Numerical analyses of deflagration initiation by a hot jet

Numerical simulations of axisymmetric reactive jets with one-step Arrhenius kinetics are used to investigate the problem of deflagration initiation in a premixed fuel–air mixture by the sudden discharge of a hot jet of its adiabatic reaction products. For the moderately large values of the jet Reynolds number considered in the computations, chemical reaction is seen to occur initially in the thin mixing layer that separates the hot products from the cold reactants. This mixing layer is wrapped around by the starting vortex, thereby enhancing mixing at the jet head, which is followed by an annular mixing layer that trails behind, connecting the leading vortex with the orifice rim. A successful deflagration is seen to develop for values of the orifice radius larger than a critical value a _c in the order of the flame thickness of the planar deflagration δ_L. Introduction of appropriate scales provides the dimensionless formulation of the problem, with flame initiation characterised in terms of a critical Damköhler number Δ_c=(a _c/δ_L)², whose parametric dependence is investigated. The numerical computations reveal that, while the jet Reynolds number exerts a limited influence on the criticality conditions, the effect of the reactant diffusivity on ignition is much more pronounced, with the value of Δ_c increasing significantly with increasing Lewis numbers . The reactant diffusivity affects also the way ignition takes place, so that for reactants with the flame develops as a result of ignition in the annular mixing layer surrounding the developing jet stem, whereas for highly diffusive reactants with Lewis numbers sufficiently smaller than unity combustion is initiated in the mixed core formed around the starting vortex. The analysis provides increased understanding of deflagration initiation processes, including the effects of differential diffusion, and points to the need for further investigations incorporating detailed chemistry models for specific fuel–air mixtures.     

Numerical simulations of the ignition of n-heptane droplets in the transition diameter range from heterogeneous to homogeneous ignition

Spontaneous ignition of single n-heptane droplets in a constant volume filled with air is numerically simulated with the spherical symmetry. The volume is closed against mass, species, and energy transfer. The numerical model is fully transient. It continues calculation even after the droplet has completely vaporized, and therefore can predict pre-vaporized ignition. Initial pressure and initial air temperature are fixed at 3 MPa and 773 K, respectively. The droplet is initially at room temperature, and its diameter is between 1 and 100 μm. When the overall equivalence ratio is fixed to be sufficiently large, there exists no ignition limit in terms of initial droplet diameter d₀, and the ignition delay takes a minimum value at certain d₀. In such a case, transition from the heterogeneous ignition to the homogeneous ignition with decreasing d₀ is observed. When d₀ is fixed to be so small that the ignition would not occur in an infinite volume of air, the ignition delay takes a minimum value at certain , which is less than unity. Two-stage ignition behavior is investigated with this model. Ignition delay of a cool flame has the dependence on d₀ that is similar to that of ignition delay of a hot flame when is unity. When is almost zero, the ignition limit for cool flame in terms of d₀ is not identified unlike that for hot flame.     

Ignition of non-premixed cyclohexane and mono-alkylated cyclohexane flames

Ignition temperatures of non-premixed cyclohexane, methylcyclohexane, ethylcyclohexane, n-propylcyclohexane, and n-butylcyclohexane flames were measured in the counterflow configuration at atmospheric pressure, a free-stream fuel/N₂ mixture temperature of 373 K, a local strain rate of 120 s^?1, and fuel mole fractions ranging from 1% to 10%. Using the recently developed JetSurf 2.0 kinetic model, satisfactory predictions were found for cyclohexane, methyl-, ethyl-, and n-propyl-cyclohexane flames, but the n-butylcyclohexane data were overpredicted by 20 K. The results showed that cyclohexane flames exhibit the highest ignition propensity among all mono-alkylated cyclohexanes and n-hexane due to its higher reactivity and larger diffusivity. The size of mono-alkyl group chain was determined to have no measurable effect on ignition, which is a result of competition between fuel reactivity and diffusivity. Detailed sensitivity analyses showed that flame ignition is sensitive primarily to fuel diffusion and also to H₂/CO and C₁–C₃ hydrocarbon kinetics.     

