Behavior Of Waves Research Articles

Wave propagation and soliton behavior in biomechanical tissues: A mathematical approach

This study presents a mathematical model for understanding wave propagation and soliton behavior in biomechanical tissues, explicitly focusing on the Achilles tendon. Utilizing the Korteweg-de Vries (KdV) equation, the research incorporates the Achilles tendons’ nonlinear elastic and viscoelastic properties to explore how mechanical waves propagate through this complex tissue. The tendon’s nonlinear elasticity leads to wave steepening, while its viscoelasticity introduces dispersive effects that counteract this steepening, resulting in the formation of solitons—stable, localized waves that maintain their shape as they propagate. Key findings from this study reveal that the formation and propagation of solitons are strongly influenced by the tendon’s mechanical properties. Numerical simulations show that stiffer tendons, characterized by a higher elasticity modulus, support faster soliton propagation, with wave speeds ranging from 18.9 m/s in damaged tendons to 28.6 m/s in stiffened tendons. Additionally, soliton amplitude increases with tissue stiffness, with the highest amplitude observed in stiffened tendons (5.1 mm) and the lowest in damaged tendons (3.2 mm). The study also demonstrates that energy dissipation due to the tendon’s viscoelasticity plays a critical role in soliton behavior. Damaged tendons exhibit the highest energy loss (18.6%), leading to shorter soliton propagation distances, while stiffer tendons retain more energy (96.1%) and allow solitons to travel further distances (up to 180 mm). Moreover, the balance between nonlinearity and dispersion is crucial for maintaining soliton stability. Excessive nonlinearity leads to unstable solitons, while higher levels of dispersion contribute to more stable waveforms.

Experimental Measurements of Explosion Effects Propagating in the Real Geological Environment—Correlation with Small-Scale Model

This research focuses on comparing small-scale and full-scale measurements of wave propagation from explosions by using scaling relationships to find significant correlations between the two. The study investigates how seismic waves generated by explosions behave in the geological environment. The research covers various aspects such as the development of the model, the explosive materials used, measurement methods, evaluation techniques, and relevant software. A scientific approach based on the principle of backward Fourier transform was used to process and evaluate the data, which helps to filter the frequencies. One of the important calculations discussed is the determination of the attenuation coefficient, which helps to describe how waves attenuate as they pass through a material. The research also deals with dynamic scaling, using the dynamic exponent as a scaling factor to provide a better understanding of the behavior of waves at different scales. By comparing real in situ data with results from small-scale models, the study provides a robust framework for predicting the effects of explosions in complex geological environments. The research results show a high correlation coherence of the statistical data files of up to 4.1%. For dynamic tasks and model scaling, an important result can be pointed out, namely the approximately fourfold decrease in the exponents of the dependence on the distance from the excitation source and the amplitudes between P-waves (0.4316) and R-waves (0.1219). Conclusions are targeted at the possibility of correlating three types of results: small-scale simulations, numerical simulations, and a real full-scale experiment.

Generalized kudryashov and extended auxiliary equation methods for novel solitons solutions to (1+1)-dimensional doubly dispersive equation of murnaghan’s rod

Abstract In this study, the Generalized Kudryashov method and the Extended Auxiliary Equations method are employed to investigate the strongly nonlinear (1+1)-dimensional Doubly Dispersive equation model of inhomogeneous Murnaghan’s rod for developing novel soliton solutions. These symbolic methods are famous for solving various problems involving nonlinear partial differential equations. The study finds novel solitons like hyperbolic, exponential, rational, and trigonometric. Moreover, 2D, 3D, and contour plots under tunable parameters depict graphical representations of the solutions that furnish dynamic wave behavior and insights into the material’s elastic properties under strain and stress.

