Dispersion Phenomena Research Articles

Flexible dispersion engineering in metasurface-based leaky-wave antennas: leveraging spatio-temporally modulated impedance surfaces

This study aims to investigate dispersion engineering mechanisms within unilateral and bilateral metasurface-based leaky-wave antennas, presenting methodologies focused on space-time modulation of impedance boundary conditions. Utilizing the generalized framework based on the Floquet-wave expansion method, the research precisely investigates the effect of periodic space-time modulation on the dispersion characteristics of the leaky-wave antenna. The beam scanning mechanism has been investigated in the momentum and frequency domains. It is shown that by choosing the appropriate spatial-temporal variations in the boundary condition, the radiation beam may be steered in the desired direction and frequency. Through a comprehensive analysis encompassing parameters such as modulation depth, average surface impedance, and space-time modulation frequencies, the paper seeks to elucidate the intricate dynamics governing dispersion phenomena. Furthermore, the inquiry delves into the "rabbit’s ears" phenomenon observed in bilateral space-time modulated leaky-wave antennas. Distinguishing this phenomenon from the conventional pure-space modulated impedance boundary conditions, the research aims to uncover its underlying mechanisms and provide insights into the antenna performance. In addressing this phenomenon, the study also proposes adjusting the temporal pumping frequency as a potential strategy to mitigate the adverse effects associated with the rabbit’s ears phenomenon.

The Multi-Soliton Solutions for the (2+1)-Dimensional Caudrey–Dodd–Gibbon–Kotera–Sawada Equation

The (2+1)-dimensional integrable Caudrey–Dodd–Gibbon–Kotera–Sawada equation is a higher-order generalization of the Kadomtsev–Petviashvili equation, which can be applied in some physical branches such as the nonlinear dispersive phenomenon. In this paper, we first present the bilinear form for this equation after constructing one Bäcklund transformation. As a result, the one-soliton solution, two-soliton solution, and three-soliton solution are shown successively and the corresponding soliton structures are constructed. These solitons and their interactions illustrate that the obtained solutions have powerful applications.

Computational and numerical solutions to the Benney–Luke equation: Insights into nonlinear long wave dynamics in dispersive media

The current investigation seeks to explore the nonlinear Benney–Luke model, a governing equation pertinent to the propagation of extended waves within dispersive media, such as those observed in water waves and plasma waves, among other nonlinear wave phenomena. This model is distinguished by its incorporation of both dispersive and nonlinear effects, rendering it a valuable instrument for delving into intricate wave dynamics. Notably, it shares similarities with other prominent nonlinear evolution equations, including the Korteweg–de Vries (KdV) equation and the Boussinesq equation, both of which have been extensively examined within the domain of water waves and associated phenomena.Employing analytical methodologies, specifically the Khater (Khat III) and modified Kudryashov (MKud) methods, the research endeavors to derive exact solutions for the Benney–Luke equation. These solutions serve to elucidate various aspects of long wave behavior in dispersive media, encompassing their propagation characteristics, stability, and potential for inter-wave interactions. Furthermore, a trigonometric-quantic-B-spline (TQBS) scheme is adopted as a numerical approach to corroborate the precision of the derived analytical solutions and demonstrate their relevance across diverse physical scenarios linked to the model under examination.The research outcomes underscore the efficacy of the analytical techniques in generating dependable solutions for the Benney–Luke model. Moreover, through the utilization of the TQBS numerical scheme, the accuracy of the derived analytical solutions is affirmed, thereby ensuring their pragmatic utility across a spectrum of physical scenarios pertinent to the investigated model. This endeavor holds significance in its contribution towards advancing the comprehension of nonlinear wave phenomena within dispersive media, with ramifications spanning multiple disciplines, including fluid dynamics, plasma physics, and nonlinear optics. The novelty of this study lies in its application of the Khater (Khat III) and modified Kudryashov (MKud) methods to the Benney–Luke equation, alongside the integration of the TQBS numerical scheme for solution validation. Positioned within the domain of nonlinear partial differential equations, this research aligns with its broader applications in physics, particularly concerning the investigation of dispersive wave phenomena.