2D computations of FREI with cool flames for n-heptane/air mixture

Two-dimensional axisymmetric numerical simulation reproduced flames with repetitive extinction and ignition (FREI) in a micro flow reactor with a controlled temperature profile with a stoichiometric n-heptane/air mixture, which have been observed in the experiment. The ignition of hot flame occurred from consumption reactions of CO that was remained in the previous cycle of FREI. Between extinction and ignition locations of hot flames, several other heat release rate peaks related to cool and blue flames were observed for the first time. After the extinction of the hot flame, cool flame by the low-temperature oxidation of n-heptane appeared first and was stabilized in a low wall temperature region. In the downstream of the stable cool flame, a blue flame by the consumption reactions of cool flame products of CH₂O and H₂O₂ appeared. After that, the hot flame ignition occurred from the remaining CO in the downstream of the blue flame. Then after the next hot flame ignition, the blue flame was swept away by the propagating hot flame. Soon before the hot flame merged with the stable cool flame, the hot flame propagation was intensified by the cool flame. After the hot flame merged with the stable cool flame, the hot flame reacted with the incoming fresh mixture of n-C₇H₁₆ and O₂.     

An experimental and numerical investigation of the catalytic-rich/gaseous-lean combustion of H2/CO/air mixtures at 8 bar

The catalytic-rich/gaseous-lean (R/L) combustion concept was investigated experimentally and numerically for syngas fuels with H₂:CO volumetric ratios 1:0, 4:1 and 1:2, catalytic-rich stoichiometries φ_rich = 2–10 (including operation without air), pressure of 8 bar and air preheat of 673 K. Experiments were performed in a subscale R/L burner with optical access to both catalytic-rich and gaseous-lean stages. OH-PLIF monitored the turbulent combustion in the gaseous-lean stage, OH*-chemiluminescence assessed the propensity for homogeneous ignition in the catalytic-rich stage, and exhaust gas analysis provided the NOx and CO emissions. Two-dimensional simulations were carried out for both stages, while a 1-D opposed-jet code modeled the NOx emissions. The exothermicity of the heterogeneous reactions promoted homogeneous ignition and flame anchoring in the upstream parts of the catalytic-rich stage and allowed for complete consumption of the deficient O₂ reactant, a process that could not be achieved by the catalytic pathway alone due to transport limitations. Homogeneous combustion in the catalytic-rich stage was beneficial for attaining the highest possible fuel pre-conversion. The catalyst not only initiated gaseous combustion but also mitigated potential NOx emissions from the catalytic-rich stage at the highest pre-conversions (lowest φ_rich) and highest CO-content mixtures. Two-sided diffusion flames were established in the gaseous-lean stage due to the recirculation of O₂-rich combustion products, which was advantageous for the burner compactness. It was shown that cardinal to the R/L concept was the fact that a decreasing φ_rich led to an increased heat transfer from the catalytic-rich stage to the bypass air, which reduced the enthalpy in the fuel stream of the gaseous-lean stage and thus lowered the peak flame temperatures (by 400 K for H₂:CO = 1:0). The reduction in flame temperatures with decreasing φ_rich led to a six-fold drop in NOx emissions, while CO emissions were less than 5 ppmv.     

Silicon diffusion in molybdenum disilicide: correlation effects

Correlation factors for silicon diffusion by a vacancy mechanism in the silicon sublattice of the tetragonal MoSi₂ structure have been calculated by combining an analytical and a Monte Carlo approach. The ratio of the silicon diffusivity perpendicular to the tetragonal axis to that parallel to the tetragonal axis is also deduced. An effect of forward correlation of tracer atom jumps in the silicon sublattice with the corresponding partial correlation factor of 1.5 appears at small frequencies of silicon atom jumps along the tetragonal axis with respect to the jump frequencies in the silicon layer perpendicular to the tetragonal axis of the MoSi₂ structure. The anisotropy of silicon diffusion in MoSi₂ measured by Salamon et al. is explained in terms of correlation effects of silicon diffusion on its own sublattice.     

Ignition and volatile combustion behaviors of a single lignite particle in a fluidized bed under O2/H2O condition

