Turbulent propagation of premixed flames in the presence of Darrieus–Landau instability

We investigate the role played by hydrodynamic instability in the wrinkled flamelet regime of turbulent combustion, where the intensity of turbulence is small compared to the laminar flame speed and the scale large compared to the flame thickness. To this end the Michelson–Sivashinsky (MS) equation for flame front propagation in one and two spatial dimensions is studied in the presence of uncorrelated and correlated noise representing a turbulent flow field. The combined effect of turbulence intensity, integral scale, and an instability parameter related to the Markstein length are examined and turbulent propagation speed monitored for both stable planar flames and corrugated flames for which the planar conformation is unstable. For planar flames a particularly simple scaling law emerges, involving quadratic dependence on intensity and a linear dependence on the degree of instability. For corrugated flames we find the dependence on intensity to be substantially weaker than quadratic, revealing that corrugated flames are more resilient to turbulence than planar flames. The existence of a threshold turbulence intensity is also observed, below which the corrugated flame in the presence of turbulence behaves like a laminar flame. We also analyze the conformation of the flame surface in the presence of turbulence, revealing primary, large-scale wrinkles of a size comparable to the main corrugation. When the integral scale is much smaller than the characteristic corrugation length we observe, in addition to primary wrinkles, secondary small-scale wrinkles contaminating the surface. The flame then acquires a multi-scale, self-similar conformation, with a fractal dimension, for one-dimensional flames, plateauing at 1.23 for large intensities. The existence of an intermediate integral scale is also found at which the turbulent speed is maximized. When two-dimensional flames are subject to turbulence, the primary wrinkling patterns give rise to polyhedral-cellular structures which bear a very close resemblance to those observed in experiments on hydrodynamically unstable expanding spherical flames.     

Darrieus–Landau instability of premixed flames enhanced by fuel droplets

Recent experiments on spray flames propagating in a Wilson cloud chamber have established that spray flames are much more sensitive to wrinkles or corrugations than single-phase flames. To propose certain elements of explanation, we numerically study the Darrieus–Landau (or hydrodynamic) instability (DL-instability) developing in premixtures that contain an array of fuel droplets. Two approaches are compared: numerical simulation starting from the general conservation laws in reactive media, and the numerical computation of Sivashinsky-type model equations for DL-instability. Both approaches provide us with results in deep agreement. It is first shown that the presence of droplets in fuel–air premixtures induces initial perturbations which are large enough to trigger the DL-instability. Second, the droplets are responsible for additional wrinkles when the DL-instability is developed. The latter wrinkles are of length scales shorter than those of the DL-instability, in such a way that the DL-unstable spray flames have a larger front surface and therefore propagate faster than the single-phase ones when subjected to the same instability.     

Diffusive–thermal oscillations of rich premixed hydrogen–air flames in a microflow reactor

In this paper the dynamics of rich hydrogen–air flames in a microflow reactor with controlled temperature of the walls is investigated numerically using the thermal-diffusion model with two-step kinetics in one spatial dimension. It is found that as the parameters of the system are varied the sequence of bifurcation occurs leading to the formation of complex spatio-temporal patterns. These include pulsating, chaotic, mixed-mode and FREI (Flames with Repetitive Extinction and Ignition) oscillations. The critical parameter values for the existence of different dynamical regimes are found in terms of equivalence ratio and flow velocity.     

On a solution of the self-interaction problem in Kohn–Sham density functional theory

We report on a methodology for the treatment of the Coulomb energy and potential in Kohn–Sham density functional theory that is free from self-interaction effects. Specifically, we determine the Coulomb potential given as the functional derivative of the Coulomb energy with respect to the density, where the Coulomb energy is calculated explicitly in terms of the pair density of the Kohn–Sham orbitals. This is accomplished by taking advantage of an orthonormal and complete basis that is an explicit functional of the density that then allows for the functional differentiation of the pair density with respect to the density to be performed explicitly. This approach leads to a new formalism that provides an analytic, closed-form determination of the exchange potential. This method is applied to one-dimensional model systems and to the atoms Helium through Krypton based on an exchange only implementation. Comparison of our total energies (denoted SIF) to those obtained using the usual Hartree–Fock (HF) and optimized effective potential (OEP) methods reveals the hierarchy $E_{\mathrm{HF}}\le E_{\mathrm{OEP}}\le E_{\mathrm{SIF}}$ that is indicative of the greater variation freedom implicit in the former two methods.     

