Resonant and antiresonant frequencies of multiple cracked bar

The natural frequencies or related resonant frequencies have been widely used for crack detection in structures by the vibration-based technique. However, antiresonant frequencies, the zeros of frequency response function, are less involved to use for the problem because they have not been thoroughly studied. The present paper addresses analysis of antiresonant frequencies of multiple cracked bar in comparison with the resonant ones. First, exact characteristic equations for the resonant and antiresonant frequencies of bar with arbitrary number of cracks are conducted in a new form that is explicitly expressed in term of crack severities. Then, the conducted equations are employed for analysis of variation of resonant and antiresonant frequencies versus crack position and depth. Numerical results show that antiresonant frequencies are indeed useful indicators for crack detection in bar mutually with the resonant ones

Full O(α)\mathcal{O}(\alpha) electroweak radiative corrections to e+e−→ttˉγe^+e^- \rightarrow t \bar{t} \gamma with GRACE-Loop

We present the full $\mathcal{O}(\alpha)$ electroweak radiative corrections to the process $e^+e^- \rightarrow t \bar{t} \gamma$ at the International Linear Collider (ILC). The computation is performed with the help of the GRACE-Loop system. We present the total cross-section and the top quark forward-backward asymmetry ($A_{FB}$) as a function of the center-of-mass energy and compare them with the process $e^+e^- \rightarrow t \bar{t}$. We find that the value of $A_{FB}$ in $t \bar{t} \gamma$ production is larger than $A_{FB}$ in $t\bar{t}$ production. It is an important result for the measurement of the top quark forward-backward asymmetry at the ILC. Applying a structure function method, we also subtract the QED correction to gain the genuine weak correction in both the $\alpha$ scheme and the $G_{\mu}$ scheme ($\delta_{W}^{G_{\mu}}$). We obtain numerical values for $\delta_{W}^{G_{\mu}}$ which are changing from 2% to -24% when we vary the center-of-mass energy from 360 GeV to 1 TeV.Comment: 13 pages, 9 figure

Spectral analysis of multiple cracked beam subjected to moving load

In present paper, the spectral approach is proposed for analysis of multiple cracked beam subjected to general moving load that allows us to obtain explicitly dynamic response of the beam in frequency domain. The obtained frequency response is straightforward to calculate time history response by using the FFT algorithm and provides a novel tool to investigate effect of position and depth of multiple cracks on the dynamic response. The analysis is important to develop the spectral method for identification of multiple cracked beam by using its response to moving load. The theoretical development is illustrated and validated by numerical case study

One-loop expressions for h→llˉγh\rightarrow l\bar{l}\gamma in Higgs extensions of the Standard Model

A systematic study of one-loop contributions to the decay channels $h\rightarrow l\bar{l}\gamma$ with $l=\nu_{e,\mu, \tau}, e, \mu$, performed in Higgs extended versions of the Standard Model, is presented in the 't Hooft-Veltman gauge. Analytic formulas for one-loop form factors are expressed in terms of the logarithm and di-logarithmic functions. As a result, these form factors can be reduced to those relating to the loop-induced decay processes $h\rightarrow \gamma\gamma, Z\gamma$, confirming not only previous results using different approaches but also close relations between the three kinds of the loop-induced Higgs decay rates. For phenomenological study, we focus on the two observables, namely the enhancement factors defined as ratios of the decay rates calculated between the Higgs extended versions and the standard model, and the forward-backward asymmetries of fermions, which can be used to search for Higgs extensions of the SM. We show that direct effects of mixing between neutral Higgs bosons and indirect contributions of charged Higg boson exchanges can be probed at future colliders.Comment: 39 pages, 9 Figures, 11 Tables of dat

Cultural evolution in Vietnam’s early 20th century: a Bayesian networks analysis of Franco-Chinese house designs

The study of cultural evolution has taken on an increasingly interdisciplinary and diverse approach in explicating phenomena of cultural transmission and adoptions. Inspired by this computational movement, this study uses Bayesian networks analysis, combining both the frequentist and the Hamiltonian Markov chain Monte Carlo (MCMC) approach, to investigate the highly representative elements in the cultural evolution of a Vietnamese city’s architecture in the early 20th century. With a focus on the façade design of 68 old houses in Hanoi’s Old Quarter (based on 78 data lines extracted from 248 photos), the study argues that it is plausible to look at the aesthetics, architecture, and designs of the house façade to find traces of cultural evolution in Vietnam, which went through more than six decades of French colonization and centuries of sociocultural influence from China. The in-depth technical analysis, though refuting the presumed model on the probabilistic dependency among the variables, yields several results, the most notable of which is the strong influence of Buddhism over the decorations of the house façade. Particularly, in the top 5 networks with the best Bayesian Information Criterion (BIC) scores and p\u3c0.05, the variable for decorations (DC) always has a direct probabilistic dependency on the variable B for Buddhism. The paper then checks the robustness of these models using Hamiltonian MCMC method and find the posterior distributions of the models’ coefficients all satisfy the technical requirement. Finally, this study suggests integrating Bayesian statistics in the social sciences in general and for the study of cultural evolution and architectural transformation in particular

Change in mode shape nodes of multiple cracked bar: II. The numerical analysis

In this paper it is numerically analyzed the change in position of mode shape nodes induced by multiple cracks in bar that has been theoretically investigated in previous paper [1] of the authors. The focus is to analyze thoroughly dislocation of node located intermediately between two cracks in dependence upon the crack parameters without assumption on the smallness of crack