Attenuation effects of seismic metamaterials based on local resonance and Rayleigh wave dispersion phenomena

Attenuation effects of seismic metamaterials based on local resonance and Rayleigh wave dispersion phenomena

Understanding of quasilinear hyperbolic systems through the investigation of their asymptotic solutions

The main aim of the study is to deepen understanding of quasilinear hyperbolic systems through the investigation of their asymptotic solutions, with specific objectives related to theoretical analysis, wave dynamics characterization, and practical applications in physics and engineering. The methods of mathematical analysis employed include asymptotic analysis, Taylor series expansions, and the formulation of transfer equations. The paper considers systems of quasilinear hyperbolic equations in partial derivatives of the first order with two independent variables. The main results of the paper are: 1) high-frequency asymptotic solutions of small amplitude for quasilinear hyperbolic systems of the first order were obtained. For fixed values of t and , values of the modulus are limited by р→∞, because the transfer equations depend on p. Thus, the moduli of the decomposition coefficients are bounded at p→∞ and at fixed u and ; 2) It has been established that for ui0= const, , , independent of t, the solution of the equation is greatly simplified because the coefficient а0 is constant. For the linear function , is also constant. Practical applications of the results lie in fields such as fluid dynamics, wave propagation, and materials science, where understanding dispersion phenomena is crucial.

Congo Red Dye Removal from Aqueous Solutions by Photocatalytic Redox Reactions Using Anatase Nano-TiO2 as a Heterogeneous Catalyst: Degradation Kinetics and Simulation Using Dispersion Model

Water pollution caused by Congo red as a textile dye is a significant concern for the aquatic environment. The photocatalytic redox reactions were carried out in a closed batch photoreactor using 0.2 g/L Anatase nano-TiO2 as a catalyst to remove different initial concentrations (32, 71, and 178 ppm COD) of the dye from its neutral aqueous solutions at 40℃. The air was supplied to the reactor as an oxygen source at a rate of 0.2 L/min. The COD removal values decreased with the increasing initial dye concentration, and the best removal value was recorded (89.47 %) for the lowest initial COD (32 ppm) after 255 minutes of radiation. The kinetics study showed that the Congo red dye removal followed a first-order reaction model. A mathematical model was developed based on the axial dispersion phenomenon to simulate the product distribution of the dye through several types of reactors (ideal and nonideal plug flow and mixed flow reactors). Effects of initial concentration, dispersion number, and space-time on the organic distribution through the reactors were studied and discussed. The simulated results show that the ideal plug flow reactor (zero dispersion) performance was better than that of the nonideal plug flow reactor, and the performance decreased with the increasing dispersion number and gave the worst performance in the mixed flow reactor (infinity dispersion).

Dynamic Phase Behavior of Amorphous Solid Dispersions Revealed with In Situ Stimulated Raman Scattering Microscopy.

This study reports the application of in situ stimulated Raman scattering (SRS) microscopy for real-time chemically specific imaging of dynamic phase phenomena in amorphous solid dispersions (ASDs). Using binary ritonavir and poly(vinylpyrrolidone-vinyl acetate) films with different drug loadings (0-100% w/w) as model systems, we employed SRS microscopy with fast spectral focusing to analyze ASD behavior upon contact with a dissolution medium. Multivariate unmixing of the SRS spectra allowed changes in the distributions of the drug, polymer, and water to be (semi)quantitatively imaged in real time, both in the film and the adjacent dissolution medium. The SRS analyses were further augmented with complementary correlative sum frequency generation and confocal reflection for additional crystallinity and phase sensitivity. In the ASDs with drug loadings of 20, 40, and 60% w/w, the water penetration front within the film, followed by both surface-directed and bulk phase separation in the film, was apparent but differed quantitatively. Additionally, drug-loading and phase-dependent polymer and drug release behavior was imaged, and liquid-liquid phase separation was observed for the 20% drug loading ASD. Overall, SRS microscopy with fast spectral focusing provides quantitative insights into water-induced ASD phase phenomena, with chemical, solid-state, temporal, and spatial resolution. These insights are important for optimal ASD formulation development.

