Extinction Transition Research Articles

Effect of the composition of the hot product stream in the quasi-steady extinction of strained premixed flames

The extinction of premixed CH 4/O 2/N 2 flames counterflowing against a jet of combustion products in chemical equilibrium was investigated numerically using detailed chemistry and transport mechanisms. Such a problem is of relevance to combustion systems with non-homogeneous air/fuel mixtures or recirculation of the burnt gases. Contrary to similar studies that were focused on heat loss/gain, depending on the degree of non-adiabaticity of the system, the emphasis here was on the yet unexplored role of the composition of counterflowing burnt gases in the extinction of lean-to-stoichiometric premixed flames. For a given temperature of the counterflowing products of combustion, it was found that the decrease of heat release with increase in strain rate could be either monotonic or non-monotonic, depending on the equivalence ratio φ b of the flame feeding the hot combustion product stream. Two distinct extinction modes were observed: an abrupt one, when the hot counterflowing stream consists of either inert gas or equilibrium products of a stoichiometric premixed flame, and a smooth extinction, when there is an excess of oxidizing species in the combustion product stream. In the latter case four burning regimes can be distinguished as the strain rate is progressively increased while the heat release decreases smoothly: an adiabatic propagating flame regime, a non-adiabatic propagating flame regime, the so-called partially-extinguished flame regime, in which the location of the peak of heat release crosses the stagnation plane, and a frozen flow regime. The flame structure was analyzed in detail in the different burning regimes. Abrupt extinction was attributed to the quenching of the oxidation layer with the entire H–OH–O radical pool being comparably reduced. Under conditions of smooth extinction, the behavior is different and the concentration of the H radical decreases the most with increasing strain rate, whereas OH and O remain comparatively abundant in the oxidation layer. As the profile of the heat release rate thickens, the oxidation layer is quenched and the attack of the fuel relies more heavily on the OH radicals.

Directed percolation and the extinction transition on a diffusive substrate

The extinction transition on a 1D heterogeneous substrate with diffusive correlations is studied. Diffusively correlated heterogeneity is shown to affect the location of the transition point, as the reactants adapt to the fluctuating environment. At the transition point the density decays like t − 0.159 , as in directed percolation. However, the scaling function describing the behavior away from the transition and other critical exponents shows significant deviations from the known DP behavior. It is suggested, thus, that the off-transition behavior of the system is governed by local adaptation to favored regions.

From nanoparticle to nanocable: Impact of size and geometrical constraints on the optical modes of Si/SiO2 core/shell nanostructures

In the extinction spectra of Si/SiO2 core/shell nanostructures, peak features in the near UV region (3–5 eV) appear when the nanostructure geometrical configuration changes from spherical nanoparticles to cylindrical nanocables, with the peak features become more intense in the nanocables of smaller core diameter. Similar feature at ∼4.2 eV is also observed in the spatially resolved electron energy loss spectra (SREELS) of individual nanocable, but not in the nanoparticle. The EELS simulations unravel the origin of such excitation as the monopolar interface plasmon in cylindrical nano-objects, being responsible for the observed near UV extinction modes in nanocables.

A Study on Flame Extinction Characteristics along a C-Curve

A study has been conducted both experimentally and numerically to clarify impacts of curtain flow and velocity ratio on low strain rate flame extinction and to further display transition of shrinking flame disk to flame-hole. Critical mole fractions at flame extinction are provided in terms of velocity ratio, nitrogen curtain flow rate, and global strain rate. Flame extinction modes are grouped into four on a C-curve, which is characterized by a flame-hole, the shrinking of edge flame, and edge flame oscillation. It is seen that varying curtain flow rate does not impact on edge flame oscillation, flame extinction, and even flame extinction modes. Variation of velocity ratio extends to the low strain rate flame extinction modes beyond the turning point. It is found that the expanding and shrinking flames always have negative flame propagation speed; it is also recognized that the decrease of flame radius is prone to extinguish due to the dominant role of radial conduction heat loss. The examination of ener...

