Waves In Periodic Structures Research Articles

MHD simulations of astrophysical and laboratory jets under different magnetic field configurations

This paper presents the results of MHD simulations of astrophysical and laboratory supersonic jets under a superposition of poloidal (Br, Bz) and toroidal (Bϕ) magnetic fields. It is shown that the escaping matter is quickly collimated by the magnetic field. A shock wave of an elongated shape is formed, which moves from the target to the boundary of the chamber, leaving behind a stable flow. A periodic shock wave structure is observed inside the main conical expanding shock wave. It is shown that the toroidal component of the magnetic field remains in the region throughout the entire calculation and plays a role in the collimation of the flow. The poloidal magnetic field decreases in the region of the jet cone, but remains in the simulation region throughout the calculation and also participates in flow collimation. Thus, both components Bz and Bϕ take part in the collimation of the flow by the magnetic field. The width of the jet and the opening angle of the cone Ɵ depend on the magnitude of the magnetic field induction. As the field increases, the jet becomes narrower and the cone angle decreases. Initially, we do not specify the rotation of the jet Ω. However, due to the presence of the Bϕ field, the substance acquires angular velocity and twists along the z axis. The simulation results are in agreement with laboratory jets arising in the experiment at the Neodymium laser installation, and with the previously obtained results of MHD modeling of jet formation separately, in poloidal or toroidal magnetic field.

Wave type fiber SPR sensor for rapid and highly sensitive detection of hyperoside.

The fiber surface plasmon resonance (SPR) sensor used for the detection of active ingredients in traditional Chinese medicine has the problems of low sensitivity and difficult specific recognition. This paper proposed a wave type fiber SPR sensor, which reduced the mode of transmitted light through a periodic wave structure and caused concentrated and total reflection of the transmitted beam at the interface between the bent peak cladding and the air. A 50 nm gold film was coated on the surface of the cladding in the wave structure area to form the SPR sensing area. By controlling the width and height of the wave structure to control the total reflection angle of the transmitted light, i.e., the SPR incidence angle, the sensitivity of the fiber SPR sensor was effectively improved to 4972 nm/RIU. Furthermore, HSP90AA protein was modified on the gold film of the sensor to achieve specific detection of hyperoside. The longest single detection time was only 3 minutes, and the detection sensitivity was 0.53 nm/(µg/ml), with a detection limit as low as 0.68µg/ml, which is comparable to liquid chromatography. The proposed wave type fiber SPR sensor is fast in production and has high structural mechanical strength, providing a new approach for the rapid, highly sensitive, and specific detection of active ingredients in traditional Chinese medicine.

On some novel solitonic structures for the Zhiber–Shabat model in modern physics

Abstract In this article, the modified Kudryashov and extended simple equation methods are employed to obtain analytical solutions for the Zhiber–Shabat problem. The outcomes of this study clearly indicate that the provided methodologies are appropriate techniques for generating some new exact solutions for nonlinear evolution equations. Furthermore, the nature of the solutions would be presented in three dimensions for various parameters applying the most advanced scientific instruments. The physical behavior of the solutions are graphically displayed, and it is established that the acquired solutions are newly constructed in the form of bright, dark, optical, singular, and bell-shaped periodic soliton wave structures. The properties of the nonlinear model have been illustrated using 3D, 2D, and contour plots by selecting an appropriate set of parameters, which is demonstrated to visualize the physical structures more productively. Finally, it is concluded that similar strategies can also be implemented to study many contemporary models. To the best of our knowledge, the current work presents a novel case study that has not been previously studied in order to generate several new solutions to the governing model appearing in diverse disciplines. The results show that the strategies that have been employed are more effective and capable than the traditional methods found in previous research.

Identifying the Onset Location of Equatorial Plasma Bubbles (EPBs) and Its Relationship With the Background Ionospheric Conditions

AbstractUsing radars and C/NOFS satellite observations we studied the spatio‐temporal evolution of Equatorial Plasma Bubbles (EPBs) and estimated its onset location across a wide longitudinal sector over Indian and Southeast Asian longitudes. The vertical E × B drift velocity measurements obtained from the Ion Velocity Meter (IVM) on board the C/NOFS satellite and collocated ionosonde observations were used to examine the background ionospheric conditions. Our study shows that the periodic EPBs were present in those longitudes where periodic wave structure in the E × B drift and elevated F layer were observed. In this case study, the comprehensive analysis using the observations from radars and satellite data provides a better understanding on the longitudinal preference of the EPB occurrence and its responsible background mechanisms. This understanding of the onset location and background conditions of EPBs over a large longitudinal area for an extended period can contribute to the development of accurate EPB forecasting models, which are essential to mitigate the detrimental effects of EPBs on communication and navigation systems.

