the objective of this work was to develop a new design of an intake manifold through a 1d simulation. it is quite familiar that a duly designed intake manifold is essential for the optimal performance of an internal combustion engine. air flow inside the intake manifold is one of the important factors, which governs the engine performance and emissions. hence the flow phenomenon inside the inta...

We consider the problem of recovering an underwater image distorted by surface waves. A large amount of video data of the distorted image is acquired. The problem is posed in terms of finding an undistorted image patch at each spatial location. This challenging reconstruction task can be formulated as a manifold learning problem, such that the center of the manifold is the image of the undistor...

In this work, we prove the existence of a center manifold for some partial functional differential equations, whose linear part is not necessarily densely defined but satisfies the Hille-Yosida condition. The attractiveness of the center manifold is also shown when the unstable space is reduced to zero. We prove that the flow on the center manifold is completely determined by an ordinary differ...

the present article serves the purpose of pursuing geometrization of heat flow on volumetrically isothermal manifold by means of rf approach. in this article, we have analyzed the evolution of heat equation in a 3-dimensional smooth isothermal manifold bearing characteristics of riemannian manifold and fundamental properties of thermodynamic systems. by making use of the notions of various curva...

In this paper, we use a feedback to change the orientation and the shape of the center manifold of a system with uncontrollable linearization. This change will directly affect the reduced dynamics on the center manifold, and hence will change the stability properties of the original system.

First we prove a general spectral theorem for the linear NavierStokes (NS) operator in both 2D and 3D. The spectral theorem says that the spectrum consists of only eigenvalues which lie in a parabolic region, and the eigenfunctions (and higher order eigenfunctions) form a complete basis in H (l = 0, 1, 2, · · · ). Then we prove the existence of invariant manifolds. We are also interested in a m...

The center manifold theorem is a model reduction technique for determining the local asymptotic stability of an equilibrium of a dynamical system when its linear part is not hyperbolic. The overall system is asymptotically stable if and only if the center manifold dynamics is asymptotically stable. This allows for a substantial reduction in the dimension of the system whose asymptotic stability...

Center-unstable manifolds are very useful in investigating nonlinear dynamics of nonlinear evolution equations. In this paper, we first present a center-unstable manifold theory for abstract semilinear Cauchy problems with nondense domain. We especially focus on the stability property of the center-unstable manifold. Then we study the stability of Hopf bifurcation, that is, stability of the bif...

in this paper we will determine the multiple point manifolds of certain self-transverse immersions in euclidean spaces. following the triple points, these immersions have a double point self-intersection set which is the image of an immersion of a smooth 5-dimensional manifold, cobordant to dold manifold $v^5$ or a boundary. we will show there is an immersion of $s^7times p^2$ in $mathbb{r}^{13...