Tensor method for optimal control problems constrained by fractional three-dimensional elliptic operator with variable coefficients

We introduce the tensor numerical method for solving optimal control problems that are constrained by fractional two- (2D) and three-dimensional (3D) elliptic operators with variable coefficients. We solve the governing equation for the control function which includes a sum of the fractional operator and its inverse, both discretized over large 3D $n\times n\times n$ spacial grids. Using the diagonalization of the arising matrix-valued functions in the eigenbasis of the one-dimensional Sturm–Liouville operators, we construct the rank-structured tensor approximation with controllable precision for the discretized fractional elliptic operators and the respective preconditioner. The right-hand side in the constraining equation (the optimal design function) is supposed to be represented in a form of a low-rank canonical tensor. Then the equation for the control function is solved in a tensor structured format by using preconditioned CG iteration with the adaptive rank truncation procedure that also ensures the accuracy of calculations, given an $\epsilon$-threshold. This method reduces the numerical cost for solving the control problem to $O(n\log n)$ (plus the quadratic term $O(n^2)$ with a small weight), which outperforms traditional approaches with $O(n^3\log n)$ complexity in the 3D case. The storage for the representation of all 3D nonlocal operators and functions involved is also estimated by $O(n\log n)$. This essentially outperforms the traditional methods operating with fully populated $n^3\times n^3$ matrices and vectors in ${?}^{n^3}$. Numerical tests for 2D/3D control problems indicate the almost linear complexity scaling of the rank truncated preconditioned conjugate gradient iteration in the univariate grid size n.     

基于碳化硅衬底的宽禁带半导体外延

宽禁带半导体具备禁带宽度大、电子饱和飘移速度高、击穿场强大等优势,是制备高功率密度、高频率、低损耗电子器件的理想材料。碳化硅(SiC)材料具有热导率高、化学稳定性好、耐高温等优点,在SiC衬底上外延宽禁带半导体材料,对充分发挥宽禁带半导体材料的优势,并提升宽禁带半导体电子器件的性能具有重要意义。得益于SiC衬底质量持续提升及成本不断降低,基于SiC衬底的宽禁带半导体电子市场占比呈现逐年增加的态势。在SiC衬底上外延生长高质量的宽禁带半导体材料是提高宽禁带半导体电子器件性能及可靠性的关键瓶颈。本文综述了近年来国内外研究者们在SiC衬底上外延SiC、氮化镓(GaN)、氧化镓(Ga₂O₃)所取得的研究进展,并展望了SiC衬底上宽禁带半导体外延的发展及应用前景。     

Morphology‐Controlled Synthesis of Organometal Halide Perovskite Inverse Opals

The booming development of organometal halide perovskites in recent years has prompted the exploration of morphology‐control strategies to improve their performance in photovoltaic, photonic, and optoelectronic applications. However, the preparation of organometal halide perovskites with high hierarchical architecture is still highly challenging and a general morphology‐control method for various organometal halide perovskites has not been achieved. A mild and scalable method to prepare organometal halide perovskites in inverse opal morphology is presented that uses a polystyrene‐based artificial opal as hard template. Our method is flexible and compatible with different halides and organic ammonium compositions. Thus, the perovskite inverse opal maintains the advantage of straightforward structure and band gap engineering. Furthermore, optoelectronic investigations reveal that morphology exerted influence on the conducting nature of organometal halide perovskites.     

Sonochemical Synthesis of Gold Nanoparticles by Using High Intensity Focused Ultrasound

The sonochemical synthesis of gold nanoparticles (GNPs) with different shapes and size distributions by using high‐intensity focused ultrasound (HIFU) operating at 463 kHz is reported. GNP formation proceeds through the reduction of Au³⁺ to Au⁰ by radicals generated by acoustic cavitation. TEM images reveal that GNPs show irregular shapes at 30 W, are primarily icosahedral at 50 W and form a significant amount of nanorods at 70 W. The size of GNPs decreases with increasing acoustic power with a narrower size distribution. Sonochemiluminescence images help in the understanding of the effect of HIFU in controlling the size and shapes of GNPs. The number of radicals that form and the mechanical forces that are generated control the shape and size of the GNPs. UV/Vis spectra and TEM images are used to propose a possible mechanism for the observed effects. The results presented demonstrate, for the first time, that the HIFU system can be used to synthesise size‐ and shape‐controlled metal nanoparticles.     

Laser Sculpting of Atomic sp,sp2, and sp3 Hybrid Orbitals

Atomic sp, sp², and sp³ hybrid orbitals were introduced by Linus Pauling to explain the nature of the chemical bond. Quantum dynamics simulations show that they can be sculpted by means of a selective series of coherent laser pulses, starting from the 1s orbital of the hydrogen atom. Laser hybridization generates atoms with state‐selective electric dipoles, opening up new possibilities for the study of chemical reaction dynamics and heterogeneous catalysis.     

Regulating Molecular Recognition with C‐Shaped Strips Attained by Chirality‐Assisted Synthesis

Chirality‐assisted synthesis (CAS) is a general approach to control the shapes of large molecular strips. CAS is based on enantiomerically pure building blocks that are designed to strictly couple in a single geometric orientation. Fully shape‐persistent structures can thus be created, even in the form of linear chains. With CAS, selective recognition between large host and guest molecules can reliably be designed de novo. To demonstrate this concept, three C‐shaped strips that can embrace a pillar[5]arene macrocycle were synthesized. The pillar[5]arene bound to the strips was a better host for electron‐deficient guests than the free macrocycle. Experimental and computational evidence is provided for these unique cooperative interactions to illustrate how CAS could open the door towards the precise positioning of functional groups for regulated supramolecular recognition and catalysis.     

Maintenance of residual activity of Bt toxin by using natural and synthetic dyes: a novel approach for sustainable mosquito vector control

Mosquito control protein from Bacillus thuringiensis gets inactivated with exposure to sunlight. To address this issue, the potential of synthetic and natural dye was investigated as sunlight protectants. Bt SV2 in absence of dyes when exposed to sunlight showed reduced effectiveness against the fourth instars of mosquito larvae. Whereas acriflavin, congo red and violacein were able to maintain 86.4%, 91.6% and 82.2% mosquito larvicidal efficacy of Bt SV2 against IVth instars larvae of Anopheles stephensi Meigen after exposure to sunlight. Similarly, beetroot dye, acriflavin, congo red and violacein maintained 98.4%, 97.1%, 90.8% and 70.7% larvicidal activities against Aedes aegypti Linnaeus after sunlight exposure. Prodigiosin was found to be the best photo-protectant by simultaneously protecting and enhancing Bt activity by 6.16% and 22.16% against A. stephensi and A. aegypti, respectively. Combination of dyes with Bt formulations can be a good strategy for mosquito control programmes in tropical and sub-tropical regions.