A Source Physics Interpretation of Nonself-Similar Double-Corner-Frequency Source Spectral Model JA19_2S

We investigate the relation between the kinematic double-corner-frequency source spectral model JA19_2S (Ji and Archuleta, 2020) and static fault geometry scaling relations proposed by Leonard (2010). We find that the nonself-similar low-corner-frequency scaling relation of JA19_2S model can be explained using the fault length scaling relation of Leonard’s model combined with an average rupture velocity ∼70% of shear-wave speed for earthquakes 5.3 < M< 6.9. Earthquakes consistent with both models have magnitude-independent average static stress drop and average dynamic stress drop around 3 MPa. Their scaled energy e˜ is not a constant. The decrease of e˜ with magnitude can be fully explained by the magnitude dependence of the fault aspect ratio. The high-frequency source radiation is generally controlled by seismic moment, static stress drop, and dynamic stress drop but is further modulated by the fault aspect ratio and the relative location of the hypocenter. Based on these two models, the commonly quoted average rupture velocity of 70%–80% of shear-wave speed implies predominantly unilateral rupture.

An Analysis of the Catastrophe Model and Catastrophe Characteristics of Traffic Flow Based on Cusp Catastrophe Theory

—The state of urban road traffic flow shows discontinuity and jumping phenomenon in the process of running. There was a data gap in the collected traffic flow data. Through the data analysis, it was found that the traffic flow state had the characteristics of multimode, mutation, inaccessibility, divergence and hysteresis, which were similar to the mutation characteristics of the basic model of catastrophe theory when the system state changed. The cusp catastrophe model of traffic flow based on traffic wave theory was established by analyzing the movement process of traffic flow. In this model, the traffic density was taken as the state variable, and traffic flow and wave speed were taken as the control variable. Referring to the basic idea of catastrophe theory, the solution method of the model was given, and the structural stability of the traffic flow state was analyzed. Through the critical equilibrium surface equation, the stability of the extreme value of the system potential function can be analyzed, and the bifurcation set equation when the traffic flow state changed can be obtained, which can be used to determine the critical range of the structural stability of the system. This paper discussed and analyzed the changing trend and constraint relationship among the wave speed, traffic density and traffic flow when the traffic flow state changed suddenly in different running environments. The analysis results were consistent with the actual road traffic flow state. A case was given, and the results showed that the cusp catastrophe model could describe the relationship among the three parameters of traffic flow from three-dimensional space, and could effectively analyze the internal relationship of the parameters when the traffic flow state changed. The validity of the model and analysis method was verified. The goal of this paper is to provide an analysis method for the judgment of urban road traffic state.

Traveling wave solutions in predator–prey models with competition

This paper studies the minimal wave speed of traveling wave solutions in predator–prey models, in which there are several groups of predators that compete among different groups. We investigate the existence and nonexistence of traveling wave solutions modeling the invasion of predators and coexistence of these species. When the positive solution of the corresponding kinetic system converges to the unique positive steady state, a threshold that is the minimal wave speed of traveling wave solutions is obtained. To finish the proof, we construct contracting rectangles and upper–lower solutions and apply the asymptotic spreading theory of scalar equations. Moreover, multiple propagation thresholds in the corresponding initial value problem are presented by numerical examples, and one threshold may be the minimal wave speed of traveling wave solutions.

Basic investigation on identification of tissue composition based on propagation speeds of longitudinal and shear waves

The elastic modulus of tissue as a useful biomarker of disease detection can be quantitatively evaluated based on shear wave speed (SWS) measurements in shear wave elastography. Although the longitudinal wave speed (LWS) is also expected to be a promising biomarker for disease detection, the elasticity is not always dominant because the LWS is affected by the bulk modulus. In other words, LWS and SWS may reflect different tissue properties. Therefore, in this study, based on the improvement in LWS measurement, the relationship between the composition of a phantom mixed with agar and glycerol and ultrasonically measured LWS and SWS was investigated. The LWS had a good sensitivity in detecting glycerol, while the SWS had a good sensitivity in detecting agar. The calculated Poisson's ratio had a better sensitivity in detecting agar. In conclusion, a simultaneous measurement of LWS and SWS may help identify the tissue composition.

