Unconstrained Optimization Methods: Conjugate Gradient Methods and Trust-Region Methods

Here, we consider two important classes of unconstrained optimization methods: conjugate gradient methods and trust region methods. These two classes of methods are very interesting; it seems that they are never out of date. First, we consider conjugate gradient methods. We also illustrate the practical behavior of some conjugate gradient methods. Then, we study trust region methods. Considering these two classes of methods, we analyze some recent results

PROPERTY ANALYSIS OF THE ASPHALT MATERIALS USING MOLECULAR DYNAMICS (MD) METHOD

The main objectives of this dissertation are to build the Molecular Dynamics (MD) model for the asphalt binders with three components, asphaltenes, aromatics and saturates, and analyze the properties of the asphalt models to discover the interactions and mechanisms of asphalt-aggregate and asphalt-modifier. The contributions of this dissertation are summarized as follows: (1) the Amber Cornell Extension Force Field (ACEFF) was assigned to each component, and most of the parameters of the force field were obtained from the General Amber Force Field (GAFF). Electrostatic Potential (ESP) charges were assigned to each atom with the NWChem calculation; (2) the modified asphalt model with the multi-layer graphite nanoplatelets (xGNP) was generated by the MD method to analyze the effect of the modifier on the asphalt binder model; (3) the aged components of the asphalt model were proposed, and the analysis of moisture susceptibility of asphalt-aggregate by the MD method; (4) the interaction or diffusion of the asphalt binder on aggregates was also realized by the MD method. The MD simulations and laboratory test evaluations show that (1) the MD asphalt model with ACEFF and ESP charges has a better prediction for the different properties than the reference model; (2) The primary aging products in the asphalt binder contain ketones, carboxylic acids and anhydrides. The difference in adhesion was observed between aggregate-asphalt and aggregate-water interfaces; (3) the addition of xGNP nanoplatelets in the asphalt model increased the density, viscosity and thermal conductivity. The same trend was observed in the experimental data. A better observation of these properties was found in the xGNP modified asphalt model compared to the base asphalt model; (4) Different moduli of the asphalt binder models had a trend similar to that of the laboratory test results; (5) The asphalt started to diffuse when the activation energy was reached, and the contact angle and area of the asphalt-aggregate interface changed. Therefore, the findings or conclusions in this dissertation have a good guidance for improving the performance of asphalt binders. Most importantly, this dissertation provides a promising way to analyze and develop the material and its properties

Fast, Scalable, and Interactive Software for Landau-de Gennes Numerical Modeling of Nematic Topological Defects

Numerical modeling of nematic liquid crystals using the tensorial Landau-de Gennes (LdG) theory provides detailed insights into the structure and energetics of the enormous variety of possible topological defect configurations that may arise when the liquid crystal is in contact with colloidal inclusions or structured boundaries. However, these methods can be computationally expensive, making it challenging to predict (meta)stable configurations involving several colloidal particles, and they are often restricted to system sizes well below the experimental scale. Here we present an open-source software package that exploits the embarrassingly parallel structure of the lattice discretization of the LdG approach. Our implementation, combining CUDA/C++ and OpenMPI, allows users to accelerate simulations using both CPU and GPU resources in either single- or multiple-core configurations. We make use of an efficient minimization algorithm, the Fast Inertial Relaxation Engine (FIRE) method, that is well-suited to large-scale parallelization, requiring little additional memory or computational cost while offering performance competitive with other commonly used methods. In multi-core operation we are able to scale simulations up to supra-micron length scales of experimental relevance, and in single-core operation the simulation package includes a user-friendly GUI environment for rapid prototyping of interfacial features and the multifarious defect states they can promote. To demonstrate this software package, we examine in detail the competition between curvilinear disclinations and point-like hedgehog defects as size scale, material properties, and geometric features are varied. We also study the effects of an interface patterned with an array of topological point-defects.Comment: 16 pages, 6 figures, 1 youtube link. The full catastroph

State of the Art in the Optimisation of Wind Turbine Performance Using CFD

Wind energy has received increasing attention in recent years due to its sustainability and geographically wide availability. The efficiency of wind energy utilisation highly depends on the performance of wind turbines, which convert the kinetic energy in wind into electrical energy. In order to optimise wind turbine performance and reduce the cost of next-generation wind turbines, it is crucial to have a view of the state of the art in the key aspects on the performance optimisation of wind turbines using Computational Fluid Dynamics (CFD), which has attracted enormous interest in the development of next-generation wind turbines in recent years. This paper presents a comprehensive review of the state-of-the-art progress on optimisation of wind turbine performance using CFD, reviewing the objective functions to judge the performance of wind turbine, CFD approaches applied in the simulation of wind turbines and optimisation algorithms for wind turbine performance. This paper has been written for both researchers new to this research area by summarising underlying theory whilst presenting a comprehensive review on the up-to-date studies, and experts in the field of study by collecting a comprehensive list of related references where the details of computational methods that have been employed lately can be obtained