Global Solutions For Systems of Quadratic Nonlinear Schr\"odinger Equations in 3D

In this work, we prove global well-posedness and scattering for systems of quadratic nonlinear Schr\"odinger equations in the critical three-dimensional case, for small, localized data. For the terms corresponding to the nonlinearity $u\bar{u}$, we need to do an $\epsilon$ regularization of this part of the nonlinearity. In order to tackle quadratic space-time resonances, after performing a Littlewood-Paley decomposition, we use integration by parts in the Duhamel term, to take advantage of the oscillations when space-time resonances are absent.Comment: 100 page

SUMMERS, Tim. 2021. China’s Hong Kong: The Politics of a Global City. 2nd ed. Newcastle: Agenda Publishing.

There has been a growing tendency to frame the discussion of developments in Hong Kong almost by default within a framework of “Beijing vis-à-vis Hong Kong” – or indeed of Beijing’s unilateral tightening of its grip on the city. Such a simplification, as Tim Summers points out, is “a misleading or at least partial interpretation of what is going on in Hong Kong” (p. 97). From this perspective, therefore, in his timely and concise monograph, Summers suggests that the ways to approach, conduct ..

Left ventricular T1-mapping in diastole versus systole in patients with mitral regurgitation

Cardiovascular magnetic resonance T1-mapping enables myocardial tissue characterisation, and is capable of quantifying both intracellular and extracellular volume. T1-mapping is conventionally performed in diastole, however, we hypothesised that systolic readout would reduce variability due to a reduction in myocardial blood volume. This study investigated whether T1-mapping in systole alters T1 values compared to diastole and whether reproducibility alters in atrial fibrillation compared to sinus rhythm. We prospectively identified 103 consecutive patients recruited to the Mitral FINDER study who had T1 mapping in systole and diastole. These patients had moderate or severe mitral regurgitation and a high incidence of ventricular dilatation and atrial fibrillation. T1, ECV and goodness-of-fit (R2) values of the T1 times were calculated offline using Circle cvi42 and in house-developed software. Systolic T1 mapping was associated with fewer myocardial segments being affected by artefact compared to diastolic T1 mapping [217/2472 (9%) vs 515/2472 (21%)]. Mean native T1 values were not significantly different when measured in systole and diastole (985 ± 26 ms vs 988 ± 29 respectively; p = 0.061) and mean post-contrast values showed similar good agreement (462 ± 32 ms vs 459 ± 33 respectively, p = 0.052). No clinically significant differences in ECV, native T1 and post-contrast T1 were identified between diastolic and systolic T1 maps in males versus females, or in patients with permanent atrial fibrillation versus sinus rhythm. A statistically significant improvement in R2 value was observed with systolic over diastolic T1 mapping in all analysed maps (n = 411) (96.2 ± 1.4% vs 96.0 ± 1.4%; p &lt; 0.001) and in subgroup analyses [Sinus rhythm: 96.1 ± 1.4 vs 96.3 ± 1.4 (n = 327); p &lt; 0.001. AF: 95.5 ± 1.3 vs 95.9 ± 1.2 (n = 80); p &lt; 0.001] [Males: 95.8 ± 1.4 vs 96.1 ± 1.3 (n = 264); p &lt; 0.001; Females: 96.2 ± 1.3 vs 96.4 ± 1.4 (n = 143); p = 0.009]. In conclusion, myocardial T1 mapping is associated with similar T1 and ECV values in systole and diastole. Furthermore, systolic acquisition is less prone to gating artefact in arrhythmia.</p

Cardiac magnetic resonance T1 and extracellular volume mapping with motion correction and co-registration based on fast elastic image registration

10.1007/s10334-017-0668-2Magnetic Resonance Materials in Physics, Biology and Medicine311115-12

Application of Patient-Specific Computational Fluid Dynamics in Coronary and Intra-Cardiac Flow Simulations: Challenges and Opportunities

The emergence of new cardiac diagnostics and therapeutics of the heart has given rise to the challenging field of virtual design and testing of technologies in a patient-specific environment. Given the recent advances in medical imaging, computational power and mathematical algorithms, patient-specific cardiac models can be produced from cardiac images faster, and more efficiently than ever before. The emergence of patient-specific computational fluid dynamics (CFD) has paved the way for the new field of computer-aided diagnostics. This article provides a review of CFD methods, challenges and opportunities in coronary and intra-cardiac flow simulations. It includes a review of market products and clinical trials. Key components of patient-specific CFD are covered briefly which include image segmentation, geometry reconstruction, mesh generation, fluid-structure interaction, and solver techniques

