Bloch–Floquet waves and controlled stop bands in periodic thermo-elastic structures

An algorithm for controlling the stop bands for elastic Bloch–Floquet waves within a periodic structure is proposed. Explicit asymptotic estimates of frequencies of translational and rotational standing waves, together with the numerical estimates of the stop band frequencies, are given. Thermal pre-stress is introduced and used to control the position of the stop bands on the dispersion diagram.     

Floquet–Bloch solutions in a sawtooth photonic crystal

Band structure of a sawtooth photonic crystal for optical wave propagation along the axis of periodicity is investigated. Floquet–Bloch solutions are found and illustrated for the bandgaps, allowed bands, and bandedges of the crystal. Special attention is given to the cases where Floquet–Bloch solutions become periodic functions.     

Dynamics of vortex–antivortex pair in a superconducting thin strip with narrow slits

In the framework of phenomenological time-dependent Ginzburg-Landau(TDGL) formalism,the dynamical properties of vortex-antivortex(V-Av) pair in a superconductor film with a narrow slit was studied.The slit position and length can have a great impact not only on the vortex dynamical behavior but also the current-voltage(Ⅰ-Ⅴ) characteristics of the sample.Kinematic vortex lines can be predominated by the location of the slit.In the range of relatively low applied currents for a constant weak magnetic field,kinematic vortex line appears at right or left side of the slit by turns periodically.We found such single-side kinematic vortex line cannot lead to a jump in the Ⅰ-Ⅴ curve.At higher applied currents the phase-slip lines can be observed at left and right sides of the slit simultaneously.The competition between the vortex created at the lateral edge of the sample and the V-Av pair in the slit will result in three distinctly different scenarios of vortex dynamics depending on slit length:the lateral vortex penetrates the sample to annihilate the antivortex in the slit;the V-Av pair in the slit are driven off and expelled laterally;both the lateral vortex and the slit antivortex are depinned and driven together to annihilation in the halfway.     

Shear Bloch waves and coupled phonon–polariton in periodic piezoelectric waveguides

Coupled electro-elastic SH waves propagating in a periodic piezoelectric finite-width waveguide are considered in the framework of the full system of Maxwell’s electrodynamic equations. We investigate Bloch–Floquet waves under homogeneous or alternating boundary conditions for the elastic and electromagnetic fields along the guide walls. Zero frequency stop bands, trapped modes as well as some anomalous features due to piezoelectricity are identified. For mixed boundary conditions, by modulating the ratio of the length of the unit cell to the width of the waveguide, the minimum widths of the stop bands can be moved to the middle of the Brillouin zone. The dispersion equation has been investigated also for phonon–polariton band gaps. It is shown that for waveguides at acoustic frequencies, acousto-optic coupling gives rise to polariton behavior at wavelengths much larger than the length of the unit cell but at optical frequencies polariton resonance occurs at wavelengths comparable with the period of the waveguide.     

On the modulation equations and stability of periodic generalized Korteweg–de Vries waves via Bloch decompositions

In this paper, we consider the relation between Evans-function-based approaches to the stability of periodic travelling waves and other theories based on long-wavelength asymptotics together with Bloch wave expansions. In previous work it was shown by rigorous Evans function calculations that the formal slow modulation approximation resulting in the linearized Whitham averaged system accurately describes the spectral stability to long-wavelength perturbations. To clarify the connection between Bloch-wave-based expansions and Evans-function-based approaches, we reproduce this result without reference to the Evans function by using direct Bloch expansion methods and spectral perturbation analysis. One of the novelties of this approach is that we are able to calculate the relevant Bloch waves explicitly for arbitrary finite-amplitude solutions. Furthermore, this approach has the advantage of being applicable in the more general multi-periodic setting where no conveniently computable Evans function has yet been devised.     

Doubly periodic waves of a discrete nonlinear Schrödinger system with saturable nonlinearity

Abstract

A system of two discrete nonlinear Schrödinger equations of the Ablowitz-Ladik type with a saturable nonlinearity is shown to admit a doubly periodic wave, whose long wave limit is also derived. As a by-product, several new solutions of the elliptic type are provided for NLS-type discrete and continuous systems.     

