Wave Speed Research Articles

Sideband Peak Count – a new nonlinear ultrasonic technique for monitoring damage progression in engineering materials

Linear ultrasonic (LU) techniques used by majority of the researchers working in material damage monitoring, are reliable for detecting relatively large defects. If the defect dimensions are in the range of the ultrasonic wavelength or larger, then those defects can be detected by analyzing the scattered ultrasonic fields. Material damage affects LU parameters such as ultrasonic wave speed and attenuation and their changes are detectable for relatively large defects. However, for small defects (when defect dimensions are significantly smaller than the wavelength of the propagating signal) the changes in the LU parameters are too small to detect or measure reliably. For detecting small defects engineers often use high frequency ultrasonic signals to make the defect dimensions greater than the wavelength. However, high frequency signals attenuate quickly and therefore, only very small regions near the ultrasonic probe can be inspected in this manner. Inspecting large structures by high frequency ultrasonic signals requires moving the probe mechanically from one point to the next and therefore, can be very time consuming. Nonlinear ultrasonic (NLU) technique on the other hand does not need to satisfy this restricting condition that the wavelength of the signal must be smaller than the defect size. NLU works well when the signal wavelength is much larger than the defect size. Therefore, relatively low frequency signals that can propagate a long distance and monitor a large area of a structure can be used for NLU measurements. Different NLU techniques can be used for detection and monitoring of small damages in a specimen. A relatively new NLU technique called the Sideband Peak Count-Index or SPC-I technique has been developed by the author and his collaborators. SPC-I technique for monitoring different types of materials – composites, metals, concrete, and other cement-based materials has been found to be effective. Along with those success stories of SPC-I the effect of topography and the advantage of topological sensing is also discussed in this presentation.

Onset and propagation of slip at adhesive elastic interfaces.

The transition from static to dynamic friction when an elastic body is slid over another is now known to result from the motion of interface rupture fronts. These fronts may be either cracklike or pulselike, with the latter involving reattachment in the wake of the front. How and why these fronts occur remains a subject of active theoretical and experimental investigation, especially given its wide ranging implications. In this work, we investigate the role of boundary loading in answering this question using an elastic lattice-network model under displacement/velocity controlled loading. Bulk elastic and interface bonds are simulated using a network of springs, with a stretch-based detachment and reattachment rule applied to interface bonds. We find that, contrary to commonly used rigid body models with Coulomb-type friction laws, the type of rupture front observed is very closely linked to the location of the applied boundary displacements. Depending on whether the sliding elastic solid is pulled, pushed or sheared-all equivalent in the rigid case-distinct interface rupture modes can occur. We quantify these rupture modes, evaluate the corresponding interface stresses that lead to their formation, and and study their subsequent propagation dynamics. Our results reveal quantitative analogies between the sliding friction problem and mode II fracture, with attendant wave speeds ranging from slow to Rayleigh. We discuss how these fronts mediate interface motion and implications for the general transition mechanism from static to dynamic friction.

Gauging force by tapping tendons? Inaccurately in the human patellar tendon

Accurately estimating in vivo tendon load non-invasively remains a major challenge in biomechanics, which might be overcome by shear-wave tensiometry. Shear-wave tensiometry measures the speed of mechanically induced tendon shear waves by skin-mounted accelerometers. To gauge the feasibility and accuracy of this novel technique, we obtained patellar tendon shear wave speeds via shear-wave tensiometry during sustained or ramp voluntary contractions of the knee extensors in two experiments (n = 8 in both). In experiment one, participants produced a constant knee extension torque of ∼ 50 Nm at five different knee joint angles (i.e. variable tendon load), which resulted in estimated patellar tendon forces between 1005 ± 6N and 1182 ± 16 N. However, wave speed squared did not correlate with estimated tendon force within participants (rrm(31) = -0.19, p = 0.278). In experiment two, averaged correlation coefficients between normalized wave speed squared and torque of maximal and submaximal voluntary contractions across participants ranged between r = 0.43 and r = 0.94, while the time-varying correlation between these normalized signals ranged from r = -0.99 to r = 1.00. Further, the mean absolute errors (MAEs) between normalized wave speed squared and normalized torque across participants ranged between 0.03 and 0.54, which were larger than the MAEs between normalized torque and normalized summed EMG amplitude from the superficial quadriceps muscles (0.03–0.54 versus 0.06–0.26, respectively). In conclusion, there was no simple relation between shear wave speed squared and patellar tendon load, which severely limits the feasibility of shear-wave tensiometry for accurately estimating in vivo tendon load at the knee joint.

