Uniform stability for a type III thermoelastic laminated beam with structural damping

In this work, we consider a thermoelastic laminated beam with structural damping, where the heat flux is given by Green and Naghdi theories. We establish the well-posedness of the system using semigroup theory. Moreover, under the condition of equal wave speeds, we prove an exponential stability result for the considered system. In the case of lack of exponential stability we show that the solution decays polynomially.

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.

The Potential Mechanisms of AMOC Multidecadal Periods in CMIP6/CMIP5 Preindustrial Simulations

Observations, theoretical analyses, and climate models show that the period of multidecadal variability of the Atlantic Meridional Overturning Circulation (AMOC) is related to westward temperature propagations in the subpolar North Atlantic, which is modulated by oceanic baroclinic Rossby waves. Here, we find major periods of AMOC variability of 12-28 years and associated westward temperature propagations in the preindustrial simulations of 9 CMIP6/CMIP5 models. Comparison with observations shows that the models reasonably simulate ocean stratifications in turn oceanic Rossby waves in the subpolar North Atlantic. The timescales of Rossby waves propagating on a static background flow across the subpolar North Atlantic basin overestimate the AMOC periods. The mean flow effects involving westward geostrophic self-advection and eastward mean advection largely shorten and greatly improve the estimate of AMOC periods through increasing Rossby wave speeds. Our results illustrate the importance of considering mean flow effects on Rossby wave propagations in the estimate of AMOC periods.

A Provably Positive, Divergence-free Constrained Transport Scheme for the Simulation of Solar Wind

In this paper, we present a provably positive, divergence-free constrained transport (CT) scheme to simulate the steady-state solar wind ambient with the three-dimensional magnetohydrodynamics numerical model. The positivity can be lost in two ways: one way is in the reconstruction process, and the other is in the updating process when the variables are advanced to the next time step. We adopt a self-adjusting strategy to bring the density and pressure into the permitted range in the reconstruction process, and use modified wave speeds in the Harten–Lax–van Leer flux to ensure the positivity in the updating process. The CT method can keep the magnetic fields divergence-free if the magnetic fields are divergence-free initially. Thus, we combine the least-squares reconstruction of the magnetic fields with the divergence-free constraints to make the magnetic fields globally solenoidal initially. Furthermore, we adopt a radial basis function method to interpolate variables at boundaries that can keep the magnetic field locally divergence-free. To verify the capability of the model in producing structured solar wind, the modeled results are compared with Parker Solar Probe (PSP) in situ observations during its first two encounters, as well as Wind observations at 1 au. Additionally, a solar maximum solar wind background is simulated to show the property of the model’s ability to preserve the positivity. The results show that the model can provide a relatively satisfactory comparison with PSP or Wind observations, and the divergence error is about 10−10 for all of the tests in this paper.

Internal Bore Evolution Across the Shelf Near Pt. Sal CA interpreted as a Gravity Current

Off the central California coast near Pt. Sal, a large amplitude internal bore was observed for 20 h over 10 km cross-shore, or 100 m to 10 m water depth (D), and 30 km alongcoast by remote sensing, 39 in situ moorings, ship surveys, and drifters. The bore is associated with steep isotherm displacements representing a significant fraction of D. Observations were used to estimate bore arrival time tB, thickness h, and bore and non-bore (ambient) temperature difference ΔT, leading to reduced gravity g′. Bore speeds c, estimated from mapped tB, varied from 0.25 m s−1 to 0.1 m s−1 from D = 50 m to D = 10 m. The h varied from 5 to 35 m, generally decreased with D, and varied regionally alongisobath. The bore ΔT varied from 0.75 to 2.15 °C. Bore evolution was interpreted from the perspective of a two-layer gravity current. Gravity current speeds U, estimated from the local bore h and g− compared well to observed bore speeds throughout its cross-shore propagation. Linear internal wave speeds based on various stratification estimates result in larger errors. On average bore thickness h = D/2, with regional variation, suggesting energy saturation. From 50–10 m depths, observed bore speeds compared well to saturated gravity current speeds and energetics that depend only on water depth and shelf-wide mean g′. This suggests that this internal bore is the internal wave analogue to a saturated surfzone surface gravity bore. Alongcoast variations in pre-bore stratification explain variations in bore properties. Near Pt. Sal, bore Doppler shifting by barotropic currents is observed.

