which avoids from using starting values. an existence and uniqueness theorem is proved and convergence isverified by using an appropriate variety of the gronwall inequality. application of the method is demonstrated for solving the ...

The governing equations of three dimensional elasticity problems include the six Beltrami-Michell stress compatibility equations, the three differential equations of equilibrium, and the six material constitutive relations; and these are usually solved subject to the boundary conditions. The system of fifteen differential equations is usually difficult to solve, and simplified methods are usual...

We deform gravity with higher curvature terms in four dimensions and argue that the non-relativistic limit is of the same form as the non-relativistic limit of the theories with large extra dimensions. Therefore the experiments that perform sub-millimeter tests of inverse-square law cannot distinguish the effects of large extra dimensions from the effects of higher dimensional operators. In oth...