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The modern imaging techniques of Positron Emission Tomography and of Single Photon Emission Computed Tomography are not only two of the most important tools for studying the functional characteristics of the brain, but they now also play a…
Quantifying material mass and electron density from computed tomography (CT) reconstructions can be highly valuable in certain medical practices, such as radiation therapy planning. However, uniquely parameterising the X-ray attenuation in…
We review briefly the fundamental equations of a semi-microscopic core-particle coupling method that makes no reference to an intrinsic system of coordinates. We then demonstrate how an intrinsic system can be introduced in the strong…
Semi-local density functionals for the exchange-correlation energy of electrons are extensively used as it produce realistic and accurate results for finite and extended systems. The choice of techniques play crucial role in constructing…
Electron energy loss spectroscopy (EELS) has emerged as a powerful tool for the investigation of plasmonic nanoparticles, but the interpretation of EELS results in in terms of optical quantities, such as the photonic local density of…
Electron microscopy is a powerful tool for studying the properties of materials down to their atomic structure. In many cases, the quantitative interpretation of images requires simulations based on atomistic structure models. These…
We present a new method for calculating electronic states in low-dimensional semiconductor heterostructures, which is based on the real-space Hamiltonian in the envelope function approximation. The numerical implementation of the method is…
We derive exact reconstruction methods for cracks consisting of unions of Lipschitz hypersurfaces in the context of Calder\'on's inverse conductivity problem. Our first method obtains upper bounds for the unknown cracks, bounds that can be…
This is the second of a series of three papers that present a methodology with the aim of creating a set of maps of the coronal density over a period of many years. This paper describes a method for reconstructing the coronal electron…
A new method for calculation of band structure has been proposed based on the Green's function theory and local sampling. Potential energy in the Hamiltonian of Schrodinger's equation is approximated with a series of sampled Dirac delta…
We present a new method for the computation of self-energy corrections in large supercells. It eliminates the explicit summation over unoccupied states, and uses an iterative scheme based on an expansion of the Green's function around a set…
Electrical impedance tomography is an imaging modality for extracting information on the conductivity distribution inside a physical body from boundary measurements of current and voltage. In many practical applications, it is a priori…
In this letter, we show that the Semiclassical Einstein's Field Equation can be recovered using the generalized entropy $S_{gen}$. This approach is reminiscent of non-equilibrium thermodynamics. Furthermore, contrary to the entanglement…
On semiconductor growth surfaces, surface reconstructions appear. Estimation of the reconstructed structures is essential for understanding and controlling growth phenomena. In this study, the stability of a mixture of two different surface…
We present a new numerical method for the isometric embedding of 2-geometries specified by their 2-metrics in three dimensional Euclidean space. Our approach is to directly solve the fundamental embedding equation supplemented by six…
In the present work we study numerical solution of the radial Dirac equation in a specific case - ab-initio pseudopotential generating process - which is needed within the electronic structure calculations using a Density Functional Theory…
We study the computation of equilibrium points of electrostatic potentials: locations in space where the electrostatic force arising from a collection of charged particles vanishes. This is a novel scenario of optimization in which…
Most density functionals have been developed by imposing the known exact constraints on the exchange-correlation energy, or by a fit to a set of properties of selected systems, or by both. However, accurate modeling of the conventional…
We consider the problem of reconstructing global quantum states from local data. Because the reconstruction problem has many solutions in general, we consider the reconstructed state of maximum global entropy consistent with the local data.…
We propose a new method for calculating total energies of systems of interacting electrons, which requires little more computational resources than standard density-functional theories. The total energy is calculated within the framework of…