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The different facets of the $R$-matrix method are presented pedagogically in a general framework. Two variants have been developed over the years: $(i)$ The "calculable" $R$-matrix method is a calculational tool to derive scattering…
A survey is given on the applications of hydrodynamic model of nucleus-nucleus collisons, focusing especially on i) the resolution of hydrodynamic equations for arbitrary configurations, by using the smoothed-particle hydrodynamic approach;…
Various applications of quantum algebraic techniques in nuclear structure physics, such as the su$_q$(2) rotator model and its extensions, the use of deformed bosons in the description of pairing correlations, and the construction of…
This article is an attempt to a pedagogical introduction and review into the elementary concepts of chiral symmetry in nuclear physics. Effective chiral models such as the linear and nonlinear sigma model will be discussed as well as the…
These lecture notes highlight the mathematical and computational structure relating to the formulation of, and development of algorithms for, the Bayesian approach to inverse problems in differential equations. This approach is fundamental…
The nucleon structure and the nuclear force are investigated in the context of the non-perturbative path-integral method of hadronization. Starting from a microscopic quark-diquark model, the nucleon is generated as a relativistic bound…
Due to the exponential increase of the numerical effort with the number of degrees of freedom, moving basis functions have a long history in quantum dynamics. In addition, spawning of new basis functions is routinely applied. Here we…
Active vibration control has been introduced and used as one of the effective approaches to suppress unwanted vibrations in different systems. Effective performance of each vibration control method is contingent to accurate design and…
We present a simple but general treatment of neutrino oscillations in the framework of quantum mechanics using plane waves and intuitive wave packet principles when necessary. We attempt to clarify some confusing statements that have…
This review is devoted to the study of stationary solutions of linear and nonlinear equations from relativistic quantum mechanics, involving the Dirac operator. The solutions are found as critical points of an energy functional. Contrary to…
The optical model is a fundamental tool to describe scattering processes in nuclear physics. The basic input is an optical model potential, which describes the refraction and absorption processes more or less schematically. Of special…
We present a new stability proof for cascaded geometric control used by aerial vehicles tracking time-varying position trajectories. Our approach uses sliding variables and a recently proposed quaternion-based sliding controller to…
Microscopic nuclear structure calculations have been performed within the framework of the unitary-model-operator approach. Ground-state and single-particle energies are calculated for nuclei around ^{14}C, ^{16}O and ^{40}Ca with modern…
In this paper, we carry a detailed study of mechanical systems with configuration space $Q\longrightarrow Q/G$ for which the base $Q/G$ variables are being controlled. The overall system's motion is considered to be induced from the base…
A powerful method for solving non-linear first-order ordinary differential equations, which is based on geometrical understanding of the corresponding dynamics of the so called Lie systems, is developed. This method allows us not only to…
In the field of quantum control, effective Hamiltonian engineering is a powerful tool that utilises perturbation theory to mitigate or enhance the effect that a variation in the Hamiltonian has on the evolution of the system. Here, we…
We present a practical implementation of the perturbation theory derived by Lynden-Bell (2015) for describing, to arbitrary precision, the orbit of a particle in an arbitrary spherically-symmetric potential. Our implementation corrects…
Reduced basis methods provide a powerful framework for building efficient and accurate emulators. Although widely applied in many fields to simplify complex models, reduced basis methods have only been recently introduced into nuclear…
An open question in experimental physics is the characterization of gravitational effects in quantum regimes. We propose an experimental set-up that uses well-tested techniques in cavity optomechanics to observe the effects of the…
This paper describes the use of a quadratic manifold for the model order reduction of structural dynamics problems featuring geometric nonlinearities. The manifold is tangent to a subspace spanned by the most relevant vibration modes, and…