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A consolidated mathematical formulation of the spherically symmetric mass-transfer problem is presented, with the quasi-stationary approximating equations derived from a perturbation point of view for the leading-order effect. For the…
This paper investigates the problem of time-harmonic acoustic scattering in an inhomogeneous medium with a complex topological structure. Specifically, the medium is anisotropic and contains several disjoint sound-soft obstacles. This model…
Inferring a diffusion equation from discretely-observed measurements is a statistical challenge of significant importance in a variety of fields, from single-molecule tracking in biophysical systems to modeling financial instruments.…
This work discusses the homogenization analysis for diffusion processes on scale-free metric graphs, using weak variational formulations. The oscillations of the diffusion coefficient along the edges of a metric graph induce internal…
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…
Integrated sensing and communication (ISAC) systems potentially encounter significant performance degradation in densely obstructed urban and non-line-of-sight scenarios, thus limiting their effectiveness in practical deployments. To deal…
For the accurate representation and reconstruction of band-limited signals on the sphere, an optimal-dimensionality sampling scheme has been recently proposed which requires the optimal number of samples equal to the number of degrees of…
Waveform inversion is theoretically a powerful tool to reconstruct subsurface structures, but a usually encountered problem is that accurate sources are very rare, causing the computation unstable and divergent. This challenging problem,…
We present the generalized iterative residual fitting (IRF) for the computation of the spherical harmonic transform (SHT) of band-limited signals on the sphere. The proposed method is based on the partitioning of the subspace of…
Modelling diffusion processes in heterogeneous media requires addressing inherent discontinuities across interfaces, where specific conditions are to be met. These challenges fall under the purview of Mathematical Analysis as…
Reconfigurable holographic surface (RHS) enables cost-effective large-scale arrays with high spatial gain. However, its amplitude-controlled holographic beamforming suffers from directional fluctuations, making it difficult to fully exploit…
We introduce a new event shape observable -- event isotropy -- that quantifies how close the radiation pattern of a collider event is to a uniform distribution. This observable is based on a normalized version of the energy mover's…
The high resolution and sensitivity provided by proposed Atacama Large Millimeter Array will reveal new small scale structures in many sources, e.g. star forming regions. Such inhomogeneities may not have been considered in the analysis of…
We describe a novel adaptive ray tracing scheme to solve the equation of radiative transfer around point sources in hydrodynamical simulations. The angular resolution adapts to the local hydrodynamical resolution and hence is of use for…
Stellar photospheric heterogeneity is a dominant astrophysical systematic impacting exoplanet transmission spectroscopy. NASA's Pandora SmallSat Mission is designed to address this challenge through contemporaneous visible photometry and…
Conventional cosmic-ray propagation models usually assume an isotropic diffusion coefficient to account for the random deflection of cosmic rays by the turbulent interstellar magnetic field. Such a picture is very successful in explaining…
The reduced speed of light approximation (RSLA) has been employed to speed up radiative transfer simulations of reionization by a factor of $\gtrsim 5-10$. However, it has been shown to cause significant errors in the HI-ionizing background…
This paper investigates the sparse optimal allocation of sensors for detecting sparse leaking emission sources. Because of the non-negativity of emission rates, uncertainty associated with parameters in the forward model, and sparsity of…
Computational modelling of diffusion in heterogeneous media is prohibitively expensive for problems with fine-scale heterogeneities. A common strategy for resolving this issue is to decompose the domain into a number of non-overlapping…
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…