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Consider the discrete 1D Schrödinger operator on Z with an odd 2k periodic potential q. For small potentials we show that the mapping: q → heights of vertical slits on the quasi-momentum domain (similar to the Marchenko-Ostrovski maping for the Hill operator) is a local isomorphism and the isospectral set consists of 2 k distinct potentials. Finally, the… (More)

- A A Kutsenko, A L Shuvalov, O Poncelet, A N Darinskii
- The Journal of the Acoustical Society of America
- 2015

One-dimensional propagation of a longitudinal wave through an infinite piezoelectric periodically layered structure is considered. The unit cell consists, in general, of piezoelectric multilayers separated by thin electrodes which are connected through a capacitor with capacity Cj that plays the role of the external electric control providing tunability of… (More)

- A A Kutsenko, A L Shuvalov, A N Norris
- The Journal of the Acoustical Society of America
- 2011

A scheme for evaluating the effective quasistatic speed of sound c in two- and three-dimensional periodic materials is reported. The approach uses a monodromy-matrix operator to enable direct integration in one of the coordinates and exponentially fast convergence in others. As a result, the solution for c has a more closed form than previous formulas. It… (More)

We consider the Schrödinger operator on the zigzag and armchair nanotubes (tight-binding models) in a uniform magnetic field B and in an external periodic electric potential. The magnetic and electric fields are parallel to the axis of the nanotube. We show that this operator is unitarily equivalent to the finite orthogonal sum of Jacobi operators. We… (More)

- Evgeny L. Korotyaev, Anton Kutsenko
- IJCSM
- 2010

Effective anti-plane quasistatic moduli for 2D piezoelectric phononic crystals of arbitrary anisotropy are formulated analytically using the plane-wave expansion (PWE) method and the recently proposed monodromy-matrix (MM) method. The latter approach employs Fourier series in one dimension with direct numerical integration along the other direction. As a… (More)

- A A Kutsenko, A L Shuvalov
- The Journal of the Acoustical Society of America
- 2013

The existence of shear horizontal (SH) surface waves in two-dimensional periodic phononic crystals with an asymmetric depth-dependent profile is theoretically reported. Examples of dispersion spectra with bandgaps for subsonic and supersonic SH surface waves are demonstrated. The link between the effective (quasistatic) speeds of the SH bulk and surface… (More)

We consider the 1D periodic Jacobi matrices. The spectrum of this operator is purely absolutely continuous and consists of intervals separated by gaps. We solve the inverse problem (including characterization) in terms of vertical slits on the quasimomentum domain. Furthermore, we obtain a priori two-sided estimates for vertical slits in terms of Jacoby… (More)

- Evgeny L. Korotyaev, Anton Kutsenko
- Asymptotic Analysis
- 2010

- A N Darinskii, A L Shuvalov, O Poncelet, A A Kutsenko
- Ultrasonics
- 2015

A theoretical study is performed of the bulk acoustic wave propagation in periodic piezoelectric structures with metallized interperiod boundaries. A crucial specific feature of such structures is that the bounded acoustic beam incident perpendicular to an interface can generate scattered (i.e. reflected and transmitted) waves over the whole area of the… (More)

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