A Gamma-convergence argument for the blow-up of a non-local semilinear parabolic equation with Neumann boundary conditions

In this paper we study a simple non-local semilinear parabolic equation with Neumann boundary condition. We give local existence result and prove global existence for small initial data. A natural non increasing in time energy is associated to this equation. We prove that the solution blows up at finite time $T$ if and only if its energy is negative at some time before $T$. The proof of this result is based on a Gamma-convergence technique

Unified methodologies, formats and outlines in online engineering education

Online education in engineering is developing as the communication technology advances. Although many online courses are being presented worldwide they have not been broadly accepted. For the online engineering education to be well successful and outperform traditional on-campus education, much has been done since ten years ago. To satisfy the five pillars in online education introduced by Sloan Consortium, there are still rooms for improvement [1]. Access, Learning effectiveness, student satisfaction, faculty satisfaction and cost effectiveness are the five metrics that drive investigations into online education

Floating time algorithm for time optimal control of multi-body dynamic systems

Moving a dynamic system in minimum time from a given initial state to a desired final state on a prescribed path is one of the oldest and most enduring technological dreams of the scientific and industrial communities. In this research, the problem of bounded-input time optimal control for applied multi-body dynamic systems subject to a full nonlinear dynamical model is solved. To solve the problem, an innovative method, called the 'floating-time' method is introduced and utilized. Compared to traditional methods, the floating-time method is an applied method not based on variational calculus. It can be applied to the full nonlinear model of the dynamical system and can handle static and dynamic constraints defined by differential or algebraic equations. The problem of time optimal control is as follows. Find the control law of bounded inputs that drive a given multi-body dynamic system (such as the gripper of a manipulator) along a pre-specified trajectory (in either configuration space or generalized coordinate space) from a given initial position to a given final position, minimizing the time of the motion as a performance index. Using variable time increments, the equations of motion of the system will be reduced to a set of algebraic equations. Searching for a set of time increments (floating-times) that make the equations to exert the maximum available effort produces the minimum possible floating-times, and minimizes the total time of motion. The applicability of the method will be shown by using three examples: a point mass sliding on a rough surface, a 2R robotic manipulator, and the well-known Brachistochrone

Autodriver algorithm for autonomous vehicles

In a recent research a superior algorithm has been introduced to design an autodriver to keep an autonomous vehicle on a given road using independent four-wheel-steering (4WS) system. The kinematic condition of steering sets the steer angles such that the kinematic center of rotation of the vehicle be controlled on a two dimensional space. The vehicle however, will turn about an actual point that is not necessarily at the road curvature center; because of the road, tire characteristics, and dynamics of the moving vehicle. The algorithm shows how the position of the dynamic turning center can be controlled by adjusting the steer angles such that it coincides with the road curvature center. Such a vehicle will move on the desired road autonomously