Application of Sasaki's numerical variational technique to the analysis of height and wind fields over Indian region

An objective analysis method based on Sasaki's numerical variational analysis technique has been taken up for the analysis of geopotential height and wind over the Indian region. The univariate optimum interpolation (UOI) method is used to generate the initial or input fields. These fields are then adjusted by the variational method. A study of this method over Indian and adjoining region for 850, 700, 500, 300 and 200 hPa levels is made from 4 to 8 July 1979 and the analyses obtained using this method are compared with the FGGE analyses.

Inverse Problems in Magnetic Resonance Velocimetry: Shape, Forcing and Boundary Condition Inference

We derive and implement an algorithm that takes noisy magnetic resonance velocimetry (MRV) images of Stokes flow and infers the velocity field, the most likely position of the boundary, the inlet and outlet boundary conditions, and any body forces. We do this by minimizing a discrepancy norm of the velocity fields between the MRV experiment and the Stokes problem, and at the same time we obtain a filtered (denoised) version of the original MRV image. We describe two possible approaches to regularize the inverse problem, using either a variational technique, or Gaussian random fields. We test the algorithm for flows governed by a Poisson or a Stokes problem, using both real and synthetic MRV measurements. We find that the algorithm is capable of reconstructing the shape of the domain from artificial images with a low signal-to-noise ratio.

Analytical model of the diffuse sound transmission loss of finite double panel structures

An analytical model for the forced sound transmission loss of finite single-leaf walls using a variational technique was previously developed and validated. As the double panel is one of the most used structures in building acoustics, the aim of this paper is to extend the analytical model to consider double panel structures. Analytical formulas for the forced part of the airborne sound insulation of finite sized double panel structures are derived using a variational technique based on the integral-differential equation of the fluid loaded panels. The formulas are valid in the entire audible frequency range. The results are compared to alternative analytical models and measurements, with reasonable agreement.

Duality theory of fractional resolvents and applications to backward fractional control systems

We study the duality theory for fractional resolvents, extending and improving some corresponding theorems on semigroups. As applications, we develop the variational technique to analyze the finite-approximate controllability of a backward fractional control system with a right-sided Riemann-Liouville fractional derivative. Moreover, validity of our theoretical findings is given by a fractional diffusion model.

A Necessary Condition for Optimal Control of Forward-Backward Stochastic Control System with Lévy Process in Nonconvex Control Domain Case

This paper analyzes one kind of optimal control problem which is described by forward-backward stochastic differential equations with Lévy process (FBSDEL). We derive a necessary condition for the existence of the optimal control by means of spike variational technique, while the control domain is not necessarily convex. Simultaneously, we also get the maximum principle for this control system when there are some initial and terminal state constraints. Finally, a financial example is discussed to illustrate the application of our result.