•Reliability estimations of fatigue life and the linear fatigue stress-life model.•The changes in fractal dimension and the two-dimensional roughness Ra.•Qualitative relationship between fractal ...dimension and crack propagation rate.•Quantitative relationship between the fractal dimension and fatigue life.
Fatigue performance is important for materials and welded joints in engineering structures. A fatigue test of A6005 aluminum alloy welded joints was conducted. When confidence level was 50%, fatigue lives were reliable for reliability levels of 50% and 97.7%. Statistical F-test evaluation proved that the linear fatigue stress-life model was rational. Metallic oxides or discrete bar-like materials led to crack nucleation. Fractal dimension characterized the fracture features, initially increased and then decreased at all stress levels. However, crack propagation rates were inversely proportional to fractal dimension. Further, fractal dimension integration equalled the fatigue life. A linear relationship was established with a good R2 obtained 0.978.
Inspired by the development in modern data science, a shift is increasingly visible in the foundation of statistical inference, away from a real space, where random variables reside, toward a ...nonmetrized and nonordinal alphabet, where more general random elements reside. While statistical inferences based on random variables are theoretically well supported in the rich literature of probability and statistics, inferences on alphabets, mostly by way of various entropies and their estimation, are less systematically supported in theory. Without the familiar notions of neighborhood, real or complex moments, tails, et cetera, associated with random variables, probability and statistics based on random elements on alphabets need more attention to foster a sound framework for rigorous development of entropy-based statistical exercises. In this article, several basic elements of entropic statistics are introduced and discussed, including notions of general entropies, entropic sample spaces, entropic distributions, entropic statistics, entropic multinomial distributions, entropic moments, and entropic basis, among other entropic objects. In particular, an entropic-moment-generating function is defined and it is shown to uniquely characterize the underlying distribution in entropic perspective, and, hence, all entropies. An entropic version of the Glivenko-Cantelli convergence theorem is also established.
During the last few decades, research activity in modeling the properties of random systems via entropies has grown noticeably across a wide spectrum of fields ....
A generalized notion of species richness is introduced. The generalization embeds the popular index of species richness on the boundary of a family of diversity indices each of which is the number of ...species in the community after a small proportion of individuals belonging to the least minorities is trimmed. It is established that the generalized species richness indices satisfy a weak version of the usual axioms for diversity indices, are qualitatively robust against small perturbations in the underlying distribution, and are collectively complete with respect to all information of diversity. In addition to a natural plug-in estimator of the generalized species richness, a bias-adjusted estimator is proposed, and its statistical reliability is gauged via bootstrapping. Finally an ecological example and supportive simulation results are given.
Piezoelectric and triboelectric nanogenerators have been developed as rising energy-harvesting devices in the past few years to effectively convert mechanical energy into electricity. Here, a novel ...hybrid piezo/triboelectric nanogenerator based on BaTiO3 NP/PDMS composite film was developed in a simple and low-cost way. The effects of the BTO content and polarization degree on the output performance were systematically studied. The device with 20 wt % BTO in PDMS and a 100-μm-thick film showed the highest output power. We also designed three measurement modes to record hybrid, triboelectric, and piezoelectric outputs separately with a simple structure that has only two electrodes. The hybrid output performance is higher than the tribo- and piezoelectric performances. This work will provide not only a new way to enhance the output power of nanogenerators, but also new opportunities for developing built-in power sources in self-powered electronics.
Mutual information is one of the essential building blocks of information theory. It is however only finitely defined for distributions in a subclass of the general class of all distributions on a ...joint alphabet. The unboundedness of mutual information prevents its potential utility from being extended to the general class. This is in fact a void in the foundation of information theory that needs to be filled. This article proposes a family of generalized mutual information whose members are indexed by a positive integer n, with the nth member being the mutual information of nth order. The mutual information of the first order coincides with Shannon’s, which may or may not be finite. It is however established (a) that each mutual information of an order greater than 1 is finitely defined for all distributions of two random elements on a joint countable alphabet, and (b) that each and every member of the family enjoys all the utilities of a finite Shannon’s mutual information.
Temperature inversion (TI) constitutes a crucial component in the physicochemical processes of the lower troposphere, but disentangling human contributions to its generation from complex ...environmental factors poses significant challenges. We leveraged the unique natural experiment prompted by the coronavirus disease 2019 (COVID‐19) pandemic to estimate changes in TI incidence and temperature difference (∆T) caused by the economic shutdown in the first half of 2020 across 500 major cities worldwide. We found that ∆T declined by 2.5% and TI incidence declined by 18.2% compared to 2016–2019, exhibiting spatial‐temporal heterogeneity and pronounced declines in cities with higher levels of economic development and emission reduction. Moreover, we demonstrated that fine particulate matter (PM2.5) may serve as a mediating pathway through which human activities influence air thermal properties, and climate categories modulate this mediating effect. Our analysis provides empirical evidence of human influence on the vertical thermal structure of the atmosphere.
