### Article

## Absolute Poisson’s ratio and the bending rigidity exponent of a crystalline two-dimensional membrane

We compute the absolute Poisson’s ratio and the bending rigidity exponent of a free-standing two-dimensional crystalline membrane embedded into a space of large dimensionality , . We demonstrate that, in the regime of anomalous Hooke’s law, the absolute Poisson’s ratio approaches material independent value determined solely by the spatial dimensionality : where . Also, we find the following expression for the exponent of the bending rigidity: . These results cannot be captured by self-consistent screening approximation.

Based on the quantum-mechanical theory of electron transfer (ET), the parameter was proposed to describe the electrochemical activity of doped graphenes. The parameter is calculated using the density of states (DOS), local density of state (LDOS) values, which are in turn obtained from the density functional theory (DFT) calculations and reorganization energies of redox system. DOS describes the contribution of the electronic structure of the electrode to the ET process, while the LDOS describes the electron density contribution of the atoms at some distance from the surface electrode. Reorganization energy corresponds to the restriction of solvation shell and bonds in redox system due to ET process. The overall contribution of these parameters enables a comprehensive assessment of the activity that is acceptable for semi-quantitative analysis. Calculations have shown that the proposed activity parameter correlates well with the calculated ET rate constants. Theoretical study of the oxygen reduction reaction (ORR) on graphene doped with p-elements in the framework of quantum-mechanical theory showed that ET activity decreases in the series P-Gr > S-Gr > N-Gr > B-Gr > O-Gr > Gr. According to our estimates, the mixed or adiabatic regime of ET is probably observed on doped graphenes for all steps of ORR. Using N- and B-graphenes as an example and activity parameter, the influence of the applied potential and the atomic fraction of the doped element on the ET activity are studied.

It is shown that the anomalous elasticity of membranes affects the profile and thermodynamics of a bubble in van der Waals heterostructures. Our theory generalizes the nonlinear plate theory as well as the membrane theory of the pressurised blister test to incorporate the power-law scale dependence of the bending rigidity and Young's modulus of a two-dimensional crystalline membrane. This scale dependence, caused by long-range interaction of relevant thermal fluctuations (flexural phonons), is responsible for the nonlinear Hooke law observed recently in graphene. It is shown that this anomalous elasticity affects the dependence of the maximal height of the bubble as a function of its radius and temperature. We determine the characteristic temperature above which the anomalous elasticity is important. It is suggested that, for graphene-based van der Waals heterostructures, the predicted anomalous regime is experimentally accessible at room temperature.

The dynamics of a two-component Davydov-Scott (DS) soliton with a small mismatch of the initial location or velocity of the high-frequency (HF) component was investigated within the framework of the Zakharov-type system of two coupled equations for the HF and low-frequency (LF) fields. In this system, the HF field is described by the linear Schrödinger equation with the potential generated by the LF component varying in time and space. The LF component in this system is described by the Korteweg-de Vries equation with a term of quadratic influence of the HF field on the LF field. The frequency of the DS soliton`s component oscillation was found analytically using the balance equation. The perturbed DS soliton was shown to be stable. The analytical results were confirmed by numerical simulations.

Radiation conditions are described for various space regions, radiation-induced effects in spacecraft materials and equipment components are considered and information on theoretical, computational, and experimental methods for studying radiation effects are presented. The peculiarities of radiation effects on nanostructures and some problems related to modeling and radiation testing of such structures are considered.