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Evaluation of the impact parameter in a single event of relativistic heavy ion collision is crucial for correct and efficient data processing and analysis. In this work we have studied the possibility of estimating the impact parameter in heavy ion collisions by using artificial neural networks applied to the charged particle data from fast microchannel plate (MCP) detectors. Charged particles' multiplicity, their spatial distribution and time-of-flight data were used as event features to be analyzed by the artificial neural network algorithms. We investigated two different configurations of microchannel plate detector layout, that have different data and computational requirements. We have shown that the developed artificial neural networks technique is capable of providing sufficiently good and fast results on the impact parameter determination in a single heavy ion collision event for both configurations of MCP detectors layout. In our first exercises, the proposed algorithm has successfully identified more than 90 of Au Au collision events with the impact parameter less than 5 fm or less than 1 fm, which suggests its use as a fast trigger. [ABSTRACT FROM AUTHOR]

The work is devoted to the analysis of Lyapunov stability of Cohen–Grossberg neural networks with time-dependent delays. For this, the stability of steady solutions of systems of linear differential equations with time-dependent coefficients and time-dependent delays is analyzed. The cases of continuous and pulsed perturbations are considered. The relevance of the study is due to two circumstances. Firstly, Cohen–Grossberg neural networks find numerous applications in various fields of mathematics, physics, and technology, and it is necessary to determine the limits of their possible application in solving each specific problem. Secondly, the currently known conditions for the stability of the Cohen–Grossberg neural networks are rather cumbersome. The article is devoted to finding the conditions for the stability of the Cohen–Grossberg neural networks, expressed via the coefficients of the systems of differential equations simulating the networks. The analysis of stability is based on the method of "freezing" time-dependent coefficients and the subsequent analysis of the stability of the solution in a vicinity of the freezing point. The analysis of systems of differential equations thus transformed uses the properties of logarithmic norms. A method is proposed making it possible to obtain sufficient stability conditions for solutions of finite systems of nonlinear differential equations with time-dependent coefficients and delays. The algorithms are efficient both in the case of continuous and pulsed perturbations. The method proposed can be used in the study of nonstationary dynamical systems described by systems of ordinary nonlinear differential equations with time-dependent delays. The method can be used as the basis for studying the stability of Cohen–Grossberg neural networks with discontinuous coefficients and discontinuous activation functions. [ABSTRACT FROM AUTHOR]

We apply a new highly efficient method of solving the Faddeev–Merkuriev equations to multichannel scattering calculations of the antihydrogen formation cross section for antiproton scattering off the ground and excited states of the positronium. Our results demonstrate good agreement with the known data on total and partial cross sections for all the reaction channels. Using moderate computational resources we have achieved a supreme energy resolution. [ABSTRACT FROM AUTHOR]

We present an illustration of using a quantumthree-body code being prepared for public release. The code is based on iterative solving of the three-dimensional Faddeev equations. The code is easy to use and allows users to perform highly-accurate calculations of quantum three-body systems. The previously known results for He ground state are well reproduced by the code. [ABSTRACT FROM AUTHOR]

A method to calculate the bound states of three atoms without resorting to an explicit partial wave decomposition is presented. The differential form of the Faddeev equations in the total angular momentum representation is used for this purpose. The method utilizes Cartesian coordinates combined with the tensor trick preconditioning for large linear systems and Arnoldi’s algorithm for eigenanalysis. As an example, we consider the He3 system in which the interatomic force has a very strong repulsive core requiring the inclusion of a large number of partial waves to achieve convergence. To improve convergence and stability in the Arnoldi’s algorithm, we modify the system of equations by introducing a background potential that removes the large number of unphysical eigenvalues stemming from the hard core. The introduction of such a modifying potential does not affect the physical spectrum of the system. The results obtained by solving the modified, three-dimensional, Faddeev equations compare favorably with other results in the field. [ABSTRACT FROM AUTHOR]

Differential Faddeev equations in total angular momentum representation are used for the first time to investigate ultra-low energy elastic scattering of a helium atom on a helium dimer. Six potential models of interatomic interaction are investigated. The results improve and extend the Faddeev equations based results known in literature. The employed method can be applied to investigation of different elastic and inelastic processes in three- and four-atomic weakly bounded systems below three-body threshold. [Copyright &y& Elsevier]

A method of direct solution of the Faddeev equations for the bound-state problem with zero total angular momentum is used to calculate the binding energies. The results for binding energies of He 2 6 Li and He 2 7 Li systems and helium atom–HeLi dimer scattering length are presented. The results show that modern potential models support two bound states in both trimers. In both cases the energy of the excited state is very close to the energy of the lowest two-body threshold. [ABSTRACT FROM AUTHOR]