Density Ratio
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Mechanika ◽  
2021 ◽  
Vol 27 (3) ◽  
pp. 187-192
Haiming HONG ◽  
Jiaying WANG ◽  
Peng LI

In this work, a new fatigue damage model considering the additive manufacturing (AM) effects is established. We first present the elastoplastic constitutive model with the newly established fatigue damage model considering AM effects. The method to calibrate the material parameters is put forward, and the numerical solution of the theoretical model is implemented. Second, the fatigue lives of two AM metal materials are predicted, and the applicability of the theoretical model is verified by the test results. Finally, the influence of the volume energy density ratio on the fatigue life of AM metal materials is analyzed, and the results show that the volume energy density ratio has a great influence on the fatigue behavior of AM metal materials. When the ratio is less than 1.0, the fatigue life increases rapidly with the increase of the ratio. The fatigue life increases with the stress ratio when the volume density ratio keeps as a constant. The research work in this paper provides a feasible method to predict the fatigue life of AM metal materials by continuum damage mechanics in engineering.

2021 ◽  
Vol 92 (6) ◽  
pp. 063509
M. Yoshinuma ◽  
K. Ida ◽  
K. Yamasaki ◽  
J. Chen ◽  
I. Murakami

Entropy ◽  
2021 ◽  
Vol 23 (6) ◽  
pp. 675
Xuze Zhang ◽  
Saumyadipta Pyne ◽  
Benjamin Kedem

In disease modeling, a key statistical problem is the estimation of lower and upper tail probabilities of health events from given data sets of small size and limited range. Assuming such constraints, we describe a computational framework for the systematic fusion of observations from multiple sources to compute tail probabilities that could not be obtained otherwise due to a lack of lower or upper tail data. The estimation of multivariate lower and upper tail probabilities from a given small reference data set that lacks complete information about such tail data is addressed in terms of pertussis case count data. Fusion of data from multiple sources in conjunction with the density ratio model is used to give probability estimates that are non-obtainable from the empirical distribution. Based on a density ratio model with variable tilts, we first present a univariate fit and, subsequently, improve it with a multivariate extension. In the multivariate analysis, we selected the best model in terms of the Akaike Information Criterion (AIC). Regional prediction, in Washington state, of the number of pertussis cases is approached by providing joint probabilities using fused data from several relatively small samples following the selected density ratio model. The model is validated by a graphical goodness-of-fit plot comparing the estimated reference distribution obtained from the fused data with that of the empirical distribution obtained from the reference sample only.

2021 ◽  
Vol 15 ◽  
Kevin Wen-Kai Tsai ◽  
Jui-Cheng Chen ◽  
Hui-Chin Lai ◽  
Wei-Chieh Chang ◽  
Takaomi Taira ◽  

ObjectiveMagnetic resonance-guided focused ultrasound (MRgFUS) is a minimum-invasive surgical approach to non-incisionally cause the thermos-coagulation inside the human brain. The skull score (SS) has already been approved as one of the most dominant factors related to a successful MRgFUS treatment. In this study, we first reveal the SS distribution of the tremor patients, and correlate the SS with the image feature from customized skull density ratio (cSDR). This correlation might give a direction to future clinical studies for improving the SS.MethodsTwo hundred and forty-six patients received a computed tomography (CT) scan of the brain, and a bone-enhanced filter was applied and reconstructed to a high spatial resolution CT images. The SS of all patients would be estimated by the MRgFUS system after importing the reconstructed CT images into the MRgFUS system. The histogram and the cumulative distribution of the SS from all the patients were calculated to show the percentage of the patients whose SS lower than 0.3 and 0.4. The same CT images of all patients were utilized to calculated the cSDR by first segmented the trabecular bone and the cortical bone from the CT images and divided the average trabecular bone intensity (aTBI) by the average cortical bone intensity (aCBI). The Pearson’s correlations between the SS and the cSDR, aTBI, and the aCBI were calculated, respectively.ResultsThere were 19.19 and 50% of the patient who had the SS lower than the empirical threshold 0.3 and 0.4, respectively. The Pearson’s correlation between the SS and the cSDR, aCBI, and the aTBI were R = 0.8145, 0.5723, and 0.8842.ConclusionHalf of the patients were eligible for the MRgFUS thalamotomy based on the SS, and nearly 20% of patients were empirically difficult to achieve a therapeutic temperature during MRgFUS. The SS and our cSDR are highly correlated, and the SS had a higher correlation with aTBI than with aCBI. This is the first report to explicitly reveal the SS population and indicate a potential way to increase the chance to achieve a therapeutic temperature for those who originally have low SS.

