Geometric inequalities for free boundary hypersurfaces in a ball

Annals of Global Analysis and Geometry - In this paper, we prove a family of sharp geometric inequalities for free boundary hypersurfaces in a ball in space forms.     

Adaptive finite time distributed 6-DOF synchronization control for spacecraft formation without velocity measurement

Nonlinear Dynamics - In this paper, the problem of distributed finite time six-degree-of-freedom (6-DOF) synchronization control for spacecraft formation flying (SFF) with the external disturbances...     

Synthesis and Characterization of Hydrophilic Trityl Radical TFO for Biomedical and Biophysical Applications

Tetrathiatriarylmethyl (TAM, trityl) radicals have found wide applications as spin probes/labels for EPR spectroscopy and imaging, and as polarizing agents for dynamic nuclear polarization. The high hydrophilicity of TAM radicals is essential for their biomedical applications. However, the synthesis of hydrophilic TAM radicals (e.g., OX063) is extremely challenging and has only been reported in the patent literature, to date. Herein, an efficient synthesis of a highly water-soluble TAM radical bis(8-carboxyl-2,2,6,6-tetramethylbenzo[1,2-d:4,5-d′]bis([1,3]dithiol-4-yl)-mono-(8-carboxyl-2,2,6,6-tetrakis(2-hydroxyethyl)benzo[1,2-d:4,5-d′]bis([1,3]dithiol-4-yl)methyl (TFO), which contains four additional hydroxylethyl groups, relative to the Finland trityl radical CT-03, is reported. Similar to OX063, TFO exhibits excellent properties, including high water solubility in phosphate buffer, low log P, low pK_a, long relaxation times, and negligible binding with bovine serum albumin. On the other hand, TFO has a sharper EPR line and higher O₂ sensitivity than those of OX063. Therefore, in combination with its facile synthesis, TFO should find wide applications in magnetic resonance related fields and this synthetic approach would shed new light on the synthesis of other hydrophilic TAM radicals.     

Possible light neutral boson and particle mass quantization

Qualities of nucleons, such as the fundamental parameter mass, might be modified in extreme conditions relative to those of isolated nucleons. We show the ratio of the EMC-effect tagged nucleon mass to that of the free one(m*/m);these values are derived from the nuclear structure function ratio between heavy nuclei and deuterium measured in the electron Deep Inelastic Scattering(DIS) reaction in 0.3≤x≤0.7. The increase in m*/mwith A-1/3 is phenomenologically interpreted via the release of a color-singlet cluster formed by sea quarks and gluons in bound nucleons holding high momentum in the nucleus, from which the mass and fraction of non-nucleonic components in nuclei can be deduced. The mass of color-singlet clusters released per short range correlated(SRC) proton in the high momentum region(k > 2 fm-1) is extracted to be 16.890 ±0.016 MeV/c2, which evidences the possibility of a light neutral boson and quantized mass of matter.     

Study on the static properties of spiral springs under static loading

Applied Mathematics and Mechanics - Spiral springs have a wide range of applications in various fields. As a result of the complexity of friction, few theoretical analyses of spring belts under...     

Large eddy simulation of high pressure spray with the focus on injection pressure

This paper presents a detailed numerical analysis of diesel engine spray structure induced by the Engine Combustion Network (ECN) Spray A at different injection pressures. The non-reacting simulations are performed using OpenFOAM where an Eulerian–Lagrangian model is adopted in the large eddy simulation (LES) framework. Effects of the LES mesh resolution as well as the spray model parameters are investigated with the focus on their impact on spray structure as the injection pressure varies. The predicted liquid and vapour penetration lengths agree well with the measurements at different injection pressures. The mixture fraction is well captured for the injection pressure of 100 and 150 MPa while a slight deviation from the measurements is observed for the injection pressure of 50 MPa near the nozzle. The parametric analysis confirms that the LES mesh resolution has significant effects on the results. A coarser mesh leads to higher liquid and vapour penetration lengths where the deviation from the measurements is larger, resulting in the highest error at the lowest injection pressure. As the mesh size increases, the droplet size distribution becomes narrower, its pick moves to the smaller droplet size and the probability of droplets with higher temperature increases. On the other hand, with increasing the mesh size, the carrier gas velocity decays slower and its radial dispersion decreases. It is found that the droplet characteristics are more affected by the mesh resolution when the injection pressure is the lowest while the opposite is true for the carrier phase. The number of Lagrangian particles also affects the droplet characteristics and the fuel-air mixing but their effects are not as significant as the mesh size. The results become less sensitive to the number of Lagrangian particles as the pressure injection decreases. Finally, the importance of the initial droplet size distribution is investigated, confirming its impact is marginal, particularly on the liquid length. It is observed that the initial droplet size is only important at very close to the nozzle and its impact on the spray structure becomes quickly insignificant due to the high rates of breakup and evaporation. This trend is consistent at different injection pressures.     

Spin-exchange relaxation of naturally abundant Rb in a K-Rb-21Ne self-compensated atomic comagnetometer

The total effective spin-exchange relaxation of naturally abundant Rb in a K–Rb–21Ne comagnetometer is analyzed,and the results show that the coexistence of 87Rb and 85Rb isotopes in the same volume can lead to a large extra spinexchange broadening compared to pure 87Rb.This broadening mainly comes from the contribution of the equivalent reduction in the Rb spin-exchange rate.On this basis,an approximate relaxation model is proposed and experimentally demonstrated to be more accurate than that from a previous work.This study also provides a method for determining the properties of alkali-metal vapor cells.     

Uncertainty quantification for dynamics of geometrically nonlinear structures coupled with internal acoustic fluids in presence of sloshing and capillarity

In this paper, we propose an uncertainty quantification analysis, which is the continuation of a recent work performed in a deterministic framework. The fluid–structure system under consideration is the one experimentally studied in the sixties by Abramson, Kana, and Lindholm from the Southwest Research Institute under NASA contract. This coupled system is constituted of a linear acoustic liquid contained in an elastic tank that undergoes finite dynamical displacements, inducing geometrical nonlinear effects in the structure. The liquid has a free surface on which sloshing and capillarity effects are taken into account. The problem is expressed in terms of the acoustic pressure field in the fluid, of the displacement field of the elastic structure, and of the normal elevation field of the free surface. The nonlinear reduced-order model constructed in the recent work evoked above is reused for implementing the nonparametric probabilistic approach of uncertainties. The objective of this paper is to present a sensitivity analysis of this coupled fluid–structure system with respect to uncertainties and to use a classical statistical inverse problem for carrying out the experimental identification of the hyperparameter of the stochastic model. The analysis show a significant sensitivity of the displacement of the structure, of the acoustic pressure in the liquid, and of the free-surface elevation to uncertainties in both linear and geometrically nonlinear simulations.     

自相似Euler方程的数值方法

Euler方程某些问题的解具有自相似特点，可以使用更准确的方法求解.提出了两种数值方法，分别称为自相似和准自相似方法，新方法可以使用现有守恒律方程的数值格式，无须设计特殊方法.对一维激波管问题、二维Riemann问题、激波反射以及激波折射问题进行了数值计算.对自相似Euler方程，一维计算结果显示数值解基本等同于精确解，二维结果也比现有文献计算的结果有更高的分辨率.对准自相似Euler方程，新方法可以求解不具有自相似性但接近自相似的问题，并在计算时间足够长时可以取得自相似Euler方程的效果.数值求解自相似Euler方程对自相似问题的研究，高分辨率、高精度格式的设计乃至Euler方程的精确解都有重要启示.