Complex systems fascinate because of the way dynamic microscopic interactions give rise to striking, often unexpected macroscopic structures: convection cells in fluids, patterns in ecosystems, ...

Department of Theoretical Chemistry, Institute of Chemical Sciences, Faculty of Chemistry, Maria Curie-Skłodowska University in Lublin, Maria Curie-Skłodowska Sq. 3, 20-031 Lublin, Poland ...

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Abstract: This article introduces a novel variational formula for modeling waveguides with uniformly curved longitudinal axes. Using the Rayleigh–Ritz method, we ...

Abstract: This article introduces a novel variational formula for modeling waveguides with uniformly curved longitudinal axes. Using the Rayleigh-Ritz method, we analyze the electromagnetic fields in ...

We give a simple proof of the well known fact that the approximate eigenvalues provided by the Rayleigh-Ritz variational method are increasingly accurate upper bounds to the exact ones. To this end, ...

The paper shows that the variational principle serves as an element of the mathematical structure of a quantum theory. The experimentally confirmed properties of the corpuscular-wave duality of a ...