Probabilistic Modeling and Tracking of Helical Particle in the Fluid

In this paper, we address the challenging problem of tracking a helically moving particle in a fluidic domain by developing a nonlinear probabilistic framework that couples stochastic transport dynamics with nanoscale sensing and an oscillatory first-passage optimization strategy. The particle’s position is assumed to be completely unobservable, and its detection is attempted by a coordinated group of three nanosensors initially located at the origin. Within this framework, potential candidate points for the particle’s trajectory are generated stochastically along three orthogonal axes, forming the basis of the tracking surface. The sensing mechanism is modeled such that one nanosensor performs oscillatory right–left displacements about a central axis, thereby enhancing the probability of interception. Beyond establishing the feasibility of the proposed method, we further investigate its optimality by quantifying the influence of the discount factor on the expected value of the first-collision time between any nanosensor and the particle. A computation experiment is employed to demonstrate the effectiveness and accuracy of the method in explaining helical transport behavior.