The effect of spatial heterogeneity on the extinction transition in stochastic population dynamics

Stochastic logistic-type growth on a static heterogeneous substrate is studied both above and below the drift-induced delocalization transition. Using agent-based simulations, the delocalization of the highest eigenfunction of the deterministic operator is connected with the large N limit of the stochastic theory. It is seen that the localization length of the deterministic theory controls the divergence of the spatial correlation length with N at the transition. It is argued that, in the presence of a strong wind, the extinction transition belongs to the directed percolation universality class, as any finite colony made of discrete agents is washed away from a heterogeneity with compact support. Some of the difficulties in the analysis of the extinction transition in the presence of a weak wind, where there is a localized active state, are discussed.

The two-dimensional structure of low strain rate counterflow nonpremixed-methane flames in normal and microgravity

The structure and extinction of low strain rate nonpremixed methane–air flames was studied numerically and experimentally. A time-dependent axisymmetric two-dimensional (2D) model considering buoyancy effects and radiative heat transfer was developed to capture the structure and extinction limits of normal gravity (1-g) and zero gravity (0-g) flames. For comparison with the 2D modelling results, a one-dimensional (1D) flamelet computation using a previously developed numerical code was exercised to provide information on the 0-g flames. A 3-step global reaction mechanism was used in both the 1D and 2D computations to predict the measured extinction limit and flame temperature. Photographic images of flames undergoing the process of extinction were compared with model calculations. The axisymmetric numerical model was validated by comparing flame shapes, temperature profiles, and extinction limits with experiments and with the 1D computational results. The 2D computations yielded insight into the extinction mode and flame structure. A specific maximum heat release rate was introduced to quantify the local flame strength and to elucidate the extinction mechanism. The contribution by each term in the energy equation to the heat release rate was evaluated to investigate the multi-dimensional structure and radiative extinction of the 1-g flames. Two combustion regimes depending on the extinction mode were identified. Lateral heat loss effects and multi-dimensional flame and flow structure were also found. At low strain rates in 1-g flames (‘regime A’), the flame is extinguished from the weak outer edge of the flame, which is attributed to a multi-dimensional flame structure and flow field. At high strain rates, (‘regime B’), the flame extinction initiates near the flame centreline owing to an increased diluent concentration in the reaction zone, similar to the extinction mode of 1D flames. These two extinction modes can be clearly explained by consideration of the specific maximum heat release rate.

The rise and fall of species: implications for macroevolutionary and macroecological studies

Knowing the geographic extents of species is crucial for understanding the causes of diversity distributions and modes of speciation and extinction. Species geographic ranges are often viewed as approximately constant in size in geological time, even though climate change studies have shown that historical and modern species geographic distributions are not static. Here, we use an extensive global microfossil database to explore the temporal trajectories of geographic extents over the entire lifespan of marine nannoplankton, diatom, planktic foraminifer and radiolarian species. We show that geographic extents are not static over geological time-scales. Temporal trajectories of species geographic ranges are asymmetric: the rise is quicker than the fall. We propose that once a species has overcome its initial difficulties in geographic establishment, it rises to its peak geographic extent. However, once this peak value is reached, it will also have a maximal number of species to interact with. The negative of these biotic interactions could then cause a gradual geographic decline. We discuss the multiple implications of our findings with reference to macroecological and macroevolutionary studies.

Bounding biomass in the Fisher equation

The Fisher-Kolmogorov-Petrovskii-Piskunov equation with a variable growth rate and advection by an incompressible velocity field is considered as a model for plankton dispersed by ocean currents. If the average growth rate is negative then the model has a survival-extinction transition; the location of this transition in the parameter space is constrained using variational arguments and delimited by simulations. The statistical steady state reached when the system is in the survival region of parameter space is characterized by integral constraints and upper and lower bounds on the biomass and productivity that follow from variational arguments and direct inequalities. In the limit of zero-decorrelation time the velocity field is shown to act as Fickian diffusion with an eddy diffusivity much larger than the molecular diffusivity: this allows a one-dimensional model to predict the biomass, productivity, and extinction transitions. All results are illustrated with a simple growth and stirring model.

