An Adaptation of the Hoshen-Kopelman Cluster Counting Algorithm for Honeycomb Networks

We develop a simplified implementation of the Hoshen-Kopelman cluster counting algorithm adapted for honeycomb networks. In our implementation of the algorithm we assume that all nodes in the network are occupied and links between nodes can be intact or broken. The algorithm counts how many clusters there are in the network and determines which nodes belong to each cluster. The network information is stored into two sets of data. The first one is related to the connectivity of the nodes and the second one to the state of links. The algorithm finds all clusters in only one scan across the network and thereafter cluster relabeling operates on a vector whose size is much smaller than the size of the network. Counting the number of clusters of each size, the algorithm determines the cluster size probability distribution from which the mean cluster size parameter can be estimated. Although our implementation of the Hoshen-Kopelman algorithm works only for networks with a honeycomb (hexagonal) structure, it can be easily changed to be applied for networks with arbitrary connectivity between the nodes (triangular, square, etc.). The proposed adaptation of the Hoshen-Kopelman cluster counting algorithm is applied to studying the thermal degradation of a graphene-like honeycomb membrane by means of Molecular Dynamics simulation with a Langevin thermostat. ACM Computing Classification System (1998): F.2.2, I.5.3

3D multi-agent models for protein release from PLGA spherical particles with complex inner morphologies

In order to better understand and predict the release of proteins from bioerodible micro- or nanospheres, it is important to know the influences of different initial factors on the release mechanisms. Often though it is difficult to assess what exactly is at the origin of a certain dissolution profile. We propose here a new class of fine-grained multi-agent models built to incorporate increasing complexity, permitting the exploration of the role of different parameters, especially that of the internal morphology of the spheres, in the exhibited release profile. This approach, based on Monte-Carlo (MC) and Cellular Automata (CA) techniques, has permitted the testing of various assumptions and hypotheses about several experimental systems of nanospheres encapsulating proteins. Results have confirmed that this modelling approach has increased the resolution over the complexity involved, opening promising perspectives for future developments, especially complementing in vitro experimentation

Correlated percolation in the fracture dynamics on a network of ionomer bundles

Motivated by predicting the lifetime of polymer electrolyte membranes (PEMs), we map the fracture dynamics of a network of ionomer bundles onto a correlated percolation model. A kinetic Monte Carlo method is employed to study these dynamics. The swelling pressure upon water uptake causes the breakage events of ionomer bundles, and the strength of the bundle-to-bundle correlations is characterized by the stress field and the stress redistribution scheme. Local load sharing (LLS) and equal load sharing (ELS) are the two most frequently studied stress transfer schemes. We adopt a stress transfer scheme that follows a power-law-type spatial decay in this thesis as an intermediate scheme between LLS and ELS. By tuning the magnitude of the stress field and the effective range of stress transfer, two fracture regimes, i.e., the random breakage (percolation-type) regime and the localization (correlated crack growth) regime, can be observed. A central property considered in this thesis is the frequency distribution of percolation thresholds. Based on this distribution, we introduce an order parameter to assess the crossover between these two fracture regimes. Moreover, the average percolation threshold is found to exhibit a peculiar variation, which has not been reported in previous correlated percolation studies

Assessment of percolation threshold simulation for individual and hybrid nanocomposites of carbon nanotubes and carbon black

Modeling electrical conductivity of polymer composites with conductive fillers has great applicability to predict conductive materials behavior. In this study, the electrical behavior of simple and hybrid systems prepared from Carbon Black (CB) and Carbon Nanotubes (CNT) was studied. There have been few advances reported in the literature regarding the modeling of hybrid systems, which motivated the development of this study. More specifically, a program was developed with the intention to describe the electric percolation threshold and the effect of synergism between the conductive fillers. Simulation was performed using the Monte Carlo method and Fortran programming language, considering concentration and geometry of conductive fillers to the system in two dimensions. Finally, simulation results were compared with the experimental results and this method proved to be effective in predicting the systems percolation threshold, being an important contribution to predict material behavior, which allows reducing the number of samples to be prepared in an experimental study20616381649CONSELHO NACIONAL DE DESENVOLVIMENTO CIENTÍFICO E TECNOLÓGICO - CNPQsem informaçã