2021 ◽  
Vol 24 (2) ◽  
pp. first
Truong V. Vu ◽  
Vinh T. Nguyen ◽  
Phan H. Nguyen ◽  
Nang X. Ho ◽  
Binh D. Pham ◽  

Introduction: Compound fluid filaments appear in many applications, e.g., drug delivery and processing or microfluidic systems. This paper focuses on the numerical simulation of an incompressible, immiscible, and Newtonian fluid for the contraction process of a fluid compound filament by solving the Navier-Stokes equations. The front-tracking method is used to solve this problem, which uses connected segments (Lagrangian grid) that move on a fixed grid (Eulerian grid) to represent the interface between the liquids. Methods: The interface points are advected by the velocity interpolated from those of the fixed grid using the area weighting function. The coordinates of the interface points are used to construct the indicators specifying the different fluids and compute the interfacial tension force. Results: The simulation results show that under the effects of the interfacial tension, the capsuleshaped filament can transform into a spherical compound droplet (i.e., non-breakup) or can break up into smaller spherical compound and simple droplets (i.e., breakup). When the density ratio of the outer to middle fluids increases, the filament changes from non-breakup to breakup upon contraction. Conclusion: Increasing the density ratio enhances the breakup of the compound filament during contraction. The breakup is also promoted by increasing the initial length of the filament.

Qingzong Xu ◽  
Qiang Du ◽  
Pei Wang ◽  
Xiangtao Xiao ◽  
Jun Liu

The aerothermal performance of interrupted slot and film holes was numerically investigated. Previous study indicates that the interrupted slot performs better compared to the conventional slot. In the meanwhile, the step formed along with the interrupted slot affects the film cooling characteristics. In this article, a row of film holes is arranged downstream of the step, and the mass flow rate for the interrupted slot is constant at 1%. Blowing ratio (BR) from 0.5 to 1.5 and density ratio from 1 to 2 were studied for the film holes. Endwall film cooling effectiveness distribution indicates that film cooling is easily affected by the secondary flow inside passage and the upstream step. Coolant traces are split into two parts due to the effects of step vortex and transverse flow. For different density ratios, increasing BR shows a different trend of film cooling effectiveness due to the variation of coolant momentum. The coolant jet is easily affected by the secondary flow when its momentum is low, but tends to liftoff when its momentum is too high. As a result, it is better to position the film holes far away from the upstream step. The total pressure loss coefficient distribution at the passage exit indicates that the coolant injection increases the total pressure loss. But density ratio has smaller effect on the loss variation. Besides, two axial positions of cooling holes were studied to improve the endwall cooling performance. Without the effect of step vortex, the film effectiveness of cooling holes is improved.

Complexity ◽  
2021 ◽  
Vol 2021 ◽  
pp. 1-15
Zhaojing Wang ◽  
Weidong Yang ◽  
Hong Zhang ◽  
Ying Zheng

Many industrial processes are operated in multiple modes due to different manufacturing strategies. Multimodality of process data is often accompanied with nonlinear and non-Gaussian characteristics, which makes data-driven monitoring more complicated. In this paper, statistics pattern analysis (SPA) is introduced to extract low- and high-order statistics from raw process data. Support vector data description (SVDD), which can deal with nonlinear and non-Gaussian problems, is applied to monitor multimode process in this paper. To improve detection performance of SVDD for training multimode data with outliers, modified local reachability density ratio (mLRDR) is proposed as a weight factor to be embedded in the weighted-SVDD (wSVDD) model, in which the local neighbors in terms of both space and time are considered. Finally, the effectiveness and superiority of our proposed method are demonstrated by the Tennessee-Eastman (TE) process and wastewater treatment process (WWTP).

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