This paper discusses the existence of the tracking model to detect a linear flows particle with a stochastic waiting time depending on the Gaussian jump length. This model is useful to measure the impurity quantification such as Radionuclides and Toxic Chemicals (particle) within the interaction medium (fluid) with minimum time and maximum probability. The particle flows linearly toward the origin (either from the left or the right). The flow line contains a nano programmed sensor (or nano UV detector). This sensor starts the tracking process for the particle (target) from the origin (filtration point) with speed equals one. We obtain the expected value of the tracking time until the sensor return to the origin with the target. Some competitive analysis depends on the uncertain values of the traveled distances which are derived to get necessary conditions for the sensor’s optimal distances. The numerical results demonstrate the efficiency of this model.

中文翻译：

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具有取决于高斯跳跃长度的随机等待时间的线性流粒子跟踪模型的存在

本文讨论了跟踪模型的存在，以检测具有取决于高斯跳跃长度的随机等待时间的线性流粒子。该模型可用于以最少的时间和最大的概率测量相互作用介质（流体）中的杂质量化，例如放射性核素和有毒化学品（粒子）。粒子线性流向原点（从左侧或右侧）。流线包含一个纳米程序传感器（或纳米紫外线检测器）。该传感器从原点（过滤点）开始跟踪粒子（目标）的过程，速度等于 1。我们获得跟踪时间的期望值，直到传感器与目标一起返回原点。一些竞争分析依赖于行进距离的不确定值，这些不确定值是为了获得传感器最佳距离的必要条件而得出的。数值结果证明了该模型的有效性。