Front Bifurcation Research Articles

The performance of reaction mechanism in prediction of the characteristics of the diffusive-thermal oscillatory instability of methane–hydrogen–air burner-stabilized flames

In this work the performance of various detailed reaction mechanisms of combustion of methane–hydrogen fuel mixtures is studied. The investigation is focused on the burner stabilized flame configuration and is undertaken for the normal pressure conditions, which is a starting point for the analysis of the combustion chemistry at elevated pressures met in rocket engine chambers. The study presents the experimental setup, computational approach and results of comparison, which allow us to access the properties of complex combustion systems in variety of dynamical regimes. The comparison of the predicted and measured characteristics of these regimes is used to test the performance of the reaction models. In particular, the critical behavior, e.g. for blow-up, onset of pulsations and quasi-steady flame front propagation and bifurcation between these regimes may be used to characterize and to study properties of combustion systems with mixed fuels. A neutral stability boundary for onset of pulsations is suggested to be used in this study. A method for automatic identification of the boundary is proposed and implemented with several detailed mechanisms. Although for pure methane the results look acceptable, they show gradual divergence with the increase of percentage of hydrogen addition. Significant quantitative differences between experiments and modeling with respects to frequencies of oscillations are reported even for 2:1 ratio of hydrogen to methane in the unburned mixture. The results of the work indicate that current reaction mechanisms need to be improved in order to gain the quantitative predictability of methane–hydrogen–air combustion at normal pressure before proceeding to the conditions fuel-oxygen high pressure combustion more relevant for rocket chamber.

Antarctica Slope Front bifurcation eddy: A stationary feature influencing CO2 dynamics in the northern Antarctic Peninsula

The Southern Ocean is a key region for analyzing environmental drivers that regulate sea-air CO2 exchanges. These CO2 fluxes are influenced by several mesoscale structures, such as meanders, eddies and other mechanisms responsible for energy dissipation. Aiming to better understand sea-air CO2 dynamics in the northern Antarctica Peninsula, we investigated an anticyclonic stationary eddy located south of Clarence Island, in the eastern basin of Bransfield Strait – named the Antarctica Slope Front bifurcation (ASFb) eddy. Physical, chemical and biological data were sampled, and remote sensing measurements taken, in the region during late summer conditions in February 2020. The eddy’s core consisted of cold (0.31 °C), salty (34.38) and carbon-rich (2247 μmol kg−1) waters with dissolved oxygen depletion (337 μmol kg−1). The core retains a mixture of local surface waters with waters derived from Circumpolar Deep Water (i.e., Warm Deep Water from the Weddell Sea and modified Circumpolar Deep Water from the Bransfield Strait) and Dense Shelf Water. The ASFb eddy acts as a CO2 outgassing structure that reaches a CO2 emission to the atmosphere of ∼1.5 mmol m−2 d–1 in the eddy’s core, mostly due to enhanced dissolved inorganic carbon (DIC). The results suggest that surface variation in DIC in the eddy’s core is modulated by (i) the entrainment of CO2-rich intermediate waters at ∼500 m, (ii) low primary productivity, associated with small phytoplankton cells such as cryptophytes and green flagellates, and (iii) respiration processes caused by heterotrophic organisms (i.e., zooplankton community). By providing a comprehensive view of these physical and biogeochemical properties of this stationary eddy, our results are key to adding new insights to a better understanding of the behavior of mesoscale features influencing sea-air CO2 exchanges in polar environments.

The influence of microstructure on the fatigue crack growth rate in marine steels in the Paris Region

AbstractThis paper presents a study on the effect of microstructure on the fatigue crack growth (FCG) rate in advanced S355 marine steels in the Paris Region of the da/dN versus ΔK log–log plot. The environments of study were air and seawater (SW), under constant amplitude sinewave fatigue loading. Fundamentally, three phenomena (crack tip diversion, crack front bifurcation and metal crumb formation) were observed to influence the rate of FCG. These phenomena appear to be a function of the material microstructure, environment and crack tip loading conditions. The three factors retarded the crack growth by reducing or redistributing the effective driving force at the main active crack tip. A crack path containing extensively the three phenomena was observed to offer strong resistance to FCG. In SW, the degree of the electrochemical dissolution of the microplastic zone appears to be an additional primary factor influencing FCG in the steels.

