相关论文: Unique determination of absorption coefficients in…
We present two uniqueness results for the inverse problem of determining an index of refraction by the corresponding acoustic far-field measurement encoded into the scattering amplitude. The first one is a local uniqueness in determining a…
Many naturally-occuring models in the sciences are well-approximated by simplified models, using multiscale techniques. In such settings it is natural to ask about the relationship between inverse problems defined by the original problem…
The linear Boltzmann equation governs the absorption and scattering of a population of particles in a medium with an ambient field, represented by a Riemannian metric, where particles follow geodesics. In this paper, we study the possible…
This paper is devoted to the investigation of inverse problems related to stationary drift-diffusion equations modeling semiconductor devices. In this context we analyze several identification problems corresponding to different types of…
Several applications in medical imaging and non-destructive material testing lead to inverse elliptic coefficient problems, where an unknown coefficient function in an elliptic PDE is to be determined from partial knowledge of its…
We investigate the asymptotic relation between the inverse problems relying on the Helmholtz equation and the radiative transfer equation (RTE) as physical models, in the high-frequency limit. In particular, we evaluate the asymptotic…
Accurate models of carrier transport are essential for describing the electronic properties of semiconductor materials. To the best of our knowledge, the current models following the framework of the Boltzmann transport equation (BTE)…
The inverse source problem for the radiative transfer equation is considered, with partial data. Here it is shown that under certain smoothness conditions on the scattering and absorption coefficients, one can recover sources supported in a…
We consider an inverse source problem in the stationary radiating transport through a two dimensional absorbing and scattering medium. Of specific interest, the exiting radiation is measured on an arc. The attenuation and scattering…
In this work, we introduce a fast numerical algorithm to solve the time-dependent radiative transport equation (RTE). Our method uses the integral formulation of RTE and applies the treecode algorithm to reduce the computational complexity…
We have studied the weakly non-linear quantum transport properties of a two-dimensional quantum wire which can be solved exactly. The non-linear transport coefficients have been calculated and interesting physical properties revealed. In…
This paper is concerned with the inverse source problem for the transport equation with external force. We show that both direct and inverse problems are uniquely solvable for generic absorption and scattering coefficients. In particular,…
The first globally convergent numerical method for a Coefficient Inverse Problem (CIP) for the Riemannian Radiative Transfer Equation (RRTE) is constructed. This is a version of the so-called \textquotedblleft convexification" method, which…
In a recent article the authors showed that the radiative Transfer equations with multiple frequencies and scattering can be formulated as a nonlinear integral system. In the present article, the formulation is extended to handle reflective…
We develop a novel wave imaging scheme for reconstructing the shape of an inhomogeneous scatterer and we consider the inverse acoustic obstacle scattering problem as a prototype model for our study. There exists a wealth of reconstruction…
We present a transport equation for the incoherent propagation of radiation inside a quasi-resonant atomic gas at low temperature. The derivation is based on a generalized Bethe-Salpeter equation taking into account the motion of the atoms.…
We are concerned with the inverse scattering problem of recovering an inhomogeneous medium by the associated acoustic wave measurement. We prove that under certain assumptions, a single far-field pattern determines the values of a…
This paper is devoted to deal with some mathematical and numerical aspects of the radiative integral transfer equations. First, the properties of the raidative integral operators are analyzed. Based on these results, the existence and…
We consider the inverse problem of determining the density coefficient appearing in the wave equation from separated point source and point receiver data. Under some assumptions on the coefficients, we prove uniqueness results.
The radiative transfer equation (RTE) models the transport of light inside photonic scattering samples such as paint, foam and tissue. Analytic approximations to solve the RTE fail for samples with strong absorption and dominant anisotropic…