Time-resolved LIF of OH in the flame front of premixed and diffusion flames at atmospheric pressure

Time-resolved fluorescence measurements are reported for the OH radical in the flame fronts of laminar atmospheric pressure flames. Effective (collision-limited) lifetimes were determined following excitation of theA ²⁺, = 0 state of OH using a picosecond dye-laser system based on the distributed-feedback principle. Measurements were made in a premixed knife-edge burner for rich CH₄/N₂O/N₂ and CH₄/air flames and in a counterflow diffusion burner for a CH₄/air flame. In the accessible range, results indicate a net dependence of lifetime on temperature intermediate betweenT andT ^0.5 for these flames.     

Anisotropic low-temperature heat transport in YBa2Cu3O6.9 single crystal

We report measurements of the low-temperature thermal conductivity of YBa₂Cu₃O_7– (0.1) single crystals (T _c =84 K) both parallel ( ^{a, b} ) and perpendicular ( ^c ) to the CuO₂ planes. Whereas ^c (T) is found to be identical, within experimental resolution, with the phonon contribution _ph (T), ^{a, b} (T) contains an additional term linear in temperature,AT. We ascribeAT to the contribution of unpaired electronic carriers residing in the chain layers. Measurements performed in external magnetic fieldsB8 T support this interpretation. Our observations can be explained by an internal multilayer (IML) model in which it is assumed that strong superconductivity is generated within the CuO₂ layers and weak superconductivity is induced in the chain layers by the proximity effect. The fit of the experimental results to the IML model reveals that approximately 15% of the electronic carriers remain unpaired in YBa₂Cu₃O₇ belowT=1 K.     

Gauge invariance of the Euler-Lagrange expressions

We prove, for a Lagrangian density L(g_ij;A _i ⁱ ;A _i ^j ), that the gauge invariance of the Euler-Lagrange expressionsE ⁱ (L) implies the existence of a gauge-invariant scalar densityL ₁, such thatE ⁱ (L) =E ⁱ (L₁). We then prove the uniqueness of the Yang-Mills field equations.     

Study ofA+A→0 with probability of reaction and diffusion in one dimension and in fractal substrata

We present Monte Carlo simulations of annihilation reactionA+A0 in one dimensional lattice and in three different fractal substrata. In the model, the particles diffuse independently and when two of them attempt to occupy the same substratum site, they react with a probabilityp. For different kinds of initial distributions and in the short an intermediate time regimes, the results for 0<p1 show that the density ofA particles approximately behaves as (t)=(t=0)f(t/t ₀), with the scaling functionf(x)1 forx1,f(x)x ^–y forx1. The crossover timet ₀, behaves ast _{0 0eff} ^–1y where theeffective initial density _0eff depends on (t=0) and on the kind of initial distribution. For a given substratum of spreading dimensiond _s, the exponenty(d _s/2<y<1) depends only onp and its value increases asp decreases (y1 whenp0). In the very long time regime it is expected thatp(t)t ^–ds/2 independently ofp.     

Spectroscopic trace-gas sensor with rapidly scanned wavelengths of a pulsed quantum cascade laser for in situ NO monitoring of industrial exhaust systems

Development of a pulsed quantum cascade laser (QCL)-based spectroscopic trace-gas sensor for sub-part-per-million detection of nitric oxide (NO) and capable of monitoring other molecular species such as CO₂, H₂O, and NH₃ in industrial combustion exhaust systems is reported. Rapid frequency modulation is applied to the QCL to minimize the influence of fluctuating non-selective absorption. A novel method utilizes only a few laser pulses within a single wavelength scan to probe an absorption spectrum at precisely selected optical frequencies. A high-temperature gas cell was used for laboratory evaluation of the NO sensor performance. A noise-equivalent sensitivity (1) of 100 ppb × m/ at room temperature and 200 ppb × m/ at 630 K was achieved by measuring the NO R(6.5) absorption doublet at 1900.075 cm^–1.     

Hydrogen-like recombination X-ray lasers using ps pulse drivers

We propose a scheme for producing high gain recombination X-ray lasers on hydrogen-like Balmer transitions by irradiating fibre targets with a 2 ps Chirped Pulse Amplification CPA beam of a Nd-glass laser facility. Very high gain coefficients for H-like C, N, O, F, Na Balmer transitions are predicted. The optimum electron density and temperature for maximum gain operation scale approximately asN _e 4 × 10¹³ Z ⁷ cm^–3 and T_e 7 × 10^–3 Z ⁴ eV, respectively, at the time when maximum lasing gain appears. Significant improvement in gain performance of recombination X-ray lasers is predicted by using CPA ps pulse drivers.     