About stability of the ignition process of small solid particle

The distributed mathematical model of magnesium particle ignition is developed taking into account the heterogeneous chemical reaction and the domain of particle thermal influence on gas. The problem solvability in the stationary case has allowed one to expand classification of regular modes of heating as well as the modes of extinction and ignition of a particle. The limiting size of a gas layer near a particle is found that determines an ignition mode. It is shown that the ignition delay time grows if we take into account the gas layer near the particle. Stability of some heating modes within the framework of finite and infinitesimal perturbations is studied. An opportunity to control the ignition process by high-frequency thermal action on the unstable particle gas states is shown.

Unbounded autocatalytic growth on diffusive substrate: The extinction transition

The effect of diffusively correlated spatial fluctuations on the proliferation-extinction transition of autocatalytic agents is investigated numerically. Reactants adaptation to spatio-temporal active regions is shown to lead to proliferation even if the mean field rate equations predict extinction, in agreement with previous theoretical predictions. While in the proliferation phase the system admits a typical time scale that dictates the exponential growth, the extinction times distribution obeys a power law at the parameter region considered.

EFFECTS OF CHANNEL WIDTH AND LEWIS NUMBER ON THE MULTIPLE FLAME REGIMES AND PROPAGATION LIMITS IN MESOSCALE

The effects of channel width and Lewis number on the propagation limits and flame transition between multiple flame regimes in mesoscale combustion were studied experimentally and numerically using methane and propane-air mixtures. The experimental results showed that both methane and propane-air flames have multiple flame regimes. It was also shown that there existed non-monotonic dependence of flame speeds on equivalence ratio. Moreover, the results also showed that there are two different flame transitions, a direct transition and an extinction transition, depending on the channel width, Lewis number, and flow velocity. For the first time, a two-dimensional numerical simulation was conducted to predict the transition between different flame regimes and to examine the effects of channel width, Lewis number, and flow rates. The results showed that flame stretch had a significant effect on the extinction limit and the flame bifurcation. The predicted results agreed qualitatively well with the experiment.

A stochastic model for integrating changes in species richness and community similarity across spatial scales

Human activities have elevated the extinction of natural populations as well as the invasion of new areas by non‐native species. These dual processes of invasion and extinction may change the richness and similarity of communities, but the form these changes take is likely to depend on the manner in which invasions and extinctions occur and the spatial scale at which the changes are measured. Here, we explore the influence of differing patterns of extinction and invasion on the similarity and richness of a meta‐community. In particular, we model simple stochastic processes analogous to realistic modes of human‐mediated introduction of non‐native species and range expansion by native species. We show that different modes of invasion and extinction can produce very different changes in diversity, and that the relative magnitude of these changes depends both on where in the meta‐community diversity is measured and the degree of initial species aggregation. At any spatial scale of measurement, changes in the richness and similarity of communities following invasion and extinction are not necessarily strongly coupled: relatively large increases in richness may or may not also be associated with relatively large increases in similarity among communities. Thus, in real systems, the influence of human‐induced invasions and extinctions on diversity will depend on both the precise mode of these processes (especially invasion), and how species populations are distributed across space.

Extinction characteristics of catalyst-assisted combustion in a stagnation-point flow reactor

As a fundamental study to understand physical and chemical characteristics in catalyst-assisted combustion, numerical simulations of a stagnation-point flow combustor with a catalytic surface are performed. The combustible mixture of methane and air is blown on top of a platinum surface, forming a classical stagnation-point flow configuration. This geometry not only represents an on-chip microcombustor considered in recent studies, but it also serves as a canonical problem of combined heterogeneous/homogeneous combustion subjected to flow straining, which is a key parameter that governs the quenching and flammability limit. One-dimensional similarity formulation is derived with full consideration of detailed surface and gas-phase chemical kinetic models. Parametric studies are conducted to investigate the effects of strain rate, equivalence ratio, heat loss on the combustion, and extinction modes. The steady results showed that catalysis can largely extend the extinction limit, while suppressing the gas-phase reaction at lower strain rates. It was also found that the extension of the catalytic reaction quenching limit is sensitive to the mixture composition, suggesting the dominance of chemical aspects in catalytic combustion. The temperature versus strain rate response curves exhibit multiple branches of stable solutions, implying a possibility of hysteresis behavior in a coupled homogeneous–heterogeneous reactor. Extensive parametric studies in terms of the mixture equivalence ratio and the conductive heat loss parameter have revealed three distinct steady response regimes: a surface-dominant monotonic response, continuous two-branch response, and separated response showing an isolated surface-reaction island. The results are expected to provide insight into improving the overall combustion stability and efficiency of catalyst-assisted combustors.

