Scattering of the three-dimensional cubic nonlinear Schrödinger equation with partial harmonic potentials

In this paper, we consider the following three dimensional defocusing cubic nonlinear Schrödinger equation (NLS) with partial harmonic potential \begin{equation} \left\{\begin{array}{l} i\partial_tu + \left(\Delta_{\mathbb{R}^3}-x^2\right)u = |u|^2u, \\ u|_{t=0} = u_0 \\ \end{array}\right. \tag{NLS} \end{equation} Out main result shows that the solution $u$ scatters for any given initial data $u_0$ with finite mass and energy. The main new ingredient in our approach is to approxmate (NLS) in the large-scale case by a relevant dispersive continuous resonant (DCR) system. The proof of global well-posedness and scattering of the new (DCR) system is greatly inspired by the fundamental works of Dodson [29, 31, 32] in his study of scattering for the mass-critical nonlinear Schrödinger equation. The analysis of (DCR) system allows us to utilize the additional regularity of the smooth nonlinear profile so that the celebrated concentration-compactness/rigidity argument of Kenig and Merle [61,62] applies

Scattering of the three-dimensional cubic nonlinear Schr\"odinger equation with partial harmonic potentials

In this paper, we consider the following three dimensional defocusing cubic nonlinear Schr\"odinger equation (NLS) with partial harmonic potential \begin{equation*}\tag{NLS} i\partial_t u + \left(\Delta_{\mathbb{R}^3 }-x^2 \right) u = |u|^2 u, \quad u|_{t=0} = u_0. \end{equation*} Our main result shows that the solution $u$ scatters for any given initial data $u_0$ with finite mass and energy. The main new ingredient in our approach is to approximate (NLS) in the large-scale case by a relevant dispersive continuous resonant (DCR) system. The proof of global well-posedness and scattering of the new (DCR) system is greatly inspired by the fundamental works of Dodson \cite{D3,D1,D2} in his study of scattering for the mass-critical nonlinear Schr\"odinger equation. The analysis of (DCR) system allows us to utilize the additional regularity of the smooth nonlinear profile so that the celebrated concentration-compactness/rigidity argument of Kenig and Merle applies.Comment: 71 page

Geodynamic effects of subducted seamount at the Manila Trench: Insights from numerical modeling

Abstract We used numerical modeling to investigate the geodynamic effects of subducted seamounts at the Manila Trench. A series of numerical modeling experiments were conducted with variable parameters, including the activation volume (Vact) and cohesion (C), which influence lithospheric rheology, the plate convergence velocity, and the age of subducting slab. Modeling results indicate that varying the Vact and C within an appropriate range have limited effects on the geodynamic process of subduction. A lower Vact allows the slab to sink more easily and results in a steeper dip angle. A slab break-off is more likely to occur under subduction at depths of 100–300 km, while the existence of a seamount further promotes the break-off process. The convergence rate is a key parameter affecting the break-off timing and depth. In contrast, under subduction where subducted oceanic plate move faster upper plate, the model results exhibit non-break-off, steady subduction. Slab age is another factor controlling break-off, where break-off time extends with slab age. A subduction without seamount will cause a ~2 Myr delay in break-off timing. We suggest that the low-velocity zone under the Manila Trench at 17o N is the result of a break-off event due to subduction of the Zhenbei-Huangyan Seamount Chain. Further to the north, such as the location at 19o N, the absence of seamount and an older oceanic crust would favor a delay in break-off timing during subduction

The duration of postoperative analgesic use after total knee arthroplasty and nomogram for predicting prolonged analgesic use

BackgroundTotal knee arthroplasty is currently a reliable treatment for end-stage knee osteoarthritis. However, chronic postsurgical pain (CPSP) is substantially thought to reduce patient satisfaction. NSAID-based oral analgesics were used to manage CPSP, but research on the duration of postoperative analgesic use (DAU) and prolonged analgesic use (PAU) are presently scarce.MethodsPreoperative, perioperative, and one-year or above postoperative follow-up data were collected from 162 patients who underwent total knee arthroplasty between 1 June 2018 and 1 March 2019, and the DAU and the discontinuation time of each patient after discharge were recorded. Observational statistical analysis, diagnostic test, and predictive nomogram construction were performed on the collected data.ResultsThe 3-month DAU has good diagnostic utility for poor outcome of postoperative months twelve (POM12). The constructed nomogram shows that gender, preoperative Numeric Rating Scale (NRS) movement pain scores, duration of surgery, postoperative days three (POD3) moderate to severe movement pain, and POD3 pain rescue medication were significant prognostic predictors of PAU after discharge. The area under the curve (AUC) of the 3-month, 6-month, and 12-month nomogram receiver operating characteristic (ROC) curves were calculated to be 0.741, 0.736, and 0.781.ConclusionPAU was defined as more than three months of NSAID-based oral analgesic use after TKA. Prognostic predictors of PAU after TKA were identified, and visualized nomogram was plotted and evaluated. The evaluation indicated that the prediction model had the good predictive ability and was a valuable tool for predicting PAU after discharge

