A study of frequency band structure in two-dimensional homogeneous anisotropic phononic K 3 -metamaterials

British council - Kiev under the Academic Partnership/Mobility Grant scheme grant No. UKR16EG/3/19.01.16

Double-logs, Gribov-Lipatov reciprocity and wrapping

We study analytical properties of the five-loop anomalous dimension of twist-2 operators at negative even values of Lorentz spin. Following L. N. Lipatov and A. I. Onishchenko, we have found two possible generalizations of double-logarithmic equation, which allow to predict a lot of poles of anomalous dimension of twist-2 operators at all orders of perturbative theory from the known results. Second generalization is related with the reciprocity-respecting function, which is a single-logarithmic function in this case. We have found, that the knowledge of first orders of the reciprocity-respecting function gives all-loop predictions for the highest poles. Obtained predictions can be used for the reconstruction of a general form of the wrapping corrections for twist-2 operators.Comment: 17 pages, references adde

Acoustic metamaterials with controllable bandgap gates based on magnetorheological elastomers

Acoustic metamaterials allow for creating selective pass- and stop-bands on the frequency spectrum. We demonstrate the possibility of designing acoustic metamaterials as core-shell 2D-phononic media with an extremely simple morphology, the frequency spectrum of which contains many real-time tunable bandgaps. The connected shells of such metamaterials form a grid with square cells filled with nuclei partitionable into two subsystems. Both subsystems are characterized by their frequency spectra, and it is the coupling between them that generates the bandgaps. If the structural elements of the metamaterial are built based on magnetoelastomers, then bandgaps can be easily controlled by an external magnetic field that changes the elastic moduli of shells/cores. We have shown the possibility of manipulating single bandgaps in different parts of the spectrum, and simultaneous control of all bandgaps up to their complete disappearance. This manipulation can be carried out, specifically, with no change in the maximum achievable frequency in the metamaterial. The results obtained can be used for selective filtering of damaging wave components, active control of seismic or blast waves, sonar systems, ultrasound imaging, impact-resistant structures, and noise cancellation protocols. The physical concepts developed are extendable to 3D-structures in a similar fashion so can benefit a wider community

Dynamics of quasi-one-dimensional structures under roughening transition stimulated by external irradiation

We studied the striking effect of external irradiation of nanowires on the dynamics of their surface morphology at elevated temperatures that do not destroy their crystal lattice. Numerical experiments performed on the basis of the Monte Carlo model revealed new possibilities for controlled periodic modulation of the cross-section of quasi-one-dimensional nanostructures for opto- and nanoelectronic elements. These are related to the fact that external irradiation stimulates the surface diffusion of atoms. On the one hand, such stimulation should accelerate the development of the well-known spontaneous thermal instability of nanowires (Rayleigh instability), which leads to their disintegration into nanoclusters. On the other hand, this leads to the forced development of the well-known roughening transition (RT) effect. Under normal circumstances, this manifests itself on selected crystal faces at a temperature above the critical one. The artificial stimulation of this effect on the lateral surface of quasi-one-dimensional structures determines many unpredictable scenarios of their surface dynamics, which essentially depend on the orientation of the nanowire axis relative to its internal crystal structure. In particular, the long-wave Rayleigh breakup observed in absence of external irradiation transforms into strongly pronounced short-wave metastable modulations of the cross-section (a chain of unduloids). The effect of the self-consistent relationship between the Rayleigh instability and RT is dimensional and can be observed only at relatively small nanowire radii. The fact is analyzed that, for the manifestation of this effect, it is very important to prevent significant heating of the nanowire when surface diffusion is stimulated. A number of developed theoretical concepts have already found confirmation in real experiments with Au and Ag nanowires irradiated by electrons and Ag+ ions, respectively