Frontiers in green radiochemistry: New optimized quantum approach to laser separation of isotopes and transmutation of radioactive waste

Two-dimensional distributed order Cable equation with non-singular kernel: A nonstandard implicit compact finite difference approach

“…Scheme (15) creates a nonlinear algebraic system of (N + 1)(M + 1)(Q + 1) equations with both initial and boundary conditions. To solve this problem, Newton's iteration approach will be applied [21]. The following section uses a Jon Von Neumann methodology to discuss the method's stability (15).…”

Chaotic dynamics of diatomic systems in an electromagnetic field: Dynamical and topological invariants

“…Chaos theory establishes that apparently complex irregular behaviour can be the result of a simple deterministic system with several dominant nonlinear interdependent variables. A large number of studies using ideas derived from chaos science to characterize, model, and predict the dynamics of various system phenomena have been witnessed over the last decade (see, for example, [11][12][13][14][15][16][17][18][19][20][21][22][23]). The results of such studies are very encouraging, as they not only showed that the dynamics of clearly irregular phenomena can be understood from a chaotic deterministic point of view, but also reported very good predictions using this approach for various systems, including those that from a classical point of view were considered nonprognostic.…”

“…Our approach to modeling the chaotic dynamics of diatomic molecules in an intense electromagnetic field is based on two blocks, namely, the universal nonlinear analysis block (e.g. [18][19][20][21][22][23]), which in our problem actually includes the computation of time series of level populations, polarization, power spectrum, and quantum-dynamic block ( e.g. [27][28][29][30]).…”

“…As the applied method has been earlier in details presented in refs. [18][19][20][21][22][23][27][28][29][30], including the quantum-dynamic method of description of the diatomic molecule in an electromagnetic field, below we will restrict yourself only by some fundamental definitions and key ideas. The quantum-dynamic approach to a diatomic molecule in an electromagnetic field is based on the solution of the time-dependent Schrödinger equation, optimized operator perturbation theory and realistic interatomic potential.…”

Collisional broadening and shift of the hyperfine lines for complex atomic systems in atmosphere of the buffer inert gases

“…The detailed description of the whole procedure can be found in Ref. [5][6][7][26][27][28]30,31]. Some results and conclusions.…”