정상 중력장에서 낮은 스트레인율을 갖는 대향류 비예혼합화염의 소화한계

The extinction characteristics of low strain rate normal gravity (1-g) nonpremixed methane-air flames were studied numerically and experimentally. A time-dependent axisymmetric two-dimensional (2D) model considering buoyancy effects and radiative heat transfer was developed to capture the structure and extinction limits of 1-g flames. One-dimensional (1D) computations were also conducted to provide information on 0-g flames. A 3-step global reaction mechanism was used in both the 1D and 2D computations to predict the measured extinction limit and flame temperature. A specific maximum heat release rate was introduced to quantify the local flame strength and to elucidate the extinction mechanism. Overall fractional contribution by each term in the energy equation to the heat release was evaluated to investigate the multi-dimensional structure and radiative extinction of 1-g flames. Images of flames were taken for comparison with the model calculation undergoing extinction. The two-dimensional numerical model was validated by comparing flame temperature profiles and extinction limits with experiments and 1D computation results. The 2D computations yielded insight into the extinction mode and flame structure of 1-g flames. Two combustion regimes depending on the extinction mode were identified. Lateral heat loss effects and multi-dimensional flame structure were also found. At low strain rates of 1-g flame (“Regime A”), the flame is extinguished from the weak outer flame edge, which is attributed to multi-dimensional flame structure and flow field. At high strain rates, (“Regime B”), the flame extinction initiates near the flame centerline due to an increased diluent concentration in reaction zone, which is the same as the extinction mode of 1D flame. These two extinction modes could be clearly explained with the specific maximum heat release rate.

Combustion characteristics and flame stability at the microscale: a CFD study of premixed methane/air mixtures

A two-dimensional elliptic, computational fluid dynamics (CFD) model of a microburner is solved to study the effects of microburner dimensions, conductivity and thickness of wall materials, external heat losses, and operating conditions on combustion characteristics and flame stability. We have found that the wall conductivity and thickness are very important as they determine the upstream heat transfer, which is necessary for flame ignition and stability, and the material's integrity by controlling the existence of hot spots. Two modes of flame extinction occur: a spatially global type for large wall thermal conductivities and/or low flow velocities and blowout. It is shown that there exists a narrow range of flow velocities that permit sustained combustion within a microburner. Large transverse and axial gradients are observed even at these small scales under certain conditions. Periodic oscillations are observed near extinction in cases of high heat loss. Engineering maps that delineate flame stability, extinction, and blowout are constructed. Design recommendations are finally made.

A complete classification of Darwinian extinction in ecological interactions.

The evolution of a population by individual-level natural selection can result in the population's extinction. Selection causes the spread of phenotypes with higher relative fitness, but at the same time, selection can also indirectly produce changes in the physical, biotic, or genotypical environment through population interactions (e.g., environment modification, interspecific interactions, and genomic conflict). Because fitness is environment dependent, this can cause mean fitness to decrease, resulting in extinction. I call this process "Darwinian extinction." Examples of Darwinian extinction include a variety of dynamics and modes of extinction, but the variation is constrained. I determine the complete classification of possible dynamics and modes of Darwinian extinction due to ecological interactions, using bifurcation theory and models with ecological and evolutionary changes occurring on different timescales. This classification is also extended to extinctions due to interactions within the population. The mode of extinction may be either sudden or gradual (requiring additional stochastic processes), and each mode has specific types of dynamics associated with it. Darwinian extinction is a robust and normal phenomenon, and this reasonably complete classification can help us understand more thoroughly its role in nature.

