Stochastic Vorticity and Associated Filtering Theory
نویسندگان
چکیده
The focus of this work is on a two-dimensional stochastic vorticity equation for an incompressible homogeneous viscous fluid. We consider a signed measure-valued stochastic partial differential equation for a vorticity process based on the Skorohod–Ito evolution of a system of N randomly moving point vortices. A nonlinear filtering problem associated with the evolution of the vorticity is considered and a corresponding Fujisaki–Kallianpur–Kunita stochastic differential equation for the optimal filter is derived.
منابع مشابه
A stochastic filtering technique for fluid flows velocity fields tracking
In this paper we present a method for the temporal tracking of fluid flows velocity fields. The technique we propose is formalized within a sequential Bayesian filtering framework. The filtering model combines an Itô diffusion process coming from a stochastic formulation of the vorticity-velocity form of the Navier-Stokes equation and discrete measurements extracted from the image sequence. In ...
متن کاملApplication of the Kalman-Bucy filter in the stochastic differential equation for the modeling of RL circuit
In this paper, we present an application of the stochastic calculusto the problem of modeling electrical networks. The filtering problem have animportant role in the theory of stochastic differential equations(SDEs). In thisarticle, we present an application of the continuous Kalman-Bucy filter for a RLcircuit. The deterministic model of the circuit is replaced by a stochastic model byadding a ...
متن کاملA New Method for Characterization of Biological Particles in Microscopic Videos: Hypothesis Testing Based on a Combination of Stochastic Modeling and Graph Theory
Introduction Studying motility of biological objects is an important parameter in many biomedical processes. Therefore, automated analyzing methods via microscopic videos are becoming an important step in recent researches. Materials and Methods In the proposed method of this article, a hypothesis testing function is defined to separate biological particles from artifact and noise in captured v...
متن کاملVortex Methods and Turbulence Theory
Vortex methods have been developed over the last fifteen years, and have found numerous applications to incompressible and slightly compressible flow, combustion theory, reaction/diffusion equations, and boundary layer theory. Vorticity dominates the mechanics of most real flows and often concentrates in small subsets of the flow field, and thus vortex methods focus effort on the variables of m...
متن کاملStochastic Coherent Adaptive Large Eddy Simulation Method
In this paper we propose a novel approach called the stochastic coherent adaptive large eddy simulation ~SCALES! method which takes advantage of both the coherent vortex simulation ~CVS! and large eddy simulation ~LES! methods. With the SCALES method a wavelet filter is applied to a turbulent field such that the maximum number of modes are resolved in the simulation, given the balance between c...
متن کامل