Periodic Discontinuities Research Articles

A new generalized perspective to establish vortex beams

Vortex beams are powerful primitives for optical operations and communications. We propose general mathematical methods to establish new vortex beams and optimize existing vortex beams. Based on these methods, two new types of vortex beams are demonstrated theoretically and experimentally. The propagation characteristics of these vortex beams can be finely controlled through specific parameters. Additionally, influences of periodic discontinuities and orbital angular momentum of two vortex beams are analyzed. The innovative concept of beam modulation and the introduction of new vortex beams in this paper indicate significant potential for applications in particle trapping, spatial communication, and quantum computation.

Paraxial forward-scatter field analysis for a THz pulse traveling down a highly overmoded iris-line waveguide

Highly overmoded iris-line structures carry desirable features for the efficient transportation of THz radiation over long distances. Previous studies have analyzed the iris line, modeled approximately as a long open-resonator structure with thin screens, using methods such as Vainstein's impedance boundary condition or perturbative mode matching. The aim in those methods was to seek the eigensolution that represents the dominant (least lossy) propagation mode in a long iris-line structure at a steady state. In this paper, a forward-traveling wave analysis is presented, wherein a short THz pulse paraxially traverses the oversized structure cell by cell, including the transient regime. The iris line's periodic discontinuities are analyzed in terms of forward-wave orthogonal mode decompositions, which are then used to build a ``forward-scatter'' model (matrix) for each cell. The presented approach predicts a diffraction loss behavior that agrees with that of the eigensolution found by the previous analytical methods for a long waveguide at the steady state but adds the ability to analyze waveguides of finite lengths, showing transients as they evolve and settle to the dominant mode down the line, and offers numerical implementation speeds that are typically an order-of-magnitude faster than those previously reported for the mode-matching method. This approach may also be easily extended to analyze iris lines with mechanical imperfections (e.g., misalignments or aperiodic defects), allowing for investigations of performance sensitivity against manufacturing tolerances.

Solving Sub-Wavelength Lattice Reduction in Full-Metal Front-Ends for Dual-Polarized Active Antennas

This article proposes an original structure of evanescent quadridge antenna (EQA) to conceive dual-polarized full-metal front-ends that can be used in active antennas (AAs) with wide field-of-view (FoV). An original design methodology is here proposed that allows to induce radiation from subwavelength squared apertures based on the use of evanescent and quadridge waveguides. The proposal is illustrated by means of a design with 4.5% bandwidth providing dual-circular polarization (CP) with good performance up to 50°-scanning even in the diagonal plane. For comparison purposes, a metallic benchmark is also proposed, which is based on the use of classical quadridge horns. Such comparative analysis allows to understand the superior performance of the proposed concept and its main advantage: it allows to avoid the excitation of the first high order mode in the squared quadridge aperture. The excitation of such spurious mode in the antenna is explained in terms of simple equivalent circuit models characterizing the aperture periodic discontinuity.

The impact of a crisis on entrepreneurial orientation of family firms: The role of organisational decline and generational change

This article critically analyses entrepreneurial orientation (EO) in family firms after a major crisis, to investigate how firms with equal initial levels of EO reach different levels over time. Based on two alternative hypotheses (stability and convergence), we analysed whether the EO of family firms remains intact, strengthens, or weakens after a crisis. Based on an examination of a database of 151 family firms collected in 2004 and 2017, our findings reveal that compared to firms with higher pre-crisis EO levels, those with lower levels saw a larger increase post crisis. Furthermore, unlike the latter group, the former was able to maintain high pre-crisis levels even after the crisis. In addition, we also we found this relationship between pre-crisis and post-crisis EO levels to be influenced by two key periodic discontinuities, namely, organisational decline and generational change contingencies. These findings advance our understanding of temporal aspects of EO and heterogeneous entrepreneurial behaviour among family firms with significant implications for both theory and practice.

Determining a technique for transmitting measuring data on the spatial positioning of the piercing head in small-size installations during controlled soil piercing