Investigation of the active tectonic in Semnan basin (South of Semnan) using geomorphological indices

Geomorphological indicators are known as very useful methods for evaluating the effects of slow and fast tectonic activities. These indices can be used to compare different land forms in real and reasonable terms. This research aims to shed light on the mechanism and effectiveness of tectonic movements in Semnan basin using such geomorphic parameters as stream length-gradient, hypsometric integral, ratio of valley floor width to valley height, reverse topographic symmetry, drainage basin asymmetry, main river crinkle, mountain front simosity, drainage density, bifurcation ratio, and basin shape. These parameters serve as the model concepts. The physical devices used in this study included IRS satellite images, topographic maps, geological maps, and a geographic information system. To conduct the research, a digital evaluation model was designed for the study area using SRTM10m topographic data. Then, by means of the ARCMAP software, streams were delineated, the indices were measured, and statistical analyses were performed of the parameters. The results were obtained in the form of a map. The results of the data analysis according to the geomorphological indexes and the use of physical tools show that the tectonic activities in the area are moderate. Calculation of 10 geomorphic parameters in the study area represents a relatively active neotectonic activity in Semnan basin. According to the IAT index classification, Semnan basin can be placed in class 3 in terms of tectonic activities. The deep v-shaped valleys in the northern part of the region serve as evidence for such activities in the basin.

Morphotectonic analysis and GNSS observations for assessment of relative tectonic activity in Alaknanda basin of Garhwal Himalaya, India

Alaknanda basin in the Garhwal Himalaya, India, is a tectonically active region owing to ongoing crustal deformation, erosion, and depositional processes active in the region. Active tectonics in this region have greatly affected the drainage system and geomorphic expression of topography and provide an ideal natural set up to investigate the influence of tectonic activity resulting from the India-Eurasia collision. We evaluated active tectonics by using high resolution digital elevation model (DEM) based on eight geomorphic indices (stream length gradient index, valley floor width-to-height ratio, hypsometric integral, drainage basin asymmetry, transverse topography symmetry factor, mountain front sinousity index, bifurcation ratio, and basin shape index) and seismicity in eight subbasins of Alaknanda basin. The integrated product, relative tectonic activity index (TAI) map, was classified into three classes such as: ‘highly active’ with values ranging up to 2.0; ‘moderately active’ with values ranging from 2.0 to 2.25; and ‘less active’ with values >2.25. Further, the results were compared with relatively high crustal movement rate of 41.10mm/y computed through high precession Global Navigation Satellite System (GNSS) based continuous operating reference station (CORS) data. Thus, we concluded that this new quantitative approach can be used for better characterization and assessment of active seismotectonic regions of the Himalaya and elsewhere.

Non-monotonic resonance in a spatially forced Lengyel-Epstein model.

We study resonant spatially periodic solutions of the Lengyel-Epstein model modified to describe the chlorine dioxide-iodine-malonic acid reaction under spatially periodic illumination. Using multiple-scale analysis and numerical simulations, we obtain the stability ranges of 2:1 resonant solutions, i.e., solutions with wavenumbers that are exactly half of the forcing wavenumber. We show that the width of resonant wavenumber response is a non-monotonic function of the forcing strength, and diminishes to zero at sufficiently strong forcing. We further show that strong forcing may result in a π/2 phase shift of the resonant solutions, and argue that the nonequilibrium Ising-Bloch front bifurcation can be reversed. We attribute these behaviors to an inherent property of forcing by periodic illumination, namely, the increase of the mean spatial illumination as the forcing amplitude is increased.

Fronts and patterns in a spatially forced CDIMA reaction.

