Adiabatic Mode Research Articles

Topological adiabatic dynamics in classical mass-spring chains with clamps

The path dependence of adiabatic evolution in classical harmonic chains with clamps is examined. It is shown that cutting and joining a chain may braid adiabatic normal mode frequencies. Accordingly, different adiabatic paths with the same endpoints may transport a normal mode to a different one, and an adiabatic cycle pumps action variables, i.e., the adiabatic invariants of integrable classical systems. Another adiabatic pump for artificial edge modes induced by clamps is shown as an application. Extensions to completely integrable systems and quantum systems are outlined.

Parallel numerical simulation of weakly range-dependent ocean acoustic waveguides by adiabatic modes based on a spectral method

With the increasing demand for underwater detection, interest in the acoustic field of range-dependent ocean waveguides is also growing. For weakly range-dependent ocean waveguides, adiabatic modes represent a compromise between accuracy and computational cost and occupy an important place in the simulation of numerical sound fields. However, either existing adiabatic-mode programs consider too few layers of media or the root-finder tends to miss roots. In addition, none of the programs can solve the acoustic field excited by a line sound source located anywhere in the plane. In this paper, we first derive an expression for the acoustic field excited by a line source by adiabatic modes and then introduce a high-precision spectral method to solve the local eigenmodes. For the lower boundary condition of the acoustic half-space, we use the eigenvalue transformation technique to transform the transcendental algebra system formed by spectral discretization into a generalized eigenvalue problem. Several representative numerical experiments are designed to verify the accuracy of the algorithm. After analyzing the parallelism, the multiprocess and multithread hybrid strategy is adopted to further accelerate the algorithm in parallel, and parallel numerical simulation is carried out on the Tianhe–2 multicore supercomputer; favorable acceleration is achieved.

Symbolic-Numerical Modeling of the Propagation of Adiabatic Waveguide Mode in a Smooth Waveguide Transition

In this work, the model of adiabatic waveguide modes is studied by means of computer algebra. Within the model, the solution of the system of Maxwell’s equations is reduced to a form expressed via the solution of a system of four ordinary differential equations and two algebraic equations for six components of the electromagnetic field. In the case of multilayer waveguides, by means of a computer algebra system, the equations are reduced to a homogeneous system of linear algebraic equations, which is studied symbolically. The condition for non-trivial solvability of the system defines a dispersion relation, which is solved by the symbolic-numerical method, while the system is solved symbolically. The paper presents solutions that describe adiabatic waveguide modes in the zeroth approximation, taking into account the small slope of the interface of the waveguide layer, which are qualitatively different from solutions that do not take into account this slope.

A Study of the GTL Process in Adiabatic Mode

Versions of the production of environmentally friendly components of motor fuels using the Fischer–Tropsch synthesis (FTS) are considered. The advantages and disadvantages of the used radial reactors are analyzed. Research on the development of a domestic technology for the production of synthetic liquid fuels from natural gas on a bench-scale process plant, which was used to solve the problems of hydrogen utilization, is described. Based on the results of this work, conclusions that allow the development of a promising scientific and practical direction were drawn.

Adiabatic guided modes of a three-layer integral optical waveguide

The numerical solution of the problem of guided propagation of polarized light in a smooth junction of a planar waveguide is considered. Within the framework of the model of adiabatic guided modes, the system of Maxwell equations is reduced to a system of four ordinary differential equations and two algebraic equations for six components of the electromagnetic field in the zeroth approximation and the same number of equations in the first approximation. The multilayer structure of waveguides makes it possible to reduce the problem to a homogeneous system of linear algebraic equations, whose nontrivial solvability condition yields the dispersion equation. Auxiliary eigenvalue problems for describing the adiabatic modes of the waveguide are solved. Keywords: smoothly irregular integrated-optical multilayer waveguides, eigenvalue and eigenvector problems, single-mode propagation of adiabatic waveguide modes.

Mode coupling in a coastal wedge due to quasi-crossing of range-dependent modal eigenvalues.

A specific mechanism of mode coupling in a waveguide propagation is studied when two range-dependent eigenvalues approach each other. This phenomenon is analogous to the so-called quasi-crossing of states in atomic physics (Landau-Zener theory). It is considered for the sound wave propagation in a coastal wedge in the presence of a sound-speed profile. The change in mode composition and the corresponding spatial variability of the sound field are analyzed by using modes coupling equations and the parabolic equation with a field decomposition over adiabatic modes, respectively.