Dispersion phenomena in EIS and DIS spectra of porous materials and their representation as transmission line bases ‘diffusion’ elements– part II - a case study of proton conductors

Porosity of materials, understood as an overall averaged parameter or as the pore-size distribution related data is an important quality of numerous functional materials including proton conductive glasses. While most of the existing techniques applied for its assessment cannot be used to monitor the behaviour of ‘live’ systems in operando conditions, it is possible to use Electrochemical Immittance Spectroscopy (EIS) for this purpose. Nevertheless, analysis of these systems still requires an approximation made using transmission lines based models, which can be equated to specific diffusion elements parameters, which can in turn be related to qualities of the porous material investigated. The changes of these parameters can be correlated with various processes– such as dehydration and phase transitions or to the material’s processing history. In this part of the material we present a case study of highly grinded, mechanochemically processed powder-pressed proton conductors: phosphate-silicate glass and two uranyl based compounds– hydroxy phosphate (HUP) and hydroxy arsenate, delivering proof that the dispersive properties of proton transporting materials can be correlated with their dehydration processes, which were followed by means of FT-IR and terahertz time domain spectroscopies.

An application of the DEM-FFT method to predict the thermal conductivity of high burnup fragmented fuel

Understanding Fuel Fragmentation, Relocation and Dispersal (FFRD) phenomena is a major item to predict the behavior of fuel rods in the event of a Pressurized Water Reactor loss-of-coolant hypothetical scenario. In order to introduce an effective medium for fragmented fuel that could be used in fuel performance codes, the heat transfer properties of UO2 granular beds in He-Kr-Xe gas mixes was studied numerically. The Discrete Element Method was first used to compute the spatial arrangement of fragments only submitted to gravity with a representative granulometric distribution. These generated geometries were then transformed into a 3D grid (voxelized) to perform numerical homogenization and compute their effective properties using a Fast Fourier Transform solver for heat transfer. Different hypotheses were made in the voxelation process about the treatment of gas-solid and solid-solid interfaces, which in turn provided different estimates of the effective properties. Due to limits on the discretization and extended particle size distributions, a two-scale scheme was introduced and numerically tested against direct computations. For several granular beds, computed thermal conductivities were compared to analytical models for granular materials. Some heat transfer properties of fragmented fuel at several burnups were then computed, taking into account approximations for Knudsen and radiation size effects.

Study on the phase transition characteristics of nano-hydrated salts based on molecular dynamics simulations

Hydrated salts possess great competitiveness in terms of enhancing utilization efficiency of heat due to large densities of heat storage and low costs. However, the existence of supercooling degree is the common phenomenon for hydrated salts, which might restrict the application prospects in partial fields. This work focuses on hydrated salts with relatively larger latent heats, namely Na2CO3·10H2O and Na2HPO4·14H2O in the absence and presence of SiO2 as well as eutectic hydrated salt prepared with 40 wt% Na2CO3·10H2O and 60 wt% Na2HPO4·12H2O. Their melting/solidification temperatures were determined and the supercooling behavior was analyzed based on molecular dynamics simulations. The simulation results of melting/solidification temperatures present small deviations of 0.17–3.24 ℃ in comparison with the experimental data. Additionally, the aggregation phenomenon among salt ions and dispersion phenomena among water molecules and between water molecules and salt ions for supercooled liquid hydrated salts are revealed, which are attributed to stronger electrostatic interactions and weaker van der Waals interactions as well as lower binding energies. Moreover, SiO2 not only lowers the melting temperatures due to its larger thermal conductivity than hydrated salts and the existence of micro-convection, but affects solidification behavior of hydrated salts. The different influences of SiO2 on the solidification temperatures of Na2HPO4·14H2O and Na2CO3·10H2O were associated with dispersion degree between water molecules and salt ions around SiO2, which would be attributed to different strengths of interaction forces between SiO2 and salt ions. On these bases, this work provides new perspectives for clarifying the phase change characteristics of nano-hydrated salts.

