Related papers: Natural orbitals in multiconfiguration calculation…
Understanding natural relative motion trajectories is critical to enable fuel-efficient multi-satellite missions operating in complex environments. This paper studies the problem of computing and efficiently parameterizing satellite…
A previously proposed computational procedure for constructing a set of nonorthogonal strongly localised one-electron molecular orbitals (O. Danyliv, L. Kantorovich - physics/0401107) is applied to a perfect $\alpha$-quartz crystal…
Colloidal self-assembly -- the spontaneous organization of colloids into ordered structures -- has been considered key to produce next-generation materials. However, the present-day staggering variety of colloidal building blocks and the…
Accurate modeling of gravitational interactions is fundamental to the analysis, prediction, and control of space systems. While the Newtonian point-mass approximation suffices for many preliminary studies, real celestial bodies exhibit…
This work presents a detailed mathematical derivation of the hierarchically correlated orbital functional theory (HCOFT), a framework based on hypercomplex orbitals. Recent study [Phys. Rev. Lett. 133, 206402] has demonstrated that…
We consider Hamiltonian diffeomorphisms of the Euclidean space, generated by compactly supported time-dependent perturbations of hyperbolic quadratic forms. We prove that, under some natural assumptions, such a diffeomorphism must have…
We propose two algorithms to provide a full preliminary orbit of an Earth-orbiting object with a number of observations lower than the classical methods, such as those by Laplace and Gauss. The first one is the Virtual debris algorithm,…
We introduce orthogonal ring patterns in the 2-sphere and in the hyperbolic plane, consisting of pairs of concentric circles, which generalize circle patterns. We show that their radii are described by a discrete integrable system. This is…
We consider principal fibre bundles with a given connection and construct almost complex structures on the total space if the adjoint bundle is isomorphic to the tangent bundle of the base. We derive the integrability condition. If the…
A fast algorithm (linear in the degrees of freedom) for the solution of linear variable-coefficient rational-order fractional integral and differential equations is described. The approach is related to the ultraspherical method for…
Spatially localized one-electron orbitals, orthogonal and nonorthogonal, are widely used in electronic structure theory to describe chemical bonding and speed up calculations. In order to avoid linear dependencies of localized orbitals, the…
The auxiliary functions provide efficient computation of integrals arising at the self-consistent field (SCF) level for molecules using Slater-type bases. This applies both in relativistic and non-relativistic electronic structure theory.…
We present a novel route to constructing cost-efficient semi-empirical approximations for the non-additive kinetic energy in subsystem density functional theory. The developed methodology is based on the use of Slater determinants composed…
Semiclassical analysis of shell structures in realistic nuclear potentials are presented using periodic-orbit theory. We adopted r^alpha potential model and examined classical-quantum correspondence using Fourier transformation technique.…
We prove that certain non-exact magnetic Hamiltonian systems on products of closed hyperbolic surfaces and with a potential function of large oscillation admit non-constant contractible periodic solutions of energy below the Ma\~n\'e…
The projection of the eigenfunctions obtained in standard plane-wave first-principle electronic-structure calculations into atomic-orbital basis sets is proposed as a formal and practical link between the methods based on plane waves and…
Abundant second-order maximally conformally superintegrable Hamiltonian systems are re-examined, revealing their underlying natural Weyl structure and offering a clearer geometric context for the study of St\"ackel transformations (also…
The non-commutative nature of 3D rotations poses well-known challenges in generalizing planar problems to three-dimensional ones, even more so in contact-rich tasks where haptic information (i.e., forces/torques) is involved. In this sense,…
This paper presents a unique approach to the problem of calculating revisit time metrics for different satellite orbits, sensor geometries, and constellation configurations with application to early lifecycle design and optimisation…
We propose a unique scheme to construct fully optimized atomic basis sets for density-functional calculations. The shapes of the radial functions are optimized by minimizing the {\it spillage} of the wave functions between the atomic…