화학 반응기 시스템을 모델링하기 위한 계산 효율적인 전략

학위논문(박사) -- 서울대학교대학원 : 공과대학 화학생물공학부(에너지환경 화학융합기술전공), 2022.2. 이종민.Many researchers in chemical engineering have been using analytical and computational models to predict the behaviors of systems and use these models to process optimization, design and control. However, until now, researchers are still forced to compromise on model fidelity and accuracy. Although high fidelity models can improve the model accuracy, simulating these models is usually time-consuming, making it difficult to perform optimization. In this thesis, computationally efficient strategies about two system are introduced which can maintain model fidelity but effectively reduce the calculation time. Polymer reactor is selected for the first system and we focused on polymer kinetics. A hybrid approach that combines the method of moments and Monte Carlo simulation to predict the molecular weight distribution of low-density polyethylene for a continuous stirred tank reactor system is proposed. A 'Block,' which is repeating reaction group, is introduced for the calculation cost-effective simulation. This model called the 'block Kinetic Monte Carlo' is ~10 to 32 times faster than Neuhaus’s model. The model can be applied to any steady state system and provide a calculation cost reduction effect, where one reaction is much faster than others; for example, the propagation reaction. Furthermore, we perform a case study on the effects of the system temperature and initiator concentration on the MWD and reaction rate ratio. Based on the simulation results of 180 case studies, we determine a quantitative guideline for the appearance of shoulder, which is a function of the rate ratio of reactions to the propagation reaction. Computational fluid dynamics (CFD) based reactor system is selected for the second system. CFD is an essential tool for solving engineering problem that involves fluid dynamics. Especially in chemical engineering, fluid motion usually has extensive effects on system states such as temperature and component concentration. However, due to the critical issue of long computational times for simulating CFD, application of CFD is limited for many real-time problems such as real-time optimization and process control. In this study, we develop the surrogate model of Continuous stirred tank reactor (CSTR) with Van de Vusse reaction using Physics-informed neural network (PINN) which can train the governing equations of system. We propose PINN architecture that can train every governing equation which chemical reactor system follows and can train multi-reference frame system. Also, we investigate that PINN can resolve the problem of neural network that needs lots of training data, are easily overfitted and cannot contain physical meaning. Furthermore, we modify the original PINN suggested by Raissi in order to solve the memory error and divergence problem with two methods: (1) Mini-batch training; (2) Weighted loss function. We also suggest a similarity based sampling strategy where the accuracy can be improved up to 5 times over the random sampling. This work can provide the guideline for developing the high performance surrogate model of chemical process.화학 공학 분야의 많은 연구자들은 분석 및 계산 모델을 이용하여 시스템의 거동을 해석하고 최적화, 설계 및 제어를 수행하고 있다. 하지만 모델의 정확도와 계산시간은 거래되는 관계에 있어 계산시간이 오래걸리는 문제 때문에 모델의 정확도를 타협할 수 밖에 없는 실상이다. 이 학위논문에서는 두 시스템에 대해 모델의 충실도를 유지하면서도 계산시간을 효과적으로 줄일 수 있는 계산 효율적인 전략을 소개한다. 첫 번째 시스템은 고분자 반응기로 고분자의 반응에 중점을 두고 있다. 연속 교반 탱크 반응기에 대한 저밀도 폴리에틸렌의 분자량 분포를 예측하기 위해 모멘트 방법과 몬테 카를로 시뮬레이션 기법을 결합한 하이브리드 접근 방식이 제안되었다. 계산 효율적인 시뮬레이션을 위해 반복되는 반응들을 집합인 ‘블락’이라는 개념이 새로이 도입되었다. ‘블락 키네틱 몬테 카를로’라고 불리는 이 모델은 Neuhaus가 제안한 모델보다 약 10~32배 빠르다. 이 모델은 모든 정상 상태시스템에 적용할 수 있으며, 특정 반응이 다른 반응들보다 훨씬 빠른 경우에 계산 시간 감소효과를 누릴 수 있다. 또한 시스템의 운전 온도 및 개시제의 농도가 분자량 분포에 미치는 영향에 대해 사례 연구를 수행하였다. 180개의 사례 연구 시뮬레이션을 바탕으로 분자량 분포가 숄더를 보이는 조건에 대한 정량적 지침을 제안하였다. 두번째 시스템은 전산유체역학 기반의 반응기 시스템이다. 전산유체역학은 유체의 흐름을 해석함에 있어 필수적인 기법이다. 특히 화학공학반응기에서 유체의 흐름은 내부의 온도나 농도에 큰 영향을 미친다. 그러나 전산유체역학은 계산시간이 오래걸린다는 단점으로 인해 실시간 최적화 및 공정 제어와 같은 응용에 사용이 제한된다. 이 학위논문에서는 시스템의 지배 방정식을 훈련할 수 있는 물리정보신경망(PINN)을 사용하여 Van de Vusse 반응이 포함된 연속 교반 탱크 반응기의 대리 모델을 개발한다. 화학 반응기 시스템이 따르는 모든 종류의 지배 방정식을 훈련할 수 있으며 다중 참조 프레임 시스템을 훈련 할 수 있는 물리정보신경망 모델 구조를 제안한다. 물리정보신경망(PINN)은 기존에 신경망 모델이 가지는 과적합 문제나 데이터가 많이 필요하다는 점 그리고 물리적 의미를 반영할 수 없다는 문제들을 해결할 수 있다. 또한 메모리 오류 및 모델의 발산 문제를 해결하기 위하여 Raissi가 제안한 기존의 물리정보신경망(PINN)을 두 가지 방법으로 수정하였다. 1) 미니 배치 훈련; 2) 가중 손실 함수. 그리고 학습 데이터를 추출함에 있어 무작위 추출에 비해 정확도를 최대 5배까지 향상시킬 수 있는 유사성 기반 추출 전략을 제안한다. 이 연구가 화학 공정의 고성능 대리 모델 개발을 위한 지침이 되기를 희망한다.Abstract i Contents iv List of Figures vii List of Tables xi Chapter 1 Introduction 1 1.1 Research motivation 1 1.2 Research objective 3 1.3 Outline of the thesis 5 Chapter 2 Molecular weight distribution modeling of LDPE in a continuous stirred-tank reactor using coupled deterministic and stochastic approach 6 2.1 Introduction 6 2.2 Methodology 10 2.2.1 Polymer reaction mechanism 10 2.2.2 Reactor model 16 2.2.3 Deterministic part 16 2.2.4 Stochastic part 20 2.3 Result 34 2.3.1 Verification 34 2.3.2 Reduction in calculation time 39 2.3.3 Case study 41 2.3.4 Shouldering condition 49 2.4 Conclusions 52 2.5 Notations 54 2.6 Abbreviations 57 Chapter 3 Physics-informed deep learning for data-driven solutions of computational fluid dynamics 58 3.1 Introduction 58 3.2 PINN 61 3.3 Model description 64 3.3.1 CFD modeling 64 3.3.2 Governing equations 67 3.3.3 PINN architecture 71 3.4 Result and Discussion 79 3.4.1 Model verification 79 3.4.2 Improvement of model performance 86 3.4.3 Comparison of PINN model with 1-D ODE model 98 3.5 Conclusion 102 3.6 Appendix 105 3.7 Notations 106 Chapter 4 Concluding Remarks 111 4.1 Summary of contributions 111 4.2 Future work 112 Reference 114 Abstract in Korean (국문초록) 121박