Investigation of complex hyperbolic and periodic wave structures to a new form of the q-deformed sinh-Gordon equation with fractional temporal evolution

This paper presents the fractional generalized q-deformed sinh-Gordon equation. The fractional effects of the temporal derivative of the proposed model are studied using a conformable derivative. The analytical solutions of the governing model depend on the specified parameters. The resulting equation is studied with two integration architectures: the sine-Gordon expansion method and the modified auxiliary equation method. These strategies extract hyperbolic, trigonometric, and rational form solutions. For appropriate parametric values and different values of fractional parameter α, the acquired findings are displayed via 3D graphics, 2D line plots, and contour plots. The graphical simulations of the constricted solutions depict the existence of bright soliton, dark soliton, and periodic waves. The considered model is useful in describing physical mechanisms that possess broken symmetry and incorporate effects such as amplification or dissipation.

Observation of photonic Peierls transition for manipulating microwave in metallic diaphragm-array periodic structures

Peierls transition that modifies electronic band structure has attracted intensive attention in solid state physics. In the present work, we report that a photonic analog of Peierls transition has been observed in a 1-D triangular metal diaphragm array, where the photonic bandgap structures have been designed at will by adjusting periodically metal diaphragm positions. It is shown by the numerical analysis that the transmission and radiation effect of the present periodic metal structure designed through the Peierls transition rule exhibits the behavior significantly different from an original periodic structure with each unit cell containing a metal diaphragm. The near- and far-field measurement results are in good agreement with our theoretical simulation. The present effect of photonic Peierls transition can serve as a working mechanism for designing new types of guided wave devices. It can be seen that the photonic Peierls transition would be one of the simplest ways for modifying the transport characteristics of electromagnetic waves in periodic structures.

Dynamics of breather, multi-wave, interaction and other wave solutions to the new (3+1)-dimensional integrable fourth-order equation for shallow water waves

PurposeThe purpose of this paper is to study the new (3 + 1)-dimensional integrable fourth-order nonlinear equation which is used to model the shallow water waves.Design/methodology/approachBy means of the Cole–Hopf transform, the bilinear form of the studied equation is extracted. Then the ansatz function method combined with the symbolic computation is implemented to construct the breather, multiwave and the interaction wave solutions. In addition, the subequation method tis also used to search for the diverse travelling wave solutions.FindingsThe breather, multiwave and the interaction wave solutions and other wave solutions like the singular periodic wave structure and dark wave structure are obtained. To the author’s knowledge, the solutions obtained are all new and have never been reported before.Originality/valueThe solutions obtained in this work have never appeared in other literature and can be regarded as an extension of the solutions for the new (3 + 1)-dimensional integrable fourth-order nonlinear equation.

Evolution of periodic wave and dromion-like structure solutions in the variable coefficients coupled high-order complex Ginzburg–Landau system

Evolution of periodic wave and dromion-like structure solutions in the variable coefficients coupled high-order complex Ginzburg–Landau system

New Complex Wave Solutions and Diverse Wave Structures of the (2+1)-Dimensional Asymmetric Nizhnik–Novikov–Veselov Equation

In this paper, we use a new, extended Jacobian elliptic function expansion method to explore the exact solutions of the (2+1)-dimensional asymmetric Nizhnik–Novikov–Veselov (aNNV) equation, which is a nonlinear physical model to describe an incompressible fluid. Combined with the mapping method, many new types of exact Jacobian elliptic function solutions are obtained. As we use two new forms of transformation, most of the solutions obtained are not found in previous studies. To show the complex nonlinear wave phenomena, we also provide various wave structures of a group of solutions, including periodic wave and solitary wave structures of ordinary traveling wave solutions, horseshoe-type wave, s-type wave and breaker-wave structures superposed by two kinds of waves: chaotic wave structures with chaotic behavior and spiral wave structures. The results show that this method is effective and powerful and can be used to construct various exact solutions for a wide range of nonlinear models and complex nonlinear wave phenomena in mathematical and physical research.

Analysis of the sound insulation performance of periodic wall structures by a virtual acoustic laboratory

The propagation of acoustic waves in periodic structures, also known as phononic crystals or PCs, is prohibited in certain frequency ranges, which are referred to as the frequency band-gaps. The existence, the location and the width of the frequency band-gaps are mainly determined by the geometrical parameters and the material properties of the PCs. In this work, a virtual acoustic laboratory based on a fully coupled fluid-structure interaction (FSI) model is developed to determine the sound insulation capacity of one-dimensional (1D) and two-dimensional (2D) periodic walls. The FSI model is discretized using the frequency-domain spectral element method (FDSEM), which is an advanced finite element method (FEM) using special high-order shape functions. Following the guidelines of the ISO10140, the setup of the developed FSI model allows us to take into account the essential physical phenomena, especially the interaction of the wall structure with the fluid domains (air). The FSI model based on the FDSEM increases the computational efficiency and accuracy in comparison with the standard FEM. Several numerical examples will be presented and discussed to show that the designed periodic walls in certain frequency ranges within the band-gaps may exhibit much better sound insulation capabilities than monolithic walls.

