Interface Fluctuations for the D = 1 Stochastic Ginzburg–Landau Equation with Nonsymmetric Reaction Term

We consider a Ginzburg–Landau equation in the interval [?ε^?1, ε^?1], ε>0, with Neumann boundary conditions, perturbed by an additive white noise of strength $\sqrt {\varepsilon } $ and reaction term being the derivative of a function which has two equal–depth wells at ±1, but is not symmetric. When ε=0, the equation has equilibrium solutions that are increasing, and connect ?1 with +1. We call them instantons, and we study the evolution of the solutions of the perturbed equation in the limit ε→0⁺, when the initial datum is close to an instanton. We prove that, for times that may be of the order of ε^?1, the solution stays close to some instanton whose center, suitably normalized, converges to a Brownian motion plus a drift. This drift is known to be zero in the symmetric case, and, using a perturbative analysis, we show that if the nonsymmetric part of the reaction term is sufficiently small, it determines the sign of the drift.     

New results in the study of Brillouin scattering in thiourea

Below T₂ = 202 K, in the incommensurate phase, a Debye relaxation appears for c₃₃; it can be attributed to a linear coupling between an acoustical mode and a phason. The relaxation time is τ = τ₀/(T₀?T) with τ₀ = 6.2 x 10^?12 sec deg and T₀ = 200.9 K. The same phenomenon appears more weakly for c₁₁. The c₆₆ elastic constant has a double discontinuity around T₁ = 169 K; this shows that in the vicinity of T₁ there are two transitions, separated by a temperature interval of 3°.     

Reflexions sur sol dur,interferences et effet d'ecran

The interference effects of the sound energy from a source and that from a reflected wave on the ground are investigated in the particular case of measurements of noise reduction due to the use of a barrier.The influence of these effects on model experiments are also investigated.     

Study of the elastic stiffness constants of thiourea by Brillouin scattering

All the elastic stiffness constants of thiourea have been measured at room temperature. The value of C₆₆(0.7 × 10¹⁰dynes/cm²) is very low. The C₁₁ and C₃₃ constants exhibit discontinuities at 169 and 202 K. The longitudinal acoustic phonons propagating in the c direction are very strongly damped in the vicinity of 202 K.     

Stark broadening and displacement of isolated He I lines

Experimental results for Stark broadened He I lines emitted by a helium plasma jet (N_e≈3×10¹⁶ cm^-3) are compared with theory; agreement is well enough for widths whereas shifts calculations present generally large discrepancies with experimental data.     

Schematicity and ground state correlations in the lead isotopes

The relationship between collectivity and ground state correlations is analyzed for the single closed shell lead isotopes. The effects of the schematic approximation are discussed, within the framework of both the quasiparticle Random Phase Approximation and the quasiparticle Tamm-Dancoff approach. The consistency of the RPA is investigated.     

Central limit theorems for empirical product densities of stationary point processes

We prove the asymptotic normality of kernel estimators of second- and higher-order product densities (and of the pair correlation function) for spatially homogeneous (and isotropic) point processes observed on a sampling window \(W_n\) , which is assumed to expand unboundedly in all directions as \(n \rightarrow \infty \,\) . We first study the asymptotic behavior of the covariances of the empirical product densities under minimal moment and weak dependence assumptions. The proof of the main results is based on the Brillinger-mixing property of the underlying point process and certain smoothness conditions on the higher-order reduced cumulant measures. Finally, the obtained limit theorems enable us to construct \(\chi ^2\) -goodness-of-fit tests for hypothetical product densities.     

Measurement of axisymmetric temperature fields using reference beam and shearing interferometry for application to flames

A unified methodology for the application of reference beam and shearing interferometry to measure axisymmetric temperature fields within flames is proposed. Sensitivity and accuracy of the techniques are analyzed basing on interferograms of reference temperature profiles and CARS measurements obtained in test laminar flames. The rapid decay of temperature measurements accuracy with increasing both intensity of errors sources and uncertainty on independent parameters is assessed. The spatial variation of mixture composition in diffusive combusting flows requires the application of complementary methods to obtain a satisfactory accuracy, while flow fields with lean premixed combustion can be treated as optically-homogeneous media. The temperature maps resulting from the investigation of the test laminar flames are presented and discussed. The capability to disclose the thermal structure and to provide reliable quantitative data is demonstrated. Received: 15 March 1999/Accepted: 29 July 1999