We use the CDIMA chemical reaction and the Lengyel-Epstein model of this reaction to study resonant responses of a pattern-forming system to time-independent spatial periodic forcing. We focus on the 2 : 1 resonance, where the wavenumber of a one-dimensional periodic forcing is about twice the wavenumber of the natural stripe pattern that the unforced system tends to form. Within this resonance, we study transverse fronts that shift the phase of resonant stripe patterns by π. We identify phase fronts that shift the phase discontinuously, and pairs of phase fronts that shift the phase continuously, clockwise and anti-clockwise. We further identify a front bifurcation that destabilizes the discontinuous front and leads to a pair of continuous fronts. This bifurcation is the spatial counterpart of the nonequilibrium Ising-Bloch (NIB) bifurcation in temporally forced oscillatory systems. The spatial NIB bifurcation that we find occurs as the forcing strength is increased, unlike earlier studies of the NIB bifurcation. Furthermore, the bifurcation is subcritical, implying a range of forcing strength where both discontinuous Ising fronts and continuous Bloch fronts are stable. Finally, we find that both Ising fronts and Bloch fronts can form discrete families of bound pairs, and we relate arrays of these front pairs to extended rectangular and oblique patterns.

Speed of traveling fronts in a sigmoidal reaction-diffusion system

We study a sigmoidal version of the FitzHugh-Nagumo reaction-diffusion system based on an analytic description using piecewise linear approximations of the reaction kinetics. We completely describe the dynamics of wave fronts and discuss the properties of the speed equation. The speed diagrams show front bifurcations between branches with one, three, or five fronts that differ significantly from the classical FitzHugh-Nagumo model. We examine how the number of fronts and their speed vary with the model parameters. We also investigate numerically the stability of the front solutions in a case when five fronts exist.

Stochastic resonance between counterpropagating Bloch walls

The nonequilibrium Ising-Bloch front bifurcation of the FitzHugh-Nagumo model with nondiffusing inhibitor provides a beautiful instance of an extended bistable system made up of propagating (Bloch) fronts. Moreover, these fronts are chiral and parity-related, and the barrier between them is nonetheless but a stationary Ising front. By means of numerical simulation in the neighborhood of this bifurcation, we demonstrate the existence of stochastic resonance in the transition between Bloch fronts of opposite chiralities, when an additive noise is included. The signal-to-noise ratio is numerically observed to scale with the distance to the critical point. This scaling law is theoretically characterized in terms of an effective nonequilibrium potential.

Pattern formation controlled by time-delayed feedback in bistable media

Effects of time-delayed feedback on pattern formation are studied both numerically and theoretically in a bistable reaction-diffusion model. The time-delayed feedback applied to the activator and/or the inhibitor alters the behavior of the nonequilibrium Ising-Bloch (NIB) bifurcation. If the intensities of the feedbacks applied to the two species are identical, only the velocities of Bloch fronts are changed. If the intensities are different, both the critical point of the NIB bifurcation and the threshold of stability of front to transverse perturbations are changed. The effect of time-delayed feedback on the activator opposes the effect of time-delayed feedback on the inhibitor. When the time-delayed feedback is applied individually to one of the species, positive and negative feedbacks make the bifurcation point shift to different directions. The time-delayed feedback provides a flexible way to control the NIB bifurcation and the pattern formation.

Stochastic resonance in extended systems

Here, three highly nontrivial instances are briefly discussed, showing both the degree of maturity achieved by the field of stochastic resonance (SR) and the wealth of potential realizations of SR in extended systems: (1) a “bound” KPZ system, for which the knowledge of its nonequilibrium potential (NEP) makes simple the solution of a very complex problem; (2) the Ising-Bloch front bifurcation in an activator-inhibitor system, a case of SR between moving fronts of opposite chirality; (3) a spatiotemporally chaotic “toy model”, useful for climate research, exhibiting internal SR due to chaos suppression.