Modeling Rayleigh wave in viscoelastic media with constant Q model using fractional time derivatives

The propagation of seismic waves within the near-surface weathering layers, characterized by their low-quality factors (Q), is often accompanied by strong attenuation and dispersion phenomena. Among these, the Rayleigh wave, with its sensitivity to dispersion, has proven to be a powerful tool for near-surface exploration. We propose a novel approach for simulating Rayleigh wave propagation in such low-Q media. Our method uses the time-domain fractional wave equation with memory effect, based on Kjartansson's constant-Q (CQ) model, for accurate characterization of the propagation process. To solve numerically the wave equation with the fractional derivatives, we employ a finite-difference method combined with the auxiliary differential equation-perfectly matched layer (ADE-PML) and the acoustic-elastic boundary approach (AEA). The algorithm's high computational accuracy is verified through comparison with the conventional integer-order wave equation based on the nearly constant-Q (NCQ) models in strong attenuation media. The research in this paper deepens our understanding of the propagation characteristics of Rayleigh waves in strongly weathering layers. This new method strongly supports those seismic imaging and inversion methods depending on seismic modeling, including the reverse time migration and the full waveform inversion of the internal structure of low-Q media.

Dispersion phenomena in EIS and DIS spectra of porous materials and their representation as transmission line bases ‘diffusion’ elements—part I: a case study of lead-acid systems

A number techniques exist to assess the porosity of materials, however a large number of them cannot be used to monitor the behaviour of such in ‘live’ systems. This problem can be overcome by the usage of Electrochemical Impedance Spectroscopy (EIS). However, porous systems and their qualities, can not be easily described using regular equivalent circuit and basic elements. An approximation of such has to be made using transmission lines, which can, in turn, be equated to specific diffusion elements. The parameters of these elements can be related to porous material qualities. And in turn, the changes of these parameters can then be related to various processes—such as ageing or degeneration. In this part of the material a case study was performed on a number of lead-acid systems—a VRLA battery, a maintenance-free one and system consisting of a lead electrode and a platinum mesh counter electrode. This was done in order to test the validity of using the Warburg impedance element in equivalent circuits. During the course of the tests it was found that not only a Gerischer element is a better choice, but the changes in its parameters can be related to different ageing-related processes.

Chaos analysis and traveling wave solutions for fractional (3+1)-dimensional Wazwaz Kaur Boussinesq equation with beta derivative

Wazwaz Kaur Boussinesq (WKB) equation can effectively simulate the behavior of water waves in shallow water, including the nonlinear effect and dispersion phenomenon of waves, which is of great significance for understanding the dynamic process of ocean, river and other water bodies. To enrich the wave equation theory, the (3+1)-dimensional integer order derivative of WKB equation is changed to the fractional one with beta derivative. The current work deals with the fractional (3+1)-dimensional WKB equation for discussing its chaotic behavior and establishing some new analytic solutions. The chaotic properties of the equation are verified by the trend of evolution along with time, Lyapunov exponents and initial sensitivity analysis. And then complete discrimination system for polynomial method is applied to derive some trigonometric, hyperbolic, Jacobi elliptic and other solutions. The graphical demonstrations are provided for part of these solutions. From these visualized graphs, the solitary, periodic and quasi-periodic wave are shown and the effect of fractional derivatives on the equation can be seen intuitively.

