Ravi Prakash

Bio: Ravi Prakash is an academic researcher from University of Concepción. The author has contributed to research in topics: Optimal control & Boundary (topology). The author has an hindex of 7, co-authored 21 publications receiving 144 citations. Previous affiliations of Ravi Prakash include Indian Institute of Science.

Generalization of unfolding operator for highly oscillating smooth boundary domains and homogenization

Abstract: Unfolding operators have been introduced and used to study homogenization problems. Initially, they were introduced for problems with rapidly oscillating coefficients and porous domains. Later, this has been developed for domains with oscillating boundaries, typically with rectangular or pillar type boundaries which are classified as non-smooth. In this article, we develop new unfolding operators, where the oscillations can be smooth and hence they have wider applications. We have demonstrated by developing unfolding operators for circular domains with rapid oscillations with high amplitude of O(1) to study the homogenization of an elliptic problem.

Periodic Controls in an Oscillating Domain: Controls via Unfolding and Homogenization

Abstract: An optimal control problem in a two-dimensional domain with a rapidly oscillating boundary is considered. The main features of this article are on two points, namely, we consider periodic controls in the thin periodic slabs of period $\epsilon >0$, a small parameter, and height $O(1)$ in the oscillatory part, and the controls are characterized using unfolding operators. We then do a homogenization analysis of the optimal control problems as $\epsilon \rightarrow 0$ with $L^2$ as well as Dirichlet (gradient-type) cost functionals.

Asymptotic analysis and error estimates for an optimal control problem with oscillating boundaries

Abstract: In this article, we consider a distributed optimal control problem associated with the Laplacian in a domain with rapidly oscillating boundary. For simplicity, we consider a rectangular region in 2d with oscillations on one part of the boundary. We consider two types of functionals, namely a functional involving the L2-norm of the state variable and another one involving its H1-norm. The homogenization of the optimality system is obtained and then we derive appropriate error estimates in both cases.

Semi-linear optimal control problem on a smooth oscillating domain

Abstract: We demonstrate the asymptotic analysis of a semi-linear optimal control problem posed on a smooth oscillating boundary domain in the present paper. We have considered a more general oscillating dom...

Randomized multi‐angle illumination for improved linear array photoacoustic computed tomography in brain

Abstract: One of the key challenges in linear array transducer‐based photoacoustic computed tomography is to image structures embedded deep within the biological tissue with limited optical energy. Here, we utilized a manually controlled multi‐angle illumination technique to allow the incident photons to interact with the imaging targets for longer periods of time and diffuse further in all directions. We have developed and optimized a compact probe that enables manual changes to the angle of illumination while acquiring photoacoustic signals. The performance has been demonstrated and evaluated by imaging complex blood vessel mimicking phantoms in‐vitro and sheep brain samples ex‐vivo. For effective image reconstruction from the data acquired by multi‐angle illumination method, we have utilized a method based on the extraction of maximum intensity. In both cases, multi‐angle illumination has out‐performed the conventional fixed angle illumination technique to improve the overall image quality. Specifically, extraction of the imaging targets located at greater axial depths was possible using this multi‐angle illumination technique.

Homogenization of the Brush Problem with a Source Term in L^1

Abstract: We consider a domain which has the form of a brush in 3D or the form of a comb in 2D, i.e. an open set which is composed of cylindrical vertical teeth distributed over a fixed basis. All the teeth have a similar fixed height; their cross sections can vary from one teeth to another one and are not supposed to be smooth; moreover the teeth can be adjacent, i.e. they can share parts of their boundaries. The diameter of every tooth is supposed to be less than or equal to e, and the asymptotic volume fraction of the teeth (as e tends to zero) is supposed to be bounded from below away from zero, but no periodicity is assumed on the distribution of the teeth. In this domain we study the asymptotic behavior (as e tends to zero) of the solution of a second order uniformly elliptic equation with a zeroth order term which is bounded from below away from zero, when the homogeneous Neumann boundary condition is satisfied on the whole of the boundary. First, we revisit the problem where the source term belongs to L^2. This is a classical problem, but our homogenization result takes place in a geometry which is more general that the ones which have been considered before. Moreover we prove a corrector result which is new. Then, we study the case where the source term belongs to L^1. Working in the framework of renormalized solutions and introducing a definition of renormalized solutions for degenerate elliptic equations where only the vertical derivative is involved (such a definition is new), we identify the limit problem and prove a corrector result.

Generalization of unfolding operator for highly oscillating smooth boundary domains and homogenization

Abstract: Unfolding operators have been introduced and used to study homogenization problems. Initially, they were introduced for problems with rapidly oscillating coefficients and porous domains. Later, this has been developed for domains with oscillating boundaries, typically with rectangular or pillar type boundaries which are classified as non-smooth. In this article, we develop new unfolding operators, where the oscillations can be smooth and hence they have wider applications. We have demonstrated by developing unfolding operators for circular domains with rapid oscillations with high amplitude of O(1) to study the homogenization of an elliptic problem.

Periodic Controls in an Oscillating Domain: Controls via Unfolding and Homogenization

Abstract: An optimal control problem in a two-dimensional domain with a rapidly oscillating boundary is considered. The main features of this article are on two points, namely, we consider periodic controls in the thin periodic slabs of period $\epsilon >0$, a small parameter, and height $O(1)$ in the oscillatory part, and the controls are characterized using unfolding operators. We then do a homogenization analysis of the optimal control problems as $\epsilon \rightarrow 0$ with $L^2$ as well as Dirichlet (gradient-type) cost functionals.