Quasi-genericity of bifurcations to high dimensional invariant tori for maps

We consider a family of maps in a Banach spaceE near the situation when the derivative at the fixed point has two pairs of complex eigenvalues lying on the unit circle, the other part of the spectrum being strictly inside the unit disc. We focus our attention on the region of the parameter space where the truncated normal form of the maps shows a bifurcation of a family of invariantT ¹-circles into a family of invariantT ²-tori. We show that this problem needs a 3 dimensional parameter unfolding and that, for the complete maps, bifurcation occurs at points _,, where is the rotation number on the non-normally hyperbolicT ¹-circle, ande ^±2i are the eigenvalues of the constant matrix conjugated to the non-contracting part of the linearization on the normal fiber bundle overT ¹. Making some non-resonance and diophantine assumptions on (, ) leading to a positive measure Cantor set inT ², we show that in paraboloïdal regions of the 3 dim. parameter space we have clean bifurcations as for the truncated normal form. The complement of these regions forms a set of bubbles such as the ones obtained by Chenciner in [Chen] for a codimension 2 problem for maps in ². The main tool here is a generalization for a matrix function onT ¹, close to a constant, of the quasi-conjugacy to a constant, modulo a minimum of additional parameters (moved quasi-conjugacy). For the infinite dimensional case we use aC decoupling result on the angular dependent linear parts into a contraction, still angular dependent, and another part quasi-conjugated to a constant matrix. This type of analysis applies for a wide range of problems, where truncated normal forms of the maps give bifurcations fromT ⁿ toT ⁿ⁺¹ tori, and this needs a (n+1)-dimensional parameter unfolding.We gratefully acknowledge the DRET (contrat 86/1445) who supported one of the authors (J.L.) during this work. This research has been also supported by the E.E.C. contract No. ST 2J-0316-C (EDB) on Mathematical problems in nonlinear Mechanics     

A Factorization of Determinant Related to Some Random Matrices

We consider the expectation of the determinant det(–X)^–1for Im >0 associated with some random N×Nmatrices and factorize it into NStieltjes transforms of probability measures. Moreover, using this factorization, we investigate the limiting behavior of the logarithm of the quantity as N.     

Cavity ring-down absorption and laser-induced fluorescence for quantitative measurements of CH radicals in low-pressure flames

The absolute, quantitative spatially resolved distribution of CH radicals was measured in the reaction zone of a low-pressure methane/air flame (25 Torr) using a combination of laser-induced fluorescence (LIF) and cavity ring-down (CRD) absorption spectroscopy operating on the A²–X²(0,0) transition. The spatially resolved 1-D image of LIF provides a direct measure of the CH distribution along the path of the laser beam in the CRD cavity. The temperature distribution was determined from measurements on a pair of rotational transitions. A series of LIF line images and CRD absorption measurements taken at various burner heights are combined to form a quantitative 2-D image of the CH distribution. This is used to interpret the CRD measurements along this inhomogeneous path. The 10 ppm peak CH concentration measured here on the centerline of the flame is in good agreement (within 15%) with earlier CH A–X LIF measurements calibrated by Rayleigh and Raman scattering. A 1-D LIF image collected simultaneously with CRD absorption was also used to quantify and optimize the spatial resolution of the CRD measurement. PACS 42.62.Fi; 82.33.Vx; 33.80.Gj     

Optic nonlinearities of a copper complex of pyrazinoporphyrazine

For the copper complex of pyrazinoporphyrazine AzaPhcCu(C(CH₃)₃)₈ in CH₂Cl₂, we use nanosecond pulses to measure its third-order nonlinear optic effects at 532 nm. The results show that its effective third-order nonlinear refractive index n ^eff ₂ (–7.85 × 10^–10 esu) is larger than that of the AzaPhcCu(C₁₂H₂₅)₄ and the CuPc(OC₅H₁₁)₈. The reverse saturable absorption (RSA) of AzaPhcCu-(C(CH₃)₃)₈ is demonstrated by the ratio of effective excited state to ground state absorption cross sections. The observed intersystem crossing lifetime _isc of AzaPhcCu(C(CH₃)₃)₈ (15 ns) and AzaPhcCu(C₁₂H₂₅)₄ (45 ns) are longer than that of CuPc(OC₅H₁₁)₈ (5.0 ns). The aza-substituents are suggested to form a S₁(n, ^*) state as their lowest excited singlet-states, and their radiationless intersystem crossing rates (1/_isc) are discussed with the spin-orbit coupling _S|H _SO|_T and the vibronic coupling _S|_T effects between S₁ and T₁ states.     

