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This paper presents an unsupervised algorithm for nonlinear unmixing of hyperspectral images. The proposed model assumes that the pixel reflectances result from a nonlinear function of the abundance vectors associated with the pure spectral…
We study linear stability of planar travelling waves for a scalar reaction-diffusion equation with non-linear anisotropic diffusion. The mathematical model is derived from the full thermo-hydrodynamical model describing the process of…
We present a unified framework that fully represents electromagnetic potentials, fields, and sources in vacuum, based on a reinterpretation of the classical Hertz-potential formalism. In this construction, $\phi$, $A$, $E$, $B$, $\rho$, and…
This article presents a multifield asymptotic homogenization scheme for the analysis of Bloch wave propagation in non-standard thermoelastic periodic materials, leveraging on the Green-Linsdsay theory that accounts for two relaxation times.…
Hyperspectral images provide much more information than conventional imaging techniques, allowing a precise identification of the materials in the observed scene, but because of the limited spatial resolution, the observations are usually…
We propose a variational approach to solve Cauchy problems for parabolic equations and systems independently of regularity theory for solutions. This produces a universal and conceptually simple construction of fundamental solution…
Transmission Electron Microscopy enables high-resolution imaging of materials, but the resulting images are difficult to interpret directly. One way to address this is exit wave reconstruction, i.e., the recovery of the complex-valued…
We revisit and present new linear spaces of explicit solutions to incompressible Euler and Navier-Stokes equations on $\mathbb{R}^n$, as well as the rotating Boussinesq equations on $\mathbb{R}^3$. We cast these solutions are superpositions…
We examine the generalized quantum electrodynamics as a natural extension of the Maxwell electrodynamics to cure the one-loop divergence. We establish a precise scenario to discuss the underlying features between photon and fermion where…
Modeling microstructure evolution in electrochemical systems is vital for understanding the mechanism of various electrochemical processes. In this work, we propose a general phase field framework that is fully variational and thus…
An inverse elastic source problem with sparse measurements is of concern. A generic mathematical framework is proposed which incorporates a low- dimensional manifold regularization in the conventional source reconstruction algorithms…
Classical theory of the electric double layer is based on the fundamental assumption of a dilute solution of point ions. There are a number of situations such as high applied voltages, high concentration of electrolytes, systems with…
We introduce a path-theoretic framework for understanding the representation theory of (quantum) symmetric and general linear groups and their higher level generalisations over fields of arbitrary characteristic. Our first main result is a…
Numerical modeling of wave propagation in heterogeneous media is important in many applications. Due to the complex nature, direct numerical simulations on the fine grid are prohibitively expensive. It is therefore important to develop…
We introduce a general, variational scheme applied to Kohn-Sham density functional theory that allows for partitioning of the ground-state density matrix into distinct spectral domains, each of which spanned by an independent diagonal…
Transformation optics offers an unconventional approach to the control of electromagnetic fields. A transformation optical structure is designed by first applying a form-invariant coordinate transform to Maxwell's equations, in which part…
We investigate the Cauchy problem and the diffusion asymptotics for a spatially inhomogeneous kinetic model associated to a nonlinear Fokker-Planck operator. We derive the global well-posedness result with instantaneous smoothness effect,…
Continuum solvation methods can provide an accurate and inexpensive embedding of quantum simulations in liquid or complex dielectric environments. Notwithstanding a long history and manifold applications to isolated systems in open boundary…
We consider the Cauchy problem for the isentropic compressible Euler-Maxwell equations under general pressure laws in a three-dimensional periodic domain. For any smooth initial electron density away from the vacuum and smooth…
Hyperspectral target detection is a task of primary importance in remote sensing since it allows identification, location, and discrimination of target features. To this end, the reflectance maps, which contain the spectral signatures and…