Heuristic modeling of macromolecule release from PLGA microspheres

Dissolution of protein macromolecules from poly(lactic-co-glycolic acid) (PLGA) particles is a complex process and still not fully understood. As such, there are difficulties in obtaining a predictive model that could be of fundamental significance in design, development, and optimization for medical applications and toxicity evaluation of PLGA-based multiparticulate dosage form. In the present study, two models with comparable goodness of fit were proposed for the prediction of the macromolecule dissolution profile from PLGA micro- and nanoparticles. In both cases, heuristic techniques, such as artificial neural networks (ANNs), feature selection, and genetic programming were employed. Feature selection provided by fscaret package and sensitivity analysis performed by ANNs reduced the original input vector from a total of 300 input variables to 21, 17, 16, and eleven; to achieve a better insight into generalization error, two cut-off points for every method was proposed. The best ANNs model results were obtained by monotone multi-layer perceptron neural network (MON-MLP) networks with a root-mean-square error (RMSE) of 15.4, and the input vector consisted of eleven inputs. The complicated classical equation derived from a database consisting of 17 inputs was able to yield a better generalization error (RMSE) of 14.3. The equation was characterized by four parameters, thus feasible (applicable) to standard nonlinear regression techniques. Heuristic modeling led to the ANN model describing macromolecules release profiles from PLGA microspheres with good predictive efficiency. Moreover genetic programming technique resulted in classical equation with comparable predictability to the ANN model

The safety case and the lessons learned for the reliability and maintainability case

This paper examine the safety case and the lessons learned for the reliability and maintainability case

Metamodel-based uncertainty quantification for the mechanical behavior of braided composites

