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Approximation of scattered data is often a task in many engineering problems. The Radial Basis Function (RBF) approximation is appropriate for large scattered (unordered) datasets in d-dimensional space. This approach is useful for a higher…
We investigate a model of solid propellant combustion involving surface pyrolysis coupled to finite activation energy gas phase combustion. Existence and uniqueness of a travelling wave solution are established by extending dynamical system…
In this paper, we formulate the Load Flow (LF) problem in radial electricity distribution networks as an unconstrained Riemannian optimization problem, consisting of two manifolds, and we consider alternative retractions and initialization…
We present an abstract method in the setting of compact metric spaces which is applied to solve a number of problems in geometric optics. In particular, we solve the one source near field refraction problem. That is, we construct surfaces…
The scattering properties of quantum particles on fractal potentials at different stages of fractal growth are obtained by means of the transfer matrix method. This approach can be easily adopted for project assignments in introductory…
We present three schemes for the numerical approximation of fractional diffusion, which build on different definitions of such a non-local process. The first method is a PDE approach that applies to the spectral definition and exploits the…
This work proposes a novel technique for the numerical calculus of the fractal dimension of fractal objects which can be represented as a closed contour. The proposed method maps the fractal contour onto a complex signal and calculates its…
The so-called non-uniform FFT (NFFT) is a family of algorithms for efficiently computing the Fourier transform of finite-length signals, whenever the time or frequency grid is nonuniformly spaced. Following the usual classification, there…
The Time-Resolved Integrative Optical Neutron (TRION) detector was developed for Fast Neutron Resonance Radiography (FNRR), a fast-neutron transmission imaging method that exploits characteristic energy-variations of the total scattering…
Radiation feedback plays a crucial role in the process of star formation. In order to simulate the thermodynamic evolution of disks, filaments, and the molecular gas surrounding clusters of young stars, we require an efficient and accurate…
Neural Radiance Fields (NeRFs) have emerged as a standard framework for representing 3D scenes and objects, introducing a novel data type for information exchange and storage. Concurrently, significant progress has been made in multimodal…
In recent years, Neural Radiance Fields (NeRFs) have demonstrated significant potential in encoding highly-detailed 3D geometry and environmental appearance, positioning themselves as a promising alternative to traditional explicit…
Calculations of the photonic band structure, transmission coefficients, and quality factors of various two-dimensional, periodic and aperiodic, dielectric photonic crystals by using the finite element method (FEM) are reported. The…
New mathematical and numerical results are given for the coupling of the temperature equation of a fluid with Radiative Transfer: existence and uniqueness and a convergent monotone numerical scheme. The technique is shown to be feasible for…
Fluorescence microscopy is an essential tool for the analysis of 3D subcellular structures in tissue. An important step in the characterization of tissue involves nuclei segmentation. In this paper, a two-stage method for segmentation of…
We consider finite approximations of a fractal generated by an iterated function system of affine transformations on $\mathbb{R}^d$ as a discrete set of data points. Considering a signal supported on this finite approximation, we propose a…
In this work, we present a mathematical model to describe the adsorption-diffusion process on fractal porous materials. This model is based on the fractal continuum approach and considers the scale-invariant properties of the surface and…
By projecting the stochastic mean-field dynamics on a suitable collective path during the entrance channel of heavy-ion collisions, expressions for transport coefficients associated with relative distance are extracted. These transport…
Perception of the full state is an essential technology to support the monitoring, analysis, and design of physical systems, one of whose challenges is to recover global field from sparse observations. Well-known for brilliant approximation…
A unified method for three-dimensional reconstruction of objects from transmission images collected at multiple illumination directions is described. The method may be applicable to experimental conditions relevant to absorption-based,…