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We analyse features of the patterns formed from a simple model for a martensitic phase transition. This is a fragmentation model that can be encoded by a general branching random walk. An important quantity is the distribution of the…
In this paper we review the importance of the Lyman alpha forest as a probe of structure formation in the universe. We first discuss the statistics used to describe the Lyman alpha forest and the numerical techniques used to produce…
We describe cosmological simulation techniques and their application to studies of cosmic structure formation, with particular attention to recent hydrodynamic simulations of structure in the high redshift universe. Collisionless N-body…
A probabilistic framework to study the dependence structure induced by deterministic discrete-time state-space systems between input and output processes is introduced. General sufficient conditions are formulated under which output…
Computational models for understanding and predicting fire in wildland and managed lands are increasing in impact. Data characterizing the fuels and environment is needed to continue improvement in the fidelity and reliability of fire…
We study the constitutive behaviour, the damage process, and the properties of bursts in the continuous damage fiber bundle model introduced recently. Depending on its two parameters, the model provides various types of constitutive…
Modelling wildfire events has been studied in the literature using the Poisson process, which essentially assumes the independence of wildfire events. In this paper, we use the fractional Poisson process to model the wildfire occurrences in…
We present new simulations of the flux power spectrum of the Lyman $\alpha$ forest as a means to investigate the effects of time-dependent dark energy on structure formation. We use a linearized parameterization of the time-dependence of…
In this article we consider a class of state-dependent delay differential equations which is modelling the dynamics of the number of adult trees in forests. We prove the boundedness of solutions for a single species model as well as a…
We establish a general framework using a diffusion approximation to simulate forward-in-time state counts or frequencies for cladogenetic state-dependent speciation-extinction (ClaSSE) models. We apply the framework to various two- and…
We investigate the growth of clusters within the forest fire model of R\'{a}th and T\'{o}th [22]. The model is a continuous-time Markov process, similar to the dynamical Erd\H{o}s-R\'{e}nyi random graph but with the addition of so-called…
A stochastic model relating the parameters of astrophysical structures to the parameters of their granular components is applied to the formation of hierarchical, large-scale structures from galaxies assumed as point-like objects. If the…
We describe two recent additions to WRF coupled with a fire spread model. Fire propagation is strongly dependent on fuel moisture, which in turn depends on the history of the atmosphere. We have implemented a equilibrium time-lag model of…
We propose Partition Tree, a novel tree-based framework for conditional density estimation over general outcome spaces that supports both continuous and categorical variables within a unified formulation. Our approach models conditional…
Tree-size distribution is one of the most investigated subjects in plant population biology. The forestry literature reports that tree-size distribution trajectories vary across different stands and/or species, while the metabolic scaling…
Consider critical site percolation on a "nice" planar lattice: each vertex is occupied with probability $p = p_c$, and vacant with probability $1 - p_c$. Now, suppose that additional vacancies ("holes", or "impurities") are created,…
We propose a model based on coupled multiplicative stochastic processes to understand the dynamics of competing species in an ecosystem. This process can be conveniently described by a Fokker-Planck equation. We provide an analytical…
We describe the physical model, numerical algorithms, and software structure of WRF-Fire. WRF-Fire consists of a fire-spread model, implemented by the level-set method, coupled with the Weather Research and Forecasting model. In every time…
In this article we present an example of a random oriented tree model on d-dimensional lattice, that is a forest in d=3 with positive probability. This is in contrast with the other random tree models in the literature which are a forest…
In surveys, the interest lies in estimating finite population parameters such as population totals and means. In most surveys, some auxiliary information is available at the estimation stage. This information may be incorporated in the…