Interfaces and typical Gibbs configurations for one-dimensional Kac potentials

Summary We consider a one dimensional Ising spin system with a ferromagnetic Kac potential J(|r|),J having compact support. We study the system in the limit, »0, below the Lebowitz-Penrose critical temperature, where there are two distinct thermodynamic phases with different magnetizations. We prove that the empirical spin average in blocks of size ^–1 (for any positive ) converges, as »0, to one of the two thermodynamic magnetizations, uniformly in the intervals of size ^–p , for any given positivep1. We then show that the intervals where the magnetization is approximately constant have lengths of the order of exp(c ^–1),c>0, and that, when normalized, they converge to independent variables with exponential distribution. We show this by proving large deviation estimates and applying the Ventsel and Friedlin methods to Gibbs random fields. Finally, if the temperature is low enough, we characterize the interface, namely the typical magnetization pattern in the region connecting the two phases.The research has been partially supported by CNR, GNFM, GNSM and by grant SC1CT91-0695 of the Commission of European Communities     

The convergence of spline collocation for strongly elliptic equations on curves

Summary Most boundary element methods for two-dimensional boundary value problems are based on point collocation on the boundary and the use of splines as trial functions. Here we present a unified asymptotic error analysis for even as well as for odd degree splines subordinate to uniform or smoothly graded meshes and prove asymptotic convergence of optimal order. The equations are collocated at the breakpoints for odd degree and the internodal midpoints for even degree splines. The crucial assumption for the generalized boundary integral and integro-differential operators is strong ellipticity. Our analysis is based on simple Fourier expansions. In particular, we extend results by J. Saranen and W.L. Wendland from constant to variable coefficient equations. Our results include the first convergence proof of midpoint collocation with piecewise constant functions, i.e., the panel method for solving systems of Cauchy singular integral equations.Dedicated to Prof. Dr. Dr. h.c. mult. Lothar Collatz on the occasion of his 75th birthdayThis work was begun at the Technische Hochschule Darmstadt where Professor Arnold was supported by a North Atlantic Treaty Organization Postdoctoral Fellowship. The work of Professor Arnold is supported by NSF grant BMS-8313247. The work of Professor Wendland was supported by the Stiftung Volkswagenwerk     

INTRAPARTICLE DIFFUSION EFFECTS IN FISCHER-TROPSCH SYNTHESIS Ⅰ. MODELING OF DIFFUSION AND REACTION

IntroductionCatal}ticrcactionsaffcctcdb}'diffosionaIlimitationincatal}'stporcshavcbccnextensive1}dcaltx`ithinlit.rat.rcll~5I.Scvcraltcchniqucsonthcspccialcase0fFischcr-Tropschs}'nthcsis(FTS)t\crcapplicdtocxplorcthebchaviorofthiscatal}ticrcactionundercxpcrimcntalandopcrationaIconditionsI3~5l.It`"ouldbeofvaluctoindicatchcrcthatthcseinvcstigationsx"ercmainl}'bascdonthesimplcstkineticsofthcfirstordcrinH2proposedbyAndersonl6]attheearIystages.However-thesetboents,striCtlyspeaking,areinvalidfor…     

R?ntgenspektrometrische Bestimmung von Eisen-55 in Luftstaub- und Niederschlagsproben

Zusammenfassung Eisen-55 wurde in Neuherberg bei München seit März 1970 in monatlich gesammelten Luftstaubproben und seit Januar 1971 in Monatsniederschlagsproben bestimmt. Nach dem Veraschen der Proben wurde Eisen durch Extraktion' mit Di-iso-propyläther abgetrennt. Zur weiteren Entfernung störender Radionuklide des Fallouts wurde eine Ionenaustauschertrennung angeschlossen. Nach der elektrolytischen Abscheidung des Eisens auf Kupferplättchen wurden die Röntgenspektren mit einem Proportionalzähler sowie einem Si(Li)-Detektor aufgenommen.Die mittlere spezifische Luftaktivität betrug in Neuherberg 1,0 fCi/m³ im Jahr 1970 (ab März), 1,2 fCi/m³ im Jahr 1971 und 0,36 fCi/m³ im Jahr 1972. Die dem Boden durch den Niederschlag zugeführte Aktivität wurde zu 697 pCi/m² · Jahr für 1971 und 178 pCi/m² · Jahr für 1972 bestimmt.Vortrag anläßlich der Tagung Spurenanalyse, 2. bis 5. April 1973 in Erlangen.     

