Hyperbolic reaction-diffusion equations for a forest fire model

Forest fire models have been widely studied from the context of self-organized criticality and from the ecological properties of the forest and combustion. On the other hand, reaction-diffusion equations have interesting applications in biology and physics. We propose here a model for fire propagation in a forest by using hyperbolic reaction-diffusion equations. The dynamical and thermodynamical aspects of the model are analyzed in detail

Directed percolation in a two dimensional stochastic fire-diffuse-fire model

In this paper we establish, from extensive numerical experiments, that the two dimensional stochastic fire-diffuse-fire model belongs to the directed percolation universality class. This model is an idealized model of intracellular calcium release that retains the both the discrete nature of calcium stores and the stochastic nature of release. It is formed from an array of noisy threshold elements that are coupled only by a diffusing signal. The model supports spontaneous release events that can merge to form spreading circular and spiral waves of activity. The critical level of noise required for the system to exhibit a non-equilibrium phase-transition between propagating and non-propagating waves is obtained by an examination of the \textit{local slope} $\delta(t)$ of the survival probability, $\Pi(t) \propto \exp(- \delta(t))$, for a wave to propagate for a time $t$.

Sensitisation waves in a bidomain fire-diffuse-fire model of intracellular Ca²⁺ dynamics

We present a bidomain threshold model of intracellular calcium (Ca²⁺) dynamics in which, as suggested by recent experiments, the cytosolic threshold for Ca²⁺ liberation is modulated by the Ca²⁺ concentration in the releasing compartment. We explicitly construct stationary fronts and determine their stability using an Evans function approach. Our results show that a biologically motivated choice of a dynamic threshold, as opposed to a constant threshold, can pin stationary fronts that would otherwise be unstable. This illustrates a novel mechanism to stabilise pinned interfaces in continuous excitable systems. Our framework also allows us to compute travelling pulse solutions in closed form and systematically probe the wave speed as a function of physiologically important parameters. We find that the existence of travelling wave solutions depends on the time scale of the threshold dynamics, and that facilitating release by lowering the cytosolic threshold increases the wave speed. The construction of the Evans function for a travelling pulse shows that of the co-existing fast and slow solutions the slow one is always unstable.

The FIREDASS (Fire Detection and Suppression Simulation) Model

The FIREDASS (FIRE Detection And Suppression Simulation) project is concerned with the development of fine water mist systems as a possible replacement for the halon fire suppression system currently used in aircraft cargo holds. The project is funded by the European Commission, under the BRITE EURAM programme. The FIREDASS consortium is made up of a combination of Industrial, Academic, Research and Regulatory partners. As part of this programme of work, a computational model has been developed to help engineers optimise the design of the water mist suppression system. This computational model is based on Computational Fluid Dynamics (CFD) and is composed of the following components: fire model; mist model; two-phase radiation model; suppression model and detector/activation model. The fire model - developed by the University of Greenwich - uses prescribed release rates for heat and gaseous combustion products to represent the fire load. Typical release rates have been determined through experimentation conducted by SINTEF. The mist model - developed by the University of Greenwich - is a Lagrangian particle tracking procedure that is fully coupled to both the gas phase and the radiation field. The radiation model - developed by the National Technical University of Athens - is described using a six-flux radiation model. The suppression model - developed by SINTEF and the University of Greenwich - is based on an extinguishment crietrion that relies on oxygen concentration and temperature. The detector/ activation model - developed by Cerberus - allows the configuration of many different detector and mist configurations to be tested within the computational model. These sub-models have been integrated by the University of Greenwich into the FIREDASS software package. The model has been validated using data from the SINTEF/GEC test campaigns and it has been found that the computational model gives good agreement with these experimental results. The best agreement is obtained at the ceiling which is where the detectors and misting nozzles would be located in a real system. In this paper the model is briefly described and some results from the validation of the fire and mist model are presented.

Geospatial data harmonization from regional level to european level: a usa case in forest fire data

Dissertation submitted in partial fulfillment of the requirements for the Degree of Master of Science in Geospatial Technologies.

The status and challenge of global fire modelling

Biomass burning impacts vegetation dynamics, biogeochemical cycling, atmospheric chemistry, and climate, with sometimes deleterious socio-economic impacts. Under future climate projections it is often expected that the risk of wildfires will increase. Our ability to predict the magnitude and geographic pattern of future fire impacts rests on our ability to model fire regimes, either using well-founded empirical relationships or process-based models with good predictive skill. A large variety of models exist today and it is still unclear which type of model or degree of complexity is required to model fire adequately at regional to global scales. This is the central question underpinning the creation of the Fire Model Intercomparison Project - FireMIP, an international project to compare and evaluate existing global fire models against benchmark data sets for present-day and historical conditions. In this paper we summarise the current state-of-the-art in fire regime modelling and model evaluation, and outline what essons may be learned from FireMIP.