Study of multiferroic properties of Mn substituted Bi0.8Sm0.1Dy0.1Fe1-xMnxO3 ceramics

Abstract Transition metal Mn substituted various multiferroic Bi0.8Sm0.1Dy0.1Fe1-xMnxO3 (x = 0.00, 0.01, 0.03 and 0.05) ceramics samples were fabricated by the solid-state reaction technique. The distorted rhombohedral perovskite structure with some phase impurity of all samples is confirmed by X-ray diffraction analysis. Field Emission Scanning Electron Microscope and Energy Dispersive X-ray spectroscopy are used for microstructural and quantitative analysis, respectively. Densities are decreased and the average grain size is increased with Mn contents. The initial permeability and relative quality factor (RQF) have found to be increased with Mn contents in the samples. The peaks in RQF shifts toward the lower frequency region with increasing Mn contents can be attributed by Snoek’s relation. All the samples show paramagnetic behavior at room temperature and magnetization slightly increases with Mn contents. The frequency dependent dielectric constant is investigated and found to consequence of space charge polarization. The dispersion behavior in dielectric constants can be explained by the Maxwell-Wagner model. The dielectric constants and dielectric loss decrease with increasing of Mn contents for all the samples. The value of electric modulus is observed to increases with the increasing of frequency and this dispersion phenomena is due to short range mobility of charge carriers in conduction. The effect of grain and grain boundaries on electric properties of samples are investigated by complex impedance analysis. The ac conductivity increases with frequency due to small polaron hopping and it can be attributed according to Jonscher’s power law.

Exchanging “Mementos of Death”: Holocaust Remains in Poland and Japan

Abstract In 1962, a Japanese delegation of peace activists visited Auschwitz-Birkenau where they participated in the annual ceremony commemorating the liberation of the camp. As part of the ceremony, the delegation engaged in an exchange of Hiroshima and Auschwitz “memontos,” receiving from the Polish side, amongst others, an urn containing ashes of the victims of the camp. The exchange was the first of several that included Holocaust urns, most of which are now in Japan, and a part of a much broader phenomenon of material dispersal of human remains instituted by Polish museums established at the former Nazi camps. In this paper, we take a critical look at this practice, its development, directionalities and meanings. Tracing the journey of the urns and their various uses, we argue, reveals the complex politics and cultural landscape of the transnational commemoration of World War II in its very local meanings in Poland, Japan and beyond.

Lax integrability and nonlinear dispersive wave phenomenon for the (3 + 1) dimensional Kudryashov–Sinelshchikov equation

A (3 + 1) dimensional Kudryashov–Sinelshchikov equation is investigated in this paper, which describes bubbles in the liquid fluctuations. By virtue of the binary Bell polynomials, the bilinear representation, bilinear Bäcklund transformation with associated Lax pair are obtained, respectively. Moreover, utilizing Hirota’s bilinear representation, four new lump solutions are constructed and the interaction phenomenon between lump and periodic solution is thoroughly examined. The work also illustrates the intriguing dynamical behavior with the aid of Maple software, which plots the three-dimensional surface, two-dimensional density, and contour profiles of the solutions constructed in this work in various planes.

Elastic reverse time migration using an efficient and accurate adaptive variable grid discretization method

Abstract The conventional reverse time migration utilizes regularly sampled computational grids to simulate wave propagation. Selecting the appropriate grid sampling is important for computational accuracy and efficiency. In general, the uniform-size grid cannot represent the complexity of the geology well. The grid may appear sparse in the low-velocity zone, especially in shallow depths where dispersion may occur. Conversely, it may appear excessively dense in the high-velocity zone, such as at greater depths or within a salt body, which results in higher computational memory and time consumption. To overcome these issues, we developed an efficient and accurate adaptive variable grid discretization method that automatically selects the vertical grid size based on the velocity, depth, and dominant frequency of the wavelet in elastic medium. Then we reformulated the elastic equations based on the adaptive variable grid by introducing a mapping relationship. To test the effectiveness, accuracy, and efficiency of the equation, we implemented it to both the forward propagation and migration of elastic wavefield. Synthetic numerical examples demonstrate that our proposed method can achieve elastic wavefield separation and no significant dispersion phenomenon. The multi-component imaging accuracy of reverse time migration is nearly equivalent to the traditional method, while significantly improving computational efficiency and saving storage space.