Influence of conductive heat-losses on the propagation of premixed flames in channels

We study the propagation of premixed flames in two-dimensional channels accounting for heat-losses by conduction to the channel’s walls and a prescribed Poiseuille flow. A diffusive-thermal model is used and the calculations reported are based on Arrhenius-type chemistry. Attention is focused on the influence of the magnitude of heat losses, the channel width, and the mean flow velocity. Special attention is devoted to the determination of the global burning rate and to extinction conditions. Depending on the channel width we discuss two possible modes of extinction: total flame extinction brought about in narrow channels by excessive losses, and partial flame extinction near the walls of wider channels. Our predictions of the quenching distance, namely the smallest channel’s width that permits flame propagation, and the dead space in the case of partial extinction are in agreement with experimentally reported values. The sensitivity of the flame to an imposed flow, being directed either towards the fresh mixture or towards the burned gas, is examined with some details.

Modes of extinction, pseudo-extinction and distribution in Middle Jurassic ammonites: terminology

Mid-Jurassic Ammonitina (Cephalopoda, Mollusca) provide good examples of true and apparent "extinctions" (i.e., taxon or clade disappearances) at the local, regional, and global scales. A terminology is presented. Extinction is the termination of a phylogenetic lineage or entire clade (not of local demes or regional populations). Extinction was often preceded by progressive range contraction that resulted in diachronous regional disappearance ("extirpation") and occurred with the elimination of the last refuge. Other range contractions, however, were not terminal, but were followed by renewed expansions, resulting in temporary absence of the lineage over part of its known range only, due to pseudo-extinction. Some lineages, called Lazarus taxa, apparently disappeared entirely for short or extended periods by pseudotermination (causing a "phylogenetic hiatus"). This is an extreme form of pseudo-extinction with unknown refuge due to small size and (or) unsuitable facies and location. Lineage or clade reappearance may be in the form of new species, whose relationship to ancestral taxa has been problematic. Some disappearances can be explained with displacive competition, where the replacement taxon is either of endemic origin or an immigrant. Recent research in previously underexplored field areas has closed some of the gaps of documentation by finding the refuges. Range contractions and expansions, together with their regional disappearances and pseudo-extinctions, including pseudotermination, were often causally related to sea-level changes, especially eustasy. Most true extinctions, however, cannot be identified precisely, because they occurred in small populations and (or) refuges. Extinctions presumably did not coincide with global geoevents.

Modes of extinction in two Devonian ostracode faunas of western Canada

The development of a prominent Middle Devonian Eifelian and an Upper Devonian Frasnian ostracode faunal sequence of western Canada is used to trace their evolutionary pathways, to illustrate evolutionary dynamics, and to evaluate the most probable causes and implications of the major and minor changes, which are clearly expressed in two sets of charts. A connection between sedimentary transgressive–regressive and evolutionary cycles is evident and documented in sample-for-sample accounts. Major changes in sea level were the primary cause for the most obvious breaks and trends in the faunal sequences and were responsible for the cyclic development of both the sedimentary and ostracode records. In contrast, numerous subordinate faunal breaks impart a distinctly punctuated pattern to both extinction and speciation pathways. Their regular spacing point to rhythmic influences that are interpreted to reflect primarily temperature fluctuations to which ostracodes are known to react in direct and indirect ways. In turn, the periodicity of the changes falls within the time frame of the Milankovitch Effect or to any one, or a combination, of its three variables. By combining the overall cyclic development with the punctuated progression of both extinction and speciation events in an "event-stratigraphic chart," a blueprint of the evolutionary dynamics emerges, which can be directly applied in sequence-stratigraphic reconstructions.

Life and death near a windy oasis.

We propose a simple experiment to study delocalization and extinction in inhomogeneous biological systems. The nonlinear steady state for, say, a bacteria colony living on and near a patch of nutrient or favorable illumination ("oasis") in the presence of a drift term ("wind") is computed. The bacteria, described by a simple generalization of the Fisher equation, diffuse, divide A --> A + A, die A --> 0, and annihilate A + A --> 0. At high wind velocities all bacteria are blown into an unfavorable region ("desert"), and the colony dies out. At low velocity a steady state concentration survives near the oasis. In between these two regimes there is a critical velocity at which bacteria first survive. If the "desert" supports a small nonzero population, this extinction transition is replaced by a delocalization transition with increasing velocity. Predictions for the behavior as a function of wind velocity are made for one and two dimensions.