Periodicities in the Hodgkin-Huxley model and versions of this model with stochastic input

A field of computational neuroscience develops mathematical models to describe neuronal systems. The aim is to better understand the nervous system. Historically, the integrate-and-fire model, developed by Lapique in 1907, was the first model describing a neuron. In 1952 Hodgkin and Huxley [8] described the so called Hodgkin-Huxley model in the article “A Quantitative Description of Membrane Current and Its Application to Conduction and Excitation in Nerve”. The Hodgkin-Huxley model is one of the most successful and widely-used biological neuron models. Based on experimental data from the squid giant axon, Hodgkin and Huxley developed their mathematical model as a four-dimensional system of first-order ordinary differential equations. One of these equations characterizes the membrane potential as a process in time, whereas the other three equations depict the opening and closing state of sodium and potassium ion channels. The membrane potential is proportional to the sum of ionic current flowing across the membrane and an externally applied current. For various types of external input the membrane potential behaves differently. This thesis considers the following three types of input: (i) Rinzel and Miller [15] calculated an interval of amplitudes for a constant applied current, where the membrane potential is repetitively spiking; (ii) Aihara, Matsumoto and Ikegaya [1] said that dependent on the amplitude and the frequency of a periodic applied current the membrane potential responds periodically; (iii) Izhikevich [12] stated that brief pulses of positive and negative current with different amplitudes and frequencies can lead to a periodic response of the membrane potential. In chapter 1 the Hodgkin-Huxley model is introduced according to Izhikevich [12]. Besides the definition of the model, several biological and physiological notes are made, and further concepts are described by examples. Moreover, the numerical methods to solve the equations of the Hodgkin-Huxley model are presented which were used for the computer simulations in chapter 2 and chapter 3. In chapter 2 the statements for the three different inputs (i), (ii) and (iii) will be verified, and periodic behavior for the inputs (ii) and (iii) will be investigated. In chapter 3 the inputs are embedded in an Ornstein-Uhlenbeck process to see the influence of noise on the results of chapter 2.

An Overview of Modelling Bulgarian Wildland Fire Behaviour by Application of a Mathematical Game Method and WRF-Fire Models

This paper presents the main achievements of the author’s PhD dissertation. The work is dedicated to mathematical and semi-empirical approaches applied to the case of Bulgarian wildland fires. After the introductory explanations, short information from every chapter is extracted to cover the main parts of the obtained results. The methods used are described in brief and main outcomes are listed. ACM Computing Classification System (1998): D.1.3, D.2.0, K.5.1.

A bidomain threshold model of propagating calcium waves

We present a bidomain fire-diffuse-fire model that facilitates mathematical analysis of propagating waves of elevated intracellular calcium (Ca) in living cells. Modelling Ca release as a threshold process allows the explicit construction of travelling wave solutions to probe the dependence of Ca wave speed on physiologically important parameters such as the threshold for Ca release from the endoplasmic reticulum (ER) to the cytosol, the rate of Ca resequestration from the cytosol to the ER, and the total [Ca] (cytosolic plus ER). Interestingly, linear stability analysis of the bidomain fire-diffuse-fire model predicts the onset of dynamic wave instabilities leading to the emergence of Ca waves that propagate in a back-and-forth manner. Numerical simulations are used to confirm the presence of these so-called "tango waves" and the dependence of Ca wave speed on the total [Ca]. The original publication is available at www.springerlink.com (Journal of Mathematical Biology)

A 45nm CMOS DESIGN OF NEUROMORPHIC SYSTEM

Neuromorphic computing has become an emerging field in wide range of applications. Its challenge lies in developing a brain-inspired architecture that can emulate human brain and can work for real time applications. In this report a flexible neural architecture is presented which consists of 128 X 128 SRAM crossbar memory and 128 spiking neurons. For Neuron, digital integrate and fire model is used. All components are designed in 45nm technology node. The core can be configured for certain Neuron parameters, Axon types and synapses states and are fully digitally implemented. Learning for this architecture is done offline. To train this circuit a well-known algorithm Restricted Boltzmann Machine (RBM) is used and linear classifiers are trained at the output of RBM. Finally, circuit was tested for handwritten digit recognition application. Future prospects for this architecture are also discussed.

