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

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

Simulation data were generated by Von-Mises Coupling.

<p>(a) From top panel to bottom panel: a 5<i>Hz</i> slow oscillation; a 40<i>Hz</i> fast oscillation; a 40 Hz fast oscillation, whose amplitude was modulated by the phase of 5<i>Hz</i> slow oscillation; Simulation data without noise; simulation data with noise (<i>σ</i> = 0.1). (b) Simulation data with different absolute amplitude levels of fast rhythm. The parameter <i>c</i> was increased from 0.5 to 1.5. (c) Simulation data with different modulation phases. The parameter <i>θ</i>₀ was changed from 0<i>π</i> to .</p

The phase-amplitude plots for the three simulation types and different coupling intensity k.

<p>The phase-amplitude plots for the three simulation types and different coupling intensity k.</p

Performance of three PAC approaches in simulation type II.

<p><b>The interferential oscillations were filtered from experimental LFP.</b> (a) The interferential oscillations were filtered from the CA1 LFP of the puberty rat. (b) The interferential oscillations were filtered from the CA3 LFP of the adult rat.</p

Phase–amplitude coupling between hippocampal DG low frequency rhythm (2–16 Hz, theta and alpha) and high frequency rhythm (30–80 Hz, gamma) measured by Modulation Index.

<p>(a) PAC between low frequency rhythm (filter bandwidth = 1 Hz) and high frequency rhythm (filter bandwidth = 1 Hz). (b) PAC between low frequency rhythm (filter bandwidth = 2 Hz) and high frequency rhythm (filter bandwidth = 1 Hz). (c) Difference (b-a). (d) PAC between low frequency rhythm (filter bandwidth = 1 Hz) and high frequency rhythm (filter bandwidth = 2 Hz). (e) Difference (d-a).</p

Cobalt-Catalyzed Cross-Dehydrogenative Coupling Reaction between Unactivated C(sp²)–H and C(sp³)–H Bonds

Catalytic oxidative cross-dehydrogenative coupling between unactivated C­(sp²)–H and C­(sp³)–H bonds is achieved by the cobalt-catalyzed <i>o</i>-alkylation reaction of aromatic carboxamides containing (pyridin-2-yl)­isopropyl amine (PIP–NH₂) as a <i>N</i>,<i>N</i>-bidentate directing group. Many different C­(sp³)–H bonds in alkanes, toluene derivatives and even in the α-position of ethers and thioethers can be used as coupling partners. This method has a broad substrate scope and the tolerance of various functional groups

Two new entangled complexes based on 4,4′-bis(1-imidazolyl)biphenyl: syntheses, structures, thermal and photoluminescent properties

<div><p>Two new entangled complexes, [Zn(bibp)(L¹)]·0.25H₂O (<b>1</b>) and [Co(bibp)(H₂L²)] (<b>2</b>) (bib<i>p</i> = 4,4′-bis(1-imidazolyl)biphenyl, H₂L¹ = 4,4′-(2,2′-oxybis(ethane-2,1-diyl)bis(oxy))dibenzoic acid, and H₄L² = 5,5′-(2,2′-oxybis(ethane-2,1-diyl)bis(oxy))diisophthalic acid), have been synthesized hydrothermally. Complex <b>1</b> features a new uninodal four-connected (6⁵·8) net with vertex symbol 6·6·6·6·6₂·8₂, which is different from all that exhibit uninodal four-connected (6⁵·8) nets found in the literature, including <b>cds</b>, <b>dmp</b>, <b>ict</b>, <b>mok</b>, <b>unl</b> and <b>unm</b>. Three of these nets interpenetrate. Complex <b>2</b> shows an unusual threefold 2-D → 3-D polythreaded framework, in which each 2-D wave-like net is formed by the intersection, at the shared Co nodes, of the 1-D left- and right-handed single-helical (H₂L²)²⁻ chains and the 1-D bibp <i>meso</i>-helices. Furthermore, the thermal and photoluminescent properties of <b>1</b> have also been studied.</p></div