Адиабатические волноводные моды трехслойного интегрально оптического волновода

The numerical solution of the problem of guided propagation of polarized light in a smooth junction of a planar waveguide is considered. Within the framework of the model of adiabatic guided modes, the system of Maxwell equations is reduced to a system of four ordinary differential equations and two algebraic equations for six components of the electromagnetic field in the zeroth approximation and the same number of equations in the first approximation. The multilayer structure of waveguides makes it possible to reduce the problem to a homogeneous system of linear algebraic equations, whose nontrivial solvability condition yields the dispersion equation. Auxiliary eigenvalue problems for describing the adiabatic modes of the waveguide are solved.

Profile thickness synthesis of thin-film waveguide Luneburg lens

In the work the link between the focusing inhomogeneity of the effective refractive index of waveguide Luneburg lens and the irregularity of the waveguide layer thickness generating this inhomogeneity is demonstrated. For the dispersion relation of irregular thin-film waveguide in the model of adiabatic waveguide modes the problem of mathematical synthesis and computer-aided design of the waveguide layer thickness profile for the Luneburg thin-film generalized waveguide lens with a given focal length is being solved. The calculations are carried out in normalized (in a special way) coordinates to adapt the used relations to computer calculations. The obtained solution is compared with the same solution within the cross-section’s method. The performance of the algorithm implemented in Delphi, was demonstrated by plotting the dispersion curves and plotting a family of dispersion curves, demonstrating a critical convergence. As an additional result, the thickness profiles of additional (irregular in thickness) waveguide layer, forming a thin film generalized waveguide Luneburg lens were synthesized. This result generalizes Southwell’s results.

Force-dependent Fluxes of Adiabatic Classical and Quantum Rocking Ratchets

We consider the adiabatic mode of Brownian particle motion in a periodic potential under the action of symmetric dichotomous fluctuations of an external force F with zero mean value (rocking ratchet), in which the fluctuation frequency is much less than the inverse relaxation time of the particle in each of the states of the dichotomous process. Expressions are given for force-dependent fluxes of an adiabatic classical rocking ratchet. In the absence of thermal fluctuations, within the semiclassical approximation, analytical expressions are obtained for the rocking-ratchet tunneling flux in a sawtooth periodic potential of arbitrary asymmetry and in the potential of two sinusoids. It is shown that the tunneling flux has a linear asymptotics in modulus of small F due to (i) the absence of reverse tunneling fluxes with respect to the direction F and (ii) the root dependence of the integrand of the Gamow formula on the potential energy. The main parameters of the model are the energy barrier V0 and the period L of the potentials, as well as the rocking force F and the asymmetry parameter ξ = l / L of the sawtooth potential with the width of one of its teeth equal to l. It is shown that the direction of quantum ratchet motion is opposite to the motion direction of the corresponding classical ratchet in a limited range of values of the rocking force |F| L / V0 < αc , where the parameter αc changes from the value α1 = (√5 − 1) / 2 ≈ 0.618 for the extremely asymmetric sawtooth potential (ξ = 1) to the value α2 = 2 / 3 ≈ 0.667 for the symmetric potential (ξ= 1 / 2). In the range of values α2 < αc < α2, the sign of the tunneling flux changes with the change in the asymmetry parameter ξ. Numerical calculations for the potential of two sinusoids corresponding to the effective value ξ ≈ 0.655 of the asymmetry lead to similar results with αc ≈ 0.81.

A Study of the GTL Process in Adiabatic Mode

A Study of the GTL Process in Adiabatic Mode

Study of acoustic propagation across an oceanic front at the edge of the New England shelf.

Propagation of low-frequency sound across a warm core ring-enhanced oceanic front at lower horizontal grazing angles is presented. The data were collected from an experimental source tow conducted during the New England Shelf Break Acoustics (NESBA) experiments in spring 2021. The 3 h tow track provides spatiotemporal measurements of acoustic propagation through the front across varying geometries. Coincident oceanographic measurements are used to estimate the strong temperature gradient of the water column and three-dimensional (3D) sound speed field. Two-dimensional (2D) adiabatic mode and full-field sound propagation models are utilized to investigate the acoustic sensitivity to the frontal structure. Then, the joint effects of acoustic ducting and bathymetric slope refraction are examined using 3D sound propagation models. Key components of the measured acoustic impulse response are captured in the 3D numerical model, and the sensitivity of low-frequency propagation to the front geometry is demonstrated.

