SOLVING SYSTEMS OF QUADRATIC EQUATIONS VIA EXPONENTIAL-TYPE GRADIENT DESCENT ALGORITHM

We consider the rank minimization problem from quadratic measurements, i.e., recovering a rank $r$ matrix $X \in \mathbb{R}^{n×r}$ from $m$ scalar measurements $y_i=a_i^T XX^T a_i,\;a_i\in \mathbb{R}^n,\;i=1,\ldots,m$. Such problem arises in a variety of applications such as quadratic regression and quantum state tomography. We present a novel algorithm, which is termed $exponential-type$ $gradient$ $descent$ $algorithm$, to minimize a non-convex objective function $f(U)=\frac{1}{4m}\sum_{i=1}^m(y_i-a_i^T UU^T a_i)^2$. This algorithm starts with a careful initialization, and then refines this initial guess by iteratively applying exponential-type gradient descent. Particularly, we can obtain a good initial guess of $X$ as long as the number of Gaussian random measurements is $O(nr)$, and our iteration algorithm can converge linearly to the true $X$ (up to an orthogonal matrix) with $m=O\left(nr\log (cr)\right)$ Gaussian random measurements.     

Novel Non-Evaporable Getter Materials and Their Possible Use in Fusion Application for Tritium Recovery

Non-evaporable getters (NEGs) are metallic compounds of the IV group, particularly titanium and/or zirconium-based alloys and are usually used as pumps in vacuum technologies since they are able to sorb, by chemical reactions, most of the active gas molecules, with particular efficacy towards hydrogen isotopes. This work suggests an alternative application of these materials to fusion nuclear reactors, where there is the need to recover small amount of tritium from the large helium flow rate composing the primary coolant loop. Starting from the tritium mass balance inside the primary coolant loop, the amount of coolant to be routed inside the coolant purification system (CPS) is identified. Then a feasibility study, based on the bulk getter theory, is presented by considering three different commercial alloys, named ST707, ST101 and ZAO. The results provide the mass, the area and the regeneration parameters of the three different alloys necessary to fulfill the requirements of the CPS unit. By comparing the features of the three alloys, the ZAO material appears the most promising for the proposed application because it requires the lower amount of material and a lower number of regeneration cycles.     

Ultraconvergence of the derivative of high-order finite element method for elliptic problems with constant coefficients

In this article, for second order elliptic problems with constant coefficients, the local ultraconvergence of the derivative of finite element method using piecewise polynomials of degrees k (k ≥ 2) is studied by the interpolation postprocessing technique. Under suitable regularity and mesh conditions, we prove that at an interior vertex, which is away from the boundary with a fixed distance, the gradient of the postprecessed finite element solution using piecewise polynomials of degrees k (k ≥ 2) converges to the gradient of the exact solution with order . Numerical experiments are used to illustrate our theoretical findings.     

Highly branched polyethylene used as sorbents for oil-spill cleanup and separation

Highly branched polyethylene (HBPE) was developed into practical application as highly efficient sorbent material for oil-spill cleanup and oil/water separation. To obtain large-scale production of HBPE, a thermal stable Ni(II)-α-diimine catalyst for ethylene polymerization in our previous work has been employed to prepare the polyolefin material in a 10-liter polymerization reactor with a high activity (>10⁶ g_PE/mol_[Ni] h). The structure, molecular weight and distribution, thermal and mechanical properties were systematically characterized by NMR, ATR-FTIR, GPC, DSC, DMA, and TGA, respectively. Through simple but feasible cross-linking process, the HBPE-based oil-absorption materials with contact angles up to 111.5° were directly applied into absorption test using various oil and pure hydrocarbons. Reusability and recovery of the absorption materials and oil or solvents were probed by drying or using the distillation method. Oil/water separation was made to determine the hydrophobic and oleophilic nature of this material. Flory-Rehner polymer swelling theory is employed to study the structure–property relationship via determining the network structure including cross-linking density ρ_c and average molecular weight M_c between two cross-links. The mixture of sorbent material after absorbing oil was regarded as crude oil component to simulate oil refinery process by thermogravimetric analysis, providing an alternative approach for oil-collection.     