Modelling Pn Wave Speeds Beneath the Central North Island, New Zealand

<p>A new method of modelling Pn-wave speeds is created. The method allows the predominant wavelength features of P-wave speeds in the uppermost mantle to be modelled, as well as estimating values of mantle anisotropy and irregularities in the crust beneath stations, using least-square collocation. A combination of National Network seismometers, local volcanic seismic monitoring networks and temporary deployments are used to collect arrival times from local events, during the period of 1990-2006. The dataset consists of approximately 11200 Pn observations from 3000 local earthquakes at 91 seismograph sites. The resulting model shows distinct variations in uppermost mantle Pn velocities. Velocities of less than 7.5 km/s are found beneath the back-arc extension region of the Central Volcanic Region, and under the Taranaki Volcanic Region, indicating the presence of water and partial melt. The region to the east shows extremely high velocities of 8.3-8.5 km/s, where the P-waves are traveling within the subducting Pacific slab. Slightly lower than normal mantle velocities of 7.8-8.1 km/s are found in the western North Island, suggesting a soft mantle. Pn anisotropy estimates throughout the North Island show predominately trench parallel fast directions, ceasing to nulls in the west. Anisotropy measurements indicate the strain history of the mantle. For the observed upper mantle Pn velocity of 7.3 km/s is one of the lowest seen in the world. Ray-tracing modelling indicate that this region extends to depths of at least 65 km, suggesting an area of elevated heat (700 - 1100 degrees C) at Moho depth. Elevated temperatures can be caused by the presence partial melt (0.4 % to 2.1 % depending on the amount of water present). Beneath the western North Island, the observed slower than normal mantle velocities, indicate a material of lowered shear modulus, susceptible to strain deformation. However, anisotropy estimations in this region, show no significant anisotropy, suggesting that this is a region of young mantle that hasn't had time to take up the signature of deformation. These observations can be explained by a detachment of the mantle lithosphere through a Rayleigh-Taylor instability more than 5 Ma.</p>

Modelling Pn Wave Speeds Beneath the Central North Island, New Zealand

<p>A new method of modelling Pn-wave speeds is created. The method allows the predominant wavelength features of P-wave speeds in the uppermost mantle to be modelled, as well as estimating values of mantle anisotropy and irregularities in the crust beneath stations, using least-square collocation. A combination of National Network seismometers, local volcanic seismic monitoring networks and temporary deployments are used to collect arrival times from local events, during the period of 1990-2006. The dataset consists of approximately 11200 Pn observations from 3000 local earthquakes at 91 seismograph sites. The resulting model shows distinct variations in uppermost mantle Pn velocities. Velocities of less than 7.5 km/s are found beneath the back-arc extension region of the Central Volcanic Region, and under the Taranaki Volcanic Region, indicating the presence of water and partial melt. The region to the east shows extremely high velocities of 8.3-8.5 km/s, where the P-waves are traveling within the subducting Pacific slab. Slightly lower than normal mantle velocities of 7.8-8.1 km/s are found in the western North Island, suggesting a soft mantle. Pn anisotropy estimates throughout the North Island show predominately trench parallel fast directions, ceasing to nulls in the west. Anisotropy measurements indicate the strain history of the mantle. For the observed upper mantle Pn velocity of 7.3 km/s is one of the lowest seen in the world. Ray-tracing modelling indicate that this region extends to depths of at least 65 km, suggesting an area of elevated heat (700 - 1100 degrees C) at Moho depth. Elevated temperatures can be caused by the presence partial melt (0.4 % to 2.1 % depending on the amount of water present). Beneath the western North Island, the observed slower than normal mantle velocities, indicate a material of lowered shear modulus, susceptible to strain deformation. However, anisotropy estimations in this region, show no significant anisotropy, suggesting that this is a region of young mantle that hasn't had time to take up the signature of deformation. These observations can be explained by a detachment of the mantle lithosphere through a Rayleigh-Taylor instability more than 5 Ma.</p>

Shallow water theory for structured bathymetry

A shallow water theory is developed which applies to surface wave propagation over structured bathymetry comprising rapid abrupt fluctuations in depth between two smoothly varying levels. Using a homogenization approach coupled to the depth-averaging process which underpins shallow water modelling, governing equations for the wave elevation are derived which explicitly relate local spatially varying anisotropy of wave speeds to properties of the microstructured bed. The model is applied to two water wave scattering problems both to demonstrate the complex wave propagation characteristics exhibited by structured beds and to provide examples of how to use structured beds to engineer bespoke wave propagation. This includes propagating waves with practically zero reflection and loss of form through circular bends in channels.