Pattern formation in the ferrocyanide-iodate-sulfite reaction: The control of space scale separation

We revisit the conditions for the development of reaction-diffusion patterns in the ferrocyanide-iodate-sulfite bistable and oscillatory reaction. This hydrogen ion autoactivated reaction is the only example known to produce sustained stationary lamellar patterns and a wealth of other spatio-temporal phenomena including self-replication and localized oscillatory domain of spots, due to repulsive front interactions and to a parity-breaking front bifurcation (nonequilibrium Ising-Bloch bifurcation). We show experimentally that the space scale separation necessary for the observation of stationary patterns is mediated by the presence of low mobility weak acid functional groups. The presence of such groups was overlooked in the original observations made with hydrolyzable polyacrylamide gels. This missing information made the original observations difficult to reproduce and frustrated further experimental exploitation of the fantastic potentialities of this system. Using one-side-fed spatial reactors filled with agarose gel, we can reproduce all the previous pattern observations, in particular the stationary labyrinthine patterns, by introducing, above a critical concentration, well controlled amounts of polyacrylate chains in the gel network. We use two different geometries of spatial reactors (annular and disk shapes) to provide complementary information on the actual three-dimensional character of spatial patterns. We also reinvestigate the role of other feed parameters and show that the system exhibits both a domain of spatial bistability and of large-amplitude pH oscillations associated in a typical cross-shape diagram. The experimental method presented here can be adapted to produce patterns in the large number of oscillatory and bistable reactions, since the iodate-sulfite-ferrocynide reaction is a prototype of these systems.

Parity-breaking front bifurcation in bistable media: link between discrete and continuous versions

The effect of space-discretization in the onset of traveling fronts in symmetrically bistable media is studied. For the FitzHugh–Nagumo model stable standing and propagating front solutions coexist. In the continuum limit this region of coexistence shrinks to a (double-zero eigenvalue) point. The unfolding of this point severely restricts the possible scenarios for the transition from standing to propagating fronts, such that the route described here and the one reported in [Phys. Rev. E 64 (2001) 065203(R)] are the most typical scenarios.

Northward and southward migrations of frontal zones during the past 40 kyr in the Kuroshio‐Oyashio transition area

The variation of sea surface temperature (SST) in the Kuroshio‐Oyashio transition area and the Okhotsk Sea during the last 40 kyr was estimated using long‐chain unsaturated alkyl ketones (alkenones). The temperature difference between the present and the last glacial period was about 5°–6°C in the Kuroshio‐Oyashio transition area, slightly larger than the 4°C previously reported. Moreover, alkenones were not detected before 18 kyr B.P. in or near the Okhotsk Sea, perhaps because of nearly year‐round sea‐ice expansion, which would have prevented the growth of alkenone producers, or because alkenones were less well preserved in surface sediments during the glacial period. The northward and southward migrations of frontal zones were evaluated using differences in alkenone temperatures between stations located in the vicinity of the Subarctic Front (SAF), Subarctic Boundary (SAB), and Kuroshio Bifurcation Front (KBF). All three frontal zones migrated southward during the glacial period, compared with their present positions, and their relative positions were different between the Holocene and glacial periods. In particular, the distance between the SAF and the SAB was reduced during the glacial period compared with at present. The northward and southward migration of the frontal zones may relate to both mid to low atmospheric circulation and polar atmospheric circulation.

Front bifurcation in a tristable reaction-diffusion system under periodic forcing.

A piecewise linear tristable reaction-diffusion equation under external forcing of periodic type is considered. A special feature of the forcing is that the force moves together with the traveling wave. Front velocity equations are obtained analytically using matching procedures for the front solutions. It is noted that there is a restriction in building of null-cline. For each choice of outer branches of null-cline the middle interfacial zone should not exceed some critical value. When this zone is larger the front does not exist. It is found that in the presence of forcing there exists a set of front solutions with different phases (matching point coordinates). The periodic forcing produces a change in the velocity-versus-phase diagram. For a specific choice of wave number, there is a bubble formation which corresponds to additional solutions when the velocity bifurcates to form three fronts.

