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This paper is concerned with time domain forward scattering and inverse scattering problems with a single moving point source as the emitter. Approximate solutions are provided for the forward scattering problem with a moving emitter.…
In the present paper we propose a coupled multigrid method for generalized Stokes flow problems. Such problems occur as subproblems in implicit time-stepping approaches for time-dependent Stokes problems. The discretized Stokes system is a…
A mechanical model and finite element method for the simultaneous solution of Stokes and incompressible Navier-Stokes flows on multiple curved surfaces over a bulk domain are proposed. The two-dimensional surfaces are defined implicitly by…
In this paper we discuss inverse medium problems. We develop the direct sampling method based on probing indices using the saddle point formulation. The medium is constructed by solutions of saddle point problems. The method improves the…
In the present work, we propose to extend to the Stokes problem a fictitious domain approach inspired by eXtended Finite Element Method and studied for Poisson problem in [Renard]. The method allows computations in domains whose boundaries…
We consider estimation of parameters defined as linear functionals of solutions to linear inverse problems. Any such parameter admits a doubly robust representation that depends on the solution to a dual linear inverse problem, where the…
In this paper a time dependent Stokes problem that is motivated by a standard sharp interface model for the fluid dynamics of two-phase flows is studied. This Stokes interface problem has discontinuous density and viscosity coefficients and…
Stokes inversion techniques are very powerful methods for obtaining information on the thermodynamic and magnetic properties of solar and stellar atmospheres. In recent years, very sophisticated inversion codes have been developed that are…
This article is devoted to the simultaneous resolution of three inverse problems, among the most important formulation of inverse problems for partial differential equations, stated for some class of diffusion equations from a single…
The Conley index of an isolated invariant set is a fundamental object in the study of dynamical systems. Here we consider smooth functions on closed submanifolds of Euclidean space and describe a framework for inferring the Conley index of…
We experimentally implement an optical algorithm for integration of a real-valued bivariate func- tion. A user-defined function is encoded in the position-dependent phase of one of the polarization components of an optical beam. The…
In this paper we cover a few topics on how to treat inverse problems. There are two different flows of ideas. One approach is based on Morse Lemma. The other is based on analyticity which proves that the number of solutions to the inverse…
The design of the performance index, also referred to as cost or reward shaping, is central to both optimal control and reinforcement learning, as it directly determines the behaviors, trade-offs, and objectives that the resulting control…
We consider a coupled model of free-flow and porous medium flow, governed by stationary Stokes and Darcy flow, respectively. The coupling between the two systems is enforced by introducing a single variable representing the normal flux…
In this article, we recover singularly-perturbed linear differential systems from their turning points and reduce the rank of the singularity in the parameter to its minimal integer value. Our treatment is Moser-based; that is to say it is…
For many biological systems that involve elastic structures immersed in fluid, small length scales mean that inertial effects are also small, and the fluid obeys the Stokes equations. One way to solve the model equations representing such…
We study an inverse source scattering problem for the Schr\"odinger equation with a quadratic nonlinearity. In general, uniqueness of inverse source problems can not be guaranteed at a fixed energy. Therefore, additional information is…
We consider the phase-integral method applied to an arbitrary ordinary linear differential equation of the second-order and study how its symmetries affect the connection matrices associated with its general solution. We reduce the obtained…
We use a method of solvable functions for solution of pursue problem at integral restriction on controls. Moreover we shall apply the method to two examples.
We solve the Stokes equations for the flow around two parallel translating and rotating cylinders using tools from complex analysis and conformal mapping. By considering cylinders of arbitrary size and separation, we generalise the…