Atomic Structure Evolution of Pt–Co Binary Catalysts: Single Metal Sites versus Intermetallic Nanocrystals

Due to their exceptional catalytic properties for the oxygen reduction reaction (ORR) and other crucial electrochemical reactions, PtCo intermetallic nanoparticle (NP) and single atomic (SA) Pt metal site catalysts have received considerable attention. However, their formation mechanisms at the atomic level during high-temperature annealing processes remain elusive. Here, the thermally driven structure evolution of Pt–Co binary catalyst systems is investigated using advanced in situ electron microscopy, including PtCo intermetallic alloys and single Pt/Co metal sites. The pre-doping of CoN4 sites in carbon supports and the initial Pt NP sizes play essential roles in forming either Pt3Co intermetallics or single Pt/Co metal sites. Importantly, the initial Pt NP loadings against the carbon support are critical to whether alloying to L12-ordered Pt3Co NPs or atomizing to SA Pt sites at high temperatures. High Pt NP loadings (e.g., 20%) tend to lead to the formation of highly ordered Pt3Co intermetallic NPs with excellent activity and enhanced stability toward the ORR. In contrast, at a relatively low Pt loading (<6 wt%), the formation of single Pt sites in the form of PtC3N is thermodynamically favorable, in which a synergy between the PtC3N and the CoN4 sites could enhance the catalytic activity for the ORR, but showing insufficient stability

Precision Higgs physics at the CEPC

The discovery of the Higgs boson with its mass around 125 GeV by the ATLAS and CMS Collaborations marked the beginning of a new era in high energy physics. The Higgs boson will be the subject of extensive studies of the ongoing LHC program. At the same time, lepton collider based Higgs factories have been proposed as a possible next step beyond the LHC, with its main goal to precisely measure the properties of the Higgs boson and probe potential new physics associated with the Higgs boson. The Circular Electron Positron Collider~(CEPC) is one of such proposed Higgs factories. The CEPC is an $e^+e^-$ circular collider proposed by and to be hosted in China. Located in a tunnel of approximately 100~km in circumference, it will operate at a center-of-mass energy of 240~GeV as the Higgs factory. In this paper, we present the first estimates on the precision of the Higgs boson property measurements achievable at the CEPC and discuss implications of these measurements.Comment: 46 pages, 37 figure

Global Solutions for Systems of Quadratic Nonlinear Schrödinger Equations in 3D

In this thesis, we prove existence of global solutions and scattering for systems of quadratic nonlinear Schr\"odinger equations in the critical three-dimensional case, for small, localized data. For the terms corresponding to the nonlinearity $u\bar{u}$, we need to do an $\epsilon$ regularization of this part of the nonlinearity. In order to tackle quadratic space-time resonances, after performing a Littlewood--Paley decomposition, we use integration by parts in the Duhamel term, to take advantage of the oscillations when space-time resonances are absent

Study on Anchor Cable instead of Single Hydraulic Prop Support in Advance Support of Deep Roadway

In order to solve the problems of complicated advanced support process, high labor intensity, affecting the rapid advance of working face and the destruction of roof bolt (cable) by advance single hydraulic prop in ultra kilometer deep mine roadway, the deformation characteristics of roadway surrounding rock is analyzed. Taking the 27304 working face of Wanglou coal mine as the engineering background, numerical simulation, field monitoring, and theoretical calculation were used to analyze the deformation characteristics of roadway surrounding rock within the advanced influence range of 27304 working face. This paper puts forward the active advance support technology scheme, in which grouting anchor cable replaces the existing single hydraulic prop in the advance influence range of the working face in the ultra-kilometer deep mine, and observes and analyzes the deformation and failure characteristics of the surrounding rock of the working face advance roadway. The numerical simulation results show that in the advanced influence range of deep roadway, grouting anchor cable was used to replace the previous single hydraulic prop, and the vertical stress at both ends of the working face decreased by 15 MPa, with a decrease rate of 33.3%; the displacement of roadway roof, floor, and two sides decreased by 10 mm, 55 mm, and 20 mm, with a decrease rate of 40%, 68.75%, and 47.6%, respectively. The field monitoring results show that the roof separation is obviously improved after using grouting anchor cable as the active advance support scheme. It solves the problem of safe and efficient production faced by the ultra-kilometer deep shaft in Wanglou coal mine and provides theoretical and technical support for unmanned double roadway advance support under the condition of safe and efficient mining