Shear Wave Tensiometry Tracks Reductions in Collateral Ligament Tension Due to Incremental Releases

Surgeons routinely perform incremental releases on overly tight ligaments during total knee arthroplasty (TKA) to reduce ligament tension and achieve their desired implant alignment. However, current methods to assess whether the surgeon achieved their desired reduction in the tension of a released ligament are subjective and/or do not provide a quantitative metric of tension in an individual ligament. Accordingly, the purpose of this study was to determine whether shear wave tensiometry, a novel method to assess tension in individual ligaments based on the speed of shear wave propagation, can detect changes in ligament tension following incremental releases. In seven medial and eight lateral collateral porcine ligaments (MCL and LCL, respectively), we measured shear wave speeds and ligament tension before and after incremental releases consisting of punctures with an 18-gauge needle. We found that shear wave speed squared decreased linearly with decreasing tension in both the MCL (r^2 avg = 0.76) and LCL (r^2 avg = 0.94). We determined that errors in predicting tension following incremental releases were 24.5 N and 12.2 N in the MCL and LCL, respectively, using specimen-specific calibrations. These results suggest shear wave tensiometry is a promising method to objectively measure the tension reduction in released structures. Clinical Significance: Direct, objective measurements of the tension changes in individual ligaments following release could enhance surgical precision during soft tissue balancing in TKA. Thus, shear wave tensiometry could help surgeons reduce the risk of poor outcomes associated with overly tight ligaments, including residual knee pain and stiffness.

Integrated rupture mechanics for slow slip events and earthquakes

Slow slip events usually occur downdip of seismogenic zones in subduction megathrusts and crustal faults, with rupture speeds much slower than earthquakes. The empirical moment-duration scaling relation can help constrain the physical mechanism of slow slip events, yet it is still debated whether this scaling is linear or cubic and a fundamental model unifying slow slip events and earthquakes is still lacking. Here I present numerical simulations that show that slow slip events are regular earthquakes with negligible dynamic-wave effects. A continuum of rupture speeds, from arbitrarily-slow speeds up to the S-wave speed, is primarily controlled by the stress drop and a transition slip rate above which the fault friction transitions from rate-weakening behaviour to rate-strengthening behaviour. This continuum includes tsunami earthquakes, whose rupture speeds are about one-third of the S-wave speed. These numerical simulation results are predicted by the three-dimensional theory of dynamic fracture mechanics of elongated ruptures. This fundamental model unifies slow slip events and earthquakes, reconciles the observed moment-duration scaling relations, and opens new avenues for understanding earthquakes through investigations of the kinematics and dynamics of frequently occurring slow slip events.

Spreading speeds and traveling wave solutions of diffusive vector-borne disease models without monotonicity

Vector-borne diseases, such as chikungunya, dengue, malaria, West Nile virus, yellow fever and Zika, pose a major global public health problem worldwide. In this paper we investigate the propagation dynamics of diffusive vector-borne disease models in the whole space, which characterize the spatial expansion of the infected hosts and infected vectors. Due to the lack of monotonicity, the comparison principle cannot be applied directly to this system. We determine the spreading speed and minimal wave speed when the basic reproduction number of the corresponding kinetic system is larger than one. The spreading speed is mainly estimated by the uniform persistence argument and generalized principal eigenvalue. We also show that solutions converge locally uniformly to the positive equilibrium by employing two auxiliary monotone systems. Moreover, it is proven that the spreading speed is the minimal wave speed of travelling wave solutions. In particular, the uniqueness and monotonicity of travelling waves are obtained. When the basic reproduction number of the corresponding kinetic system is not larger than one, it is shown that solutions approach to the disease-free equilibrium uniformly and there is no travelling wave solutions. Finally, numerical simulations are presented to illustrate the analytical results.

Travelling-wave analysis of a model of tumour invasion with degenerate, cross-dependent diffusion

In this paper, we carry out a travelling-wave analysis of a model of tumour invasion with degenerate, cross-dependent diffusion. We consider two types of invasive fronts of tumour tissue into extracellular matrix (ECM), which represents healthy tissue. These types differ according to whether the density of ECM far ahead of the wave front is maximal or not. In the former case, we use a shooting argument to prove that there exists a unique travelling-wave solution for any positive propagation speed. In the latter case, we further develop this argument to prove that there exists a unique travelling-wave solution for any propagation speed greater than or equal to a strictly positive minimal wave speed. Using a combination of analytical and numerical results, we conjecture that the minimal wave speed depends monotonically on the degradation rate of ECM by tumour cells and the ECM density far ahead of the front.

Comparison of volcanic explosions in Japan using impulsive ionospheric disturbances

Using the ionospheric total electron content (TEC) data from ground-based Global Navigation Satellite System (GNSS) receivers in Japan, we compared ionospheric responses to five explosive volcanic eruptions 2004–2015 of the Asama, Shin-Moe, Sakurajima, and Kuchinoerabu-jima volcanoes. The TEC records show N-shaped disturbances with a period ~ 80 s propagating outward with the acoustic wave speed in the F region of the ionosphere. The amplitudes of these TEC disturbances are a few percent of the background absolute vertical TEC. We propose to use such relative amplitudes as a new index for the intensity of volcanic explosions. Graphical Abstract