Spontaneous synchronization of two bistable pyridine-furan nanosprings connected by an oligomeric bridge

The intensive development of nanodevices acting as two-state systems has motivated the search for nanoscale molecular structures whose long-term conformational dynamics are similar to the dynamics of bistable mechanical systems such as Euler arches and Duffing oscillators. Collective synchrony in bistable dynamics of molecular-sized systems has attracted immense attention as a potential pathway to amplify the output signals of molecular nanodevices. Recently, pyridin-furan oligomers of helical shape that are a few nanometers in size and exhibit bistable dynamics similar to a Duffing oscillator have been identified through molecular dynamics simulations. In this article, we present the case of dynamical synchronization of these bistable systems. We show that two pyridine-furan springs connected by a rigid oligomeric bridge spontaneously synchronize vibrations and stochastic resonance enhances the synchronization effect

Temperature dependent network stability in simple alcohols and pure water: The evolution of Laplace spectra

A number of computer-generated models of water, methanol and ethanol are considered at room temperature and ambient pressure, and also as a function of temperature (for water and ethanol), and the potential model (for water only). The Laplace matrices are determined, and various characteristics of them, such as eigenvalues and eigenvectors, as well as the corresponding Laplace spectra are calculated. It is revealed how the width of the spectral gap in the Laplace matrix of H-bonded networks may be applied for characterising the stability of the network. A novel method for detecting the presence percolated network in these systems is also introduced

On boundedness of solutions of periodic systems: a multivariable cell structure approach

A wide range of practical systems exhibits dynamics, which are periodic with respect to several state variables and which possess multiple invariant solutions. Yet, when analyzing stability of such systems, many classical techniques often fall short in that they only permit to establish local stability properties. Motivated by this, we present a new sufficient criterion for global stability of such a class of nonlinear systems. The proposed approach is characterized by two main properties. First, it develops the conventional cell structure framework to the case of multiple periodic states. Second, it extends the standard Lyapunov theory by relaxing the usual definiteness requirements of the employed Lyapunov functions to sign-indefinite functions. The stability robustness with respect to exogenous perturbations is analyzed. The efficacy of the proposed approach is illustrated via the global stability analysis of a nonlinear system