Effects of nonlinearity and a new nonlinear resonance in two-path phonon transmittance in lattices with two-dimensional arrays of atomic defects.

The paper is devoted to analytical and numerical studies of the effects of nonlinearity on the two-path phonon interference in the transmission through two-dimensional arrays of atomic defects embedded in a lattice. The emergence of transmission antiresonance (transmission node) in the two-path system is demonstrated for the few-particle nanostructures, which allow us to model both linear and nonlinear phonon transmission antiresonances. The universality of destructive-interference origin of transmission antiresonances of waves of different nature, such as phonons, photons, and electrons, in two-path nanostructures and metamaterials is emphasized. Generation of the higher harmonics as a result of the interaction of lattice waves with nonlinear two-path atomic defects is considered, and the full system of nonlinear algebraic equations is obtained to describe the transmission through nonlinear two-path atomic defects with an account for the generation of second and third harmonics. Expressions for the coefficients of lattice energy transmission through and reflection from the embedded nonlinear atomic systems are derived. It is shown that the quartic interatomic nonlinearity shifts the antiresonance frequency in the direction determined by the sign of the nonlinear coefficient and enhances in general the transmission of high-frequency phonons due to third harmonic generation and propagation. The effects of the quartic nonlinearity on phonon transmission are described for the two-path atomic defects with a different topology. Transmission through the nonlinear two-path atomic defects is also modeled with the simulation of the phonon wave packet, for which the proper amplitude normalization is proposed and implemented. It is shown that the cubic interatomic nonlinearity red shifts in general the antiresonance frequency for longitudinal phonons independently of the sign of the nonlinear coefficient, and the equilibrium interatomic distances (bond lengths) in the atomic defects are changed by the incident phonon due to cubic interatomic nonlinearity. For longitudinal phonons incident on a system with the cubic nonlinearity, the new narrow transmission resonance on the background of a broad antiresonance is predicted to emerge, which we relate to the opening of the additional transmission channel for the phonon second harmonic through the nonlinear defect atoms. Conditions of the existence of the new nonlinear transmission resonance are determined and demonstrated for different two-path nonlinear atomic defects. A two-dimensional array of embedded three-path defects with an additional weak transmission channel, in which a linear analog of the nonlinear narrow transmission resonance on the background of a broad antiresonance is realized, is proposed and modeled. The presented results provide better understanding and detailed description of the interplay between the interference and nonlinearity in phonon propagation through and scattering in two-dimensional arrays of two-path anharmonic atomic defects with a different topology.

The "sugar" coarse-grained DNA model.

More than 20 coarse-grained (CG) DNA models have been developed for simulating the behavior of this molecule under various conditions, including those required for nanotechnology. However, none of these models reproduces the DNA polymorphism associated with conformational changes in the ribose rings of the DNA backbone. These changes make an essential contribution to the DNA local deformability and provide the possibility of the transition of the DNA double helix from the B-form to the A-form during interactions with biological molecules. We propose a CG representation of the ribose conformational flexibility. We substantiate the choice of the CG sites (six per nucleotide) needed for the "sugar" GC DNA model, and obtain the potentials of the CG interactions between the sites by the "bottom-up" approach using the all-atom AMBER force field. We show that the representation of the ribose flexibility requires one non-harmonic and one three-particle potential, the forms of both the potentials being different from the ones generally used. The model also includes (i) explicit representation of ions (in an implicit solvent) and (ii) sequence dependence. With these features, the sugar CG DNA model reproduces (with the same parameters) both the B- and A- stable forms under corresponding conditions and demonstrates both the A to B and the B to A phase transitions. Graphical Abstract The proposed coarse-grained DNA model allows to reproduce both the B- and A- DNA forms and the transitions between them under corresponding conditions.