Abstract 4139162: Optical coherence tomography measures mechanical contractile properties of the beating murine heart

Introduction: Optical imaging techniques can characterize properties of tissue at high temporal and spatial resolution, offering unique insights into electrically excitable tissues such as nerve and muscle. We hypothesized that the gated high-speed optical coherence tomography (OCT) could profile the contractile properties of mouse myocardial tissue and facilitate investigations of microscale mechanical function in the beating heart. Methods: C57BL/6 male mice (n=6) underwent a sternotomy while anesthetized and ventilated and were imaged at baseline with OCT. Another cohort of C57BL/6 male mice (n=6) were sacrificed and the hearts were ex vivo perfused with crystalloid using a Langendorff system. These hearts were imaged at baseline and after inhibition of contractile function with blebbistatin. OCT was performed using a custom tissue stabilizer and a Thorlabs TEL 321 OCT system, which was synchronized to physiologic signals using custom hardware and software and cardiac pacing protocols (Fig. 1A and 1B). OCT cross-sectional B-scan images (Fig. 1C) were obtained throughout multiple cardiac cycles in both in vivo and ex vivo preparations. Data were processed in MATLAB and ImageJ using the workflow in Fig. 1D. Results: Highly reproducible cross-sectional mean intensity changes were observed over the contractile cycle in vivo and ex vivo (Fig. 1E, left and middle). With mechanical contraction inhibited by blebbistatin, this cyclical intensity extinguished, linking the optical scattering change measured by OCT to myocardial contraction (Fig. 1E, right). B-scan curves averaged over multiple mice and temporally aligned with the ECG waveform (Fig. 1F) demonstrate a signal intensity waveform that reproducibly varies with the contractile cycle for both in vivo and ex vivo preparations. In vivo and ex vivo baseline waveforms both had peak intensity during systole and minimum in end-diastole (Fig. 1F). Reproducibility in ex vivo beating heart preparations without blood perfusion provides evidence that myocardial mechanical properties, not red blood cell flow, generate the intensity changes. Conclusion: Gated high-speed OCT imaging can quantify the mechanical contraction wave in the myocardium. Combined with gated OCT angiography, OCT techniques will provide high resolution imaging of both blood flow and mechanical contractility of the beating heart in small animal models of heart disease.

Exact boundary-value solution for an electromagnetic wave propagating in a linearly varying index of refraction

The propagation of electromagnetic waves in a linearly varying index of refraction is a fundamental problem in wave physics, being relevant in fusion science for describing certain wave-based heating and diagnostic schemes. Here, an exact solution is obtained for a given incoming wavefield specified on the boundary transverse to the direction of inhomogeneity by performing a spectral, rather than asymptotic, matching. Two case studies are then presented: a Gaussian beam at oblique incidence and a speckled wavefield at normal incidence. For the Gaussian beam, it is shown that when the waist $W$ is sufficiently large, oblique incidence manifests simply as rigid translation and focal shift of the corresponding diffraction pattern at normal incidence. The destruction of the hyperbolic umbilic caustic (corresponding to a critically focused beam) as $W$ is reduced is then demonstrated. The caustic disappears once $W \lesssim \delta _a \sqrt {L}$ ( $L$ being the medium length scale normalized by the Airy skin depth $\delta _a$ ), at which point the wave behaviour is increasingly described by Airy functions, but experiences less focusing as a result. To maximize the intensity of a launched Gaussian beam at a turning point, one should therefore minimize the imaginary part of the launched complex beam parameter while having the real part satisfy critical focusing. For the speckled wavefield, it is shown that the transverse speckle pattern only couples to the Airy longitudinal pattern when the coupling parameter $\eta = \sqrt {L}/f_{\#}$ is large, with $f_{\#}$ being the f-number of the launching aperture. When $\eta \ll 1$ , a reduced description of the total wavefield can be obtained by simply multiplying the incoming speckle pattern with the Airy swelling.