Natural Gas Storage Filled with Peat-Derived Carbon Adsorbent: Influence of Nonisothermal Effects and Ethane Impurities on the Storage Cycle.

Adsorbed natural gas (ANG) is a promising solution for improving the safety and storage capacity of low-pressure gas storage systems. The structural-energetic and adsorption properties of active carbon ACPK, synthesized from cheap peat raw materials, are presented. Calculations of the methane-ethane mixture adsorption on ACPK were performed using the experimental adsorption isotherms of pure components. It is shown that the accumulation of ethane can significantly increase the energy capacity of the ANG storage. Numerical molecular modeling of the methane-ethane mixture adsorption in slit-like model micropores has been carried out. The molecular effects associated with the displacement of ethane by methane molecules and the formation of a molecule layered structure are shown. The integral molecular adsorption isotherm of the mixture according to the molecular modeling adequately corresponds to the ideal adsorbed solution theory (IAST). The cyclic processes of gas charging and discharging from the ANG storage based on the ACPK are simulated in three modes: adiabatic, isothermal, and thermocontrolled. The adiabatic mode leads to a loss of 27-33% of energy capacity at 3.5 MPa compared to the isothermal mode, which has a 9.4-19.5% lower energy capacity compared to the thermocontrolled mode, with more efficient desorption of both methane and ethane.

Efficient Dual-Mode Fiber-Chip Edge Coupler Using an Adiabatic Mode Evolution Trident

We propose and demonstrate a silicon based dual-mode fiber-chip edge coupler. By utilizing an adiabatic mode evolution trident structure combined with triple inverse tapers, efficient TE0-LP01 and TE1-LP11 mode coupling with low loss, low crosstalk and compact footprint could be achieved simultaneously. Design details and the corresponding simulation results are presented. Experimental results show insertion losses for TE0-LP01 and TE1-LP11 mode coupling are 9.78 dB and 7.82 dB, while crosstalk are −13.9 dB and −22.5 dB within 1520–1580 nm. Total length of the fabricated device is <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\sim 220~\mu \text{m}$ </tex-math></inline-formula> . The proposed dual-mode coupler could be utilized in the interconnection of multi-mode fiber-chip transmission networks.

Investigation of interfacial structure and dynamic mechanical behavior of titanium alloy laminated composites

Explosive welding is widely used in the manufacture of dissimilar metal composite plates. In this work, TC4/TA1/Ti6321 titanium alloy laminated composites were successfully prepared by explosive welding. The interfacial characteristics of the laminated composites were studied by energy dispersive spectroscopy (EDS), electron backscattered diffraction (EBSD), transmission electron microscope (TEM), and other characterization methods. The dynamic mechanical properties of the laminated composites were investigated by using the split Hopkinson pressure bar (SHPB). The results show that the interface of laminated composites was well bonded. There was a high density of crystal defects including dislocations and twins near the interface. The composite plates showed a hard/soft/hard hardness distribution as a whole, and the microhardness increased near the interface. Due to the existence of the interface, the dynamic mechanical properties of laminated composites show different results. The dynamic compressive stress-strain curve of laminated composites showed an equilibrium type, and the strain strengthening effect was lower than that of homogeneous materials. The failure mode of laminated composites was adiabatic shear failure mode.

Galaxy number-count dipole and superhorizon fluctuations

In view of the growing tension between the dipole anisotropy of number counts of cosmologically distant sources and of the cosmic microwave background (CMB), we investigate the number count dipole induced by primordial perturbations with wavelength comparable to or exceeding the Hubble radius today. First, we find that neither adiabatic nor isocurvature superhorizon modes can generate an intrinsic number count dipole. However a superhorizon isocurvature mode does induce a relative velocity between the CMB and the (dark) matter rest frames and thereby affects the CMB dipole. We revisit the possibility that it has an intrinsic component due to such a mode, thus enabling consistency with the galaxy number count dipole if the latter is actually kinematic in origin. Although this scenario is not particularly natural, there are possible links with other anomalies and it predicts a concommitant galaxy number count quadrupole which may be measurable in future surveys. We also investigate the number count dipole induced by modes smaller than the Hubble radius, finding that subject to CMB constraints this is too small to reconcile the dipole tension.

Fabrication tolerant and broadband polarization splitter-rotator based on adiabatic mode evolution on thin-film lithium niobate

A polarization splitter-rotator device can facilitate on-chip polarization-division multiplexing to enhance the transmission data rate. Here, we propose and experimentally demonstrate a polarization splitter-rotator based on adiabatic mode evolution on the thin-film lithium niobate platform. The measured results for a fabricated device show low insertion losses of <-0.5 dB and large extinction ratios of >20 dB over the 110-nm band. Large fabrication tolerance is also demonstrated with extinction ratios of >15 dB in the wavelength range of 1465-1630 nm for a waveguide width variation of 80 nm.