O₂/H₂O combustion, as a new evolution of oxy-fuel combustion, has gradually gained more attention recently for carbon capture in a coal-fired power plant. The physical and chemical properties of steam e.g. reactivity, thermal capacity, diffusivity, can affect the coal combustion process. In this work, the ignition and volatile combustion characteristics of a single lignite particle were first investigated in a fluidized bed combustor under O₂/H₂O atmosphere. The flame and particle temperatures were measured by a calibrated two-color pyrometry and pre-buried thermocouple, respectively. Results indicated that the volatile flame became smaller and brighter as the oxygen concentration increased. The ignition delay time of particle in dense phase was shorter than that in dilute phase due to its higher heat transfer coefficient. Also, the volatile flame was completely separated from particles (defined as off-flame) in dense phase while the flame lay on the particle surface (defined as on-flame) in dilute phase. The self-heating of fuel particles by on-flame in dilute phase was more obvious than that in dense phase, leading to earlier char combustion. At low oxygen concentration, the flame in the H₂O atmosphere was darker than that in the N₂ atmosphere because the heat capacity of H₂O is higher than that of N₂. With the increase of oxygen concentration, the flame temperature in the O₂/H₂O atmosphere was dramatically enhanced rather than that in the O₂/N₂ atmosphere, where the diffusion rate of oxygen in O₂/N₂ atmosphere became the dominant factor.     

Single-shot laser-induced fluorescence imaging of formaldehyde with XeF excimer excitation

Single-shot formaldehyde laser-induced fluorescence (LIF) imaging measurements in a technical scale turbulent flame have been obtained using XeF excimer laser excitation in the ?¹A₂-˜X¹A₁ transition at 353.2 nm. Measurements have been carried out in a 150 kW natural gas swirl burner where formaldehyde distribution fields have the potential, in combination with OH concentration fields, to visualize the heat release distribution and therefore give an optimal visualization of flame-front positions. The extended areas where formaldehyde was detected in the swirl flame indicates the presence of low temperature chemistry in preheated gas pockets before ignition. Received: 31 January 2000 / Revised version: 2 March 2000 / Published online: 5 April 2000     

Direct ignition and S-curve transition by in situ nano-second pulsed discharge in methane/oxygen/helium counterflow flame

A well-defined plasma assisted combustion system with novel in situ discharge in a counterflow diffusion flame was developed to study the direct coupling kinetic effect of non-equilibrium plasma on flame ignition and extinction. A uniform discharge was generated between the burner nozzles by placing porous metal electrodes at the nozzle exits. The ignition and extinction characteristics of CH₄/O₂/He diffusion flames were investigated by measuring excited OH¹ and OH PLIF, at constant strain rates and O₂ mole fraction on the oxidizer side while changing the fuel mole fraction. It was found that ignition and extinction occurred with an abrupt change of OH¹ emission intensity at lower O₂ mole fraction, indicating the existence of the conventional ignition-extinction S-curve. However, at a higher O₂ mole fraction, it was found that the in situ discharge could significantly modify the characteristics of ignition and extinction and create a new monotonic and fully stretched ignition S-curve. The transition from the conventional S-curves to a new stretched ignition curve indicated clearly that the active species generated by the plasma could change the chemical kinetic pathways of fuel oxidation at low temperature, thus resulting in the transition of flame stabilization mechanism from extinction-controlled to ignition-controlled regimes. The temperature and OH radical distributions were measured experimentally by the Rayleigh scattering technique and PLIF technique, respectively, and were compared with modeling. The results showed that the local maximum temperature in the reaction zone, where the ignition occurred, could be as low as 900 K. The chemical kinetic model for the plasma–flame interaction has been developed based on the assumption of constant electric field strength in the bulk plasma region. The reaction pathways analysis further revealed that atomic oxygen generated by the discharge was critical to controlling the radical production and promoting the chain branching effect in the reaction zone for low temperature ignition enhancement.     

Radial excitations of heavy-light mesons

The recent discovery of D_s states suggests the existence of radial excitations. Our semirelativistic quark potential model succeeds in reproducing these states within one to two percent of accuracy compared with the experiments, D _s0(2860) and D _s ^*(2715), which are identified as 0⁺ and 1^- radial excitations (n = 2). We also present calculations of radial excitations for B/B _s heavy mesons. The relation between our formulation and the modified Goldberger-Treiman relation is also described.     

