Study on Date–Jimbo–Kashiwara–Miwa Equation with Conformable Derivative Dependent on Time Parameter to Find the Exact Dynamic Wave Solutions

In this article, we construct the exact dynamical wave solutions to the Date–Jimbo–Kashiwara–Miwa equation with conformable derivative by using an efficient and well-established approach, namely: the two-variable G’/G, 1/G-expansion method. The solutions of the Date–Jimbo–Kashiwara–Miwa equation with conformable derivative play a vital role in many scientific occurrences. The regular dynamical wave solutions of the abovementioned equation imply three different fundamental functions, which are the trigonometric function, the hyperbolic function, and the rational function. These solutions are classified graphically into three categories, such as singular periodic solitary, kink soliton, and anti-kink soliton wave solutions. Furthermore, the effect of the fractional parameter on these solutions is discussed through 2D plots.

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.

DETERMINATION OF WAVE SLAMMING LOADS ON HIGH-SPEED CATAMARANS BY HYDROELASTIC SEGMENTED MODEL EXPERIMENTS

A 2.5m hydroelastic segmented catamaran model has been developed based on the 112m INCAT wave-piercer catamaran to simulate the vibration response during the measurement of dynamic slam loads in head seas. Towing tank tests were performed in regular seas to measure the dynamic slam loads acting on the centre bow and vertical bending moments acting in the demihulls of the catamaran model as a function of wave frequency and wave height to establish the operational loads acting on the full-scale 112m INCAT catamaran vessel. Peak slam forces measured on the bow of the model are found to approach the weight of the model, this being similar to the findings of full-scale vessel trials. A review of the motions of the hydroelastic segmented catamaran model found that the heave and pitch motions give a good indication of slamming severity in terms of the dimensionless heave and pitch accelerations. The dynamic wave slam forces are closely related to the relative motion between the bow and the incident wave profile.

Full-range birefringence control with piezoelectric MEMS-based metasurfaces

Dynamic polarization control is crucial for emerging highly integrated photonic systems with diverse metasurfaces being explored for its realization1–6, but efficient, fast, and broadband operation remains a cumbersome challenge. While efficient optical metasurfaces (OMSs) involving liquid crystals suffer from inherently slow responses1, other OMS realizations are limited either in the operating wavelength range (due to resonances involved)2,3 or in the range of birefringence tuning4–6. Capitalizing on our development of piezoelectric micro-electro-mechanical system (MEMS) based dynamic OMSs7, we demonstrate reflective MEMS-OMS dynamic wave plates (DWPs) with high polarization conversion efficiencies (~ 75%), broadband operation (~ 100 nm near the operating wavelength of 800 nm), fast responses (< 0.4 milliseconds) and full-range birefringence control that enables completely encircling the Poincaré sphere along trajectories determined by the incident light polarization and DWP orientation. Demonstrated complete electrical control over light polarization opens new avenues in further integration and miniaturization of optical networks and systems8,9.

Stormwater Runoff Modelling in an Urban Catchment to Plan Risk Management for Contaminant Spills for Stormwater Harvesting

Water quality is a key consideration for urban stormwater harvesting via aquifers. This study assessed catchment spill management options based on a calibrated dynamic wave routing model of stormwater flow in an urban catchment. The study used measured travel times, pluviometer and gauging station observations from 21 storms to calibrate a stormwater model to simulate transport of pollutants from spill locations to the point of harvest. The simulations considered the impact of spill locations, spill durations, storm intensities and storm durations on the pollutant concentration at the point of harvest and travel time of a pollutant spill to the harvesting point. During dry weather, spill events travelled slower than spills occurring during wet weather. For wet weather spills, the shortest travel times tended to occur in higher intensity storms with shorter duration, particularly when a spill occurred in the middle of the storm. Increasing the intensity of rainfall reduced the peak concentration of pollutant at the harvest point via dilution, but it also reduced the time of travel. On a practical level, due to the short response times in urban catchments, management of spills should be supported by automated detection/diversion systems to protect stormwater harvesting schemes.

A software package for modeling the propagation of dynamic wave disturbances in heterogeneous multi-scale media

The paper considers a software package designed to simulate the propagation of dynamic wave disturbances in heterogeneous media. One of the main features of the considered software package is numerical algorithms with an explicit selection of inhomogeneities. Within the framework of the work, such inhomogeneities as pores, fractures and interfaces between media (contact boundaries) are considered. The considered algorithms make it possible to perform calculations in different scale settings in micro and macro sizes. The mathematical model is based on the equations of the linear theory of elasticity. For the calculation, block structural meshes are used. The software package is parallelized using MPI and OpenMP technologies. Separate parts of the algorithm are parallelized using graphics accelerators such as GPGPU. The paper describes the features of the algorithms under consideration and provides examples of calculations that demonstrate the capabilities of the algorithm.