New analytical wave structures for generalized B-type Kadomtsev–Petviashvili equation by improved modified extended tanh function method

Abstract Recently, solving the complicated nonlinear partial differential equations has become very important demand in order to simulate their physical phenomena. This manuscript focuses on extracting the wave solutions of (3 + 1)-dimensional generalized B-type Kadomtsev-Petviashvili equation (GBKPE), which demonstrates the behavior of nonlinear waves in fluid mechanics. The improved modified extended Tanh function (IMETF) method is the suggested method to do this task as it gives different types of solutions. This method enables us to obtain many solutions, such as Jacobi elliptic, dark soliton, and singular soliton, exponential, and singular periodic wave solutions. Additionally, for more illustrations graphical visual representations of some solutions are provided.

Instability of isolator shocks to fuel flow rate modulations in a strut-stabilised scramjet combustor

Abstract Reynolds-Averaged Navier–Stokes (RANS) simulations, both steady and unsteady, are used to investigate supersonic, chemically reacting, flow fields inside a strut-stabilised supersonic combustion ramjet (scramjet) engine operating under different fuel flow rates. Fully supersonic, fully subsonic and mixed modes of operations inside the combustor, obtained at different fuel flow rates, are studied numerically through shock wave visualisations and top-wall static-pressure probing. The effect of changing fuel flow rates, imposed both suddenly and gradually, on the behaviour of shock waves and wall pressure profiles are studied in detail. For certain modes of combustion characterised by the presence of oblique shocks at the strut, shockwaves in the combustor respond predictably to an increase or decrease in fuel flow rate attaining the steady state flow fields as predicted by RANS simulations for those fuel flow rates. For certain other modes of combustion, characterised by the presence of shockwaves in the isolator and the absence of oblique shocks at the leading edge of the strut, shockwaves in the flow field appear unstable to fuel flow rate modulations. For such cases, any change in fuel flow rates, sudden or gradual, increase or decrease, causes the isolator shocks to immediately move upstream and eventually out of the isolator. A plausible physics-based explanation of the observed phenomena is presented.

Manipulation of circular polarization and mechanical waves in gyroscopic metamaterials

Manipulation of circular polarization and mechanical waves in gyroscopic metamaterials

Exploring stoneley wave behavior in size-dependent couple stress solids with imperfect interfaces under Wiechert conditions

Exploring stoneley wave behavior in size-dependent couple stress solids with imperfect interfaces under Wiechert conditions

Einstein’s spacetime curvature and gravitational waves: Elucidating the gradient flow of scalar invariants, variations in the Ricci scalar, and gravitational wave propagation

In the general theory of relativity initially rationalized by Einstein, the gravity is considered as an occurrence ensuing from the spacetime curvature, which is in turn triggered by the presence of mass. This article provides a detailed analysis of spacetime curvature and gravitational waves, enhancing our understanding of general relativity and astrophysics. Using both analytical and numerical methods, we examined the gradient flow of scalar invariants, variations in the Ricci scalar, and gravitational wave propagation. New findings include the identification of unique curvature patterns around rotating black holes, a detailed comparison of gradient flow behavior in different spacetime geometries, and the discovery of a correlation between scalar invariant fluctuations and gravitational wave amplitudes. These findings validate numerical techniques and reveal how different parameters affect gravitational wave characteristics. While simplified models are used, the present study offers a robust framework for future research. Our work aligns with previous studies but also reveals unique aspects of wave behavior, with implications for quantum gravity and cosmology.

Tin can telephone-inspired self-powered mechanical wave communication integrated with self-charge excitation triboelectric nanogenerator

As an alternative to electromagnetic wave communication, mechanical waves (MW) retain their advantage in several aspects, including cost-effectiveness, simplicity, interference resistance, and short-distance transmission. Here, a string-vibrated self-powered mechanical wave communication system (SSMWC) is proposed. Inspired by tin can telephone, modulated voltage signals are converted into MW by a vibrator and then transmitted along a string to the receiver. The receiver integrates a string-vibrated triboelectric nanogenerator (SV-TENG) and a self-charge excitation triboelectric nanogenerator (SCE-TENG). The SV-TENG can detect MW and convert them into electrical signals without external power sources, while the SCE-TENG is integrated to improve the sensitivity of the receiver. After charges pumping of SCE-TENG, the average output of SV-TENG can increase by 88 times within the frequency range of 0-1000Hz, indicating the successful application of self-charge excitation in triboelectric sensing for the first time. Furthermore, a demonstration of information coding and real-time decoding proves the potential application of SSMWC as an alternative in specific environments. This work shows the breakthrough of the bottlenecks faced by triboelectric sensors that the essential preparatory contact electrification before packaging, which indeed affect sensitivity and durability. Therefore, this scheme can be widely applied for output enhancement, especially for triboelectric sensors with lower output.

Diurnal Off-Mountain Propagation of Rainfall and Low-Level Vertical Velocity over the Lee Side of the Yungui Plateau

Abstract Diurnal off-mountain propagation is a distinctive feature of rainfall over terrestrial areas, whereas the causes of this phenomenon are not well understood. Focused on the rainfall downstream of the Yungui Plateau (YGP), this study aims to examine whether the gravity waves stimulated by an assumed terrain-related thermal forcing could explain the feature. The results show that the rainfall diurnal phase propagates eastward at a speed of approximately 13 m s−1 over the lee side of YGP during warm seasons. The diurnal amplitude reaches its zonally maximum over the slope of the YGP and drops sharply downstream the terrain. The low-level vertical velocity exhibits similar diurnal characteristics. A linear model forced by a hollow heating is proposed to mimic the thermal forcing related to a mountain. Experiments with the model show that there are mainly two branches of waves around the terrain. One is over the upstream with upwind-tilting phase lines that move toward −z and −x directions. The other branch exists over the lee side of terrain with downwind-tilting phase lines that move toward −z and +x directions, which is considered to be relevant to the off-mountain propagation feature. The wave behavior over the YGP is then reproduced using the model. It is shown that the main features of the diurnal phase lag and the zonal amplitude distribution pattern of the low-level updraft could be captured by the model, suggesting an important role of the gravity wave in driving the diurnal propagation of vertical velocity and rainfall downstream large terrains. Significance Statement The purpose of this study is to better understand why diurnal off-mountain rainfall propagation exists over the downstream of Yungui Plateau (YGP). This is important because the off-mountain rainfall propagation influences the rainfall events over the lee side of mountains and can further influence people’s lives therein. Inspired by previous studies on coastal rainfall, we proposed a simplified linear gravity wave model forced by a topography-related heating function. The results showed that the thermally forced gravity waves could reproduce the main features of the propagating phase and amplitude pattern of upward motion disturbance over the lee side of the YGP. Our results highlight the importance of gravity waves stimulated by topography-related heating on the diurnal propagation features over the downstream of mountains.

Polarization-Selective Metamaterial Absorber Using Tailored Y-Shaped SRR for UWB Device and Doppler Navigation Aids Applications

In this paper, we present an unprecedented metamaterial absorber design exhibiting exceptional characteristics in electromagnetic wave absorption. The proposed bent Y-shaped structure, fabricated on an FR-4 substrate with copper patches, showcases remarkable performance across a diverse frequency spectrum. Through exhaustive simulations in CST, this design manifests eight distinct resonant frequencies, achieving absorption rates exceeding 90% at each resonance. The resonances, strategically spanning from L-band (3.728 GHz) through S-band, C-band, X-band, Ku-band, and K-band up to 22.664 GHz, signify unparalleled versatility and efficacy in mitigating electromagnetic radiation. It investigates the equivalent circuit parameters of a proposed metamaterial absorber design, focusing on inductance (L), capacitance (C), and resistance (R). This paper investigates the applications of UWB devices at 3.728 GHz and Doppler navigation aids at the 13.4 GHz frequency as regulated by the Federal Communications Commission. It includes a discussion on near-zero refractive Index Metamaterials (NZRIM), highlighting their potential utilization in achieving extraordinary control over wave behaviour. Notably, the absorber's inherent polarization insensitivity fortifies its adaptability in various applications. Additionally, the metamaterial exhibits near-zero or negative permittivity, altering electric response, while simultaneously demonstrating permeability absolute zero throughout all frequency bands sparking new avenues for exploration and challenging conventional electromagnetic theories.