Plain Language Summary
Near‐surface temperature inversion (TI) is a typical indicator reflecting the vertical structure of the atmosphere and is closely related to human socioeconomic activities. However, due to the complicated interplay between anthropogenic and natural factors, quantifying human contributions to TI generation poses significant challenges. In this study, we utilized the economic shutdown during the first wave of COVID‐19 (the first half of 2020) across 500 cities worldwide to estimate changes in TI incidence and temperature difference (∆T) between atmospheric pressure layers compared to parallel levels in 2016–2019. We found that ∆T declined by 2.5% and TI incidence declined by 18.2% during the shutdown period as a consequence of disrupted socioeconomic activities. The magnitude of this effect varies with urban climate and economic level and is highly correlated with anthropogenic emissions. Furthermore, we demonstrated that fine particulate matter (PM2.5) may serve as a mediating pathway through which human activities impact atmospheric thermal properties. Notably, the effect of PM2.5 is climate‐dependent, being most pronounced in boreal cities but least significant in tropical regions. This study enriches our understanding of human influence on the vertical thermal structure of the atmosphere.
Key Points
Reduced human activities during the COVID‐19 led to a 18.2% decrease in the incidence of temperature inversion (TI) across global cities
TI responses monotonously to reduced economic activities, prominent for urban areas with greater reduction in anthropogenic emissions
PM2.5 serves as a mediator through which humans impact the vertical thermal structure, with the effect size being climate‐dependent
In English and Chinese, irrealis sentences which contain auxiliaries of modality can be very complex. Aiming at this hard nut, the present study takes the recent generative syntax approach to ...tentatively explain the mechanism to generate these sentences. The basic strategy is to consider the auxiliaries in them as head of the modality phrase which can be further divided into epistemic and deontic modalities. Then in the syntactic cartography, mood layer is inserted which is divided into knowledge mood and development mood. We draw this tentative conclusions: Irrealis is base generated at the knowledge mood layer, and in an irrealis sentence, an implicit negation exists at the tense layer. The syntactic operation of mood match exists in conditional sentence of irrealis. In Chinese, the knowledge mood marker might exist in both simple and conditional sentences of irrealis. The two languages also differ in combination of mood, modality and aspect.
Magnetic plasmons (MPs) refer to the coupling of external electromagnetic waves with a strong magnetic response induced inside the nanostructures. MPs have been widely employed as artificial magnetic ...atoms to fabricate negative-permeability or negative-refractive-index metamaterials with peculiar electromagnetic properties. Here, we propose a refractive index sensing by utilizing the MP resonances excited in a simple one-dimensional (1D) metallic nanogroove array. We demonstrate a sensitivity up to 1200 nm/RIU with a figure of merit (FOM*) of 15 thanks to the MP resonances that are extremely sensitive to the surrounding media. Importantly, the influence of the local environment effects on the sensing ability is studied. An equivalent inductor-capacitor (LC) model is used to give a precise quantitative description of the sensing performance and reveal the underlying mechanism. Such a MP-based sensor with the ease of fabrication may provide great potentials in designing broadband sensing devices with high performance and compactness.
Turing's formula is, perhaps, the only known method for estimating beyond the range of known data without making any parametric or semi-parametric assumptions. This book presents a unified and broad ...presentation of Turing's formula and its connections to statistics. Topics with applications in a variety of different fields of study are included such as information theory; statistics; probability; computer science inclusive of artificial intelligence, machine learning; big data; biology; ecology; and genetics. The author provides an accessible and clear introduction to Turing's formula and features examinations of many core statistical issues within modern data science from Turing's perspective. Recently, a clear and systematic description of Turing's formula and its statistical properties and implications has evolved, and the newly found statistical implications have brought about substantial gains for some of the most important areas of modern data science. A systematic approach to long-standing problems, such as entropy and mutual information estimation, diversity index estimation, domains of attraction on general alphabets, and tail probability estimation are discussed in light of the most up-to-date understanding of Turing's formula. Featuring numerous exercises and examples throughout, the author presents a summary of the known properties of Turing's formula and explains how and when it works well; discusses the approach that led to Turing's formula in order to estimate a variety of quantities, all of which mainly come from information theory, but are also important for machine learning and for ecological applications; and uses Turing's formula to estimate the tail index of certain heavy tailed distributions.
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