Infrared phonon spectra of 3d-metal doped YBa2(Cu1-x M x )3O7-δ

Infrared (IR) absorption spectra of doped YBa₂(Cu_1–x M _x )₃O_7–, with M representing Co, Fe, Ni, and Zn were observed as a function of concentrationx. TheB _1u IR mode at 580 cm^–1 was observed for all samples which were in the orthorhombic phase, which includes all the Ni and Zn doped samples and the lower concentrations (x<2.5%) for Fe and Co samples. The tetragonal phase of Co and Fe systems (x%>2.5%) shows three new IR modes at 655 cm^–1, 340 cm^–1, and 175 cm^–1. The frequency of the B_1u mode at 580 cm^–1 remains unchanged for all the Ni and Zn concentrations. In contrast, this mode shows a strong monotonic frequency softening with increase in Co substitution, while in the Fe-system it shows a comparable monotonic mode softening for 3%x%0%, and then remains unchanged for 12%x%3%. These observations indicate that Fe and Co substitute on the Cu(1) sites, whereas Ni and Zn most likely substitute on Cu(2) sites. We attribute the difference in the mode softening for Co and Fe to different Cu(1) local environments for these two elements. Indication for a chain-plane charge transfer based on our results is also discussed.     

Unstable neutrinos can do it!

We present a cosmological scenario with unstable neutrinos which decay into a light neutrino and a relativistic boson. Theoretical and observational constraints severely narrow the values of mass and of lifetime of neutrinos. However, within this range, we can construct models with (i) = 1, (ii) age of the universe 13 billion years (b.y.) and (iii)h ₀ –0.5. The dynamical modeling shows that (a) the initial condensates of primordial _L are disrupted by the decay, lowering their masses to acceptable values ~10¹² M, (b) the relativistic boson contributes nearly 0.25 to, and (c) there emerge two prominent scales in dark matter distribution, one with a mass ~10¹² M distributed over 200 kpc around galaxies and another component with density 10^–27 g cm^–3 distributed over 1 Mpc. The model agrees with observations at all scales.This essay received an honorable mention from the Gravity Research Foundation for 1986-Ed.     

The random-phase-approximation in the weak coupling regime of the square lattice half-filled Hubbard model

We re-examine the random-phase approximation (RPA) in the antiferromagnetic spin-density-wave state of the half-filled square lattice repulsive Hubbard model. It is shown that forU/t1 the RPA yields a vanishing spinwave velocity, c(2t)^–1(U/t)^1/2, a diverging uniform transverse susceptibility, (2t)^–1(U/t ^–1/2, and a constant spin stiffness, _s 2t)^–2 t. The behavior of _s shows that the RPA cannot be correct in the weak coupling regime, because _s should vanish in the limitU/t0. We give a formally exact expression for _s and identify the term which is neglected within the RPA.     

Two-dimensional quenching lifetime measurement of OH:A 2 Σ +(υ′ = 1) and NO:A 2 Σ(υ′ = 0) in atmospheric-pressure flames

Planar laser-induced fluorescence is currently widely applied to research on combustion. However, conventional approaches for semi-quantitative measurement could not provide the satisfactory solution and the problem due to collisional quenching remains to be solved. This paper describes the two-dimensional (2D) quenching-time-constant measurement of OH:A ^{2 +}( = 1) and NO:A ² ( = 0) in flame cross sections at atmospheric pressure. These measurements involve 1–2 ns decay time of the excited state using a high-speed image intensifier and a tunable laser with a pulse duration of 3 ns at FWHM. The correlation factors of the exponential fits for the fluorescence decays after the laser pulse were larger than 0.999 in all experiments presented in this study. Furthermore, the measured Stern-Volmer plots of the quenching rate at 1.0, 1/2, 1/3, and 1/4 atm pressure using the same experimental apparatus was confirmed to have a linear relationship for both OH and NO, showing that the 2D decay-time measurements of 1–2 ns have been successful. For NO:A ² ( = 0), the obtained quenching rates inside the inner cone and in the outer flame in the NO-seeded methane-air Bunsen flame were 8.7 × 10⁸ and 7.8 × 10⁸ s^–1, respectively, and for OH:A ² ( = 1), the obtained quenching rate mapping in the outer flame was around 5.6 × 10⁸ s^–1 in the methane-air flame.     

Deep bandtail states picosecond intensity-dependent carrier dynamics of GaN epilayer under high excitation

Picosecond carrier dynamics of deep bandtail states (3.1 eV) in an unintentionally n-doped GaN epilayer at room temperature under high excitation densities (i.e., N ₀ = 1.0× 10¹⁹– 1.1× 10²⁰ cm^–3) have been investigated with nondegenerate femtosecond pump–probe (267/400 nm) reflectance ( R/R ₀). All R/R ₀ traces possess a 2 ps buildup time that represents an overall time for the initial non-thermal carrier population to relax towards the continuum extremes and then into the probed tail states. We observe a saturation of R/R ₀ initial (first 10 ps) recovery rate _i at a density of 5– 6×10¹⁹ cm^–3 close to the Mott transition threshold obtained from time-integrated PL measurements. Such a saturation phenomenon has been identified as the trap-bottleneck due to the bandtail states and deep traps. As N ₀ is further increased, _i accelerates due to the onset of Auger recombination as the trap-bottleneck becomes effective. The best fit by the Auger model for N ₀ in the range of the mid-10¹⁹–10²⁰ cm^–3 yields an Auger coefficient of C _a 5.0× 10^–30 cm⁶ s^–1.     

