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6 papers · 1 filter
Atomic Super-Resolution Tomography
Poulami Somanya Ganguly, Felix Lucka, Hermen Jan Hupkes +1
We consider the problem of reconstructing a nanocrystal at atomic resolution from electron microscopy images taken at a few tilt angles. A popular reconstruction approach called di…
Stability of inverse transport equation in diffusion scaling and Fokker-Planck limit
Ke Chen, Qin Li, Li Wang
We consider the inverse problem of reconstructing the scattering and absorption coefficients using boundary measurements for a time dependent radiative transfer equation (RTE). As…
A new numerical approach to inverse transport equation with error analysis
Qin Li, Ruiwen Shu, Li Wang
The inverse radiative transfer problem finds broad applications in medical imaging, atmospheric science, astronomy, and many other areas. This problem intends to recover the optica…
Uniform regularity for linear kinetic equations with random input based on hypocoercivity
Qin Li, Li Wang
In this paper we study the effect of randomness in kinetic equations that preserve mass. Our focus is in proving the analyticity of the solution with respect to the randomness, whi…
Efficient determination of critical parameters of nonlinear Schrödinger equation with point-like potential using generalized polynomial chaos methods
Debananda Chakraborty, Jae-Hun Jung, Emmanuel Lorin
We consider the nonlinear Schrödinger equation with a point-like source term. The soliton interaction with such a singular potential yields a critical solution behavior. That is, f…
Efficient determination of the critical parameters and the statistical quantities for Klein-Gordon and sine-Gordon equations with a singular potential using generalized polynomial chaos methods
Debananda Chakraborty, Jae-Hun Jung
We consider the Klein-Gordon and sine-Gordon type equations with a point-like potential, which describes the wave phenomenon in disordered media with a defect. The singular potenti…