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In the present work, we investigate the possibility of obtaining stellar interiors for static self-gravitating systems describing an anisotropic matter distribution in the framework of Rastall gravity through gravitational decoupling by…
Fast and accurate integration of geodesics in Kerr spacetimes is an important tool in modeling the orbits of stars and the transport of radiation in the vicinities of black holes. Most existing integration algorithms employ Boyer-Lindquist…
From the point of view of canonical quantum gravity, it has become imperative to find a framework for quantization which provides a {\em general} prescription to find the physical inner product, and is flexible enough to accommodate…
Generalized complex geometry, as developed by Hitchin, contains complex and symplectic geometry as its extremal special cases. In this thesis, we explore novel phenomena exhibited by this geometry, such as the natural action of a B-field.…
This article presents original work combining a NURBS-based inverse analysis with both kinematic and constitutive nonlinearities to recover the applied loads and deformations of thin shell structures. The inverse formulation is tackled by…
We combine advanced image reconstruction techniques from computed X-ray micro tomography (XCT) with state-of-the-art discrete element method simulations (DEM) to study granular materials. This "virtual-laboratory" platform allows us to…
With the exception of q-hypergeometric summation, the use of computer algebra packages implementing Zeilberger's "holonomic systems approach" in a broader mathematical sense is less common in the field of q-series and basic hypergeometric…
This paper develops a novel mathematical framework for collaborative learning by means of geometrically inspired kernel machines which includes statements on the bounds of generalisation and approximation errors, and sample complexity. For…
Computer simulations are enabling researchers to investigate systems which are extremely difficult to handle analytically. In the particular case of General Relativity, numerical models have proved extremely valuable for investigations of…
We present a boundary integral method for numerical computation of the capacity of generalized condensers. The presented method applies to a wide variety of generalized condenser geometry including the cases when the plates of the…
Accurately describing many-body effects in multi-orbital systems remains a major challenge in theoretical condensed matter physics. At present, there is a significant methodological gap between the numerical tools used in ab initio…
Evaluation of relativistic molecular integrals over exponential-type spinor orbitals require using the relativistic auxiliary functions in prolate spheroidal coordinates. They have derived recently by the author [Physical Review E 91,…
Full-potential electronic structure calculations for periodic systems retain the Coulomb singularity at the nuclei, which induces cusp behavior of the orbitals near the nuclei while leaving the interstitial region smooth. This multiscale…
An adjoint-based shape optimization method for solid bodies subjected to both rarefied and continuum gas flows is proposed. The gas-kinetic BGK equation with the diffuse-reflection boundary condition is used to describe the multiscale gas…
In this video we highlight the application of Computational Geometry to our understanding of the formation and dynamics of the Cosmic Web. The emergence of this intricate and pervasive weblike structure of the Universe on Megaparsec scales…
We introduce a coupled finite and boundary element formulation for acoustic scattering analysis over thin shell structures. A triangular Loop subdivision surface discretisation is used for both geometry and analysis fields. The…
Geometrization of physical theories have always played an important role in their analysis and development. In this contribution we discuss various aspects concerning the geometrization of physical theories: from classical mechanics to…
Drachmann's regularization approach is implemented for floating explicitly correlated Gaussians (fECGs) and molecular systems. Earlier applications of drachmannized relativistic corrections for molecular systems were hindered due to the…
In this paper, we consider the hull of an algebraic geometry code, meaning the intersection of the code and its dual. We demonstrate how codes whose hulls are algebraic geometry codes may be defined using only rational places of Kummer…
We revise general relativity (GR) from the perspective of calculus for moving surfaces (CMS). While GR is intrinsically constructed in pseudo-Riemannian geometry, a complete understanding of moving manifolds requires embedding in a higher…