On the origin of the phase–space diffusion limit in (dis)ordered protein aggregation

Derivation of a phase–space diffusion limit (D-L) allows to obtain a useful formula for a characteristic width of the macroion-channeling filter, controlling model (dis)ordered protein aggregations in a non-ideal aqueous solution. The channel’s width is estimated at the order of an inner half-width of the Stern-type double layer circumventing the growing object and depends in turn on an interplay of the local thermal and electrostatic conditions. The interfacial channeling effect manifests at the edge of biomolecular hydration-duration dependent (non)Markovianity of the system. The interface vs. solution aggregation late-time dynamics are discussed in such local (non)isothermal context with the aim to suggest their experimental assessment.     

On the effects of a varied diffusion time in vivo: is the diffusion in white matter restricted?

The aim of this work was to study the diffusion-related signal attenuation curves (signal-vs.-b curves) measured perpendicular and parallel to the neuronal fibers of the corticospinal tract in vivo and to determine whether effects of restricted diffusion could be observed when varying the diffusion time (T_D). A biexponential model and a two-compartment model including exchange according to the Kärger formalism were employed to analyze the signal-vs.-b curves. To validate the two-compartment model, restricted diffusion with exchange was simulated for uniformly sized cylinders, using different diameters and exchange times. The model was shown to retrieve the simulated parameters well, also when the short gradient pulse approximation was not met. The in vivo measurements performed perpendicular to the tracts, using b values up to 28000 s/mm² and T_D values between 64 and 256 ms, did not show the effects of restricted diffusion as expected from previous ex vivo studies. The applied two-compartment model yielded an average axonal diameter of about 4 μm and an intracellular exchange time of about 300 ms, but did not fit statistically well to the data. In conclusion, this study indicates that if the diffusion is modeled as two compartments, of which one is restricted, exchange must be included in the model.     

Effects of preferential and differential diffusion on the mutual annihilation of two premixed hydrogen–air flames

The unsteady process of upstream head-on quenching of two laminar premixed hydrogen–air flames at different equivalence ratios in one dimension is investigated numerically in the presence of preferential and differential diffusion effects. Important chemical and transport characteristics of the mutual annihilation process are studied during the two primary stages of upstream mutual annihilation, preheat layers' and reaction layers' interactions. Because of the diffusive mobility of the fuel, hydrogen, relative to heat and the oxidizer, preferential and differential diffusion effects result in a shift in the equivalence ratio in the reaction zone to leaner conditions. This shift, in turn, affects the subsequent reaction layers' interactions through qualitative and quantitative changes in the rates of reactants' consumption and radicals' production. Another consequence of this shift is the presence of excess and ‘unburnt’ fuel or oxidizer at the end of the mutual annihilation process. The process of mutual annihilation occurs over time scales that are significantly shorter than characteristic residence times associated with flames.     

The precise time-dependent solution of the Fokker–Planck equation with anomalous diffusion

We study the time behavior of the Fokker–Planck equation in Zwanzig’s rule (the backward-Ito’s rule) based on the Langevin equation of Brownian motion with an anomalous diffusion in a complex medium. The diffusion coefficient is a function in momentum space and follows a generalized fluctuation–dissipation relation. We obtain the precise time-dependent analytical solution of the Fokker–Planck equation and at long time the solution approaches to a stationary power-law distribution in nonextensive statistics. As a test, numerically we have demonstrated the accuracy and validity of the time-dependent solution.     

On the physical parametrization and magnetic analogs of the Emparan–Teo dihole solution

The Emparan–Teo non-extremal black dihole solution is reparametrized using Komar quantities and the separation distance as arbitrary parameters. We show how the potential A₃$A_3$ can be calculated for the magnetic analogs of this solution in the Einstein–Maxwell and Einstein–Maxwell-dilaton theories. We also demonstrate that, similar to the extreme case, the external magnetic field can remove the supporting strut in the non-extremal black dihole too.     

Parametric magnon–phonon instability in the structure of YIG films

The effects of parametric magnon–phonon instability and the self-modulation of magnetostatic and fast magnetoelastic waves are revealed. It is found that instabilities are caused by the decay of the initial waves stimulated by high-Q acoustic resonances. Decays of the first and the second order (three- and four-magnon–phonon decays) are observed. Their characteristics and existing conditions are determined. Magnetostatic wave decays have both upper and lower thresholds. It is shown that magnetoelastic waves become stable above the upper thresholds. The existence of the upper threshold is due to several competing decay scenarios.     