OEDG: Oscillation-eliminating discontinuous Galerkin method for hyperbolic conservation laws

Suppressing spurious oscillations is crucial for designing reliable high-order numerical schemes for hyperbolic conservation laws, yet it has been a challenge actively investigated over the past several decades. This paper proposes a novel, robust, and efficient oscillation-eliminating discontinuous Galerkin (OEDG) method on general meshes, motivated by the damping technique (see J. Lu, Y. Liu, and C. W. Shu [SIAM J. Numer. Anal. 59 (2021), pp. 1299–1324]). The OEDG method incorporates an oscillation-eliminating (OE) procedure after each Runge–Kutta stage, and it is devised by alternately evolving the conventional semidiscrete discontinuous Galerkin (DG) scheme and a damping equation. A novel damping operator is carefully designed to possess both scale-invariant and evolution-invariant properties. We rigorously prove the optimal error estimates of the fully discrete OEDG method for smooth solutions of linear scalar conservation laws. This might be the first generic fully discrete error estimate for nonlinear DG schemes with an automatic oscillation control mechanism. The OEDG method exhibits many notable advantages. It effectively eliminates spurious oscillations for challenging problems spanning various scales and wave speeds, without necessitating problem-specific parameters for all the tested cases. It also obviates the need for characteristic decomposition in hyperbolic systems. Furthermore, it retains the key properties of the conventional DG method, such as local conservation, optimal convergence rates, and superconvergence. Moreover, the OEDG method maintains stability under the normal Courant–Friedrichs–Lewy (CFL) condition, even in the presence of strong shocks associated with highly stiff damping terms. The OE procedure is nonintrusive, facilitating seamless integration into existing DG codes as an independent module. Its implementation is straightforward and efficient, involving only simple multiplications of modal coefficients by scalars. The OEDG approach provides new insights into the damping mechanism for oscillation control. It reveals the role of the damping operator as a modal filter, establishing close relations between the damping technique and spectral viscosity techniques. Extensive numerical results validate the theoretical analysis and confirm the effectiveness and advantages of the OEDG method.

Periodic traveling waves of a SIR model with renewal and delay in one-dimensional lattice

This paper is primarily addressed to the (non)existence and asymptotic behaviors of periodic traveling waves for a SIR model with renewal and delay in one-dimensional lattice, which generalizes the conclusions of SIR models in one-dimensional continuous space. Especially, the challenge of establishing the asymptotic behaviors of periodic traveling waves when periodicity arises is solved by integral and analytic techniques. Moreover, the spreading speed is equal to the minimal wave speed can be obtained by our results.

Pseudo grid-based physics-informed convolutional-recurrent network solving the integrable nonlinear lattice equations

Traditional discrete learning methods involve discretizing continuous equations using difference schemes, necessitating considerations of stability and convergence. Integrable nonlinear lattice equations possess a profound mathematical structure that enables them to revert to continuous integrable equations in the continuous limit, particularly retaining integrable properties such as conservation laws, Hamiltonian structure, and multiple soliton solutions. The pseudo grid-based physics-informed convolutional-recurrent network (PG-PhyCRNet) is proposed to investigate the localized wave solutions of integrable lattice equations, which significantly enhances the model’s extrapolation capability to lattice points beyond the temporal domain. We conduct a comparative analysis of PG-PhyCRNet with and without pseudo grid by investigating the multi-soliton solutions and rational solitons of the Toda lattice and self-dual network equation. The results indicate that the PG-PhyCRNet excels in capturing long-term evolution and enhances the model’s extrapolation capability for solitons, particularly those with steep waveforms and high wave speeds. Finally, the robustness of the PG-PhyCRNet method and its effect on the prediction of solutions in different scenarios are confirmed through repeated experiments involving pseudo grid partitioning.

An extended cellular automation model for bicycles with group and retrograde behaviors at signalized intersections

The rise of shared bicycles has increased the demand for group riding, integrating bicycles into social groups. Additionally, retrograde riding, where cyclists travel against the designated direction, is a common behavior observed in bicycle flows. The interaction and self-organization phenomenon of group and retrograde behaviors are complex, significantly impacting traffic efficiency. This paper develops a two-dimensional Extended Moore Neighborhood and constructs state-updating rules for regular riding, group riding and retrograde riding. Each rule comprises a psychological decision layer and a physical execution layer, forming a cellular automaton model for group and retrograde bicycles. Field experiments are conducted to calibrate the model parameters and verify the behavioral characteristics. Finally, we execute numerical simulations at a signalized intersection to explore the coupling effects of group and retrograde behaviors on self-organization within the bicycle flow and the traffic capacity. The results indicate that group behavior increases queue length while reducing start wave speed and expansion degree. Retrograde behavior intensifies the negative effects on bicycle flow. These findings provide insights for managing both forward and retrograde bicycle flows.