For laying of underground utility systems in urban conditions by the method of horizontally directed soil piercing, small-sized units are designed. Such units should have measurement systems for determining the spatial position of the piercing head. In known systems, the surface layer of the soil is used as a data transmission line for transmitting measurement information. This method of transmitting information signals in urban conditions is not very acceptable. Ground-based objects reflect electromagnetic radiation of the head transmitter which leads to distortion of the directional diagram of the emitter and complicates the reliable reception of measurement information. It was proposed to use an autonomous measuring system with an operating frequency of 5 GHz based on Wi-Fi technologies and an unconventional method of transmitting measurement information using hollow steel bars in the piercing unit itself. This transmission line has periodic discontinuities because of the bar design. These discontinuities accumulate as the piercing head advances. For the basic vibration type Н 11 , more accurate analytical expressions were obtained for calculating the power transfer coefficient of the measurement signal in such non-uniform lines. It was shown that inhomogeneity of the transmission line in comparison with its surface resistance does not significantly affect the transmission coefficient. For example, damping in the line increased by 1.2 dB with the maximum length of inhomogeneity of 5 mm and the total length of jointed bars of 50 m. It has been theoretically proven that the range of soil piercing with reliable signal reception can be up to 50 meters. The proposed method for transmitting information signals makes it possible to reduce the transmitter power, ensure noise immunity of the measuring system, and reliable reception of the measuring information throughout the entire piercing path

Multifunctional Filtering Leaky-Wave Antenna Exhibiting Simultaneous Rapid Beam-Scanning and Frequency-Selective Characteristics Based on Radiative Bandpass Filter Concept

In this article, the concept of radiative bandpass filter (RBPF) is proposed and investigated for developing a class of multifunctional filtering leaky-wave antennas (LWAs) which exhibit the simultaneous rapid frequency-dependent beam-scanning and frequency-selective characteristics. A substrate-integrated waveguide (SIW) is periodically loaded with closed (nonradiative) discontinuities acting as a bandpass filter, where the lower and higher stopbands are, respectively, stemmed from the SIW natural cutoff and the Bragg effect bandgap or bandstop caused by periodic discontinuities. By adequately adjusting the periodicity of filter unit cells and loading effects of closed discontinuities, filtering and dispersion behaviors of the periodic SIW can be flexibly engineered. Open (radiative) discontinuities are then deliberately introduced into the bandpass filter to generate a controllable radiation leakage, thereby accomplishing the design of the RBPF, i.e., the proposed LWA. With this concept, both filtering/dispersion and radiation tasks can be independently managed by different modules for LWAs. For demonstration purposes, two kinds of closed discontinuities, namely nonradiative longitudinal slot-pair (capacitive) and iris (inductive), are separately exploited for periodic SIWs with bandpass and high dispersion characteristics, whereas transverse slot (open discontinuity) is mainly aimed for radiation leakage. Two RBPF-based LWAs are simulated, fabricated, and measured. The simulated and measured results are in a reasonable agreement, and both demonstrate the rapid beam-scanning and filtering behaviors, thereby validating the proposed concept.

Simulation of sedimentation of two spheres with different densities in a square tube

We simulated the sedimentations of two unequal spheres with different densities in a square tube for Galileo numbers (Ga) from 5 to 25, resulting in a Reynolds number range of based on the terminal settling velocity. The sedimentation of spheres with different densities is dynamically more complex than that of identical spheres. At high Ga the spheres oscillate in the centreline plane of the tube, where they are initially released from rest. By contrast, the spheres move to the diagonal or reverse–diagonal plane of the tube at low Ga, reaching a steady or periodic state depending on the density difference between them. A phase diagram illustrates the transitions between different sedimentation behaviours depending on Ga and the density difference. A possible mechanism for these behaviours is also presented. Furthermore, we compare two-dimensional (2-D) and three-dimensional computations for our system to attain a better understanding of the hydrodynamic interactions between two unequal spheres at low but finite Reynolds number. Comparing relative trajectories, periods of oscillation and flow features shows that 2-D circular cylinders oscillate much more strongly and frequently than spheres under the same flow conditions. In particular, spheres do not have the discontinuity in period that arises in the 2-D case from the change in rotation sign of a heavy particle.

Spectral analysis and structural response of periodic and quasi-periodic beams

Periodic structures have found a big interest in engineering applications because they introduce frequency band effects, due to the impedance mismatch generated by periodic discontinuities in the geometry, material, or boundary conditions, which can improve the vibroacoustic performances. However, the presence of defects or irregularity in the structure leads to a partial lost of regular periodicity (called quasi-periodic structure) that can have a noticeable impact on the vibrational and/or acoustic behavior of the elastic structure. The irregularity can be tailored to have impact on dynamical behavior. In the present paper, numerical studies on the vibrational analysis of one-dimensional finite, periodic, and quasi-periodic structures are presented. The contents deal with the finite element models of beams focused on the spectral analysis and the damped forced responses. The quasi-periodicity is defined by invoking the Fibonacci sequence for building the assigned variations (geometry and material) along the span of finite element model. Similarly, the same span is used as a super unit cell with Floquet–Bloch conditions waves for analyzing the infinite periodic systems. Considering both longitudinal and flexural elastic waves, the frequency ranges corresponding to band gaps are investigated. The wave characteristics in quasi-periodic beams, present some elements of novelty and could be considered for designing structural filters and controlling the properties of elastic waves.