Ring Resonator Gap Determination Design Rule and Parameter Extraction Method for Sub-GHz Resolution Whole C-Band Si3N4 Integrated Spectrometer

A panoramic ultra-high resolution photonic integrated circuit spectrometer is under development by the authors. The architecture comprises a tunable ring resonator (RR) stage and an AWG stage. The resolution defines the bandwidth of the RR, determined by the cross-coupled power and hence the gap between the access and ring waveguides. The AWG channel frequency spacing determines the required free-spectral range (FSR) and hence the perimeter of the ring resonator. The specified &lt;1 GHz resolution combined with an FSR of 50 GHz renders accurate simulation difficult, obstructing the design process. In this report, a simplified design rule to determine the minimum gap between straight access waveguides and a circular ring waveguide is proposed. Realistic assumptions such as the existence of local bisymmetry and adiabatic mode evolution throughout the coupling region permit a simple mode solver to determine the relationship between the cross-coupled power and the minimum gap size. A parameter extraction method is also formulated for add-drop rings equipped with two nominally identical couplers that disentangles the loss and coupling ring parameters from intensity-only transmission measurements. The proposed rule is applied to the design of ring resonators fabricated on a Si3N4 platform. The parameter extraction method is used to analyze the measured characterization data of the ring resonators. The results show good agreement within ~43 nm between the design rule and the gaps size determined by the parameters extracted from the measured data and provide experimental confirmation of the technological viability of the ring resonators required by the spectrometer.

Numerical method for designing ultrashort and efficient adiabatic mode converters

This paper proposes a fully numerical method for designing adiabatic mode converters (NM-AMCs). The proposed method can help compute efficient adiabatic guided-wave shapes for mode converters using a nonuniform section division technique. Such a scheme reduces the memory requirement and computational time for the design of adiabatic devices. Furthermore, the adiabatic mode converter comprises a ridge waveguide, which is difficult to design using analytical methods. This complex case of an adiabatic mode converter is used to demonstrate how the proposed method can readily generate a guided-wave shape that gives the same mode-connection power transfer with a far shorter length compared with a linear-shape converter. The efficiency of the device designed using this NM-AMC is significantly better than that of linear-shape converters; this designed adiabatic mode converter can enable a broad operating bandwidth. Moreover, the efficiency of the adiabatic mode converter that was designed using the NM-AMC method considerably exceeds that obtained using an analytical method proposed for a strip waveguide.

Magnetic field back reaction on the matter power spectrum

At lowest order comoving magnetic fields which are frozen-into the expanding cosmic fluid do not evolve in time. At next-to-leading order the induction equation is sourced by the interaction term between the baryon velocity and the magnetic field amplitude which leads to a non-trivial evolution of the comoving magnetic field. Moreover, it induces non-trivial cross correlations between the adiabatic curvature mode and the magnetic mode. This cross correlation together with the evolution of the induced matter perturbation leads to interesting effects on the total matter power spectrum at small scales.

Loading rate effect and failure mechanisms of ultra-high-strength steel under mode II fracture

40Cr and 30CrMnSiNi2A are both ultra-high-strength steel (UHSS) that is usually used in engineering structures such as aircraft landing gear, wing girder, and fastening bolts. Under dynamic loading, fracture properties of such materials are very important for structural design. A novel mode II dynamic fracture testing technique is adopted to study the mode II dynamic fracture characteristics of these two materials under high loading rates. The mode II dynamic fracture specimen is designed for the SHPB equipment, and the stress intensity factor curve at the crack tip is determined by an experimental-numerical method. The crack initiation time of the specimen is determined by the strain gage method. In the end, the mode II dynamic fracture toughness (KIId) of the two materials is obtained, and the loading rate effects are compared and analyzed in detail. The results show that within the loading rate range of this research (1.08 ∼ 7.73 TPa·m1/2/s), the KIId of the two materials has a positive correlation to the loading rate. Both of the materials exhibit a gradual transition process from tensile failure to adiabatic shearing failure mode. According to the fracture morphologies of the two materials, the failure mechanism of the two materials is analyzed for different failure modes. Failure mode transition (FMT) is specially investigated with the increase of the loading rate for both of the materials.