Related papers: Compact Formulae for Three-Center Nuclear Attracti…
We provide an elegant way of solving analytically the third post-Newtonian (3PN) accurate Kepler equation, associated with the 3PN-accurate generalized quasi-Keplerian parametrization for compact binaries in eccentric orbits. An additional…
The paper proposes an approximate expression for calculating very complex one-dimensional integrals depending on the parameter $a$. These integrals often occur in computational problems theory of magnetic solitons. The resulting analytical…
In the present paper, we study the uncertainties in modeling the collision of complex nuclei (heavy ions) resulting in capture of the nuclei into orbital motion. The effective interaction energy of the nuclei (effective potential) consists…
The well-known spatial integration schemes in molecular electronic structure theory, immune to cusps and point singularities of some kind at atomic positions, use a set of weighting functions to split the integrand into a sum of…
We consider the computation of the matrix logarithm by using numerical quadrature. The efficiency of numerical quadrature depends on the integrand and the choice of quadrature formula. The Gauss--Legendre quadrature has been conventionally…
The numerical simulation of three-dimensional charged-particle dynamics (CPD) under strong magnetic field is a basic and challenging algorithmic task in plasma physics. In this paper, we introduce a new methodology to design two-scale…
The computation of the matrix exponential is a ubiquitous operation in numerical mathematics, and for a general, unstructured $n\times n$ matrix it can be computed in $\mathcal{O}(n^3)$ operations. An interesting problem arises if the input…
This article presents two methods, in parallel, of solving more complex integrals, among which is the Poisson's integral, in order to emphasize the obvious advantages of a new method of integration, which uses the supermathematics circular…
The Slater-type orbital basis with non-integer principal quantum numbers is a physically and mathematically motivated choice for molecular electronic structure calculations in both non-relativistic and relativistic theory. The…
We present an efficient algorithm for one- and two-component relativistic exact-decoupling calculations. Spin-orbit coupling is thus taken into account for the evaluation of relativistically transformed (one-electron) Hamiltonian. As the…
I discuss the accuracy requirements on numerical relativity calculations of inspiraling compact object binaries whose extracted gravitational waveforms are to be used as templates for matched filtering signal extraction and physical…
We derive density-dependent corrections to the in-medium nucleon-nucleon interaction from the leading-order chiral three-nucleon force. To this order there are six distinct one-loop diagrams contributing to the in-medium nucleon-nucleon…
We present new nuclear matter calculations based on low-momentum interactions derived from chiral effective field theory potentials. The current calculations use an improved treatment of the three-nucleon force contribution that includes a…
The precise description of quantum nuclear fluctuations in atomistic modelling is possible by employing path integral techniques, which involve a considerable computational overhead due to the need of simulating multiple replicas of the…
An analytically derived 'integral operator' approach is introduced to estimate the expectation value of a quantum operator for an evolving state weighted with an exponential function. This allows to compute quantities useful in Nuclear…
We study the problem of computing the matrix exponential of a block triangular matrix in a peculiar way: Block column by block column, from left to right. The need for such an evaluation scheme arises naturally in the context of option…
The matrix element technique provides a superior statistical sensitivity for precision measurements of important parameters at hadron colliders, such as the mass of the top quark or the cross section for the production of Higgs bosons. The…
The method of McCurdy, Baertschy, and Rescigno, J. Phys. B, 37, R137 (2004) is generalized to obtain a straightforward, surprisingly accurate, and scalable numerical representation for calculating the electronic wave functions of molecules.…
In order to interpret precise measurements of molecular properties the finite nuclear mass corrections to the Born-Oppenheimer approximation have to be accounted for. It is shown that they can be obtained systematically in the perturbative…
The electromagnetic form factors of the three-nucleon bound states were calculated in Complete Impulse Approximation in the framework of the Covariant Spectator Theory for the new high-precision two-nucleon interaction models WJC-1 and…