Numerical investigations and experimental measurements on the structural dynamic behaviour of quasi-periodic meta-materials

Abstract The periodic structures have various applications in vibroacoustic engineering fields since they introduce frequency band effects due to the periodic discontinuities in the geometrical or material configurations: this can lead to increased performances. This paper is focused on the analysis of quasi-periodic structures: instead of using strictly repeated patterns, a certain degree of irregularity is introduced. Quasi-periodic lattices are defined as assemblies of two different elements in two directions. The assembly follows a Thue-Morse Morphism sequence which results in asymmetry in both directions. Numerical studies and experimental measurements on two-dimensional periodic and quasi-periodic lattices are thus performed. First validations are carried out by comparing the quasi-periodic lattice modelled by using finite element model with a prototype manufactured by laser machine. The wave characteristics in quasi-periodic lattice introduce elements of novelty for designing wider frequency stop bands in low frequency ranges.

On the behaviour of infinite, periodic, mono-coupled waveguides using a transmission coefficient phase method

Abstract Wave propagation in a one dimensional, mono-coupled waveguide composed of an infinite wave-bearing structure supported by periodic discontinuities is analysed in terms of the transmission and reflection coefficients of a single discontinuity, expressions for which are often available in the literature. The general solution is presented and is applicable for arbitrary transmission and reflection coefficients. For conservative discontinuities, conservation of energy imposes relationships on the complex values of these coefficients and yields a simplified expression for the propagation constant, which is a function of the phase of the transmission coefficient, and a second phase angle which arises from the conditions of continuity and equilibrium at the discontinuity. Expressions for the bounding frequencies between pass and stop bands, the bandwidth of a stop band, and the upper bound of attenuation within a stop band are also given in terms of these phases. For some common systems, the phase of the transmission coefficient determines the behaviour of the entire system and thus provides a straightforward analysis. The proposed approach for mono-coupled waveguides can also be applied to some multi-coupled waveguides such as beams under the assumption that nearfield waves are negligible. The approach is then applied to an infinite periodic string on arbitrary supports, an Euler-Bernoulli beam on periodic arbitrary supports, and a system of thin beams that are hinged at periodic intervals with arbitrary supports.

Analysis of the variability of pesticide concentration downstream of inline mixers for direct nozzle injection systems

The injection of pesticide directly into spray nozzles results in concentration variations, both periodic discontinuities and pulses, caused by the use of injection pumps and solenoid valves. Such variations can lead to inaccurate application of pesticide. To avoid using long pipelines, long lag times and inaccurate application, efficient mixers are required to shorten the distance between the injection point and the spray nozzle. To analyse concentration variations and periodic pulses, a set of methods based on image processing were proposed and were tested using three inline mixers, a jet mixer (A), a layered mixer (B) which was specially designed, and simplified layered-jet mixer (C) which was developed as combination of mixer A and some simplified structures of mixer B. Results showed the characteristics of concentration variability for three mixers were generally different. The application conditions, carrier flow rate, mixing ratio, and injection frequency, need to be comprehensively considered to achieve improved concentration consistency and improve spraying accuracy. Concentration variability was the most obvious for mixer A with the average Coefficient of Variation (CV) as high as 4.12%. Using auto-correlation and complexity analysis, the concentration series exhibited strong periodicity and relatively lower complexity. Concentration variability for mixer B was less prominent with an average CV value 1.25% and concentration periodicity sometimes being indeterminable. Mixer C showed moderate concentration variability (CV 2.26%) although pulsation was still detectable. Mixers with similar structures to mixer C could be applied for direct nozzle injection systems to improve the spraying accuracy.

Acoustic reflection and transmission by sub-critical and super-critical elastic partitions with structural discontinuities forced by multiple-angle oblique broadband sound waves

