Statistics for Spatial Data.

Deep eutectic solvents (DESs) are an emerging class of mixtures characterized by significant depressions in melting points compared to those of the neat constituent components. These materials are promising for applications as inexpensive "designer" solvents exhibiting a host of tunable physicochemical properties. A detailed review of the current literature reveals the lack of predictive understanding of the microscopic mechanisms that govern the structure-property relationships in this class of solvents. Complex hydrogen bonding is postulated as the root cause of their melting point depressions and physicochemical properties; to understand these hydrogen bonded networks, it is imperative to study these systems as dynamic entities using both simulations and experiments. This review emphasizes recent research efforts in order to elucidate the next steps needed to develop a fundamental framework needed for a deeper understanding of DESs. It covers recent developments in DES research, frames outstanding scientific questions, and identifies promising research thrusts aligned with the advancement of the field toward predictive models and fundamental understanding of these solvents.

Deep Eutectic Solvents: A Review of Fundamentals and Applications.

생체의 모델링과 Simulation

Thick electrodes for Li-ion batteries: A model based analysis

Definitions and basic properties of the Voronoi diagram generalizations of the Voronoi diagram algorithms for computing Voronoi diagrams poisson Voronoi diagrams spatial interpolation models of spatial processes point pattern analysis locational optimization through Voronoi diagrams.

Spatial tessellations. Concepts and Applications of Voronoi diagrams

Since the beginning of electronic computing, people have been interested in carrying out random experiments on a computer. Such Monte Carlo techniques are now an essential ingredient in many quantitative investigations. Why is the Monte Carlo method MCM so important today? This article explores the reasons why the MCM has evolved from a 'last resort' solution to a leading methodology that permeates much of contemporary science, finance, and engineering. WIREs Comput Stat 2014, 6:386-392. doi: 10.1002/wics.1314

https://people.smp.uq.edu.au/DirkKroese/ps/whyMCM_fin.pdf

Why the Monte Carlo method is so important today

Stochastic 3D modeling of the microstructure of lithium-ion battery anodes via Gaussian random fields on the sphere

The analysis of polycrystalline materials benefits greatly from accurate quantitative descriptions of their grain structures. Laguerre tessellations approximate such grain structures very well. However, it is a quite challenging problem to fit a Laguerre tessellation to tomographic data, as a high-dimensional optimization problem with many local minima must be solved. In this paper, we formulate a version of this optimization problem that can be solved quickly using the cross-entropy method, a robust stochastic optimization technique that can avoid becoming trapped in local minima. We demonstrate the effectiveness of our approach by applying it to both artificially generated and experimentally produced tomographic data.

/pdf/fitting-laguerre-tessellation-approximations-to-tomographic-4znfkhordb.pdf

Fitting Laguerre tessellation approximations to tomographic image data

A compact and tractable representation of the grain structure of a material is an extremely valuable tool when carrying out an empirical analysis of the material’s microstructure. Tessellations have proven to be very good choices for such representations. Most widely used tessellation models have convex cells with planar boundaries. Recently, however, a new tessellation model — called the generalised balanced power diagram (GBPD) — has been developed that is very flexible and can incorporate features such as curved boundaries and non-convexity of cells. In order to use a GBPD to describe the grain structure observed in empirical image data, the parameters of the model must be chosen appropriately. This typically involves solving a difficult optimisation problem. In this paper, we describe a method for fitting GBPDs to tomographic image data. This method uses simulated annealing to solve a suitably chosen optimisation problem. We then apply this method to both artificial data and experimental 3D electron b...

/pdf/3d-reconstruction-of-grains-in-polycrystalline-materials-f92ii99np0.pdf

Tim Brereton

Papers

Why the Monte Carlo method is so important today

Stochastic 3D modeling of the microstructure of lithium-ion battery anodes via Gaussian random fields on the sphere

Fitting Laguerre tessellation approximations to tomographic image data

Fitting Laguerre tessellation approximations to tomographic image data

3D reconstruction of grains in polycrystalline materials using a tessellation model with curved grain boundaries