C0 Interior Penalty Methods for Cahn-Hilliard Equations

In this work we study C0 interior penalty methods for Cahn-Hilliard equations. In Chapter 1 we introduce Cahn-Hilliard equations and the time discretization that leads to linear fourth order boundary value problems. In Chapter 2 we review related fundamentals of finite element methods and multigrid methods. In Chapter 3 we formulate the discrete problems for linear fourth order boundary value problems with the boundary conditions of the Cahn-Hilliard type, which are called C0 interior penalty methods, and we carry out the convergence analysis. In Chapter 4 we consider multigrid methods for the C0 interior penalty methods. We present two smoothing schemes and compare their performance. In Chapter 5 we apply the C0 interior penalty methods and the time discretization scheme to nonlinear time-dependent Cahn-Hilliard equations. Numerical examples for phase separation and image processing are presented

A Domain-adaptive Physics-informed Neural Network for Inverse Problems of Maxwell's Equations in Heterogeneous Media

Maxwell's equations are a collection of coupled partial differential equations (PDEs) that, together with the Lorentz force law, constitute the basis of classical electromagnetism and electric circuits. Effectively solving Maxwell's equations is crucial in various fields, like electromagnetic scattering and antenna design optimization. Physics-informed neural networks (PINNs) have shown powerful ability in solving PDEs. However, PINNs still struggle to solve Maxwell's equations in heterogeneous media. To this end, we propose a domain-adaptive PINN (da-PINN) to solve inverse problems of Maxwell's equations in heterogeneous media. First, we propose a location parameter of media interface to decompose the whole domain into several sub-domains. Furthermore, the electromagnetic interface conditions are incorporated into a loss function to improve the prediction performance near the interface. Then, we propose a domain-adaptive training strategy for da-PINN. Finally, the effectiveness of da-PINN is verified with two case studies.Comment: 5 pages,4 figure

Inherent SM Voltage Balance for Multilevel Circulant Modulation in Modular Multilevel DC--DC Converters

The modularity of a modular multilevel dc converter (MMDC) makes it attractive for medium-voltage distribution systems. Inherent balance of submodule (SM) capacitor voltages is considered as an ideal property, which avoids a complex sorting process based on many measurements thereby reducing costs and enhancing reliability. This article extends the inherent balance concept previously shown for square-wave modulation to a multilevel version for MMDCs. A switching duty matrix dU is introduced: it is a circulant matrix of preset multilevel switching patterns with multiple stages and multiple durations. Inherent voltage balance is ensured with a full-rank dU . Circulant matrix theory shows that this is equivalent to a simplified common factor criterion. A nonfull rank dU causes clusters of SM voltage rather than a single common value, with the clusters indicated by the kernel of the matrix. A generalized coprime criterion is developed into several deductions that serve as practical guidance for design of multilevel circulant modulation. The theoretical development is verified through full-scale simulations and downscaled experiments. The effectiveness of the proposed circulant modulation in achieving SM voltage balance in an MMDC is demonstrated

Comparative genomic and transcriptomic analysis revealed genetic characteristics related to solvent formation and xylose utilization in Clostridium acetobutylicum EA 2018

<p>Abstract</p> <p>Background</p> <p><it>Clostridium acetobutylicum</it>, a gram-positive and spore-forming anaerobe, is a major strain for the fermentative production of acetone, butanol and ethanol. But a previously isolated hyper-butanol producing strain <it>C. acetobutylicum </it>EA 2018 does not produce spores and has greater capability of solvent production, especially for butanol, than the type strain <it>C. acetobutylicum </it>ATCC 824.</p> <p>Results</p> <p>Complete genome of <it>C. acetobutylicum </it>EA 2018 was sequenced using Roche 454 pyrosequencing. Genomic comparison with ATCC 824 identified many variations which may contribute to the hyper-butanol producing characteristics in the EA 2018 strain, including a total of 46 deletion sites and 26 insertion sites. In addition, transcriptomic profiling of gene expression in EA 2018 relative to that of ATCC824 revealed expression-level changes of several key genes related to solvent formation. For example, <it>spo0A </it>and <it>adhEII </it>have higher expression level, and most of the acid formation related genes have lower expression level in EA 2018. Interestingly, the results also showed that the variation in CEA_G2622 (CAC2613 in ATCC 824), a putative transcriptional regulator involved in xylose utilization, might accelerate utilization of substrate xylose.</p> <p>Conclusions</p> <p>Comparative analysis of <it>C. acetobutylicum </it>hyper-butanol producing strain EA 2018 and type strain ATCC 824 at both genomic and transcriptomic levels, for the first time, provides molecular-level understanding of non-sporulation, higher solvent production and enhanced xylose utilization in the mutant EA 2018. The information could be valuable for further genetic modification of <it>C. acetobutylicum </it>for more effective butanol production.</p

Component-based isosurface extraction for multiple dataset visualization

In the situations where isosurfaces are comprised of many disjoint components, two or more datasets can be visualized simul- taneously by processing only a subset of isosurface components. The components of interest can be selected by exploiting interdataset coherency at the level of individual voxels and components. Thus, only those components (identified as voxel cov- erages or voxel sets) which differ significantly among the datasets under consideration are extracted as needed while the similar components were extracted only once from a reference dataset. Since the polygons are extracted/rendered as a whole com- ponent, the rendered isosurfaces are crack-free. We use three user-defined thresholds to control multiple dataset visualization (MDV) so that important relationships (differences and similarities) among the datasets can be explored with an improvement in the overall performance. If the data-coherency can not be defined easily, MDV can still benefit from the on-the-fly processing of the individual components

Optical Model and Optimization for Coherent-Incoherent Hybrid Organic Solar Cells with Nanostructures

Embedding nanostructures in organic solar cells (OSCs) is a well-known method to improve the absorption efficiency of the device by introducing the plasma resonance and scattering effects without increasing the active layer thickness. The introduction of nanostructures imposes greater demands on the optical analysis method for OSCs. In this paper, the generalized rigorous coupled-wave analysis (GRCWA) is presented to analyze and optimize the performance of coherent-incoherent hybrid organic solar cells (OSCs) with nanostructures. Considering the multiple reflections of light scattered within the glass substrate by the device, the correction vector g is derived, then the modified expressions for the field and absorption distribution in OSCs are provided. The proposed method is validated by comparing the simulated results of various structures with results obtained by the generalized transfer matrix method (GTMM) and the &ldquo;equispaced thickness method&rdquo; (ETM). The results demonstrate that the proposed method can reduce the number of simulations by at least half compared to the ETM while maintaining accuracy. With the proposed method, we discussed the device performance depending on the geometrical parameters of nanostructures, and the optimization and analysis are accomplished for single and tandem OSCs. After optimization based on the proposed method, the performance of OSCs are significantly improved, which further demonstrates the practicality of the method

Biharmonic volumetric mapping using fundamental solutions

We propose a biharmonic model for cross-object volumetric mapping. This new computational model aims to facilitate the mapping of solid models with complicated geometry or heterogeneous inner structures. In order to solve cross-shape mapping between such models through divide and conquer, solid models can be decomposed into subparts upon which mappings is computed individually. The biharmonic volumetric mapping can be performed in each subregion separately. Unlike the widely used harmonic mapping which only allows (C0) continuity along the segmentation boundary interfaces, this biharmonic model can provide (C1) smoothness. We demonstrate the efficacy of our mapping framework on various geometric models with complex geometry (which are decomposed into subparts with simpler and solvable geometry) or heterogeneous interior structures (whose different material layers can be segmented and processed separately). © 1995-2012 IEEE