Rayleigh wave manipulation based on phase shift between two periodic surface corrugations

The propagation of Rayleigh waves along solid surfaces has attracted great attention due to its ubiquity in seismic waves, non-destructive evaluation, acoustic surface wave devices, and so on. Moreover, Rayleigh waves in periodic structures and their related band gaps caused by Bragg resonances have also been investigated. In this paper, we theoretically and experimentally demonstrate the propagation mechanism of Rayleigh waves along the side wall of a periodically corrugated aluminum plate. As expected, the band gap structures are observed in the spectrum of Rayleigh waves. However, not all the band gaps are caused by the Bragg resonances. The additional band gaps created by the interference of different transverse modes are observed. Different from the well-known Bragg resonance, the different mode interference, producing stronger energy attenuation and wider band gap, is called non-Bragg resonances. The two resonances can be manipulated by varying the phase shift of two sidewall corrugations, achieving an effective prohibition of Rayleigh wave propagation. These findings on Rayleigh wave propagation in periodic structures provide a comprehensive understanding of wave-structure interactions, which can be used to regulate elastic waves in various applications, such as multifunctional elastic wave separators, filters, and modulators.

Investigation on frequency influence on the transverse pulsed jet in a supersonic crossflow

AbstractThe pulsed jet is a novel and effective active mixing enhancement approach. For the transverse pulsed jet in the supersonic crossflow, the frequency influence is investigated using the three-dimensional Reynolds-averaged Navier–Stokes (RANS) equations coupled with the SST k-ω turbulence model. The averaged flow field properties of the pulsed jet are better than those of the steady jet when considering mixing efficiency and jet penetration depth, especially for the case with the pulsed frequency being 50kHz. The flow field structures of the pulsed jet are connected with the time, with periodic wave structures generating in the flow field and moving downstream. The size of the wave structures and its distance are related to the frequency, namely the size and flow distance are relatively small at 50kHz, and it takes some time for the pulsed jet to establish its influence in the full flow field. At low frequencies, the flow field produces large fluctuations, and this may be detrimental to the stable operation of the engine.

PERIODIC WAVE STRUCTURE OF THE FRACTAL GENERALIZED FOURTH-ORDER BOUSSINESQ EQUATION TRAVELING ALONG THE NON-SMOOTH BOUNDARY

In this study, we present a fractal generalized fourth-order Boussinesq equation which can describe the shallow water waves with the non-smooth boundary (such as the fractal boundary). Aided by the semi-inverse method, we establish its variational principle, which is proved to have a strong minimum condition via the He–Weierstrass theorem. Then, two powerful approaches namely the variational method (VM) and energy balance theory (EBT) are utilized to search for the periodic wave solutions. As expected, the results obtained by the two methods are almost the same. Furthermore, the impact of the fractal orders on the periodic wave structure is illustrated via the 3D plot and 2D curve. The results of this paper are expected to provide a reference for the study of periodic wave theory in fractal space.

Continuous limit and position adjustable rogue wave solutions for the semi-discrete complex coupled system associated with 4 × 4 Lax pair

In this letter, we propose a new semi-discrete complex coupled system associated with 4 × 4 Lax pair. Firstly, the continuous limit technique is used to map this semi-discrete system to two new continuous complex equations. Then, the discrete generalized (m,N−m)-fold Darboux transformation for this system is first proposed. Finally, through applying the resulting Darboux transformation, some novel rogue wave and periodic wave structures with position adjustable parameters are investigated and discussed graphically. In particular, it is found that in the same semi-discrete system, the first-order rogue wave can have one or two fundamental rogue waves, and the second-order rogue wave can have three or six fundamental rogue waves.

Doubly periodic wave structure of the modified Schrödinger equation with fractional temporal evolution

Abundant Jacobi elliptic type solutions with distinct physical structures of complex nonlinear conformable time-fractional modified Schrödinger equation are obtained by using the generalized Jacobi elliptic function (GJEF) method. The Jacobi function expansions may lead to new doubly periodic wave solutions, soliton solutions, and triangular periodic solutions. Nowadays the conformable operator is being used for a better description of the dynamical systems. Motivated by the potential applications of the governed equation in nonlinear optics, biological sciences, and fluid dynamics, these solutions may be significant in the study of wave propagation in the desired field. Symbolic computations are made with the aid of Maple.

