Finite element approximation of steady flows of generalized Newtonian fluids with concentration-dependent power-law index

We consider a system of nonlinear partial differential equations describing the motion of an incompressible chemically reacting generalized Newtonian fluid in three space dimensions. The governing system consists of a steady convection-diffusion equation for the concentration and a generalized steady power-law-type fluid flow model for the velocity and the pressure, where the viscosity depends on both the shear-rate and the concentration through a concentration-dependent power-law index. The aim of the paper is to perform a mathematical analysis of a finite element approximation of this model. We formulate a regularization of the model by introducing an additional term in the conservation-of-momentum equation and construct a finite element approximation of the regularized system. We show the convergence of the finite element method to a weak solution of the regularized model and prove that weak solutions of the regularized problem converge to a weak solution of the original problem.Comment: arXiv admin note: text overlap with arXiv:1703.0476

Finite element approximation of an incompressible chemically reacting non-Newtonian fluid

We consider a system of nonlinear partial differential equations modelling the steady motion of an incompressible non-Newtonian fluid, which is chemically reacting. The governing system consists of a steady convection-diffusion equation for the concentration and the generalized steady Navier-Stokes equations, where the viscosity coefficient is a power-law type function of the shear-rate, and the coupling between the equations results from the concentration-dependence of the power-law index. This system of nonlinear partial differential equations arises in mathematical models of the synovial fluid found in the cavities of moving joints. We construct a finite element approximation of the model and perform the mathematical analysis of the numerical method in the case of two space dimensions. Key technical tools include discrete counterparts of the Bogovski\u{\i} operator, De Giorgi's regularity theorem in two dimensions, and the Acerbi-Fusco Lipschitz truncation of Sobolev functions, in function spaces with variable integrability exponents.Comment: 40 page

A novel approach for wafer defect pattern classification based on topological data analysis

In semiconductor manufacturing, wafer map defect pattern provides critical information for facility maintenance and yield management, so the classification of defect patterns is one of the most important tasks in the manufacturing process. In this paper, we propose a novel way to represent the shape of the defect pattern as a finite-dimensional vector, which will be used as an input for a neural network algorithm for classification. The main idea is to extract the topological features of each pattern by using the theory of persistent homology from topological data analysis (TDA). Through some experiments with a simulated dataset, we show that the proposed method is faster and much more efficient in training with higher accuracy, compared with the method using convolutional neural networks (CNN) which is the most common approach for wafer map defect pattern classification. Moreover, our method outperforms the CNN-based method when the number of training data is not enough and is imbalanced

Organ Transplants and Governmental Regulations Restricting Individual Bodies

Honors (Bachelor's)Asian StudiesUniversity of Michiganhttp://deepblue.lib.umich.edu/bitstream/2027.42/98946/1/chanbaik.pd

SIZE MODIFICATION AND COATING OF TITANIUM DIOXIDE USING A PREMIXED HYDROGEN/AIR FLAME

A study was conducted of the effect of flame processing on the size distribution of titania nanoparticles, and a flame process was developed for producing TiO2/SiO2 coreshell particles from aqueous suspensions of TiO2 and SiO2 nanoparticles. Both were performed using a premixed hydrogen/air flame. At the adiabatic flame temperature of 2400 K, the number mean diameter of titania primary particle increased considerably from an initial value of 44 nm to 96 nm, presumably by atomic diffusion, and viscous flow coalescence. Moreover, the majority of product particles from this high flame temperature were smooth and spherical. Based on the results of size modification experiments, coating experiments were performed. The dominant morphology observed in the product particles from coating experiments was silica coated titania. The silica coating was very smooth and dense. The total particle size and the shell volume of the product particles were in reasonable agreement with values predicted from the atomized droplet size distribution and the droplet concentration

Robotic Interestingness via Human-Informed Few-Shot Object Detection

Interestingness recognition is crucial for decision making in autonomous exploration for mobile robots. Previous methods proposed an unsupervised online learning approach that can adapt to environments and detect interesting scenes quickly, but lack the ability to adapt to human-informed interesting objects. To solve this problem, we introduce a human-interactive framework, AirInteraction, that can detect human-informed objects via few-shot online learning. To reduce the communication bandwidth, we first apply an online unsupervised learning algorithm on the unmanned vehicle for interestingness recognition and then only send the potential interesting scenes to a base-station for human inspection. The human operator is able to draw and provide bounding box annotations for particular interesting objects, which are sent back to the robot to detect similar objects via few-shot learning. Only using few human-labeled examples, the robot can learn novel interesting object categories during the mission and detect interesting scenes that contain the objects. We evaluate our method on various interesting scene recognition datasets. To the best of our knowledge, it is the first human-informed few-shot object detection framework for autonomous exploration

DramaQA: Character-Centered Video Story Understanding with Hierarchical QA

Despite recent progress on computer vision and natural language processing, developing video understanding intelligence is still hard to achieve due to the intrinsic difficulty of story in video. Moreover, there is not a theoretical metric for evaluating the degree of video understanding. In this paper, we propose a novel video question answering (Video QA) task, DramaQA, for a comprehensive understanding of the video story. The DramaQA focused on two perspectives: 1) hierarchical QAs as an evaluation metric based on the cognitive developmental stages of human intelligence. 2) character-centered video annotations to model local coherence of the story. Our dataset is built upon the TV drama "Another Miss Oh" and it contains 16,191 QA pairs from 23,928 various length video clips, with each QA pair belonging to one of four difficulty levels. We provide 217,308 annotated images with rich character-centered annotations, including visual bounding boxes, behaviors, and emotions of main characters, and coreference resolved scripts. Additionally, we provide analyses of the dataset as well as Dual Matching Multistream model which effectively learns character-centered representations of video to answer questions about the video. We are planning to release our dataset and model publicly for research purposes and expect that our work will provide a new perspective on video story understanding research.Comment: 21 pages, 10 figures, submitted to ECCV 202