A new approach to the description of plasma Langmuir waves

After finding an exact solution to the Vlasov–Boltzmann kinetic equation (i.e., finding distribution functions for plasma particles), we consider the description of Landau damping using Poisson's equation, since with the complete distribution function, there is no need to split the kinetic equation into equilibrium and perturbed parts for the subsequent implementation of the pole bypass in the integrand expression. The found distribution function depends, in addition to velocity, on the coordinates and can be used to analytically consider different cases and configurations of the spatial confinement of the plasma. General distribution function for electrons is discussed. We consider the behavior of Langmuir waves, also at the nonlinear stage.

Dynamic response mechanism of layered coatings under impacts: Insights from the perspective of stress wave

Precision machining operations often lead to the failure of protective coatings on cutting tools due to common issues such as cracking, delamination, and peeling from cyclic impacts. While material selection and structural design are crucial for enhancing impact resistance, they primarily focus on static performance with limited consideration from the dynamic sights. This paper presents a novel dynamic design method for coatings, viewed through the lens of stress waves. We investigate the propagation behavior of stress waves in TaN/TiN and CrN/TiN coatings with layered structures. Our findings indicate that the attenuation of stress waves is dominated by the physical properties on both sides of the interface and the stride length. For interfaces with similar physical properties, the attenuation of stress waves is insensitive to the stride length, while for interfaces with different physical properties, the attenuation is regulated by the ratio of single-layer thickness to the full width at half maximum of the stress wave. These insights offer a strategy for extending the life of coatings and improving process safety under dynamic shocks.

Determination of grout compactness in rebar grouted splice sleeves using frequency domain characteristics of the excitation process

Grouted splice sleeves are widely used in assembly building connections. However, void defects within the sleeve directly affect the load-bearing capacity of the building structure. This paper presents a new method for detecting void defects inside a grouted splice sleeve based on the frequency domain characteristics of mechanical vibration waves. This method analyses the grouted spliced casing containing void defects as a gas-liquid two-phase flow system. To confirm the validity of the method, this paper builds a test setup for testing. The results showed that the test method can effectively detect the void defects and the volume of the defects inside the grouted splice sleeves when the grout is not solidified.

Dam break flow through rigid-emergent vegetation

Dam failures pose a significant threat to life and property. This study investigates the potential of rigid emergent vegetation to attenuate dam break waves, reducing their destructive impact. Experiments explored the effect of varying vegetation field lengths on wave propagation. Wooden cylinders with consistent diameter (1.0 cm) and density (0.067) simulated the rigid vegetation in a straight, flat rectangular channel. Four different vegetation lengths and three bore conditions for different reservoir and tailwater depths were examined to analyze their influence on dam break wave behavior. The results demonstrate the effectiveness of vegetation in dissipating wave energy, leading to a rapid decrease in wave height and celerity. Interestingly, increasing vegetation length significantly attenuates the wave height downstream of the vegetation zone, while having no significant impact on the reflection wave height upstream of the vegetation. This finding highlights the targeted effectiveness of strategically placed vegetation in shielding downstream areas. The study also clarifies that celerity can be calculated using shallow water equations for both upstream and downstream regions with wave height and tailwater depth. However, within the vegetation, drag forces significantly reduce celerity. A novel equation, derived from wavefront profiles, was proposed and validated to accurately calculate celerity within the vegetation field. These findings provide valuable data for validating numerical models simulating dam break wave interactions with vegetation.Graphical abstract