An analysis is presented for acoustic reflection and transmission from an infinite fluid-loaded flexible barrier with spatially periodic discontinuities. The plate, with similar or dissimilar acoustic fluids on both sides, is excited by an oblique wave incident acoustic field. The fully-coupled structural/acoustic problem is treated by Analytical-Numerical Matching (ANM) which improves the numerical accuracy and convergence rate. Periodic spatial discontinuities, modelled by various boundary conditions, create deviations from specular directivity. For super-critical structural wave speeds, the scattering is characterized by a distribution of reflection and transmission angles centered around the Mach Angles. For sub-critical structural waves, energy redistribution is most pronounced at the structural resonances. These results are compared to a baffled finite barrier analyzed by approximate means. For the subcritical finite barrier, a fluid loading correction is introduced to the structural wavenumber to approximate the effects of the fluid coupling and radiation damping. For subsonic flexural waves, the radiation is analyzed in terms of the wavenumber transform and interpreted as a series of edge singularities dependent on the boundary conditions. For the super-critical configuration, the effects of the fluid loading are introduced by approximating the structural wavenumber from the dispersion relation of the free response of the unbounded structure.An analysis is presented for acoustic reflection and transmission from an infinite fluid-loaded flexible barrier with spatially periodic discontinuities. The plate, with similar or dissimilar acoustic fluids on both sides, is excited by an oblique wave incident acoustic field. The fully-coupled structural/acoustic problem is treated by Analytical-Numerical Matching (ANM) which improves the numerical accuracy and convergence rate. Periodic spatial discontinuities, modelled by various boundary conditions, create deviations from specular directivity. For super-critical structural wave speeds, the scattering is characterized by a distribution of reflection and transmission angles centered around the Mach Angles. For sub-critical structural waves, energy redistribution is most pronounced at the structural resonances. These results are compared to a baffled finite barrier analyzed by approximate means. For the subcritical finite barrier, a fluid loading correction is introduced to the structural wavenumber to a...

Acoustics of locally bilinear periodic metamaterials

The scope of traditional metamaterials is expanded by analyzing bilinear discontinuities in an otherwise continuous medium. This amplitude independent nonlinearity is sought for its practicality and utility. Wave propagation has to be solved for in the time domain due to the difference in energy transfer from compression to rarefaction across an interface. Various sizes, orientations and shapes of the discontinuities are analyzed on a unit cell level. Periodic chains with the same type of material discontinuity have recently been shown to exhibit a rich dispersion behavior, such as negatively sloped dispersion branches [Titovich (2017), J. Acoust. Soc. Am. 141(5), 3698]. These waves are now investigated in a continuum, where the discontinuity is modelled as displacement-dependent complex impedance relating the interface tractions. The onset of chaotic behavior as well as its effect on absorption is discussed. Also, the ability of such periodic discontinuities to produce nonlinear non-reciprocity is invest...

Reflection and transmission of acoustic energy by an elastic plate with structural discontinuities forced by multiple angle oblique broadband sound waves

An analysis is presented for acoustic reflection and transmission from an infinite fluid-loaded plate with spatially periodic discontinuities. The plate, with similar or dissimilar acoustic fluids on both sides, is excited by an oblique wave incident acoustic field. The fully-coupled structural/acoustic problem is treated by the method of Analytical-Numerical Matching (ANM). The ANM framework separates the problem into global numerical and local analytical solutions, and handles rapid spatial variation around the structural discontinuities in closed form, improving the numerical accuracy and convergence rate. The ANM approach includes a novel way to handle difficulties associated with coincidence frequencies. The periodic spatial discontinuities, modeled by various boundary conditions, create deviations from specular directivity with multiple reflection and transmission angles, the effect being most pronounced at structural resonances. The periodic discontinuities redirect part of the structural energy in...

Band-gaps in long Josephson junctions with periodic phase-shifts

We investigate analytically and numerically a long Josephson junction on an infinite domain, having arbitrary periodic phase shift of κ, that is, the so-called 0–κ long Josephson junction. The system is described by a one-dimensional sine-Gordon equation and has relatively recently been proposed as artificial atom lattices. We discuss the existence of periodic solutions of the system and investigate their stability both in the absence and presence of an applied bias current. We find critical values of the phase-discontinuity and the applied bias current beyond which static periodic solutions cease to exist. Due to the periodic discontinuity in the phase, the system admits regions of allowed and forbidden bands. We perturbatively investigate the Arnold tongues that separate the region of allowed and forbidden bands, and discuss the effect of an applied bias current on the band-gap structure. We present numerical simulations to support our analytical results.