A Generalized Methodology to Characterize Composite Materials for Pyrolysis Models

The predictive capabilities of computational fire models have improved in recent years such that models have become an integral part of many research efforts. Models improve the understanding of the fire risk of materials and may decrease the number of expensive experiments required to assess the fire hazard of a specific material or designed space. A critical component of a predictive fire model is the pyrolysis sub-model that provides a mathematical representation of the rate of gaseous fuel production from condensed phase fuels given a heat flux incident to the material surface. The modern, comprehensive pyrolysis sub-models that are common today require the definition of many model parameters to accurately represent the physical description of materials that are ubiquitous in the built environment. Coupled with the increase in the number of parameters required to accurately represent the pyrolysis of materials is the increasing prevalence in the built environment of engineered composite materials that have never been measured or modeled. The motivation behind this project is to develop a systematic, generalized methodology to determine the requisite parameters to generate pyrolysis models with predictive capabilities for layered composite materials that are common in industrial and commercial applications. This methodology has been applied to four common composites in this work that exhibit a range of material structures and component materials. The methodology utilizes a multi-scale experimental approach in which each test is designed to isolate and determine a specific subset of the parameters required to define a material in the model. Data collected in simultaneous thermogravimetry and differential scanning calorimetry experiments were analyzed to determine the reaction kinetics, thermodynamic properties, and energetics of decomposition for each component of the composite. Data collected in microscale combustion calorimetry experiments were analyzed to determine the heats of complete combustion of the volatiles produced in each reaction. Inverse analyses were conducted on sample temperature data collected in bench-scale tests to determine the thermal transport parameters of each component through degradation. Simulations of quasi-one-dimensional bench-scale gasification tests generated from the resultant models using the ThermaKin modeling environment were compared to experimental data to independently validate the models.

Gap junctions and emergent rhythms

Gap junction coupling is ubiquitous in the brain, particularly between the dendritic trees of inhibitory interneurons. Such direct non-synaptic interaction allows for direct electrical communication between cells. Unlike spike-time driven synaptic neural network models, which are event based, any model with gap junctions must necessarily involve a single neuron model that can represent the shape of an action potential. Indeed, not only do neurons communicating via gaps feel super-threshold spikes, but they also experience, and respond to, sub-threshold voltage signals. In this chapter we show that the so-called absolute integrate-and-fire model is ideally suited to such studies. At the single neuron level voltage traces for the model may be obtained in closed form, and are shown to mimic those of fast-spiking inhibitory neurons. Interestingly in the presence of a slow spike adaptation current the model is shown to support periodic bursting oscillations. For both tonic and bursting modes the phase response curve can be calculated in closed form. At the network level we focus on global gap junction coupling and show how to analyze the asynchronous firing state in large networks. Importantly, we are able to determine the emergence of non-trivial network rhythms due to strong coupling instabilities. To illustrate the use of our theoretical techniques (particularly the phase-density formalism used to determine stability) we focus on a spike adaptation induced transition from asynchronous tonic activity to synchronous bursting in a gap-junction coupled network.

Current status of a model system: the gene Gp-9 and its association with social organization in fire ants.

The Gp-9 gene in fire ants represents an important model system for studying the evolution of social organization in insects as well as a rich source of information relevant to other major evolutionary topics. An important feature of this system is that polymorphism in social organization is completely associated with allelic variation at Gp-9, such that single-queen colonies (monogyne form) include only inhabitants bearing B-like alleles while multiple-queen colonies (polygyne form) additionally include inhabitants bearing b-like alleles. A recent study of this system by Leal and Ishida (2008) made two major claims, the validity and significance of which we examine here. After reviewing existing literature, analyzing the methods and results of Leal and Ishida (2008), and generating new data from one of their study sites, we conclude that their claim that polygyny can occur in Solenopsis invicta in the U.S.A. in the absence of expression of the b-like allele Gp-9(b) is unfounded. Moreover, we argue that available information on insect OBPs (the family of proteins to which GP-9 belongs), on the evolutionary/population genetics of Gp-9, and on pheromonal/behavioral control of fire ant colony queen number fails to support their view that GP-9 plays no role in the chemosensory-mediated communication that underpins regulation of social organization. Our analyses lead us to conclude that there are no new reasons to question the existing consensus view of the Gp-9 system outlined in Gotzek and Ross (2007).