Uncertainty Cost Functions for Wave Energy

Wave energy is considered as an important energy source for people living near coastal areas to meet their basic energy needs. Innovative and new technologies can be used for this energy utilization to run the loads from sea waves. Due to its uncertain power availability, we can use uncertainty cost functions based on probability distributions for the availability of the operation of the wave energy microgrid. These probability distributions are based on several mapping models designed for the wave energy, wave height, and wave speed mapping to make the energy more stable and reliable. In contrast to other renewable energy sources, wave energy is inherently unpredictable, making it impossible to model with a single, globally applicable probability distribution function (PDF). The prediction of the behavior of primary wave energy for this purpose is completely based on several probability distribution functions (PDFs) which can be considered as the best for all conditions. In this paper, we have used the Weibull-Rayleigh probability distribution model to develop the uncertainty cost function for wave energy. The Monte-Carlo process is carried out to get the results supported by the Rayleigh probability distribution model consisting of wave height, and uncertain cost histograms. Cost is minimized by using the Weibull Rayleigh model for both overestimation and underestimation costs of wave energy. Monte-Carlo simulation results are further compared with analytical calculation and error between them.

High-order accurate well-balanced energy stable finite difference schemes for multi-layer shallow water equations on fixed and adaptive moving meshes

This paper develops high-order accurate well-balanced (WB) energy stable (ES) finite difference schemes for multi-layer (the number of layers M⩾2) shallow water equations (SWEs) with non-flat bottom topography on both fixed and adaptive moving meshes, extending our previous work on the single-layer shallow water magnetohydrodynamics [25] and single-layer SWEs on adaptive moving meshes [58]. To obtain an energy inequality, the convexity of an energy function for an arbitrary M is proved by finding recurrence relations of the leading principal minors or the quadratic forms of the Hessian matrix of the energy function with respect to the conservative variables, which is more involved than the single-layer case due to the coupling between the layers in the energy function. An important ingredient in developing high-order semi-discrete ES schemes is the construction of a two-point energy conservative (EC) numerical flux. In pursuit of the WB property, a sufficient condition for such EC fluxes is given with compatible discretizations of the source terms similar to the single-layer case. It can be decoupled into M identities individually for each layer, making it convenient to construct a two-point EC flux for the multi-layer system. To suppress possible oscillations near discontinuities, WENO-based dissipation terms are added to the high-order WB EC fluxes, which gives semi-discrete high-order WB ES schemes. Fully-discrete schemes are obtained by employing high-order explicit strong stability preserving Runge-Kutta methods and proved to preserve the lake at rest. The schemes are further extended to moving meshes based on a modified energy function for a reformulated system, relying on the techniques proposed in [58]. Numerical experiments are conducted for some two- and three-layer cases to validate the high-order accuracy, WB and ES properties, and high efficiency of the schemes, with a suitable amount of dissipation chosen by estimating the maximal wave speed due to the lack of an analytical expression for the eigenstructure of the multi-layer system.

Studi Motion Sickness Incidence (MSI) Pada Kapal Patroli (KAL-28) Katamaran

Motion sickness or seasickness is a condition caused by the movement of a ship that results in dizziness, nausea, and vomiting. The Motion Sickness Incidence (MSI) Study on the Patrol Catamaran (KAL-28) aims to evaluate the comfort level of passengers and the safety of the ship's crew during operations, following the ISO 2631/1997 standards. The evaluation is conducted on the vertical acceleration response of the ship under various wave conditions, speeds, and wave directions. Mapping is performed in various areas of the ship, including the deck, navigation room, and engine room, considering wave heights of 0.875 meters and 2 meters at speeds of 15 knots, 22.5 knots, and 30 knots. The research results indicate that at a speed of 15 knots, the deck area, navigation room, and engine room meet the criteria from comfortable to somewhat uncomfortable. However, at speeds of 22.5 knots and 30 knots, these areas are rated as somewhat uncomfortable to very uncomfortable. This study emphasizes the need for ship design that considers both passenger comfort and safety, especially for patrol catamarans

Time periodic traveling wave solutions of a time-periodic reaction–diffusion SEIR epidemic model with periodic recruitment

This paper focuses on the existence and nonexistence of a time periodic traveling wave solution of a time-periodic reaction–diffusion SEIR epidemic model. The main feature of the model is the possible deficiency of the classical comparison principle such that many known results do not directly work. If the basic reproduction number of the model, denoted by R0, is larger than one, there exists a minimal wave speed c∗>0 satisfying for each c>c∗, the system admits a nontrivial time periodic traveling wave solution with wave speed c and for c<c∗, there exists no nontrivial time periodic traveling waves such that the system; if R0<1, the system admits no nontrivial time periodic traveling waves.