The main design requirement for any high-performance structure is minimal dead weight. Producing lighter structures for aerospace and automotive industry directly leads to fuel efficiency and, hence, cost reduction. For wind energy, lighter wings allow larger rotor blades and, consequently, better performance. Prosthetic implants for missing body parts and athletic equipment such as rackets and sticks should also be lightweight for augmented functionality. Additional demands depending on the application, can very often be improved fatigue strength and damage tolerance, crashworthiness, temperature and corrosion resistance etc. Fiber-reinforced composite materials lie within the intersection of all the above requirements since they offer competing stiffness and ultimate strength levels at much lower weight than metals, and also high optimization and design potential due to their versatility. Braided composites are a special category with continuous fiber bundles interlaced around a preform. The automated braiding manufacturing process allows simultaneous material-structure assembly, and therefore, high-rate production with minimal material waste. The multi-step material processes and the intrinsic heterogeneity are the basic origins of the observed variability during mechanical characterization and operation of composite end-products. Conservative safety factors are applied during the design process accounting for uncertainties, even though stochastic modeling approaches lead to more rational estimations of structural safety and reliability. Such approaches require statistical modeling of the uncertain parameters which is quite expensive to be performed experimentally. A robust virtual uncertainty quantification framework is presented, able to integrate material and geometric uncertainties of different nature and statistically assess the response variability of braided composites in terms of effective properties. Information-passing multiscale algorithms are employed for high-fidelity predictions of stiffness and strength. In order to bypass the numerical cost of the repeated multiscale model evaluations required for the probabilistic approach, smart and efficient solutions should be applied. Surrogate models are, thus, trained to map manifolds at different scales and eventually substitute the finite element models. The use of machine learning is viable for uncertainty quantification, optimization and reliability applications of textile materials, but not straightforward for failure responses with complex response surfaces. Novel techniques based on variable-fidelity data and hybrid surrogate models are also integrated. Uncertain parameters are classified according to their significance to the corresponding response via variance-based global sensitivity analysis procedures. Quantification of the random properties in terms of mean and variance can be achieved by inverse approaches based on Bayesian inference. All stochastic and machine learning methods included in the framework are non-intrusive and data-driven, to ensure direct extensions towards more load cases and different materials. Moreover, experimental validation of the adopted multiscale models is presented and an application of stochastic recreation of random textile yarn distortions based on computed tomography data is demonstrated

The Effect of Composition and Architecture on Polymer Behavior in Homopolymer Blends and Inter-filament Bonding in 3D Printed Models

This dissertation presents work that increases our understanding of the effects of composition and architecture on copolymer structure and dynamics and how they affect material diffusion between filaments in a 3D printed model. Copolymers are polymer chains made up of at least two different monomers. The ordering and arrangement of the two monomer species within a copolymer can have drastic effects on the behavior and properties of the copolymer. The first chapter of this dissertation examines how the copolymer composition affects the structure and dynamics of the chain in a homopolymer blend. This study used a modified Monte Carlo BFM to simulate random polystyrene(PS)-polymethymethacrylate(PMMA) copolymers in a PMMA matrix. The results suggest that the faster moving PS segments in the copolymer chain dominate the chain’s motion. However, concentration fluctuations in the local volume around segments of the chain ultimately slow the chain down. This work sheds light into why a randomly distributed copolymer will move faster than a di-block copolymer of the same monomer composition. The next project focused on the effect of copolymer architecture on the structure and dynamics of branched polymers in a homopolymer matrix using a Monte Carlo simulation. In these simulations, branched polymer consisted of a backbone and the side-chains being unlike monomer species. The number and the molecular weight of the branches was varied to study the effects of branch packing densities on homopolymer copolymer comb structure and motion. Additionally, the temperature varied to determine the effect of available thermal energy on each architectural copolymer configuration. The results of this project concluded that the structure and motion of a branched polymer are a result of the balance in the thermodynamic environment surrounding the copolymer. Finally, the effect of inter-filament heat and copolymer diffusion on inter-filament bonding in 3D printed part was examined. In this study the importance of thermal history in the print environment was determined quantitatively and its effect on the adhesion between acrylonitrile-butadiene-styrene (ABS) copolymer filaments was probed. Additionally, the interface between ABS filaments was improved using a chemical cross-linker. These studies provide insight into improving the mechanical strength of 3D printed parts

Monte-Carlo-Simulation-Based, Product-Quality-Focused Analysis Of Nanocoating Curing And Post Curing Process

ABSTRACT MONTE CARLO SIMULATION BASED PRODUCT QUALITY ANALYSIS OF POLYMER COATING CURING AND POST CURING By Jianming Zhao May 2017 Advisor：Dr. Yinlun Huang Major: Chemical Engineering Degree: Master of Science To achieve better property of polymer coatings, different categories of nanoparticles are applied before coating’s curing process. However, one of the adverse effects is the change of final property, which leads the difficulty of product quality control. Using mathematical modeling method can actually improve the cost and time to get a prediction of product quality. Still now, different series of models are developed for various purposes. For example, Monte-Carlo simulation suits short-term usage prediction; kinetics simulation suits long-term usage prediction; potential energy simulation suits to model microcosmic particle’s energy change. To solve the difficulty of quality control, Monte-Carlo simulation is used to provide relatively accurate data under given conditions. A series of models are redesigned, based on those developed by Xiao et al. (2009, 2010). From the simulation data, a visualized conversion and final Young’s modulus change can be clearly seen. In this thesis, a linear plot of the general curing process is gained. Monte Carlo simulation methodology is a new method to describe the conversion change. The post-curing process is also simulated, with the contrast of the real data from Yari (2014), the post-curing process and principle can be explained. The effect of the nanoparticle can also be gained in this work. Additionally, with the work of this thesis, people can control the product quality more easily