Prediction of reflection and transmission by an elastic barrier with periodic structural discontinuities forced by oblique acoustic waves

An analysis method is developed for acoustic reflection and transmission from an infinite fluid-loaded flexible barrier with spatially periodic discontinuities. The barrier has acoustic fluids on both sides, which can be dissimilar. The structure is excited by an oblique-wave incident acoustic field. The fully-coupled structural/acoustic problem is treated by the method of Analytical-Numerical Matching (ANM). The ANM framework separates the problem into a global numerical solution and local analytical solutions. ANM handles rapid spatial around the structural discontinuities, improving the accuracy and convergence rate of reflected and transmitted pressures. Furthermore, the ANM approach offers a way to handle the mathematical difficulties associated with coincidence frequencies. The periodic spatial discontinuities create variations from simple specular-like directivity with multiple reflection and transmission angles, the effect being most pronounced at structural resonances. The periodic discontinuities can be thought of as redirecting a portion of the structural energy into resonant substructures having wavenumbers different from the oblique wave forcing, reradiating reflection and transmission fields with different directivity patterns. Discrete frequency and broadband results are presented. The goal is to develop efficient first-principles methods for structural-acoustic reflection and transmission between coupled acoustic spaces and into surrounding media.

Phase space of partially coherent light with discontinuous surfaces

We propagate partially coherent light through discontinuous surfaces and analyze the optical effects in phase space. The discontinuous surfaces are classified into two types, those with discontinuity in space and those with discontinuity in slope. Results are discussed based on the Wigner function. This approach explains the performance of segmented elements during the transition from the refractive into the diffractive regime. At first the diffraction effects generated by a single discontinuity (e.g. a phase step and a linear axicon) are investigated. Later on we discuss surfaces with periodic discontinuities, e.g. gratings, to study the formation of multiple diffracted orders. A kinoform lens is given as a further example to visualize the change from pure refraction to diffraction. Moreover, we present the beam homogenizing effect in phase space generated by lens arrays.

Chronic disease prevalence and discontinuation of medications among young mothers with a relationship to the child welfare system

ObjectivesTo describe the prevalence of chronic conditions in the reproductive period among young mothers with a relationship to child welfare and to describe medication discontinuity from the preconception to postpartum period. MethodsRetrospective cohort of mothers aged 15 to 24 delivering an infant between 2007 and 2010 in a large, Mid-Atlantic city. Descriptive and chi square statistics were used to: 1) describe the prevalence of chronic conditions and medication fills in the preconception, pregnancy and postpartum periods and, 2) determine differences in these outcomes by child welfare involvement status. ResultsNearly half (43%) of all mothers with Medicaid-financed births had a relationship with the child welfare system. The prevalence of asthma and HIV were significantly elevated among child welfare involved mothers as compared to non-involved mothers. With the exception of anxiety and intellectual disability, all mental and behavioral conditions occurred more frequently among child welfare involved mothers than non-involved mothers. Among mothers with diagnosed mental illness receiving psychotropic medications prior to pregnancy, more than half experienced discontinuity of medications in the postpartum year and discontinuity was significantly increased among child welfare exposed mothers. ConclusionsYoung mothers with a relationship to child welfare experience increased morbidity and are at high risk for treatment discontinuity in the postpartum period. Bridging reproductive and behavioral health services is critical for this population; in addition, public health systems should support the delivery of trauma-informed services for adolescents to meet needs of young mothers with child welfare involvement.

Filter Helix for Harmonic Suppression in Traveling Wave Tubes

Increasing the efficiency of traveling wave tubes (TWTs) is a basic development strategy. In this paper, second harmonic suppression is introduced as a possible mean. For this purpose, a filter consisting of periodic pitch discontinuities is implemented in the helix transmission line (TL) of a tube. A method is developed to obtain the reflection coefficients of adjustable pitch discontinuities. A filter design for a low frequency TWT is tested in a helical TL without electron beam and implemented in the tube. Both simulation and measurement confirm a stopband at the second harmonic and thus a significant reduction of this harmonic at the output. An additional filter is designed and tested at S-band. It is shown to improve both the output power and the linearity of the tube.

Improvements to the Frequency Division-Based Subaperture Algorithm for Motion Compensation in Wide-Beam SAR

Motion compensation (MoCo) is pivotal in the processing of airborne synthetic aperture radar (SAR) data. Motion errors are space variant according to the data acquisition geometry, which can be split into range-variant and azimuth-variant components. In the processing of wide-beam SAR data, the azimuth variance must be considered. Several approaches have been proposed, among which the subaperture algorithm based on frequency division (FD) is a good choice if motion errors involve high-frequency components. However, there are two drawbacks to using this algorithm in conditions where the magnitude of motion errors is large, i.e., the invalidation of the time-frequency relation in an FD with too many subapertures and paired echoes caused by periodic discontinuities in the azimuth phase history. Theoretical analysis and simulations are presented to demonstrate these two drawbacks. Improvements are then made on the traditional algorithm: implementing the FD after the subaperture MoCo instead of before it and adopting a nonuniform FD scheme rather than a uniform one. Finally, the validity of the improved algorithm is further demonstrated by experimental results with real data.