Droplet growth for three-dimensional Kawasaki dynamics

 The goal of this paper is to describe metastability and nucleation for a local version of the three-dimensional lattice gas with Kawasaki dynamics at low temperature and low density. Let $\Lambda\subseteq{\mathbb Z}^3$ be a large finite box. Particles perform simple exclusion on $\Lambda$, but when they occupy neighboring sites they feel a binding energy $-U<0$ that slows down their dissociation. Along each bond touching the boundary of $\Lambda$ from the outside, particles are created with rate $\rho=e^{-\Delta\beta}$ and are annihilated with rate 1, where $\beta$ is the inverse temperature and $\D>0$ is an activity parameter. Thus, the boundary of $\Lambda$ plays the role of an infinite gas reservoir with density $\rho$. We consider the regime where $\Delta\in (U,3U)$ and the initial configuration is such that $\Lambda$ is empty. For large $\beta$, the system wants to fill $\Lambda$ but is slow in doing so. We investigate how the transition from empty to full takes place under the dynamics. In particular, we identify the size and shape of the critical droplet\/ and the time of its creation in the limit as $\beta\to\infty$. Received: 23 February 2002 / Revised version: 24 June 2002 / Published online: 24 October 2002 Mathematics Subject Classification (2000): 60K35, 82B43, 82C43, 82C80 Key words or phrases: Lattice gas – Kawasaki dynamics – Metastability – Critical droplet – Large deviations – Discrete isoperimetric inequalities     

Correlation structure of intermittency in the parabolic Anderson model

Consider the Cauchy problem ∂u(x, t)/∂t = ℋu(x, t) (x∈ℤ^d, t≥ 0) with initial condition u(x, 0) ≡ 1 and with ℋ the Anderson Hamiltonian ℋ = κΔ + ξ. Here Δ is the discrete Laplacian, κ∈ (0, ∞) is a diffusion constant, and ξ = {ξ(x): x∈ℤ ^d } is an i.i.d.random field taking values in ℝ. G?rtner and Molchanov (1990) have shown that if the law of ξ(0) is nondegenerate, then the solution u is asymptotically intermittent. In the present paper we study the structure of the intermittent peaks for the special case where the law of ξ(0) is (in the vicinity of) the double exponential Prob(ξ(0) > s) = exp[−e ^{s /θ}] (s∈ℝ). Here θ∈ (0, ∞) is a parameter that can be thought of as measuring the degree of disorder in the ξ-field. Our main result is that, for fixed x, y∈ℤ ^d and t→∈, the correlation coefficient of u(x, t) and u(y, t) converges to ∥w _ρ∥⁻² _ℓ2Σ_{z ∈ℤd} w _ρ(x+z)w _ρ(y+z). In this expression, ρ = θ/κ while w _ρ:ℤ^d→ℝ⁺ is given by w _ρ = (v _ρ)^{⊗ d} with v _ρ: ℤ→ℝ⁺ the unique centered ground state (i.e., the solution in ℓ²(ℤ) with minimal l ²-norm) of the 1-dimensional nonlinear equation Δv + 2ρv log v = 0. The uniqueness of the ground state is actually proved only for large ρ, but is conjectured to hold for any ρ∈ (0, ∞). empty It turns out that if the right tail of the law of ξ(0) is thicker (or thinner) than the double exponential, then the correlation coefficient of u(x, t) and u(y, t) converges to δ _{x, y} (resp.the constant function 1). Thus, the double exponential family is the critical class exhibiting a nondegenerate correlation structure. Received: 5 March 1997 / Revised version: 21 September 1998     

A contribution to the application of flame photometry on Ca, Sr, Ba and Li

Summary Test solutions containing Li, Ca, Sr and Ba salts were sprayed into a flame photometer of simple design. The line-to-background ratio, the detection limit, interference effects, filter leakage and the form of the standard graphs were investigated. With each element readings were made with a series of interference filters of varying central wavelength and with an acetylene-air and propane-air flame, for comparison. From the results obtained conclusions can be drawn concerning the optimum measuring conditions to be used in routine analysis. Also an approach is made to the quantitative understanding of the form of the standard graphs with Ca, Sr and Ba, in the lower concentration range, based on the underlying ionization and dissociation processes. A characteristic saturation effect of the photomultiplier tube used is reported.     

Liquid order at the interface of KDP crystals with water: evidence for icelike layers

We present a surface x-ray diffraction study on the KDP-water interface in which the structure of both the crystalline and liquid part of the interface has been measured. We have been able to determine the ordering components in the liquid in both the perpendicular and parallel directions. We find interface-induced ordering in the first four layers of water molecules. The first two layers behave icelike and are strongly bound to the surface. The next two layers are more diffuse and show only minor lateral and perpendicular ordering. Subsequent layers are found to behave similar to a bulk liquid.     

Saturation of sodium fluorescence in a flame irradiated with a pulsed tunable dye laser

Theoretical and experimental saturation curves and associated saturation parameters for the Na-D doublet in an H₂-O₂-Ar flame at 1 atm (T=1700 K) are compared. These parameters are found to agree within the experimental error of 25%. An explanation based on the spatial and temporal distribution of the laser intensity is given for the deviating saturation curves reported by various authors. The shape of the fluorescence pulse is shown to depend on the O₂ concentration in the flame. A lower limit for the rate constant of the doublet mixing transition is estimated from the ratio of the saturated fluorescence intensities of the Na-D components and found to be 3x10⁸s^-1. Conclusions are drawn which restrict the use of saturated atomic fluorescence intensities as a measure for the total atomic number density in the flame.     

Wireless random-access networks with bipartite interference graphs

We consider random-access networks where nodes represent servers with a queue and can be either active or inactive. A node deactivates at unit rate, while it activates at a rate that depends on its queue length, provided none of its neighbors is active. We consider arbitrary bipartite graphs in the limit as the initial queue lengths become large and identify the transition time between the two states where one half of the network is active and the other half is inactive. The transition path is decomposed into a succession of transitions on complete bipartite subgraphs. We formulate a randomized greedy algorithm that takes the graph as input and gives as output the set of transition paths the network is most likely to follow. Along each path we determine the mean transition time and its law on the scale of its mean. Depending on the activation rates, we identify three regimes of behavior.     

Some observations on the collisional broadening and shift of the Sr 4607.33 Å line in H2/O2/Ar flames

Spectral profiles of the 4607.33 Å Sr emission line $\text{(}{}^1\text{P}{}_1\text{?}{}^1\text{S}{}_0\text{transition}\text{)}$ were measured with a pressure-scanned Fabry-Pérot interferometer in a set of pre-mixed, laminar shielded H₂/O₂/Ar flames at 1 atm with temperatures ranging from 1765 to 2365 K. Some additional integrated line profile measurements were carried out.From the full width at one-half maximum (FWHM), δλ_T, and shift of the optically thin line profiles, adiabatic cross sections for broadening and for shift were determined for SrAr and SrH₂O.