M-integral analysis for cracks in a viscoplastic material with extended finite element method

The M-integral can be used to quantify complex damage in materials subjected to mechanical deformation. However, the effect of viscoplasticity on the damage level associated with the M-integral has not been studied yet. In this paper, the variation of the M-integral associated with viscoplastic deformation was investigated numerically using a user-defined material subroutine. Effects of creep deformation and loading rate on the M-integral were also evaluated. In particular, the association of crack growth with the evolution of the M-integral was captured by the extended finite element method for different crack configurations. It was found that viscoplastic deformation has a great effect on the damage evolution of viscoplastic materials characterized by the M-integral. Crack growth leads to an increase of the M-integral, indicating progressive damage of the materials. Concerning the secondary cracks formed around a major crack, the results show that the M-integral is highly dependent on the numbers and locations of those secondary cracks. Shielding effect is mostly evident for microcracks with centres located just behind or vertically in line with the major crack tip. With the increasing number of microcracks, the shielding effect tends to decrease as reflected by the increasing M-integral value

Multilinear Algebra in High-Order Data Analysis: Retrieval, Classification and Representation

One of the fundamental problems in data analysis is how to represent the data. Real-world signals of practical interest such as color imaging, video sequences and multi-sensor networks, are usually generated by the interaction of multiple factors and thus can be intrinsically represented by higher-order tensors. Application of conventional linear analysis methods to higher-order data tensor representation is typically performed by conversion of the data to very long vectors, thus inevitably losing spatial locality as well as imposing a huge computational and memory burden. As a result, great efforts have been made to extend conventional linear analysis methods that rely on data representation in the form of vectors, for higher-order data analysis. This thesis is dedicated to the study of higher-order data analysis including retrieval, classification and representation, within the mathematical framework provided by multilinear algebra. We first present a higher-order singular value decomposition (HOSVD)-based method for robust indexing and retrieval of higher-order data in responding to various query structures. We prove theoretically that the set of HOSVD unitary matrices of a sub-tensor is equivalent to the corresponding subset of HOSVD unitary matrices of the original tensor. Therefore, if we first arrange all tensors in the database compactly as a higher-order tensor, then we only need to conduct HOSVD once on the total tensor. We then extend linear discriminant analysis (LDA) for higher-order data classification. We propose two multilinear discriminant analysis methods, Direct General Tensor Discriminant Analysis (DGTDA) and Constrained Multilinear Discriminant Analysis (CMDA). Both DGTDA and CMDA seek a tensor-to-tensor projection onto a lower-dimensional tensor subspace, which is most efficient for discrimination. Finally, we propose Generalized Tensor Compressive Sensing (GTCS)--a unified framework for compressive sensing of higher-order tensors. GTCS offers an efficient means for representation of multidimensional data by providing simultaneous acquisition and compression from all tensor modes

Compressive Sensing of Sparse Tensors

Compressive sensing (CS) has triggered an enormous research activity since its first appearance. CS exploits the signal's sparsity or compressibility in a particular domain and integrates data compression and acquisition, thus allowing exact reconstruction through relatively few nonadaptive linear measurements. While conventional CS theory relies on data representation in the form of vectors, many data types in various applications, such as color imaging, video sequences, and multisensor networks, are intrinsically represented by higher order tensors. Application of CS to higher order data representation is typically performed by conversion of the data to very long vectors that must be measured using very large sampling matrices, thus imposing a huge computational and memory burden. In this paper, we propose generalized tensor compressive sensing (GTCS)-a unified framework for CS of higher order tensors, which preserves the intrinsic structure of tensor data with reduced computational complexity at reconstruction. GTCS offers an efficient means for representation of multidimensional data by providing simultaneous acquisition and compression from all tensor modes. In addition, we propound two reconstruction procedures, a serial method and a parallelizable method. We then compare the performance of the proposed method with Kronecker compressive sensing (KCS) and multiway compressive sensing (MWCS). We demonstrate experimentally that GTCS outperforms KCS and MWCS in terms of both reconstruction accuracy (within a range of compression ratios) and processing speed. The major disadvantage of our methods (and of MWCS as well) is that the compression ratios may be worse than that offered by KCS

Compressive Sensing of Sparse Tensors

Compressive sensing (CS) has triggered an enormous research activity since its first appearance. CS exploits the signal's sparsity or compressibility in a particular domain and integrates data compression and acquisition, thus allowing exact reconstruction through relatively few nonadaptive linear measurements. While conventional CS theory relies on data representation in the form of vectors, many data types in various applications, such as color imaging, video sequences, and multisensor networks, are intrinsically represented by higher order tensors. Application of CS to higher order data representation is typically performed by conversion of the data to very long vectors that must be measured using very large sampling matrices, thus imposing a huge computational and memory burden. In this paper, we propose generalized tensor compressive sensing (GTCS)-a unified framework for CS of higher order tensors, which preserves the intrinsic structure of tensor data with reduced computational complexity at reconstruction. GTCS offers an efficient means for representation of multidimensional data by providing simultaneous acquisition and compression from all tensor modes. In addition, we propound two reconstruction procedures, a serial method and a parallelizable method. We then compare the performance of the proposed method with Kronecker compressive sensing (KCS) and multiway compressive sensing (MWCS). We demonstrate experimentally that GTCS outperforms KCS and MWCS in terms of both reconstruction accuracy (within a range of compression ratios) and processing speed. The major disadvantage of our methods (and of MWCS as well) is that the compression ratios may be worse than that offered by KCS

