相关论文: Convexification With the Viscocity Term for Electr…
Determining the adsorption isotherms is an issue of significant importance in preparative chromatography. A modern technique for estimating adsorption isotherms is to solve an inverse problem so that the simulated batch separation coincides…
In this work, the inverse problem of quantitative thermoacoustic tomography is studied. In quantitative thermoacoustic tomography, dielectric parameters of an imaged target are estimated from an absorbed energy density induced by an…
We propose a new globally convergent numerical method to solve Hamilton-Jacobi equations in $\mathbb{R}^d$, $d \geq 1$. This method is named as the Carleman convexification method. By Carleman convexification, we mean that we use a Carleman…
We introduce a kind of electromagnetism, which we call viscoelastic-electromagnetism, to investigate viscoelastic transport phenomena. It is shown that Cartan's formalism of general relativity is essential for viscoelastic theory, and then…
This paper presents a static electrical impedance tomography (EIT) technique that evaluates abdominal obesity by estimating the thickness of subcutaneous fat. EIT has a fundamental drawback for absolute admittivity imaging because of its…
We extend the relative entropy identity to the class of hyperbolic-parabolic systems whose hyperbolic part is symmetrizable. The resulting identity, in the general theory, is useful to provide stability of viscous solutions and yields a…
Ultrasound modulated optical tomography, also called acousto-optics tomography, is a hybrid imaging modality that aims to combine the high contrast of optical waves with the high resolution of ultrasound. We follow the model of the…
A method for including a priori information in the 2-D D-bar algorithm is presented. Two methods of assigning conductivity values to the prior are presented, each corresponding to a different scenario on applications. The method is tested…
We develop a variational approach to the vanishing discount problem for fully nonlinear, degenerate elliptic, partial differential equations. Under mild assumptions, we introduce viscosity Mather measures for such partial differential…
We develop a virtual element method to solve a convective Brinkman-Forchheimer problem coupled with a heat equation. This coupled model may allow for thermal diffusion and viscosity as a function of temperature. Under standard…
In Electrical Impedance Tomography (EIT), the internal conductivity of a body is recovered via current and voltage measurements taken at its surface. The reconstruction task is a highly ill-posed nonlinear inverse problem, which is very…
This paper presents a modified general viscosity iterative process designed to solve variational inclusion and fixed point problems involving multi-valued quasi-nonexpansive and demi-contractive operators. The modified iterative process…
The paper surveys recent progress in establishing uniqueness and developing inversion formulas and algorithms for the thermoacoustic tomography. In mathematical terms, one deals with a rather special inverse problem for the wave equation.…
The Electrical Resistance Tomography (ERT) technique is applied to the measurement of sheet conductance maps of both uniform and patterned conductive thin films. Images of the sheet conductance spatial distribution, and local conductivity…
We explore the potential applications of virtual elements for solving the Sobolev equation with a convective term. A conforming virtual element method is employed for spatial discretization, while an implicit Euler scheme is used to…
When time reversal is broken the viscosity tensor can have a non vanishing odd part. In two dimensions, and only then, such odd viscosity is compatible with isotropy. Elementary and basic features of odd viscosity are examined by…
We consider Inverse Electrical Impedance Tomography (EIT) problem on recovering electrical conductivity and potential in the body based on the measurement of the boundary voltages on the $m$ electrodes for a given electrode current. The…
Here, we study the large-time limit of viscosity solutions of the Cauchy problem for second-order Hamilton--Jacobi--Bellman equations with convex Hamiltonians in the torus. This large-time limit solves the corresponding stationary problem,…
Photothermal imaging is a powerful noncontact and nondestructive technique for subsurface inspection of composite materials, yet its performance is fundamentally limited by the diffusive and irreversible nature of heat transport, leading to…
We derive, by means of Gamma-convergence, the equations of homogenized bending rod starting from $3D$ nonlinear elasticity equations. The main assumption is that the energy behaves like h^2 (after dividing by the order h^2 of vanishing…