Validation and parametric study of FFRD model in DRACCAR code

The recent revision of Emergency Core Cooling System (ECCS) regulations in Korea has necessitated the consideration of Fuel Fragmentation, Relocation, and Dispersal (FFRD) phenomena in nuclear reactor safety analyses. Consequently, the Korea Atomic Energy Research Institute (KAERI) has developed and integrated the FFRD model into the domestically licensed safety analysis code, SPACE. Globally, US NRC’s FRAPTRAN and IRSN’s DRACCAR are available for evaluating FFRD phenomena. The FRAPTRAN code incorporates the FFR model, developed by Quantum Technology, while the fuel dispersal model is currently not included. In contrast, the DRACCAR code functions as an integrated analysis platform capable of modeling multi-dimensional thermal, hydraulic, mechanical, and chemical phenomena during a Loss of Coolant Accident (LOCA). This study conducts a thorough examination of the FFRD model in the DRACCAR code and validates its applicability through analysis using the Halden IFA-650 tests. The results demonstrate satisfactory predictive capabilities. Furthermore, a parametric study of key FFRD model parameters enhances the understanding of the FFRD model in the DRACCAR code. The development of detailed physical models in the FFRD model could significantly enhance the performance of the DRACCAR code, warranting the establishment of a comprehensive framework for these advancements. In the future, code-to-code comparisons between the DRACCAR code and other domestically developed integrated analysis platforms will be conducted to investigate various phenomena in depth.

NUMERICAL COMPUTATION OF ONE- AND TWO-LAYER SHALLOW FLOW MODEL

In this research, we study a proficient computational model designed to simulate shallow flows involving one- and two-layer shallow flow. This numerical model is built upon the Saint Venant equations, which are widely used in hydraulics to depict the behavior of shallow water flow. The numerical scheme used here is constructed based on the conventional leapfrog technique implemented on a staggered grid framework, referred to as MCS. The primary objective of this research is to re-examine and implement the MCS in accurately modelling the free surface and interface waves produced by different flows passing through irregular geometries. Unlike the conventional MCS, we modify the momentum conservation principle to be more general, accommodating a non-negative wet cross-sectional area due to irregular geometry. We successfully conduct numerous numerical simulations by examining various scenarios involving one-layer and two-layer flow through irregularly shaped channels or structures. Our results show that the correct surface wave profile generated by a one-dimensional dam break through the triangular obstacle in the open channel can be simulated very well. Comparison with the existing experimental data seems promising although some disparities are being found due to dispersive phenomena with RMSE less than 5%. Furthermore, our scheme is successfully extended to simulate the steady sub-maximal exchange in two-layer flows using specific boundary conditions. The alignment between the submaximal numerical results with exchange flow theory is noticeable in the interface profile, characteristics of flow conditions and the flux values achieved when the steady situation occurs. These satisfying results indicate that our proposed numerical model can be used for practical needs involving various flow situations both one and two-layer cases

Study of inclusions-removal and slag-metal dispersion phenomenon in gas-stirred ladle

Abstract The slag-metal interface serves as a crucial locus for both chemical reactions and the adsorption of inclusions during secondary refining. This study first comprehensively reviews the methods of inclusions removal and then establishes a cold-state experiment using a water-oil system to reappear the phenomenon of slag-metal dispersion and inclusion adsorption. The distribution of slag droplets under varying slag volumes is analyzed in terms of the effect of bottom blow rates. Simultaneously, the volumetric fraction of oxygen on the slag-eye surface is analyzed. The result proved that the increase in oil layer thickness or the gas flow rate increase the volume of entrained oil. The dimensionless depth of entrained droplets was positively associated with gas flow rate or oil thickness. The dimensionless depth of “large droplets” and “small droplets” was in the range of 0–25 % and 0–60 %, respectively. Moreover, analysis of the gas composition above the slag-eye in a water-oil system is used to determine the degree of secondary oxidation. The oxygen volume fraction over the surface of the slag-eye decreases with the increase of gas flow rate. The oxygen volume fraction over the surface of the slag-eye is 1.51 % when the gas flow rate is 9 L/min.