Entanglements in a coupled cavity–array with one oscillating end-mirror

We theoretically investigate the entanglement properties in a hybrid system consisting of an optical cavity–array coupled to a mechanical resonator. We show that the steady state of the system presents bipartite continuous variable entanglement in an experimentally accessible parameter regime. The effects of the cavity–cavity coupling strength on the bipartite entanglements in the field–mirror subsystem and in the field–field subsystem are studied. We further find that the entanglement between the adjacent cavity and the movable mirror can be entirely transferred to the distant cavity and mirror by properly choosing the cavity detunings and the coupling strength in the two-cavity case. Surprisingly, such a remote macroscopic entanglement tends to be stable in the large coupling regime and persists for environment temperatures at above 25 K in the three-cavity case. Such optomechanical systems can be used for the realization of continuous variable quantum information interfaces and networks.     

Propagation of elastic waves in a plate with rough surfaces

Abstract The characteristics of Lamb wave propagating in a solid plate with rough surfaces are studied on the basis of small perturbation approximation. The Rayleigh-Lamb frequency equation expressed with SA matrix is presented. The Rayleigh-Lamb frequency equation fora rough surface plate is different from that for a smooth surface plate, resulting in a small perturbation Δk on Lamb wave vector k. The imaginary part of Δk gives the attenuation caused by wave scattering. An experiment is designed to test our theoretical predications.By using wedge-shape pipes, different Lamb Wave modes are excited. The signals at different positions are received and analyzed to get the dispersion curves and attenuations of different modes. The experimental results are compared with the theoretical predications.     

Sound waves in a liquid with polydisperse vapor–gas bubbles

A mathematical model is presented for the propagation of plane, spherical, and cylindrical sound waves in a liquid containing polydisperse vapor–gas bubbles with allowance for phase transitions. A system of integro-differential equations is constructed to describe perturbed motion of a two-phase mixture, and a dispersion relation is derived. An expression for equilibrium sound velocity is obtained for a gas–liquid or vapor–liquid mixture. The theoretical results agree well with the known experimental data. The dispersion curves obtained for the phase velocity and the attenuation coefficient in a mixture of water with vapor–gas bubbles are compared for various values of vapor concentration in the bubbles and various bubble distributions in size. The evolution of pressure pulses of plane and cylindrical waves is demonstrated for different values of the initial vapor concentration in bubbles. The calculated frequency dependence of the phase sound velocity in a mixture of water with vapor bubbles is compared with experimental data.     

Floquet spectrum and optical behaviors in dynamic Su–Schrieffer–Heeger modeled waveguide array

Floquet topological insulators(FTIs) have been used to study the topological features of a dynamic quantum system within the band structure. However, it is difficult to directly observe the dynamic modulation of band structures in FTIs. Here, we implement the dynamic Su–Schrieffer–Heeger model in periodically curved waveguides to explore new behaviors in FTIs using light field evolutions. Changing the driving frequency produces near-field evolutions of light in the high-frequency curved waveguide array that are equivalent to the behaviors in straight arrays. Furthermore, at modest driving frequencies,the field evolutions in the system show boundary propagation, which are related to topological edge modes. Finally, we believe curved waveguides enable profound possibilities for the further development of Floquet engineering in periodically driven systems, which ranges from condensed matter physics to photonics.     

Invariant analysis with conservation law of time fractional coupled Ablowitz–Kaup–Newell–Segur equations in water waves

ABSTRACT

In this paper, the symmetry analysis and conservation laws of time fractional coupled Ablowitz–Kaup–Newell–Segur (AKNS) equations have been presented. Initially, the Lie symmetry method has been used for similarity reduction of time fractional coupled AKNS equations. Here, the Erdélyi–Kober differential operators have been used for symmetry reduction. Also, the new conservation vectors for time fractional coupled AKNS equations have been derived by using the new conservation theorem with formal Lagrangian.     

An Asymptotic Limit of a Navier–Stokes System with Capillary Effects

A combined incompressible and vanishing capillarity limit in the barotropic compressible Navier–Stokes equations for smooth solutions is proved. The equations are considered on the two-dimensional torus with well prepared initial data. The momentum equation contains a rotational term originating from a Coriolis force, a general Korteweg-type tensor modeling capillary effects, and a density-dependent viscosity. The limiting model is the viscous quasi-geostrophic equation for the “rotated” velocity potential. The proof of the singular limit is based on the modulated energy method with a careful choice of the correction terms.     

