We prove existence, uniqueness and optimal regularity of solutions to the stationary obstacle problem defined by the fractional Laplacian operator with drift, in the subcritical regime. As in [1], we localize our problem by considering a suitable extension operator introduced in [2]. The structure of the extension equation is different from the one constructed in [1], in that the obstacle funct...

In an excitable medium, wave breaks are essential for spiral wave formation. Although wave breaks can result from collisions between a wave and an obstacle, it is only when the resultant wave fragments separate from the obstacle ~wave-front–obstacle separation! that a spiral wave will begin to develop. We explored collisions between a piecewise linear obstacle and an incident wave front while v...

Spatio-temporal gaze behaviour patterns were analysed as normal participants wearing a mobile eye tracker approached and stepped over obstacles of varying height in the travel path. We examined the frequency and duration of three types of gaze fixation with respect to the participants' stepping patterns: obstacle fixation (ObsFix); travel fixation (TravFix) (when the gaze is stable and travelli...

We developed a novel locomotor task in which cats step over obstacles that move at a different speed from that of the treadmill on which the cat is walking: we refer to this as a visual dissociation locomotion task. Slowing the speed of the obstacle with respect to that of the treadmill sometimes led to a major change in strategy so that cats made two steps with the hindlimbs before stepping ov...

The present paper deals with an exact semi-analytical formulation of a combined conductive-radiative heat transfer, applied to two-dimensional semi-transparent medium carrying square centered obstacle. gray participating black boundaries absorbs, emits but does not scatter radiation. One intends evaluate the temperature and radiative flux distributions within medium. transfer equation has been ...

In this paper, the bisection of the local mesh refinement in self adaptive finite element is applied to the obstacle problem of elliptic variational inequalities .We try to find the approximated region of the contact in the obstacle problem efficiently .Numerical examples are given for the obstacle problem. Key-Words: obstacle problem, variational inequalities, self adaptive finite element, bis...

This paper proposes a novel vector field navigation method by using the velocity vector of a robot to avoid obstacles in dynamic environment. Shifting vector and virtual obstacle are proposed to derive the center of repulsive field which makes the robot move away from the obstacle: The shifting vector is derived from the velocity vector of the robot and the obstacle and the virtual obstacle is ...

The obstacle problem is a linearized version of the problem of stretching an elastic membrane over an obstacle. One of its central features is that the solution will divide the original domain into a set of points where the membrane lies strictly above the obstacle and satisfies a partial differential equation, and its complement, where the membrane touches the obstacle. The fact that these set...

We examined the ways in which memories of previously seen obstacles can alter the stepping of walking cats. Cats were paused after the forelegs, but not the hindlegs, had stepped over an obstacle. Near the beginning of a variable delay period, the obstacle was lowered. On the subsequent step, the path of the hindlegs allowed us to make inferences about whether the memory of the obstacle was inf...