Synthesis of Coumarins, 4-Hydroxycoumarins, and 4-Hydroxyquinolinones by Tellurium-Triggered Cyclizations¹

Coumarins, 4-hydroxycoumarins, and 4-hydroxyquinolin-2(1H)-ones can be conveniently prepared by treatment of α-halocarboxylic acid esters of salicylaldehyde, o-hydroxyacetophenone, methyl salicylate, and methyl N-methyl- or N-phenylanthranilates with sodium or lithium telluride. Phenylketene formation competes with cyclization of the α-chlorophenylacetate ester of methyl salicylate as demonstrated by a trapping experiment with benzylamine. Elemental tellurium may be recovered and reused

Pd-Catalyzed Asymmetric Three-Component Allenol Carbopalladation and Allylic Cycloaddition Cascade: A Route to Functionalized Tetrahydrofurans

The first Pd-catalyzed asymmetric three-component reaction of 2,3-allenol, aryl iodides, and 2-arylmethylenemolononitriles has been developed via an allenol carbopalladation and an allylic cycloaddition cascade. This process allows rapid access to substituted tetrahydrofurans bearing diverse functional groups in good yields with high diastereoselectivities and excellent enantioselectivities. The concise total synthesis of a lignan, (−)-2-episesaminone, has been achieved by the elaboration of a functionalized tetrahydrofuran obtained from this reaction

DataSheet_1_Observational Study on the Variability of Mixed Layer Depth in the Bering Sea and the Chukchi Sea in the Summer of 2019.pdf

Based on the CTD data from 58 stations in the Bering Sea and the Chukchi Sea in the summer of 2019, the values of mixed layer depth (MLD) were obtained by using the density difference threshold method. It was concluded that the MLD can be estimated more accurately by using a criterion of 0.125 kg/m3 in this region. The average MLD in the Bering Sea basin was larger than that in the Bering Sea shelf, and both of them were smaller than that in the Bering Sea slope. The MLD increased northward in both the Chukchi Sea shelf and the Chukchi Sea slope. The farther northward, the greater the difference between the MLD calculated from temperature (MLDt) and the MLD calculated from density (MLDd). The water masses and their interaction played an important role in the variation of MLD in the northern Bering Sea shelf and Chukchi Sea. The MLD was large due to the vertically homogeneous Anadyr Water in the northwestern Bering Sea shelf. The horizontal advection of Bering Sea Anadyr Water and Alaska Coastal Water in the Bering Sea shelf led to shallower MLD in the central northern Bering Sea shelf. The westward advection of the Alaska Coastal Water caused shallow mixed layers (MLs) in some regions of the Chukchi Sea shelf in the summer of 2019. The observed large MLD at BL01 station near the Aleutian Island was caused by an anticyclonic eddy. The northward increase in the MLD in the Chukchi Sea was related to the low-salinity seawater from sea ice melting in summer. The spatial variation of MLD was also closely related to the surface momentum flux and the sea surface buoyancy flux. Stratification plays an even more important role in determining the variation of MLD. The ML in 2019 was shallower and warmer than those in previous years, especially in the Bering Sea shelf and Chukchi Sea where sea ice volume, thickness, and coverage were significantly larger than the Bering Sea basin, which was related to the small sea ice volume in winter and spring of 2019 compared to previous years.</p

Performance of three PAC approaches in simulation type II.

The interferential oscillations were sinusoidal oscillations. (a) Simulation data were constructed without noise. (b) Noise level σ = 0.1. (c) Noise level σ = 0.2.</p

Cobalt-Catalyzed Secondary Alkylation of Arenes and Olefins with Alkyl Ethers through the Cleavage of C(sp²)–H and C(sp³)–O Bonds

A novel cobalt-catalyzed C–H alkylation of arenes and olefins is achieved with (pyridin-2-yl)­isopropyl amine as an N,N-bidentate directing group. Different linear, branched, and cyclic alkyl ethers were used as practical secondary alkylating reagents through cleavage of C­(sp3)–O bond, providing an efficient approach to the synthesis of verstile o-alkylated arylamides and tetrasubstituted acrylamides. Mechanistic studies indicate that cleavage of the inert C­(sp3)–O bond involves a cobalt-promoted radical process and that cleavage of the inert C­(sp2)–H bond by a cobalt catalyst is a rate-limiting step

A Precise Annotation of Phase-Amplitude Coupling Intensity

<div><p>Neuronal information can be coded in different temporal and spatial scales. Cross-frequency coupling of neuronal oscillations, especially phase-amplitude coupling (PAC), plays a critical functional role in neuronal communication and large scale neuronal encoding. Several approaches have been developed to assess PAC intensity. It is generally agreed that the PAC intensity relates to the uneven distribution of the fast oscillation amplitude conditioned on the slow oscillation phase. However, it is still not clear what the PAC intensity exactly means. In the present study, it was found that there were three types of interferential signals taking part in PAC phenomenon. Based on the classification of interferential signals, the conception of PAC intensity is theoretically annotated as the proportion of slow or fast oscillation that is involved in a related PAC phenomenon. In order to make sure that the annotation is proper to some content, simulation data are constructed and then analyzed by three PAC approaches. These approaches are the mean vector length (MVL), the modulation index (MI), and a new permutation mutual information (PMI) method in which the permutation entropy and the information theory are applied. Results show positive correlations between PAC values derived from all three methods and the suggested intensity. Finally, the amplitude distributions, i.e. the phase-amplitude plots, obtained from different PAC intensities show that the annotation proposed in the study is in line with the previous understandings.</p></div