Spectral series of the Schrödinger operator in a thin waveguide with a periodic structure. 2. Closed three-dimensional waveguide in a magnetic field

In the paper, which is the second part of the paper by J. Brüning, S. Dobrokhotov, S. Sekerzh-Zenkovich, T. Tudorovskiy, “Spectral series of the Schrödinger operator in thin waveguides with a periodic structure. 1,” Russ. J. Math. Phys. 13 (4), 401–420 (2006), using the adiabatic approximation, diverse quantum states of the stationary Schrödinger equation for a particle in a thin waveguide in a magnetic field are constructed. The problems of “destruction” of the adiabatic approximation as the value of energy increases and of replacing this approximation by the approximation of V. P. Maslov’s theory of complex germ (the complex WKB method) are studied.     

Correction of located points in a hyperbolical locating system with a short-baseline plane array

Here is reported an iteration method,which corrects the coordinatesof an underwater moving target obtained by a hyperbolic locating system with ashort-baseline plane array when the sound velocity varies with depth.A seriesof differential difference equations are used for determining the iterative values.The calculated results show that under the same conditions,the location error isabout several meters or tens of meters without correction and less than 0.5 mwith correction.The method can be applied to various types of arrays.     

Bose-Einstein condensates in standing waves: the cubic nonlinear Schrödinger equation with a periodic potential

We present a new family of stationary solutions to the cubic nonlinear Schr?dinger equation with an elliptic function potential. In the limit of a sinusoidal potential our solutions model a quasi-one-dimensional dilute gas Bose-Einstein condensate trapped in a standing light wave. Provided that the ratio of the height of the variations of the condensate to its dc offset is small enough, both trivial phase and nontrivial phase solutions are shown to be stable. Recent developments allow for experimental investigation of these predictions.     

Asymptotic freedom of Yang–Mills theory with gravity

We study the behaviour of Yang–Mills theory under the inclusion of gravity. In the weak-gravity limit, the running gauge coupling receives no contribution from the gravitational sector, if all symmetries are preserved. This holds true with and without cosmological constant. We also show that asymptotic freedom persists in general field-theory-based gravity scenarios including gravitational shielding as well as asymptotically safe gravity.     

Solitons in PT–symmetric optical lattices with spatially periodic modulation of nonlinearity

We study the existence and stability of solitons forming in PT–symmetric optical lattices with spatially periodic modulation of the local strength of the nonlinear media. We found that the spatial modulation of the nonlinearity significantly affects the stability of solitons in PT–symmetric optical lattices. With the decrease of the strength of nonlinear refractive index modulation, the soliton's stability domain increases, whereas with the increase of the period of nonlinear refractive index modulation, the corresponding soliton's stability range narrows. In addition, we also investigate the influence of variation of the amplitude of the linear PT–symmetric lattice potential on soliton dynamics, in the presence of spatially periodic modulation of nonlinearity.     

The structure of ion-acoustic waves in a low-frequency three-component electron–ion space plasma with two-electron populations

In the present paper, we have studied the binding energy of the shallow donor hydrogenic impurity, which is confined in an inhomogeneous cylindrical quantum dot (CQD) of \(\hbox {GaAs-Al}_{x}\hbox {Ga}_{1-x}\hbox {As}\). Perturbation method is used to calculate the binding energy within the framework of effective mass approximation and taking into account the effect of dielectric mismatch between the dot and the barrier material. The ground-state binding energy of the donor is computed as a function of dot size for finite confinement. The result shows that the ground-state binding energy decreases with the increase in dot size. The result is compared with infinite dielectric mismatch as a limiting case. The binding energy of the hydrogenic impurity is maximum for an on-axis donor impurity.     

Resonance energy transfer in a dense array of II–VI quantum dots

Förster resonance energy transfer in inhomogeneous dense arrays of epitaxial CdSe/ZnSe quantum dots is demonstrated by time- and space-resolved photoluminescence spectroscopy. The specific feature of this process is the dipole–dipole interaction between the ground exciton levels of small quantum dots and the excited levels of large dots. This interaction brings efficient energy collection and spectral selection of a limited number of emitters. Results of theoretical modeling of optical transitions in spheroidal quantum dots with a Gaussian potential profile agree with the observed features of optical spectra induced by the change of the dominant energy transfer mechanism.