Synthesis Method and Experimental Research of Ku-band Antennas Based on Tensorial Metasurfaces

Antennas based on metasurfaces with tensorial impedance is a relatively new type of antennas appeared in the last decade. They have a simple design, but a complex synthesis procedure. The synthesis procedure can be based on analysis of the properties of waves in periodic structures or on representing the antenna as a phase hologram. Due to the novelty of this type of antennas, researching of various synthesis methods, obtaining new experimental results and on their basis assessment of realistically achievable characteristics is of interest. The purpose of the work was an experimental research of antennas based on metasurfaces with tensorial surface impedance, synthesized according to the method proposed by the authors. To carry out the research, mathematical modeling, electrodynamic modeling, and nearfield measurements of antenna prototypes were used. As a result, it was experimentally confirmed that the proposed tensorial metasurface antennas synthesis method makes it possible to obtain antennas with a given radiation direction and polarization, which have an aperture efficiency of up to 50 %, a bandwidth of up to 8 %, and a cross-polarization level below minus 20 dB. The results of measurements are in a good agreement with the electrodynamic calculation and the parameters specified during the synthesis. The type of antennas described in the work and the given synthesis method, according to the authors, are promising for various applications, for example, in satellite and mobile communications

Multistability and dynamic behavior of non-linear wave solutions for analytical kink periodic and quasi-periodic wave structures in plasma physics

Multistability and dynamic behavior of non-linear wave solutions of unperturbed and perturbed with FitzHugh–Nagumo (FHN) equation is measured using analytical and numerical methods. For unperturbed model a variety of solitonic structures are calculated using a direct algebraic method. Thereafter, the examine model is transformed into a dynamic system with the help of the Galilean transformation and a bifurcation behavior is reported. To choose various particular values of the parameters, we determine single soliton, kinky periodic, bell type waves. In particular, we find both kink waves and the bright and dark bell type from solutions and interactions between waves at different times and solitons. In this work, the dynamics of the low-level model, which controls the interaction between the operator associated with a non-linear wave solution and the multi-stability due to periodic and quasi-periodic deviations, are investigated. Different kinds of cyclic firing diagram emanate abruptly saddle node bifurcations. The parameter territory in which different periodic solutions is also found. In addition, sensitivity analysis is used for a variety of initial values to analyze periodic and quasi-periodic behavior.

Design of circularly polarized planar leaky‐wave antenna using characteristic mode analysis

In the present study, a characteristic mode analysis (CMA) is proposed for the first time to design a periodic leaky-wave antenna (LWA). By applying CMA to the unit cell of a periodic travelling wave structure, the open stopband is suppressed and circular polarization (CP) radiation is achieved. Also, some parametric studies are added to clarify the design processes. Eventually, to optimize the design, the series and shunt analysis is applied to the unit cell of the periodic travelling wave structure. Based on the proposed analysis, a wideband CP long microstrip LWA (MLWA) is designed and simulated. The MLWA can sweep the main beam from around −30° to +10° continuously through broadside by sweeping the frequency from 7.5 to 12.25 GHz. The proposed structure is designed to have CP in the entire operating frequency. Eventually, the fabricated antenna showed excellent agreement between measured, modelled, and simulated results.

The Influence of Stationary Periodic Wave Structures on the Local Strength of an Ice Field

The influence of nonlinear wave structures on the local hardness of an ice field of a dynamic type of formation is studied. Wave structures are formed by the interference of flexural–gravitational and longitudinal waves. The source of oscillations is coherent radiation in the ice itself. The difference in the local hardness of ice in the nodes and antinodes of standing waves (up to 60%) is explained by the dynamic metamorphism of ice. The dependences of the local ice hardness on the coordinates in the longitudinal and transverse profiles of the ice field have the form of periodic curves. The texture scales were determined, and the phase surface of the wave structures was constructed, which is not monochrome and reflects the spatial heterogeneity of the strength properties of the ice field. The effect of the wave action depends on the conditions at the interface between the ice and the pool walls. The influence of wave structures on the strength properties of the ice field as one of the possible factors of the spatial variability of ice under various modes of occurrence in situ is quantified.

Nonlinear electron plasma waves in fully relativistic plasmas

Propagation of nonlinear electron plasma waves is investigated in a fully relativistic election-ion plasma using two-fluid hydrodynamic model. The relationship between pressure and density is assumed to be of polytropic form for relativistic electrons. The conditions for the validity of adiabatic equation of state for electron fluid is also discussed. The well-known pseudopotential approach is employed for arbitrary amplitude wave analysis and superluminous and subluminous wave phase speed cases are discussed in two special frames of references transformed under Lorentz-transformation. The set of model equations is solved analytically as well as numerically to obtain nonlinear periodic wave structures of electron plasma waves in a fully relativistic plasmas. A special case of solitary wave structure formed in subluminous phase speed case is also discussed in detail, which has not been done in the previous published literature. The effects of electron temperature and phase speed of the plasma wave (i.e., for subluminous and superluminous wave phase speed cases) on the amplitude of nonlinear periodic wave and solitary wave structures are also presented with its possible applications to the astorphysical environment.