A numerical study of the superadiabatic flame temperature phenomenon in HN3 flames

The phenomenon of superadiabatic flame temperature (SAFT) was discovered and investigated in a low-pressure HN₃/N₂ flame using numerical modelling. A previously developed mechanism of chemical reactions in the HN₃/N₂ flame at the pressure 50 Torr and the initial temperature T₀ = 296 K was revised. Rate constants of several important reactions involving HN₃ (HN₃ (+N₂) = N₂ + NH (+N₂), R1; HN₃ (+HN₃) = N₂ + NH (+HN₃), R2; HN₃ + H = N₂ + NH₂, R4; HN₃ + N = N₂ + NNH, R5; and HN₃ + NH₂ = NH₃ + N₃, R7) were calculated using quantum chemistry and reaction rate theories. Modified Arrhenius expressions for these reactions are provided for the 300–3500 K temperature range. Modelling of the flame structure and flame propagation velocity of the HN₃/N₂ flame at p = 50 Torr and T₀ = 296 K was performed using the revised mechanism. The results demonstrate the presence of the SAFT phenomenon in the HN₃/N₂ flame. Analysis of the flame structure and the kinetic mechanism indicates that the cause of SAFT is in the kinetic mechanism: exothermic reactions of radicals with hydrogen atoms occur in the post flame zone, which results in the formation of super equilibrium H₂ concentrations. The flame propagation velocity is largely determined by the second-order HN₃ decomposition reaction and not by the reaction of HN₃ with H, as was previously assumed. Calculation of the flame propagation velocity according to the Zeldovich-Frank-Kamenetsky theory with the decomposition reaction as a limiting stage yielded a value that agrees with that obtained in numerical modelling using the complete reaction mechanism.     

Nonlinear kinematic response of premixed flames to harmonic velocity disturbances

This paper analyzes the nonlinear dynamics of premixed flames responding to harmonic velocity disturbances. These nonlinear dynamics were studied by solving a constant flame speed front tracking equation for the flame’s response to harmonically oscillating velocity disturbances. The solution to these equations is used to quantify the transfer function relating the ratio of the normalized flame area to velocity fluctuations, G = (A′/A_o)/(u′/u_o), upon the amplitude of velocity oscillations, ε = u′/u_o. Due to nonlinearities, the amplitude of this transfer function relative to its linear value decreases with increasing amplitude of velocity oscillation, u′/u_o. In contrast, the transfer function phase exhibits almost no amplitude dependence. The velocity amplitude where transfer function nonlinearities become significant depends strongly upon three parameters: a Strouhal number, St = ωL_f/u_o (where L_f is the flame length), the ratio of the flame length to width, β = L_f/R, and the flame shape in the absence of perturbations (i.e., conical, inverted wedge, etc.). In the linear case, the transfer function, G, depends only upon an algebraic combination of the first two parameters, given by St₂ = St (1 + β²)/β². In general, however, G exhibits a distinct dependence upon both parameters St and β. In particular, we show that the nonlinear response of G is an intrinsically dynamic phenomenon; i.e., its quasi-steady response (St 1) is purely linear. As such, nonlinearity is enhanced with increasing Strouhal numbers. In contrast, nonlinearity is suppressed at large β values; as such, the response of a long flame remains quite similar to its linear value, even at large ε values where the flame front exhibits substantial corrugation and cusping. Finally, we show that the response of conical flames remains much more linear at comparable disturbance amplitudes than for “V” or wedge-shaped flames. These predictions are shown to be consistent with available experimental data.     

A contrastive study on the influences of radial and three-dimensional satellite gravity gradiometry on the accuracy of the Earth's gravitational field recovery

The accuracy of the Earth’s gravitational field measured from the gravity field and steady-state ocean circulation explorer(GOCE),up to 250 degrees,influenced by the radial gravity gradient V zz and three-dimensional gravity gradient V ij from the satellite gravity gradiometry(SGG) are contrastively demonstrated based on the analytical error model and numerical simulation,respectively.Firstly,the new analytical error model of the cumulative geoid height,influenced by the radial gravity gradient V zz and three-dimensional gravity gradient V ij are established,respectively.In 250 degrees,the GOCE cumulative geoid height error measured by the radial gravity gradient V zz is about 2 1/2 times higher than that measured by the three-dimensional gravity gradient V ij.Secondly,the Earth’s gravitational field from GOCE completely up to 250 degrees is recovered using the radial gravity gradient V zz and three-dimensional gravity gradient V ij by numerical simulation,respectively.The study results show that when the measurement error of the gravity gradient is 3×10 12 /s 2,the cumulative geoid height errors using the radial gravity gradient V zz and three-dimensional gravity gradient V ij are 12.319 cm and 9.295 cm at 250 degrees,respectively.The accuracy of the cumulative geoid height using the three-dimensional gravity gradient V ij is improved by 30%-40% on average compared with that using the radial gravity gradient V zz in 250 degrees.Finally,by mutual verification of the analytical error model and numerical simulation,the orders of magnitude from the accuracies of the Earth’s gravitational field recovery make no substantial differences based on the radial and three-dimensional gravity gradients,respectively.Therefore,it is feasible to develop in advance a radial cold-atom interferometric gradiometer with a measurement accuracy of 10 13 /s 2-10 15 /s 2 for precisely producing the next-generation GOCE Follow-On Earth gravity field model with a high spatial resolution.     