Local spherical collapsing box in Athena++ : Numerical implementation and benchmark tests

We implement a local model for a spherical collapsing or expanding gas cloud in the Athena++ magnetohydrodynamic code. This local model consists of a Cartesian periodic box with time-dependent geometry. We present a series of benchmark test problems, including nonlinear solutions and linear perturbations of the local model, confirming the code's desired performance. During a spherical collapse, a horizontal shear flow is amplified, corresponding to angular momentum conservation of zonal flows in the global problem; wave speed and the amplitude of sound waves increase in the local frame, due to the reduction in the characteristic length scale of the box, which can lead to an anisotropic effective sound speed in the local box. Our code conserves both mass and momentum-to-machine precision. This numerical implementation of the local model has potential applications to the study of local physics and hydrodynamic instabilities during protostellar collapse, providing a powerful framework for better understanding the earliest stages of star and planet formation.

Reconstruction of excitation waves from mechanical deformation using physics-informed neural networks

Non-invasive assessment of the electrical activation pattern can significantly contribute to the diagnosis and treatment of cardiac arrhythmias, due to faster and safer diagnosis, improved surgical planning and easier follow-up. One promising path is to measure the mechanical contraction via echocardiography and utilize this as an indirect way of measuring the original activation pattern. To solve this demanding inversion task, we make use of physics-informed neural networks, an upcoming methodology to solve forward and inverse physical problems governed by partial differential equations. In this study, synthetic data sets were created, consisting of 2D excitation waves coupled to an isotropic and linearly deforming elastic medium. We show that for both focal and spiral patterns, the underlying excitation waves can be reconstructed accurately. We test the robustness of the method against Gaussian noise, reduced spatial resolution and projected tri-planar data. In situations where the data quality is heavily reduced, we show how to improve the reconstruction by additional regularization on the wave speed. Our findings suggest that physics-informed neural networks hold the potential to solve sparse and noisy bio-mechanical inversion problems and may offer a pathway to non-invasive assessment of certain cardiac arrhythmias.

Simulation Study on Constraining Gravitational Wave Propagation Speed by Gravitational Wave and Gamma-ray Burst Joint Observation on Binary Neutron Star Mergers

Theories of modified gravity suggest that the propagation speed of gravitational waves (GW) v g may deviate from the speed of light c. A constraint can be placed on the difference between c and v g with a simple method that uses the arrival time delay between GW and electromagnetic wave simultaneously emitted from a burst event. We simulated the joint observation of GW and short gamma-ray burst signals from binary neutron star merger events in different observation campaigns, involving advanced LIGO (aLIGO) in design sensitivity and Einstein Telescope (ET) joint-detected with Fermi/GBM. As a result, the relative precision of constraint on v g can reach ∼10−17 (aLIGO) and ∼10−18 (ET), which are one and two orders of magnitude better than that from GW170817, respectively. We continue to obtain the bound of graviton mass m g ≤ 7.1(3.2) × 10−20 eV with aLIGO (ET). Applying the Standard-Model Extension test framework, the constraint on v g allows us to study the Lorentz violation in the nondispersive, nonbirefringent limit of the gravitational sector. We obtain the constraints of the dimensionless isotropic coefficients s¯00(4) at mass dimension d = 4, which are −1×10−15<s¯00(4)<9×10−17 for aLIGO and −4×10−16<s¯00(4)<8×10−18 for ET.

Schallamach waves in the rolling inception of rubber wheel

Rubber wheel exhibits complex behaviors during high-acceleration rolling, but the behind mechanism is not yet clear. Although rigorous research has been conducted on the Schallamach waves in the sliding of rubber, it is nevertheless unknown whether they exist during the rolling contact. Through micromechanical modeling and transient analysis, we found that the adhesion energy and startup acceleration jointly determine the contact behaviors in the rolling inception, with the result that Schallamach waves can emerge when rubber wheel rolls with high-acceleration and strong-adhesion. We analyzed the speed of Schallamach waves and the associated stick-slip friction, and discussed the possible drawback of surface creasing. The findings from this investigation provide new insights into the mechanisms governing the rolling friction of rubber wheels.