Effect of gas pressure and pulse length on the isotopically selective multiphoton dissociation of CF3Cl under CO2 laser pulses

The multiphoton dissociation of CF₃Cl induced by TEA-CO₂ laser pulses has been studied in a focused beam geometry. TheR(10) [00°1–02°0] ( ) laser line was used, so as to dissociate preferentially the minor isotopic component¹³CF₃Cl. The isotopic selectivityS and the dissociation probability per pulse ω were measured in the pressure range between 0.25 and 8 Torr. With short laser pulses (90 ns FWHM),S is found to increase slightly with gas pressure up to 2 Torr, and ω, to increase almost linearly over the whole pressure range studied. A schematic model is proposed which satisfactorily explains these results if the transition rates across the energy level spectrum of the CF₃Cl molecules are assumed to increase with gas pressure.     

A central limit theorem for age- and density-dependent population processes

Consider a population consisting of one type of individual living in a fixed region with area A. In [8], we constructed a stochastic population model in which the death rate is affected by the age of the individual and the birth rate is affected by the population density P_A(t), i.e., the population size divided by the area A of the given region. In [8], we proposed a continuous deterministic model which in general is a nonlinear Volterra type integral equation and proved that under appropriate conditions the sequence P_A(t) would converge to the solution P(t) of our integral equation in the sense that

$\text{lim}\text{→∞}\text{P}\text{sup}\text{0?s?t}\text{|P}{}_{\mathrm{A}}\text{(s) ? P(s)|>ε}\text{=0}\text{for every}\text{ε > 0}$

.In this paper, we obtain a “central limit theorem” for the random element √A(P_A(t)?P(t)). We prove that under appropriate conditions √A(P_A(t)?P(t)) will converge to a Gaussian process. (See Theorem 3.4 for the explicit formula of this Gaussian process.)     

Investigation of m-nitroaniline formation during the Zimmermann reaction

The Zimmermann reaction for the determination of 17-ketosteroids was tested under both room-temperature and steam-distillation reaction conditions. meta-Nitroaniline was isolated from the residue of the steam distillation by ether extraction and thin-layer chromatography. Conclusive identification was by infrared spectroscopy. In contrast, m-nitroaniline was not formed under room-temperature reaction conditions, even when allowed to react for 24 hr. Similar results were also obtained for the reaction between acetone and m-dinitrobenzene under alkaline conditions. In conclusion, the results indicate that m-nitroaniline formation cannot account for the conversion of structure I to structure II under room-temperature reaction conditions as investigated herein.     

KT-nearfields of rank 2

Summary Nearfields of rank 2 over their kernel which are not Dickson nearfields have recently been constructed by H. Zassenhaus. Here it is shown that KT-nearfields of rank 2 over their kernels and of characteristic 2 are necessarily Dickson nearfields which are coupled to quadratic field extensions and their Dickson group is isomorphic to ₂. Using results of Gröger one obtains all KT-nearfields of rank 2 over the field of rational numbers.     

Linear optical properties of frequency doubling polymers

Measurements of linear optical properties of methylmethacrylate copolymers with non-linear optical 4-alkoxy-4-alkylsulfone stilbene side-chains are presented. From there two methods for phase matching are discussed; one aiming to equalize the refractive indices of the fundamental and the second harmnic wave, the other to suppress the destructive character of the interference. The matter of photo stability of frequency doubling polymers is also discussed.