Ignition of hydrogen in unsteady nonpremixed flows

The effects of unsteady strain on hydrogen (H₂) ignition in nonpremixed flows are investigated with both experimental measurements and numerical computations. A mixing layer is established in a counterflow configuration with a fuel stream containing N₂–diluted H₂ (X_H2=0.08) flowing against heated air. A reproducible ignition process is initiated by introducing atomic oxygen into the mixing layer with a pulsed ArF excimer laser, which photodissociates heated O₂ from the oxidizer stream. The temporal evolution of OH during ignition is measured by planar laser-induced fluorescence. Following the induction phase, the measured OH mole fraction increases rapidly to a super-equilibrium value that is 60% greater than the OH mole fraction in a steady diffusion flame. The peak OH mole fraction occurs at approximately 6 ms after the excimer laser pulse. To study the OH time history under transient strain, the fuel stream is pulsed at a fixed time after the initiation of ignition. The response of the ignition kernel is extremely sensitive to the time delay of the flow transient. The unsteady strain can delay the ignition time or extinguish the kernel. Comparisons between computations and experiments are made for the evolution of OH during autoignition both for steady and unsteady strain. For both steady and unsteady strain, the transient one-dimensional counterflow computations show excellent agreement with the experiment in terms of predicting ignition delays and the rate of OH accumulation during the induction period. The computations also capture the super-equilibrium OH during the transition to the formation of a steady flame, although not to the degree observed experimentally. The computations are further used to understand the influence of unsteady strain on the kernel evolution. It is found that the degree of super-equilibrium OH is sensitive to strain transients applied close to the time of thermal runaway.     

Current-voltage characteristics for a Peierls-conducting point contact

Current-voltage (J-V) and differential-conductivity-voltage ( dJ/dV-V) characteristics are analytically calculated at zero temperature for a point contact consisting of: two Peierls conductors P ( = 1, 2) separated by an insulator (I). Here P is a conductor with charge density wave (CDW). The J-V and dJ/dV-V characteristics depend on the CDW phases ( = 1, 2) in the mean field approximation. To calculate them analytically we assumed, = ≡Δ where ( = 1, 2) are the energy gaps of P ( = 1, 2). The current J has a discontinuous jump at eV = 2Δ for ϕ ₁ = ϕ ₂≠ 0. The differential conductivity dJ/dV has a singularity at eV = 2Δ for ϕ ₁ = ϕ ₂≠ 0. The relation J(V,ϕ ₁,ϕ ₂) = - J(- V,ϕ ₁ + π,ϕ ₂ + π) is obtained. Received 4 July 2001 and Received in final form 13 September 2001     

An improved high-order scheme for DNS of low Mach number turbulent reacting flows based on stiff chemistry solver

We present an improved numerical scheme for numerical simulations of low Mach number turbulent reacting flows with detailed chemistry and transport. The method is based on a semi-implicit operator-splitting scheme with a stiff solver for integration of the chemical kinetic rates, developed by Knio et al. [O.M. Knio, H.N. Najm, P.S. Wyckoff, A semi-implicit numerical scheme for reacting flow II. Stiff, operator-split formulation, Journal of Computational Physics 154 (2) (1999) 428–467]. Using the material derivative form of continuity equation, we enhance the scheme to allow for large density ratio in the flow field. The scheme is developed for direct numerical simulation of turbulent reacting flow by employing high-order discretization for the spatial terms. The accuracy of the scheme in space and time is verified by examining the grid/time-step dependency on one-dimensional benchmark cases: a freely propagating premixed flame in an open environment and in an enclosure related to spark-ignition engines. The scheme is then examined in simulations of a two-dimensional laminar flame/vortex-pair interaction. Furthermore, we apply the scheme to direct numerical simulation of a homogeneous charge compression ignition (HCCI) process in an enclosure studied previously in the literature. Satisfactory agreement is found in terms of the overall ignition behavior, local reaction zone structures and statistical quantities. Finally, the scheme is used to study the development of intrinsic flame instabilities in a lean H₂/air premixed flame, where it is shown that the spatial and temporary accuracies of numerical schemes can have great impact on the prediction of the sensitive nonlinear evolution process of flame instability.     