Photorefractive measurements on electron-irradiated semi-insulating GaAs

We present photorefractive measurements at 1.06 m and 1.3 m performed in electron-irradiated GaAs. Irradiation with electrons of kinetic energies 1 MeV introduces intrinsic electrically active defects which modify the Fermi-level position and allow to modify the electron-hole competition mechanism of the photorefractive effect. Furthermore, it is shown that the optical absorption in the 1.3–1.5 m spectral range can be increased, which might allow to enlarge the useful spectral range of GaAs towards optical telecommunication windows. The native and irradiation-induced defects are assessed by electron paramagnetic resonance and optical absorption spectroscopy conducted at T=300 K and 77 K. The direct influence of an irradiation-induced mid-gap defect on the photorefractive effect is experimentally and theoretically demonstrated.     

The Split of the Dirac Hamiltonian into Precisely Predictable Energy Components

We are dealing with the Dirac Hamiltonian H = H₀ + V with no magnetic field and radially symmetric electrostatic potential V = V(r), preferably the Coulomb potential. While the observable H is precisely predictable, its components H₀ (relativistic mass) and V (potential energy) are not. However they both possess precisely predictable approximations H₀ and V which approximate accurately if the particle is not near its nucleus. On the other hand, near 0, H₀ and V are practically unpredictable, perhaps in agreement with the fact, that a neutrino also should be in the game. [We have not yet studied the corresponding observables for the ( 12-dimensional) problem of electro-weak interaction.] Mathematically we are focusing on the spectral theory of the unbounded self-adjoint operators H₀ and V . We can prove that V is unitarily equivalent to V(r) again, by a unitary map given as Wiener-Hopf-type singular integral operator in the standard separation of variables for radially symmetric Dirac Hamiltonians. [This is, as far as the continuous spectrum is concerned.] Very similar unitary equivalence holds for H ₀ and H ₀. We are tempted to regard this as a form of renormalization.     

Glueball spectroscopy in strongly coupled lattice gauge theories

We study the mass spectrum up to –7 (1–) log of pure three-dimensional lattice gauge theories with action (g _P) for real irreducible and small . Besides the lowest excitationm ₀–4log, we find two nearly degenerate excited statesm ₁,m ₂ withm _i–6log (i=1, 2) and (m ₁–m ₂) at leastO().Work partially supported by CNPq (Brasil)     

Neutron scattering study of the two-dimensional spinS=1/2 square-lattice Heisenberg antiferromagnet Sr2CuO2Cl2

We have carried out a neutron scattering investigation of the static structure factorS(q _2D ) (q _2D is the in-plane wave vector) in the two-dimensional spinS=1/2 square-lattice Heisenberg antiferromagnet Sr₂CuO₂Cl₂. For the spin correlation length we find quantitative agreement with Monte Carlo results over a wide range of temperature. The combined Sr₂CuO₂Cl₂-Monte Carlo data, which cover the length scale from 1 to 200 lattice constants, are predicted without adjustable parameteres by renormalized classical theory for the quantum nonlinear sigma model. For the structure factor peakS(0), on the other hand, we findS(0) ² for the reduced temperature range 0.16<T/2 _s <0.36, whereas current theories predict that at low temperaturesS(0)T ^{2 2}. This discrepancy has important implications for the interpretation of many derivative quantities such as NMR relaxation rates. In the ordered phase, we have measured the temperature dependence of the out-of-plane spin-wave gap. Its low-temperature value of 5.0 meV corresponds to an XY anisotropyJ _XY /J=1.4×10^–4. From measurements of the sublattice mangetization we obtain =0.22±0.01 for the order parameter exponent. This may either reflect tricricality as in La₂CuO₄, or it may indicate finite-size two-dimensional XY behavior as suggested by Bramwell and Holdsworth. As in theS=1 system K₂NiF₄, the gap energy in Sr₂CuO₂Cl₂ scales linearly with the order parameter up to the Néel temperature. We also reanalyze static structure factor data for K₂NiF₄ using the exact low temperature result for the correlation length of Hasenfratz and Niedermayer and including the Ising anisotropy explicitly. Excellent agreement between experiment and theory is obtained for the correlation length, albeit with the spin-stiffness _s reduced by 20% from the spin-wave value. As in Sr₂CuO₂Cl₂ we find thatS(0) ² for the reduced temperature range 0.22<T/2 _s <0.47.