Front Bifurcations in an Excitatory Neural Network

We show how a one-dimensional excitatory neural network can exhibit a symmetry breaking front bifurcation analogous to that found in reaction diffusion systems. This occurs in a homogeneous network when a stationary front undergoes a pitchfork bifurcation leading to bidirectional wave propagation. We analyze the dynamics in a neighborhood of the front bifurcation using perturbation methods, and we establish that a weak input inhomogeneity can induce a Hopf instability of the stationary front, leading to the formation of an oscillatory front or breather. We then carry out a stability analysis of stationary fronts in an exactly solvable model and use this to derive conditions for oscillatory fronts beyond the weak input regime. In particular, we show how wave propagation failure occurs in the presence of a large stationary input due to the pinning of a stationary front; a subsequent reductionin the strength of the input then generates a breather via a Hopf instability of the front. Finally, we derive conditions for the locking of a traveling front to a moving input, and we show how locking depends on both the amplitude and velocity of the input.

Evans Functions for Integral Neural Field Equations with Heaviside Firing Rate Function

In this paper we show how to construct the Evans function for traveling wave solutions of integral neural field equations when the firing rate function is a Heaviside. This allows a discussion of wave stability and bifurcation as a function of system parameters, including the speed and strength of synaptic coupling and the speed of axonal signals. The theory is illustrated with the construction and stability analysis of front solutions to a scalar neural field model, and a limiting case is shown to recover recent results of Zhang [Differential Integral Equations, 16 (2003), pp. 513--536]. Traveling fronts and pulses are considered in more general models possessing either a linear or piecewise constant recovery variable. We establish the stability of coexisting traveling fronts beyond a front bifurcation and consider parameter regimes that support two stable traveling fronts of different speeds. Such fronts may be connected, and depending on their relative speed the resulting region of activity can widen or contract. The conditions for the contracting case to lead to a pulse solution are established. The stability of pulses is obtained for a variety of examples, in each case confirming a previously conjectured stability result. Finally, we show how this theory may be used to describe the dynamic instability of a standing pulse that arises in a model with slow recovery. Numerical simulations show that such an instability can lead to the shedding of a pair of traveling pulses.

Effect of Lewis number on flame front fragmentation in narrow closed channels

This work is concerned with the numerical investigation of the influence of the ratio of thermal conductivity to diffusivity of a combustible gas mixture on the dynamics of adiabatic flame propagation in narrow closed planar channels under zero gravity. Reynolds numbers are less than 100. A low Mach number limit of the Navier-Stokes system for the A → B reaction was used. The appearance of a flame front bifurcation, resulting in flame inversion, was obtained numerically for low Lewis numbers. The combined effect of a specific hydrodynamic flow field in a closed channel and of the domination of diffusivity over thermal conductivity, similar to the mechanism of thermal-diffusive instability, was found to be the main driving force of the bifurcation. It was concluded that, both numerically and experimentally, the inverted flame front has the same general shape. However, this shape is unlikely to be attributed to the same physical mechanism of its formation over the entire range of regimes. Fragmentation of inverted flames into two segments is clearly observed for low Lewis numbers.

Kinematic equations for front motion and spiral-wave nucleation

We present a new set of kinematic equations for front motion in bistable media. The equations extend earlier kinematic approaches by coupling the front curvature with the order parameter associated with a parity-breaking front bifurcation. In addition to naturally describing the core region of rotating spiral waves, the equations can be used to study the nucleation of spiral-wave pairs along uniformly propagating fronts. The analysis of spiral-wave nucleation reduces to the simpler problem of droplet, or domain, nucleation in one space dimension.

Holes and chaotic pulses of traveling waves coupled to a long-wave mode

It is shown that localized traveling-wave pulses and holes can be stabilized by a coupling to a long-wave mode. Simulations of suitable real Ginzburg-Landau equations reveal a small parameter regime in which the pulses exhibit a breathing motion (presumably related to a front bifurcation), which subsequently becomes chaotic via period-doubling bifurcations.