Structure and propagation of two-dimensional,partially premixed,laminar flames in diesel engine conditions

We investigate the influence of inflow velocity (V_in) and scalar dissipation rate (χ) on the flame structure and stabilisation mechanism of steady, laminar partially premixed n-dodecane edge flames stabilised on a convective mixing layer. Numerical simulations were performed for three different χ profiles and several V_in (V_in = 0.2 to 2.5m/s). The ambient thermochemical conditions were the same as the Engine Combustion Network’s (ECN) Spray A flame, which in turn represents conditions in a typical heavy duty diesel engine. The results of a combustion mode analysis of the simulations indicate that the flame structure and stabilisation mechanism depend on V_in and χ. For low V_in the flame is attached. Increasing V_in causes the high-temperature chemistry (HTC) flame to lift-off, while the low-temperature chemistry (LTC) flame is still attached. A unique speed S_R associated with this transition is defined as the velocity at which the lifted height has the maximum sensitivity to changes in V_in. This transition velocity is negatively correlated with χ. Near $V_{in}=S_R$ a tetrabrachial flame structure is observed consisting of a triple flame, stabilised by flame propagation into the products of an upstream LTC branch. Further increasing the inlet velocity changes the flame structure to a pentabrachial one, where an additional HTC ignition branch is observed upstream of the triple flame and ignition begins to contribute to the flame stabilisation. At large V_in, the LTC is eventually lifted, and the speed at which this transition occurs is insensitive to χ. Further increasing V_in increases the contribution of ignition to flame stabilisation until the flame is completely ignition stabilised. Flow divergence caused by the LTC branch reduces the χ at the HTC branches making the HTC more resilient to χ. The results are discussed in the context of identification of possible stabilisation modes in turbulent flames.     

On the Bose-Einstein condensation of free relativistic bosons with or without mass

The Bose-Einstein condensation of free relativistic particles [=(M ² c ⁴ +c ² p ² ) ^1/2 –Mc ² ] is studied rigorously. For massless bosons (=cp), the condensation transition of third (second) order occurs in2 (3) dimensions (D). The molar heat capacity follows the T ² (T ³ ) law below the condensation temperature T_c [k ^B T_c=(2 ² c ² n/1.645) ^1/2 [( ^{2 3} c ³ n/1.202) ^1/3 ], reaches4.38 (10.8) R at T=T_c, and approaches the high-temperature-limit value2 (3) R with no jump (a jump equal to6.75R) in2 (3)D. For finite-mass (M) bosons, the phase transition occurs only in3D with the condensation temperature T_c always smaller than that of the corresponding nonrelativistic bosons [=(2M) ^–1 p ² ]. If the mass M is reduced to zero, the condensation temperature T_c grows monotonically and reaches eventually that of massless relativistic bosons. This mass-dependence of T_c is therefore distinct from the case of nonrelativistic bosons, where T_c grows to infinity as M 0. A brief discussion is given for a possible connection with the normal-to-super transition of the independently moving Cooper pairs (bosons).     

Experimental study of laser-induced thermal ignition in O2/O3 mixtures

O₂/O₃ mixtures are ignited by absorption of laser pulses of a TEA CO₂ laser along the axis of a cylindrical cell. The dependence of the radial propagation of the O₃ decomposition, detected by uv absorption of the ozone, on laser fluence and on O₃ concentration is investigated. Oscillations of the signals are identified to be the first radial acoustic mode of the cell. For mixtures of 0.35 bar and 0.70 bar total pressure and O₃ percentages within 20–50%, the ignition limit is in the order of 0.1–0.2 J/cm³ (absorbed energy density). These values are in reasonable agreement with the results of the corresponding numerical simulations.     

A New Duality Transformation for Fourth-order Gravity

We prove that for non-linear L = L(R), G = dL/dR 0 the Lagrangians L and ^L(^R) with ^L = 2R/G³ - 3L/G⁴, ^g_ij = G² g_ij and ^R = 3R/G² - 4L/G³ give conformally equivalent fourth-order field equations being dual to each other. The proof represents a new application of the fact that the operator - R/6 is conformally invariant.