Optimization of the shape memory effect in shape memory polymers

In this article, we show that given a thermoresponsive shape memory polymer, it is possible to alter a number of its properties, such as the recovery temperature, shape fixity ratio, maximum recovery stress, and final recovery stress (and even a right combination of some of them, e.g., the maximum recovery stress and final recovery stress), simply by means of selecting the programming temperature to achieve optimized performance. Some concerns for the implementation in real engineering practice are also discussed. Although the focus is on the case of a fixed maximum strain in programming, alternative programming approaches can be investigated in a similar way for optimized performance as well. © 2011 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem, 2011     

Hydrophobic polyurethane polyHIPEs templated from mannitol within nonaqueous high internal phase emulsions for oil spill recovery

Although amphiphilicity is an integral component for the applications of polyHIPEs (PHs), it is challenging to produce hydrophobic PHs from hydrophilic monomers. Herein, hydrophobic polyurethane (PU) PHs have been fabricated from a water‐soluble mannitol within block copolymer surfactant‐stabilized, nonaqueous high internal phase emulsions (HIPEs). These highly porous, interconnected, macroporous PU PHs were hydrophobic with water contact angles between 102° and 140°, demonstrating that water‐soluble monomers could be used for fabrication of hydrophobic PHs. The block copolymer surfactant acted not only as the HIPE stabilizer, but also as a monomer, enhancing hydrophobicity and overcoming some drawbacks imposed by conventional inert stabilizers. The solvents used for PU PH synthesis and purification were easily recovered and reused, showing that nonaqueous HIPE templating for PU PH preparation is an efficient and facile route. The PU PHs were investigated for oil spill reclamation and they were demonstrated to be an ideal candidate for such an application. © 2019 Wiley Periodicals, Inc. J. Polym. Sci., Part A: Polym. Chem. 2019, 57, 1315–1321     

多通道可回收型中试亚临界流体萃取装置的改造及功能拓展

以中试亚临界流体萃取装置为基础,将萃取金属滤筐改造为多通道非对称性微孔复合陶瓷膜滤芯、增加萃取溶剂回收系统以及相关重要部件的安装与调试,实现了系统压力在1.55±0.05 Mpa范围内波动,稳定可控.植物油萃取效率提高到95%以上,平均提取时间缩短了75%左右.对植物油中脂肪酸、挥发性有效成分可进行准确定性、定量分析.平均回收率在93%左右,实现了萃取溶剂有效回收利用,节能减排,从而实现了仪器的多通道可回收型升级改造,达到了仪器萃取能力提升的目的.     

冰下运动目标主动探测技术研究*

使用主动声呐探测冰下目标时，混响是无法回避的问题。在大面积冰层覆盖的水域中，混响具有强度大、作用范围广的特点，导致主动声呐对目标探测的性能大大下降。本文针对有着强混响的冰下水域这一应用背景，重点研究了基于低秩矩阵恢复理论的冰下运动目标主动探测方法。该方法运用常规波束形成获取多组方位时间历程图像，然后利用低秩矩阵恢复算法分离图像中的混响背景与运动目标。仿真表明不精确的增广拉格朗日乘子法(Inexact Augmented Lagrange Multiplier, IALM)在等间隔直线阵、非等距线阵和均匀间隔圆形阵三种阵型下均有较好的效果。同时与经典的背景差分法做了对比，表明了低秩矩阵恢复算法具有更好的适应性。松花江冰下实验验证了在线阵情况下低秩矩阵恢复算法的实际应用性。     

Difference approach to the analysis of resistivity recovery data for irradiated short-range ordered alloys

Electrical resistivity recovery (RR) data for irradiated concentrated alloys typically consist of two inseparable parts, one resulting from defect annihilation and the other from short-range order (SRO) effects. These parts exhibit different behaviour and often follow opposite trends. Therefore, in this case, analysis of RR data within the conventional method is too complicated. A new approach to data analysis of such a two-component RR is proposed. The approach involves a new quantity, the difference RR (DRR), which is composed of RR dependences of two similar samples irradiated to different defect concentrations. It is shown that the SRO formation proper and the stages corresponding to the onset of long-range migration of Frenkel pair defects, formed in each part of RR, can be clearly related to certain features of the DRR plots. This interrelationship allows detecting and identifying these stages in each part of RR separately. The validity of the approach is illustrated by analysis of the available pairwise RR data for Fe–16Cr–20Ni and Fe–4Cr alloys. It makes it possible to detect the small contribution from the SRO formation to RR in Fe–4Cr, which we failed to observe previously. It is shown that stage III of Fe–4Cr, which has a negligible contribution to the part of RR induced by defect annihilation, is clearly observed in the part induced by SRO formation.