Applicability Of Continuum Fracture Mechanics In Atomistic Systems

By quantitating the amplitude of the unbounded stress, the continuum fracture mechanics defines the stress intensity factor K to characterize the stress and displacement fields in the vicinity of the crack tip, thereby developing the relation between the stress singularity and surface energy (energy release rate G). This G-K relation, assigning physical meaning to the stress intensity factor, makes these two fracture parameters widely used in predicting the onset of crack propagation. However, due to the discrete nature of the atomistic structures without stress singularity, there might be discrepancy between the failure prediction and the reality of nanostructured materials. Defining the local atomistic stress with convergence within one lattice ensures the near-tip stress in the discrete systems displays the detailed stress concentration. Through comparison to the equivalent continuum finite element models, although these atomistic near-tip stress distributions preserve the trend of inverse square root singularity, the corresponding fracture toughness in terms of critical stress intensity factor (or energy release rate) is size dependent (i.e., varying with the size of the singular stress zone, K-dominance zone). Consequently, the failure load predicted by constant fracture toughness deviates from what a nanostructure can sustain if the singular stress is not dominant. The two-parameter model, including the contributions from both singular and non-singular terms, is utilized to improve the inadequacy of continuum fracture mechanics. On the other hand, since the magnitude of the atomistic near-tip stress is finite, the maximum stress criterion is valid in atomistic systems, proven by the close match between the peak stress and the theoretic strength under the failure condition. Furthermore, the surface energy determined by the overall energy balance over the crack growth within several sizes of lattice constant is shown to be size-independent, in contrast to the size-dependent results obtained by the G-K relatio

On Bergman kernel functions and weak Morse inequalities

We give simple and unified proofs of weak holomorhpic Morse inequalities on complete manifolds, $q$-convex manifolds, pseudoconvex domains, weakly $1$-complete manifolds and covering manifolds. This paper is essentially based on the asymptotic Bergman kernel functions and the Bochner-Kodaira-Nakano formulas

NAD tagSeq reveals that NAD+-capped RNAs are mostly produced from a large number of protein-coding genes in Arabidopsis.

The 5' end of a eukaryotic mRNA transcript generally has a 7-methylguanosine (m7G) cap that protects mRNA from degradation and mediates almost all other aspects of gene expression. Some RNAs in Escherichia coli, yeast, and mammals were recently found to contain an NAD+ cap. Here, we report the development of the method NAD tagSeq for transcriptome-wide identification and quantification of NAD+-capped RNAs (NAD-RNAs). The method uses an enzymatic reaction and then a click chemistry reaction to label NAD-RNAs with a synthetic RNA tag. The tagged RNA molecules can be enriched and directly sequenced using the Oxford Nanopore sequencing technology. NAD tagSeq can allow more accurate identification and quantification of NAD-RNAs, as well as reveal the sequences of whole NAD-RNA transcripts using single-molecule RNA sequencing. Using NAD tagSeq, we found that NAD-RNAs in Arabidopsis were produced by at least several thousand genes, most of which are protein-coding genes, with the majority of these transcripts coming from <200 genes. For some Arabidopsis genes, over 5% of their transcripts were NAD capped. Gene ontology terms overrepresented in the 2,000 genes that produced the highest numbers of NAD-RNAs are related to photosynthesis, protein synthesis, and responses to cytokinin and stresses. The NAD-RNAs in Arabidopsis generally have the same overall sequence structures as the canonical m7G-capped mRNAs, although most of them appear to have a shorter 5' untranslated region (5' UTR). The identification and quantification of NAD-RNAs and revelation of their sequence features can provide essential steps toward understanding the functions of NAD-RNAs

A Heuristic Approach to Solve an Industrial Scalability Problem

In recent years, the rapid change of market demand is increasing the need for scalability as a key characteristic of manufacturing systems. Scalability allows production capacity to be rapidly and cost-effectively reconfigured in different situation with different requirements and constraints. Our industrial partners are facing quarterly scalability problems involving a multi-unit and multi-product manufacturing system. In this paper, an original approach is presented to solve this kind of problems. Starting from the original manufacturing system configuration and process plan, a set of practical principles are introduced to seek for the feasible configurations; a GA is designed to search in the global solution space. A balancing objective function is defined and used to rank the proposed configurations. A real case study with 4-unit / 4-product situation demonstrates both the validity and efficiency of the proposed approach

Representation Class and Geometrical Invariants of Quantum States under Local Unitary Transformations

We investigate the equivalence of bipartite quantum mixed states under local unitary transformations by introducing representation classes from a geometrical approach. It is shown that two bipartite mixed states are equivalent under local unitary transformations if and only if they have the same representation class. Detailed examples are given on calculating representation classes.Comment: 11 page

A New Design for Low Impact Development in Urban Area- Infiltration Pipe and Gravel Pile

Source: ICHE Conference Archive - https://mdi-de.baw.de/icheArchive

Certain Class of Analytic Functions Based on qq-difference operator

In this paper, we considered a generalized class of starlike functions defined by Kanas and R\u{a}ducanu\cite{10} to obtain integral means inequalities and subordination results. Further, we obtain the for various subclasses of starlike functions.Comment: