Scaling for a random polymer

LetQ _n ^β be the law of then-step random walk on ?^d obtained by weighting simple random walk with a factore ^?β for every self-intersection (Domb-Joyce model of “soft polymers”). It was proved by Greven and den Hollander (1993) that ind=1 and for every β∈(0, ∞) there exist θ^*(β)∈(0,1) and such that under the lawQ _n ^β asn→∞: $$\begin{array}{l} (i) \theta ^* (\beta ) is the \lim it empirical speed of the random walk; \\ (ii) \mu _\beta ^* is the limit empirical distribution of the local times. \\ \end{array}$$ A representation was given forθ ^*(β) andµ _β ^β in terms of a largest eigenvalue problem for a certain family of ? x ? matrices. In the present paper we use this representation to prove the following scaling result as β?0: $$\begin{array}{l} (i) \beta ^{ - {\textstyle{1 \over 3}}} \theta ^* (\beta ) \to b^* ; \\ (ii) \beta ^{ - {\textstyle{1 \over 3}}} \mu _\beta ^* \left( {\left\lceil { \cdot \beta ^{ - {\textstyle{1 \over 3}}} } \right\rceil } \right) \to ^{L^1 } \eta ^* ( \cdot ) . \\ \end{array}$$ The limitsb ^*∈(0, ∞) and are identified in terms of a Sturm-Liouville problem, which turns out to have several interesting properties. The techniques that are used in the proof are functional analytic and revolve around the notion of epi-convergence of functionals onL ²(?⁺). Our scaling result shows that the speed of soft polymers ind=1 is not right-differentiable at β=0, which precludes expansion techniques that have been used successfully ind≧5 (Hara and Slade (1992a, b)). In simulations the scaling limit is seen for β≦10^?2.     

Quenching of excited strontium atomic state measured in H2- and CO-flames

The efficiency of resonance fluorescence, Y, of the strontium resonance line (¹P₁→¹S₀ transition) at 4607.33 Å was measured in CO/N₂O, CO/O₂/Ar, and H₂/O₂/CO₂/N₂ flames at atmospheric pressure. From these data, the specific quenching cross sections, σ_qu, for CO₂ and CO were found to be (60 ± 10) Ų and  (300 ± 60) Ų, respectively. The experimental cross sections were confronted with the intermediate ionic-state curve-crossing model and chemical quenching model, respectively.     

Possible Loss and Recovery of Gibbsianness¶During the Stochastic Evolution of Gibbs Measures

We consider Ising-spin systems starting from an initial Gibbs measure ν and evolving under a spin-flip dynamics towards a reversible Gibbs measure μ≠ν. Both ν and μ are assumed to have a translation-invariant finite-range interaction. We study the Gibbsian character of the measure νS(t) at time t and show the following: (1) For all ν and μ, νS(t) is Gibbs for small t. (2) If both ν and μ have a high or infinite temperature, then νS(t) is Gibbs for all t > 0. (3) If ν has a low non-zero temperature and a zero magnetic field and μ has a high or infinite temperature, then νS(t) is Gibbs for small t and non-Gibbs for large t. (4) If ν has a low non-zero temperature and a non-zero magnetic field and μ has a high or infinite temperature, then νS(t) is Gibbs for small t, non-Gibbs for intermediate t, and Gibbs for large t. The regime where μ has a low or zero temperature and t is not small remains open. This regime presumably allows for many different scenarios. Received: 26 April 2001 / Accepted: 10 October 2001     

Construction of the Incipient Infinite Cluster for Spread-out Oriented Percolation Above 4 + 1 Dimensions

 We construct the incipient infinite cluster measure (IIC) for sufficiently spread-out oriented percolation on ℤ ^d × ℤ₊, for d +1 > 4+1. We consider two different constructions. For the first construction, we define ℙ ⁿ (E) by taking the probability of the intersection of an event E with the event that the origin is connected to (x,n)  ℤ ^d × ℤ₊, summing this probability over x  ℤ ^d , and normalising the sum to get a probability measure. We let n → ∞ and prove existence of a limiting measure ℙ_∞, the IIC. For the second construction, we condition the connected cluster of the origin in critical oriented percolation to survive to time n, and let n → ∞. Under the assumption that the critical survival probability is asymptotic to a multiple of n ⁻¹, we prove existence of a limiting measure ℚ_∞, with ℚ_∞ = ℙ_∞. In addition, we study the asymptotic behaviour of the size of the level set of the cluster of the origin, and the dimension of the cluster of the origin, under ℙ_∞. Our methods involve minor extensions of the lace expansion methods used in a previous paper to relate critical oriented percolation to super-Brownian motion, for d+1 > 4+1. Received: 13 December 2001 / Accepted: 11 July 2002 Published online: 29 October 2002 RID="*" ID="*" Present address: Department of Mathematics and Computer Science, Eindhoven University of Technology, P.O. Box 513, 5600 MB Eindhoven, The Netherlands. E-mail: rhofstad@win.tue.nl     

Detection of autocatalytic decomposition behavior of energetic materials using APTAC

Characterization of autocatalytic decomposition reactions is important for the safe handling and storage of energetic materials. Isothermal differential scanning calorimetry (DSC) has been widely used to detect autocatalytic decomposition of energetic materials. However, isothermal DSC tests are time consuming and the choice of experimental temperature is crucial. This paper shows that an automatic pressure tracking calorimeter (APTAC) can be a reliable and efficient screening tool for the identification of autocatalytic decomposition behavior of energetic materials. Hydroxylamine nitrate (HAN) is an important member of the hydroxylamine family. High concentrations of HAN are used as liquid propellants, and low concentrations of HAN are used primarily in the nuclear industry for decontamination of equipment. Because of its instability and autocatalytic decomposition behavior, HAN has been involved in several incidents.     

Excitation energies of strontium mono-hydroxide bands measured in flames

Experiments are described to yield more decisive information about the excitation energies of visible strontium monohydroxide bands appearing in flames. Excitation energy differences are derived directly from the ratio of thermal band intensities measured as a function of temperature. Absolute excitation energies are derived from the temperature dependence of the ratio of thermal band to strontium line intensity, while assuming a value for the dissociation energy of SrOH. Flames with temperatures ranging from 1907 to 2886 K were used. A level diagram is proposed for the strontium bands at 6060, 6470, 6690, and 6820 Å. From the results obtained, two conclusions may be drawn: (i) the bands considered are non-resonance bands and (ii) the uncertainty in the excitation energy as a result of the unknown molecular configuration is 0·25 eV.     

Synthesis of polyurethanes from fluorinated diisocyanates

A number of polyurethanes based on fluorinated aliphatic diisocyanates, perfluorinated aromatic diisocyanates, and chlorinated aromatic diisocyanates have been prepared. The polyurethane prepared from perfluorotrimethylene diisocyanate and hexafluoropentanediol was a rubbery solid which hydrolyzed readily in air to a liquid or sticky solid but was stable if protected from moisture. The products of hydrolysis were isolated and identified. Polyurethanes based on hexafluoropentamethylene diisocyanate were synthesized by reaction of hexafluoropentanediamine with hexafluoropentamethylene bischloroformate and with tetrafluoro-p-phenylene bischloroformate. Polyurethanes were synthesized by reaction of tetrafluoro-p-phenylene diisocyanate with hexafluoropentanediol and pentanediol. Other perfluoroaryl diisocyanate-based polyurethanes were synthesized by reaction of tetrafluoro-m-phenylene diisocyanate with hexafluoropentanediol and with tetrafluoro-p-hydroquinone. Polyurethanes were also synthesized by reaction of tetrachloro-p-phenylene diisocyanate and 2,3,5,6-tetrachloro-p-xylylene-α,α′-diisocyanate with hexafluoropentanediol.     

Ultrafast magneto-optics in nickel: magnetism or optics?

Several magnetic and optical processes contribute to the magneto-optical response of nickel thin films after excitation by a femtosecond laser pulse. We achieved a first complete identification by explicitly measuring the time-resolved Kerr ellipticity and rotation, as well as its temperature and magnetic field dependence in epitaxially grown (111) and (001) oriented Cu/Ni/Cu wedges. The first hundreds of femtoseconds the response is dominated by state filling effects. The true demagnetization takes approximately 0.5-1 ps. At the longer (sub-ns) time scales the spins are found to precess in their anisotropy field. Simple and transparent models are introduced to substantiate our interpretation.