A review of wildland fire spread modelling, 1990-present 3: Mathematical analogues and simulation models

In recent years, advances in computational power and spatial data analysis (GIS, remote sensing, etc) have led to an increase in attempts to model the spread and behvaiour of wildland fires across the landscape. This series of review papers endeavours to critically and comprehensively review all types of surface fire spread models developed since 1990. This paper reviews models of a simulation or mathematical analogue nature. Most simulation models are implementations of existing empirical or quasi-empirical models and their primary function is to convert these generally one dimensional models to two dimensions and then propagate a fire perimeter across a modelled landscape. Mathematical analogue models are those that are based on some mathematical conceit (rather than a physical representation of fire spread) that coincidentally simulates the spread of fire. Other papers in the series review models of an physical or quasi-physical nature and empirical or quasi-empirical nature. Many models are extensions or refinements of models developed before 1990. Where this is the case, these models are also discussed but much less comprehensively.Comment: 20 pages + 9 pages references + 1 page figures. Submitted to the International Journal of Wildland Fir

Cellular automata simulations of field scale flaming and smouldering wildfires in peatlands

In peatland wildfires, flaming vegetation can initiate a smouldering fire by igniting the peat underneath, thus, creating a positive feedback to climate change by releasing the carbon that cannot be reabsorbed by the ecosystem. Currently, there are very few models of peatland wildfires at the field-scale, hindering the development of effective mitigation strategies. This lack of models is mainly caused by the complexity of the phenomena, which involves 3-D spread and km-scale domains, and the very large computational resources required. This thesis aims to understand field-scale peatland wildfires, considering flaming and smouldering, via cellular automata, discrete models that use simple rules. Five multidimensional models were developed: two laboratory-scale models for smouldering, BARA and BARAPPY, and three field-scale models for flaming and smouldering, KAPAS, KAPAS II, and SUBALI. The models were validated against laboratory experiments and field data. BARA accurately simulates smouldering of peat with realistic moisture distributions and predicts the formation of unburned patches. BARAPPY brings physics into BARA and predicts the depth of burn profile, but needs 240 times more computational resources. KAPAS showed that the smouldering burnt area decreases exponentially with higher peat moisture content. KAPAS II integrates daily temporal variation of moisture content, and revealed that the omission of this temporal variation significantly underestimates the smouldering burnt area in the long term. SUBALI, the ultimate model of the thesis, integrates KAPAS II with BARA and considers the ground water table to predict the carbon emission of peatland wildfires. Applying SUBALI to Indonesia, it predicts that in El Niño years, 0.40 Gt-C in 2015 (literature said 0.23 to 0.51 Gt-C) and 0.16 Gt-C in 2019 were released, and 75% of the emission is from smouldering. This thesis provides knowledge and models to understand the spread of flaming and smouldering wildfires in peatlands, which can contribute to efforts to minimise the negative impacts of peatland wildfires on people and the environment, through faster-than-real-time simulations, to find the optimum firefighting strategy and to assess the vulnerability of peatland in the event of wildfires.Open Acces

Modeling, Characterizing and Reconstructing Mesoscale Microstructural Evolution in Particulate Processing and Solid-State Sintering

abstract: In material science, microstructure plays a key role in determining properties, which further determine utility of the material. However, effectively measuring microstructure evolution in real time remains an challenge. To date, a wide range of advanced experimental techniques have been developed and applied to characterize material microstructure and structural evolution on different length and time scales. Most of these methods can only resolve 2D structural features within a narrow range of length scale and for a single or a series of snapshots. The currently available 3D microstructure characterization techniques are usually destructive and require slicing and polishing the samples each time a picture is taken. Simulation methods, on the other hand, are cheap, sample-free and versatile without the special necessity of taking care of the physical limitations, such as extreme temperature or pressure, which are prominent issues for experimental methods. Yet the majority of simulation methods are limited to specific circumstances, for example, first principle computation can only handle several thousands of atoms, molecular dynamics can only efficiently simulate a few seconds of evolution of a system with several millions particles, and finite element method can only be used in continuous medium, etc. Such limitations make these individual methods far from satisfaction to simulate macroscopic processes that a material sample undergoes up to experimental level accuracy. Therefore, it is highly desirable to develop a framework that integrate different simulation schemes from various scales to model complicated microstructure evolution and corresponding properties. Guided by such an objective, we have made our efforts towards incorporating a collection of simulation methods, including finite element method (FEM), cellular automata (CA), kinetic Monte Carlo (kMC), stochastic reconstruction method, Discrete Element Method (DEM), etc, to generate an integrated computational material engineering platform (ICMEP), which could enable us to effectively model microstructure evolution and use the simulated microstructure to do subsequent performance analysis. In this thesis, we will introduce some cases of building coupled modeling schemes and present the preliminary results in solid-state sintering. For example, we use coupled DEM and kinetic Monte Carlo method to simulate solid state sintering, and use coupled FEM and cellular automata method to model microstrucutre evolution during selective laser sintering of titanium alloy. Current results indicate that joining models from different length and time scales is fruitful in terms of understanding and describing microstructure evolution of a macroscopic physical process from various perspectives.Dissertation/ThesisDoctoral Dissertation Materials Science and Engineering 201

A review of mathematical models for the formation of vascular networks

Two major mechanisms are involved in the formation of blood vasculature: vasculogenesis and angiogenesis. The former term describes the formation of a capillary-like network from either a dispersed or a monolayered population of endothelial cells, reproducible also in vitro by specific experimental assays. The latter term describes the sprouting of new vessels from an existing capillary or post-capillary venule. Similar mechanisms are also involved in the formation of the lymphatic system through a process generally called lymphangiogenesis. A number of mathematical approaches have been used to analyse these phenomena. In this article, we review the different types of models, with special emphasis on their ability to reproduce different biological systems and to predict measurable quantities which describe the overall processes. Finally, we highlight the advantages specific to each of the different modelling approaches. The research that led to the present paper was partially supported by a grant of the group GNFM of INdA

Common metrics for cellular automata models of complex systems

The creation and use of models is critical not only to the scientific process, but also to life in general. Selected features of a system are abstracted into a model that can then be used to gain knowledge of the workings of the observed system and even anticipate its future behaviour. A key feature of the modelling process is the identification of commonality. This allows previous experience of one model to be used in a new or unfamiliar situation. This recognition of commonality between models allows standards to be formed, especially in areas such as measurement. How everyday physical objects are measured is built on an ingrained acceptance of their underlying commonality. Complex systems, often with their layers of interwoven interactions, are harder to model and, therefore, to measure and predict. Indeed, the inability to compute and model a complex system, except at a localised and temporal level, can be seen as one of its defining attributes. The establishing of commonality between complex systems provides the opportunity to find common metrics. This work looks at two dimensional cellular automata, which are widely used as a simple modelling tool for a variety of systems. This has led to a very diverse range of systems using a common modelling environment based on a lattice of cells. This provides a possible common link between systems using cellular automata that could be exploited to find a common metric that provided information on a diverse range of systems. An enhancement of a categorisation of cellular automata model types used for biological studies is proposed and expanded to include other disciplines. The thesis outlines a new metric, the C-Value, created by the author. This metric, based on the connectedness of the active elements on the cellular automata grid, is then tested with three models built to represent three of the four categories of cellular automata model types. The results show that the new C-Value provides a good indicator of the gathering of active cells on a grid into a single, compact cluster and of indicating, when correlated with the mean density of active cells on the lattice, that their distribution is random. This provides a range to define the disordered and ordered state of a grid. The use of the C-Value in a localised context shows potential for identifying patterns of clusters on the grid

PATTERN FORMATION AND PHASE TRANSITION OF CONNECTIVITY IN TWO DIMENSIONS

This dissertation is devoted to the study and analysis of different types of emergent behavior in physical systems. Emergence is a phenomenon that has fascinated researchers from various fields of science and engineering. From the emergence of global pandemics to the formation of reaction-diffusion patterns, the main feature that connects all these diverse systems is the appearance of a complex global structure as a result of collective interactions of simple underlying components. This dissertation will focus on two types of emergence in physical systems: emergence of long-range connectivity in networks and emergence and analysis of complex patterns. The most prominent theory which deals with the emergence of long-range connectivity is the percolation theory. This dissertation employs many concepts from the percolation theory to study connectivity transitions in various systems. Ordinary percolation theory is founded upon two main assumptions, namely locality and independence of the underlying components. In Chapters 2 and 3, we relax these assumptions in different manners and show that relaxing these assumptions leads to irregular behaviors such as appearance of different universality classes and, in some instances, violation of universality. Chapter 2 deals with relaxing the assumption of locality of interactions. In this Chapter, we define a hierarchy of various measures of robust connectivity. We study the phase transition of these robustness metrics as a function of site/bond occupation/removal probability on the square lattice. Furthermore, we perform extensive numerical analysis and extract these robustness metrics\u27 critical thresholds and critical behaviors. We show that some of these robustness metrics do not fall under the regular percolation universality class. The extensive numerical results in this work can serve as a foundation for any researcher who aims to design/study various degrees of connectivity in networks. In Chapter 3, we study the non-equilibrium phase transition of long-range connectivity in a multi-particle interacting system on the square lattice. The interactions between different particles translate to relaxing the assumption of independence in the percolation theory. Using extensive numerical simulations, we show that the phase transition observed in this system violates the regular concept of universality. However, it conforms well with the concept of weak-universality recently introduced in the literature. We observe that by varying inter-particle interaction strength in our model, one can control the critical behavior of this phase transition. These observations could be pivotal in studying phase transitions and universality classes. Chapter 4 focuses on the analysis of reaction-diffusion patterns. We utilize a multitude of machine learning algorithms to analyze reaction-diffusion patterns. In particular, we address two main problems using these techniques, namely, pattern regression and pattern classification. Given an observed instance of a pattern with a known generative function, in the pattern regression task, we aim to predict the specific set of reaction-diffusion parameters (i.e. diffusion constant) which can reproduce the observed pattern. We employ supervised learning techniques to successfully solve this problem and show the performance of our model in some real-world instances. We also address the task of pattern classification. In this task, we are interested in grouping different instances of similar patterns together. This task is usually performed visually by the researcher studying certain natural phenomena. However, this method is tedious and can be inconsistent among different researchers. We utilize supervised and unsupervised machine learning algorithms to classify patterns of the Gray-Scott model. We show that our methods show outstanding performance both in supervised and unsupervised settings. The methods introduced in this Chapter could bridge the gaps between researchers studying patterns in different fields of science and engineering

Computer generation and application of 3-D reconstructed porous structure :: from 2-D images to the prediction of permeability /

Tese (Doutorado) - Universidade Federal de Santa Catarina, Centro Tecnológico