On the possibility of generation of high-power low-frequency radiation as a result of evolution of explosive instability in the flow–nonisothermal plasma system

We discuss the possibility of realization of explosive instability in a resonance triplet of longitudinal waves, specifically, an ion Langmuir mode and two beam modes (slow and fast ones) in the system of a beam of charged particles and nonisothermal plasma. Estimates for the plasmasphere of the Earth are given.     

A new type of the evolution of the bubble front in the Richtmyer–Meshkov instability

We study the coherent motion of bubbles and spikes in the Richtmyer–Meshkov instability. The theoretical solutions capturing the interplay of harmonics in the nonlinear dynamics are found, and a new type of the evolution of the bubble front is predicted.     

Solid–state diffusion–controlled growth of the phases in the Au–Sn system

The solid state diffusion-controlled growth of the phases is studied for the Au–Sn system in the range of room temperature to 200 °C using bulk and electroplated diffusion couples. The number of product phases in the interdiffusion zone decreases with the decrease in annealing temperature. These phases grow with significantly high rates even at the room temperature. The growth rate of the AuSn₄ phase is observed to be higher in the case of electroplated diffusion couple because of the relatively small grains and hence high contribution of the grain boundary diffusion when compared to the bulk diffusion couple. The diffraction pattern analysis indicates the same equilibrium crystal structure of the phases in these two types of diffusion couples. The analysis in the AuSn₄ phase relating the estimated tracer diffusion coefficients with grain size, crystal structure, the homologous temperature of experiments and the concept of the sublattice diffusion mechanism in the intermetallic compounds indicate that Au diffuses mainly via the grain boundaries, whereas Sn diffuses via both the grain boundaries and the lattice.     

On the Effect of Stochastic Fluctuations in the Dynamics of the Lifshitz–Slyozov–Wagner Model

In this paper the dynamics of a system of spherical particles that fill a small volume fraction of the space and that evolves in a concentration field is discussed. Corrections to the Lifshitz–Slyozov–Wagner (LSW) model that take into account the stochastic character of the problem are computed. It is proved, under suitable smallness assumptions for the volume fraction filled by the particles, that the effect of these corrections does not modify much the dynamics of the self-similar solutions of the LSW system of equations.     

On the onset condition of fast-time instability in Liñán's premixed-flame regime

The fast-time instability of Liñán's premixed-flame regime is revisited in order to resolve the unrealistic result, previously obtained by Peters, that the inner reaction zone becomes unstable under all subadiabatic conditions. The problem is posed as that of finding the stable range of the heat-loss parameter, defined as the ratio of the downstream heat loss to the total chemical energy influx, near the adiabatic condition. Central to the analysis is rescaling near the adiabatic condition by employing a distinguished limit that the heat-loss parameter is of the order of the inverse of the Zel'dovich number, which enables us to take into account the stabilizing effect of the outer diffusive layers on the inner reaction zone. For a general diffusion flamelet model, the critical value of the heat-loss parameter at the neutral-stability condition is obtained to form a bound for the stable subadiabatic range of the heat–loss parameter.     

On the development of a dispersion-relation-preserving dual-compact upwind scheme for convection–diffusion equation

In this paper a dual-compact scheme, which accommodates a better dispersion relation for the convective terms shown in the transport equation, is proposed to enhance the convective stability of the convection–diffusion equation by virtue of the increased dispersive accuracy. The dispersion-relation-preserving compact scheme has been rigorously developed within the three-stencil point framework through the dispersion and dissipation analyses. To verify the proposed method, several problems that are amenable to the exact and benchmark solutions will be investigated. The results with good rates of convergence are demonstrated for all the investigated problems.     

On the infrared scaling solution of SU(N) Yang–Mills theories in the maximally Abelian gauge

An improved method for extracting infrared exponents from functional equations is presented. The generalizations introduced allow for an analysis of quite complicated systems such as Yang–Mills theory in the maximally Abelian gauge. Assuming the absence of cancellations in the appropriately renormalized integrals the only consistent scaling solution yields an infrared enhanced diagonal gluon propagator in support of the Abelian dominance hypothesis. This is explicitly shown for SU(2) and subsequently verified for SU(N), where additional interactions exist. We also derive the most infrared divergent scaling solution possible for vertex functions in terms of the propagators’ infrared exponents. We provide general conditions for the existence of a scaling solution for a given system and comment on the cases of linear covariant gauges and ghost–anti-ghost symmetric gauges.