Chemical compositions and precipitation timing of basement calcium carbonate veins from the South China Sea

Sixteen calcium carbonate veins (CCVs) within the igneous basement recovered from both East and Southwest Sub-basin, close to the fossil spreading ridge of the South China Sea during the Integrated Ocean Drilling Program (IODP) Expedition 349 were investigated. The CCVs are composed primarily of either calcite or aragonite, and some of mixed aragonite and calcite. The delta O-18 values of CCVs range from 25.5 to 31.896e VSMOW, indicating these are typical low temperature basement carbonates precipitated at temperatures of 12-40 degrees C. The Sr-87/Sr-86 ratios of CCVs from Site U1431 show a strong negative correlation with delta O-18-calculated temperatures, regardless of carbonate phases - calcite or aragonite, indicating CCVs with lower Sr-87/Sr-86 ratios have precipitated from moderately warmer and more geochemically evolved hydrothermal fluids, and reflecting that precipitation of CCVs might have occurred any time between 14.5 and 0 Ma at Site U1431. The formation timing of CCVs at Site U1431 is consistent with the ongoing hydrothermal flow and circulation led by recharging seawater into the volcanic basement through the nearby outcropped seamount. The oldest ages of CCVs from Site U1433 at the Southwestern sub-basin of SCS were determined to be similar to 18-11 Ma, based on basement age of 18.5 Ma and the well-established seawater Sr-87/Sr-86 ratio curve. It indicates that the hydrothermal circulation at Site U1433 which is more distal to a recharging/discharging site was only active until similar to 11 Ma. In consequence, the CCVs within basalts from Sites U1431 and U1433 provide more insights into the past hydrologic conditions and hydrothermal circulation along the fossil ridge flank in the SCS

Chemical compositions and precipitation timing of basement calcium carbonate veins from the South China Sea

Sixteen calcium carbonate veins (CCVs) within the igneous basement recovered from both East and Southwest Sub-basin, close to the fossil spreading ridge of the South China Sea during the Integrated Ocean Drilling Program (IODP) Expedition 349 were investigated. The CCVs are composed primarily of either calcite or aragonite, and some of mixed aragonite and calcite. The delta O-18 values of CCVs range from 25.5 to 31.8%o VSMOW, indicating these are typical low temperature basement carbonates precipitated at temperatures of 12-40 degrees C. The Sr-87/Sr-86 ratios of CCVs from Site U1431 show a strong negative correlation with delta O-18-calculated temperatures, regardless of carbonate phases calcite or aragonite, indicating CCVs with lower Sr-87/Sr-86 ratios have precipitated from moderately warmer and more geochemically evolved hydrothermal fluids, and reflecting that precipitation of CCVs might have occurred any time between 14.5 and 0 Ma at Site U1431. The formation timing of CCVs at Site U1431 is consistent with the ongoing hydrothermal flow and circulation led by recharging seawater into the volcanic basement through the nearby outcropped seamount. The oldest ages of CCVs from Site U1433 at the Southwestern sub-basin of SCS were determined to be similar to 18-11 Ma, based on basement age of 18.5 Ma and the well-established seawater Sr-87/Sr-86 ratio curve. It indicates that the hydrothermal circulation at Site U1433 which is more distal to a recharging/discharging site was only active until similar to 11 Ma. In consequence, the CCVs within basalts from Sites U1431 and U1433 provide more insights into the past hydrologic conditions and hydrothermal circulation along the fossil ridge flank in the SCS

Influence of Different Industrial Waste Residues on Engineering Properties of High Liquid Limit Soil and Its Microscopic Mechanism

High liquid limit soil has unfavorable engineering geological characteristics, such as strong disintegration, dry shrinkage and easy cracking, and easy uplift when encountering water, which will cause various problems to the engineering. At present, the relationship between the physical and mechanical properties of high liquid limit soil and the characteristics of water-soil interaction is still not clear enough. In this study, the high liquid limit soil of Zhanjiang Avenue was selected to explore the influence of different ratios of three kinds of industrial waste residues (blast furnace slag, carbide slag, and tailing sand) on the high liquid limit soil. Aiming at the common adverse engineering geological phenomena of high liquid limit soil, such as easy disintegration, dry shrinkage crack, and easy uplift in water, the effects of different industrial waste residues on the water-soil interaction characteristics of high liquid limit soil are explored through disintegration and crack tests. In addition, the effects of different kinds and ratios on the free expansion rate, pH, unconfined compressive strength, and shear strength parameters of high liquid limit soil were studied. The improvement mechanism of different industrial waste residues on the engineering properties of high liquid limit soil is discussed in terms of mineral composition and microstructure. Based on the experimental results of this study and considering the cost and engineering practice, it is suggested that the modified carbide slag optimal ratio of high liquid limit soil of Zhanjiang Avenue is 8%. The results can provide certain guidance for the improvement and application of different industrial waste residues on high liquid limit soil to achieve the effect of sustainable development