Editorial

This topical issue collects contributions to the interdisciplinary study of the interacting global systems of public health, energy production, and climate change, in order to provide physicists with an opportunity to explore these fields of application of great societal importance.     

Synchronization in power-law networks

We consider realistic power-law graphs, for which the power-law holds only for a certain range of degrees. We show that synchronizability of such networks depends on the expected average and expected maximum degree. In particular, we find that networks with realistic power-law graphs are less synchronizable than classical random networks. Finally, we consider hybrid graphs, which consist of two parts: a global graph and a local graph. We show that hybrid networks, for which the number of global edges is proportional to the number of total edges, almost surely synchronize.     

Rich-club and page-club coefficients for directed graphs

Rich-club and page-club coefficients and their null models are introduced for directed graphs. Null models allow for a quantitative discussion of the rich-club and page-club phenomena. These coefficients are computed for four directed real-world networks: Arxiv High Energy Physics paper citation network, Web network (released from Google), Citation network among US Patents, and email network from a EU research institution. The results show a high correlation between rich-club and page-club ordering. For journal paper citation network, we identify both rich-club and page-club ordering, showing that “elite” papers are cited by other “elite” papers. Google web network shows partial rich-club and page-club ordering up to some point and then a narrow declining of the corresponding normalized coefficients, indicating the lack of rich-club ordering and the lack of page-club ordering, i.e. high in-degree (PageRank) pages purposely avoid sharing links with other high in-degree (PageRank) pages. For UC patents citation network, we identify page-club and rich-club ordering providing a conclusion that “elite” patents are cited by other “elite” patents. Finally, for email communication network we show lack of both rich-club and page-club ordering. We construct an example of synthetic network showing page-club ordering and the lack of rich-club ordering.     

Exploring the possibilities to control the molecular switching properties and dynamics: A field-switchable rotor-stator molecular system

A bistable, dipolar stator-rotor molecular system-candidate for molecular electronics is investigated. We demonstrate that it is possible to control the intramolecular torsional states and dynamics in this system by applying an appropriate additional electric field (instead of biasing one), achieving fine tuning and modulation of the relevant properties. The electric field effects on the quantities responsible for torsional dynamics (potential energy surface, potential barrier height, quantum and classical transition probabilities, correlation time, HOMO-LUMO gap) are studied from first principles. Our results indicate that it is possible to artificially stabilize the metastable conformational state of the studied molecule. The importance of this is evident, as the current-voltage characteristics of the metastable state are clearly distinguishable from the current-voltage characteristics of the two stable states. We report for the first time exact calculations related to the possibilities to control the thermally induced stochastic switching, and reduce the noise in a practical application. Thus, we believe that the molecule studied in this paper could operate as a field-switchable molecular device under real conditions.     

Topological description of a chaotic attractor with spiral structure

We compute the template of a chaotic attractor with spiral structure. The template describes the topological properties of periodic orbits embedded in the attractor. It is confirmed by investigating orbits of higher period.     

Infrared spectra of permanganate anions in potassium perchlorate matrices: vibrational anharmonicity,effective symmetry and vibrational mode mixing effects

Fourier transform infrared spectra of MnO4- anions isomorphously isolated in potassium perchlorate matrices were recorded at room and low temperature (LT, approximately 100 K). On the basis of the detected second-order vibrational transitions involving the dopant species nu3 mode components, anharmonicity constants and harmonic eigenvalues for these modes were calculated. Despite the fact that, rigorously speaking, the appearance of the spectra of dopant permanganate anions may be explained in terms of a Cs site symmetry, the nu3 stretching region resembles an approximate A1+E splitting (characteristic for a local C3nu or even higher symmetry), which is not expected, even within the latent symmetry approach. We explain such spectral patterns on the basis of vibrational mode mixing (a 'Fermi-like' resonance) of the MnO4- nu1 mode with the nu3, site-group component. With the results of degenerate case stationary perturbation theory, we show that in the present case the Fermi-like resonance is predominantly responsible for the observed spectral features. The appearance of the region of second-order vibrational transitions in the spectra of dopant permanganate anions may be better explained in terms of the (rigorous) crystallographic Cs site group (corresponding to the crystallographic Pnma space group), instead of the 'latent' (effective) symmetry site group C2nu (corresponding to the latent symmetry space group Imma).     

Splitting of Spectra in Anharmonic Oscillators Described by Kratzer Potential Function

A perturbation theory model that describes splitting of the spectra in highly symmetrical molecular species in electrostatic field is proposed. An anahrmonic model of a two-dimensional oscillator having Kratzer potential energy functionis used to model the molecular species and to represent the unperturbed system. A selection rule for the radial quantum number of the oscillator is derived. The eigenfunctions of a two-dimensional anharmonic oscillator in cylindrical coordinates are used for the matrix elements representing the probability for energy transitions in dipole approximation to be calculated. Several forms of perturbation operators are proposed to model the interactionbetween the polyatomic molecular species and an electrostatic field. It is found that the degeneracy is removed in the presence of the electric field and spectral splitting occurs. Anharmonic approximation for the unperturbed system is more accurate and reliable representation of a real polyatomic molecular species.     

Theory and practice of chaotic cryptography

In this Letter we address some basic questions about chaotic cryptography, not least the very definition of chaos in discrete systems. We propose a conceptual framework and illustrate it with different examples from private and public key cryptography. We elaborate also on possible limits of chaotic cryptography.     

Computational investigation of the weakly bound dimers HOX...SO(3) (X = F, Cl, Br)

The electronic structure and thermochemical stability of the HOX-SO(3) (X = F, Cl, Br) complexes is studied using second-order M?ller-Plesset perturbation theory (MP2). The calculated dissociation energies of the HOF-SO(3), HOCl-SO(3), and HOBr-SO(3) complexes are 5.43, 6.02, and 5.98 kcal mol(-1) at MP2/6-311++G(3df,3pd) level, respectively. Anharmonic OH stretching frequencies of the HOX (X = F, Cl, Br) moieties along with the frequency shifts upon complex formation are calculated at the MP2/6-311++G(2df,2p) level. AIM and NBO analyses were also performed. Theoretical data strongly encourage performing of matrix-isolation studies of the title complexes and their spectroscopic identification.