Numerical investigation of bandgap characteristics in integrated metallic metafilters for nonlinear guided wave applications

Guided waves propagating in nonlinear media, featuring second harmonic generation, represent a promising avenue for early-stage damage detection due to their high sensitivity and long-range propagation capabilities. However, nonlinear ultrasonic measurements are hindered by nonlinearities induced by the experimental system, necessitating careful calibrations that have restricted their application to laboratory settings. While several phononic crystal and metamaterial designs have been devised to enhance nonlinear-based ultrasonic testing, most are tailored for suppressing second harmonics within a frequency range of 100–300 kHz, primarily utilizing low-frequency excitation. In this paper, we propose a metallic ring-shaped metafilter designed to explore high-order bandgaps. To fully understand the bandgap characteristics, we begin by analyzing mode shapes, providing insights into the underlying wave mechanics. The efficacy of the designed filter is subsequently assessed through 3D time step elastodynamic simulations. In addition, this study underscores the significance of parameters such as the number of rings employed in the filter, signal duration, and bandgap width in optimizing its performance. Furthermore, the observed mode conversion phenomena from S0 to A0 guided wave modes underscore the filter’s capacity to influence guided wave propagation. The defect localization technique, based on the time difference of arrival of second-order wave modes, accurately predicts the defect location with an error margin of less than 0.2%. The present investigation showcases advancements in the sensitivity of nonlinear-based guided wave testing for characterizing microstructural changes, promising substantial potential for detecting incipient damage in practical structural health monitoring applications.

Time‐domain spectra of ultrasonic wave transmitted through granite and gypsum samples containing artificial defects

AbstractThe internal defects in rock masses can significantly impact the quality and safety of geotechnical projects. Mechanical waves, as a common nondestructive testing (NDT) method, can reflect the external and internal structures of rock or rock masses. Analyses on the reflected and transmitted waves enable nondestructive identification and assessment of potential defects within rocks. Previous studies mainly focused on the variation of single or limited wave features like main frequency, amplitude and energy between the intact and non‐intact samples. In fact, most information contained in the waveforms is neglected. Techniques of data mining can provide a powerful tool to reveal this information and therefore a more accurate determination of the internal structures. In this study, 995,412 NDT data from 14 types of granite and gypsum samples with different cross‐section shapes and different types of defects are recorded by an ultrasonic wave generation and collection system. This dataset can be used not only as the training data for defect classification in NDT but also as a good reference for conventional NDT analyses. Besides, time‐series data analysis is an opportunity and challenging issue, this dataset holds great potential for broader application in general time‐series classification analysis.

Air effects on solitary waves impinging and overtopping an impermeable seawall

Considering the presence or absence of air, the solitary waves impinging on an impermeable structure were numerically investigated to discuss solitary wave characteristics such as surface elevation, pressure, vorticity, eddy viscosity, and force on structures under different initial conditions. The volume of fluid (VOF) model (Wu, 2004) was employed to simulate solitary waves impinging an impermeable structure. Besides, the LES turbulent module was utilized to capture the turbulent phenomenon generated by wave-structure interactions, particularly after wave breaking. The present model was verified by comparing the simulation results with the experimental data (Hsiao and Lin, 2010). The findings demonstrated that the model more accurately represents tsunami wave behavior compared to simulations that did not account for air, especially in cases where wave breaking occurs prior to overtopping, entraining more air into the water. Detailed comparisons between simulations with and without air presence reveal that simulations excluding air exhibited delayed wave breaking, a more distant breaking point, and the absence of an air pocket behind the seawall. Despite these differences, the simulations showed excellent agreement with the laboratory results. Moreover, it was shown that the presence of air dissipated part of wave energy. Earlier the stage of waves broke, the more air was entrained, making the effects of air on the waves more noticeable. The highest fluid velocity was observed at the breaking point in front of the structure, while the strongest forces were experienced by the structure at the breaking location behind it.