Revisiting Einstein-Gauss-Bonnet theories after GW170817

In this work we study the inflationary framework of Einstein-Gauss-Bonnet theories which produce a primordial gravitational wave speed that respects the constraint imposed by the GW170817 event, namely |cT2−1|<6×10−15 in natural units. For these theories in general, the scalar Gauss-Bonnet coupling function ξ(ϕ) is arbitrary and unrelated to the scalar potential. We develop the inflationary formalism of this theory, and present analytic forms for the slow-roll indices, the observational indices and the e-foldings number, assuming solely a slow-roll era and also that the constraints imposed by the GW170817 event hold true. We present in detail an interesting class of models that produces a viable inflationary era. Finally, we investigate the behavior of the Einstein-Gauss-Bonnet coupling function during the reheating era, in which case the evolution of the Hubble rate satisfies a constant-roll-like relation H˙=δH2. As we show, the behavior of the scalar Gauss-Bonnet coupling during the reheating is different from that of the inflationary era. This is due to the fact that the evolution governing the reheating is different compared to the inflationary era.

Effect of Recycled Fibers on the Mechanical Properties and Durability of Sand Concrete

Recycling waste in construction materials is part of a sustainable development approach aimed at creating new materials with characteristics that have been shown to be competitive with traditional materials. In this context, this study aims to recover steel, copper and aluminum wastes from blacksmiths’ workshops together with the reuse thereof in the form of reinforcing fibers in sand concrete. However, in order to assess the impact of this waste on the concrete properties, we introduced such wastes in the form of fibers at different proportions (0.4 %, 0.8 % and 1.2 %). Further, a series of tests was then carried out to determine the evolution of the concrete characteristics in the fresh state (workability and density) and in the hardened state (compressive strength, flexural strength, compressive strength obtained using a sclerometer and the speed of ultrasonic waves), as well as the concrete’s durability (absorption coefficient by immersion, by capillarity and the porosity accessible to water). In closing, the behavior of the concrete was assessed in the face of a chemical attack by H2SO4 and HCl by measuring mass loss. In virtue of thus, the results obtained demonstrated a positive evolution of certain properties of sand concrete as a function of the type and percentage of fibers incorporated into the composition of the concrete.

Traveling wave solutions of a susceptible-infectious model

This paper studies the traveling wave solutions of a susceptible and infectious (SI) mathematical model with and without recruitment rates. Our research provides numerical solutions for the proposed models, confirming the existence of traveling wave solutions. We meticulously calculate the minimal traveling wave speeds and analytically determine the spreading speed without turnover for the susceptible population. The paper also investigates the relationship between the spreading speeds and the model parameters. Additionally, we identify the threshold density of susceptible individuals, a crucial point below which the disease cannot persist. Our findings also confirm that the disease ceases to exist if the death rates surpass the rate of new cases of infections.

Study on the characteristics and predictive model of autoignition induced by shock wave from high-pressure hydrogen leakage

Faced with climate change and increasing environmental pollution, countries around the world are actively exploring strategies for clean, renewable energy. However, under high-pressure conditions, hydrogen leaks can lead to spontaneous combustion, which significantly raises the safety risk of hydrogen applications. This study employs fluid dynamic simulation methods to investigate the development process of shock waves within tubes. It analyzes the effect of release conditions on the propagation speed and shock wave intensity, revealing the impact of shock wave intensity on the temperature distribution and gas composition variation within the hydrogen-air mixture boundary layer. The results show that the tube length and bends have relatively little impact on the shock waves, while discharge pressure and tube diameter significantly affect the propagation speed and intensity of shock waves. Combined with dimensional analysis and data fitting, a predictive model for autoignition of high-pressure hydrogen leakage is established: (Pr/Pa)((DXrx(H₂)rO₂))/Vs2) = 1505(X/D)−1.329.

Propagation dynamics of a three-species nonlocal dispersal predator–prey system with two weak competing aborigine preys

This paper is concerned with the propagation dynamics of a three-species nonlocal dispersal predator–prey system with two weak competing aborigine preys. Precisely, our main concern is the invading process of an alien predator into the habitat of two aborigine preys, when two preys are weak competitors in the absence of predator. This invasion process can be characterized by the spreading speed of the predator as well as the traveling wave solutions connecting the predator-free state to other states. First, by applying Schauder’s fixed point theorem with the help of two pairs of upper and lower solutions, we prove that there exists a positive number [Formula: see text], when the wave speed is large than or equals to [Formula: see text], the system admits a traveling wave solution connecting the predator-free state to the co-existence state, which indicates the occurrence of invasion-coexistence phenomenon. Then the invading speed of the predator is investigated by using the comparison argument. Our results show that (i) the weak interspecific competition between two preys will not affect the phenomenon of invasive-coexistence; (ii) the invading speed of the predator coincides with the minimal wave speed [Formula: see text].