The development of structural adhesive systems suitable for use with liquid oxygen Summary report, 1 Mar. - 30 Nov. 1967

Structural adhesives prepared from fluorinated polyurethanes for use with liquid oxyge

Synthesis of various highly halogenated monomers and polymers

Halogenated polyurethane and polycarbonate are synthesized and found to be LOX compatible but dependent upon the type nitrogen bonding

Intermittency in a catalytic random medium

In this paper, we study intermittency for the parabolic Anderson equation $\partial u/\partial t=\kappa\Delta u+\xi u$, where $u:\mathbb{Z}^d\times [0,\infty)\to\mathbb{R}$, $\kappa$ is the diffusion constant, $\Delta$ is the discrete Laplacian and $\xi:\mathbb{Z}^d\times[0,\infty)\to\mathbb {R}$ is a space-time random medium. We focus on the case where $\xi$ is $\gamma$ times the random medium that is obtained by running independent simple random walks with diffusion constant $\rho$ starting from a Poisson random field with intensity $\nu$. Throughout the paper, we assume that $\kappa,\gamma,\rho,\nu\in (0,\infty)$. The solution of the equation describes the evolution of a ``reactant'' $u$ under the influence of a ``catalyst'' $\xi$. We consider the annealed Lyapunov exponents, that is, the exponential growth rates of the successive moments of $u$, and show that they display an interesting dependence on the dimension $d$ and on the parameters $\kappa,\gamma,\rho,\nu$, with qualitatively different intermittency behavior in $d=1,2$, in $d=3$ and in $d\geq4$. Special attention is given to the asymptotics of these Lyapunov exponents for $\kappa\downarrow0$ and $\kappa \to\infty$.Comment: Published at http://dx.doi.org/10.1214/009117906000000467 in the Annals of Probability (http://www.imstat.org/aop/) by the Institute of Mathematical Statistics (http://www.imstat.org

Intermittency on catalysts

The present paper provides an overview of results obtained in four recent papers by the authors. These papers address the problem of intermittency for the Parabolic Anderson Model in a \emph{time-dependent random medium}, describing the evolution of a ``reactant'' in the presence of a ``catalyst''. Three examples of catalysts are considered: (1) independent simple random walks; (2) symmetric exclusion process; (3) symmetric voter model. The focus is on the annealed Lyapunov exponents, i.e., the exponential growth rates of the successive moments of the reactant. It turns out that these exponents exhibit an interesting dependence on the dimension and on the diffusion constant.Comment: 11 pages, invited paper to appear in a Festschrift in honour of Heinrich von Weizs\"acker, on the occasion of his 60th birthday, to be published by Cambridge University Pres

Intermittency on catalysts: three-dimensional simple symmetric exclusion

We continue our study of intermittency for the parabolic Anderson model $\partial u/\partial t = \kappa\Delta u + \xi u$ in a space-time random medium $\xi$, where $\kappa$ is a positive diffusion constant, $\Delta$ is the lattice Laplacian on $\Z^d$, $d \geq 1$, and $\xi$ is a simple symmetric exclusion process on $\Z^d$ in Bernoulli equilibrium. This model describes the evolution of a \emph{reactant} $u$ under the influence of a \emph{catalyst} $\xi$. In G\"artner, den Hollander and Maillard (2007) we investigated the behavior of the annealed Lyapunov exponents, i.e., the exponential growth rates as $t\to\infty$ of the successive moments of the solution $u$. This led to an almost complete picture of intermittency as a function of $d$ and $\kappa$. In the present paper we finish our study by focussing on the asymptotics of the Lyaponov exponents as $\kappa\to\infty$ in the \emph{critical} dimension $d=3$, which was left open in G\"artner, den Hollander and Maillard (2007) and which is the most challenging. We show that, interestingly, this asymptotics is characterized not only by a \emph{Green} term, as in $d\geq 4$, but also by a \emph{polaron} term. The presence of the latter implies intermittency of \emph{all} orders above a finite threshold for $\kappa$.Comment: 38 page

Intermittency on catalysts: Voter model

In this paper we study intermittency for the parabolic Anderson equation $\partial u/\partial t=\kappa\Delta u+\gamma\xi u$ with $u:\mathbb{Z}^d\times[0,\infty)\to\mathbb{R}$, where $\kappa\in[0,\infty)$ is the diffusion constant, $\Delta$ is the discrete Laplacian, $\gamma\in(0,\infty)$ is the coupling constant, and $\xi:\mathbb{Z}^d\times[0,\infty)\to\mathbb{R}$ is a space--time random medium. The solution of this equation describes the evolution of a ``reactant'' $u$ under the influence of a ``catalyst'' $\xi$. We focus on the case where $\xi$ is the voter model with opinions 0 and 1 that are updated according to a random walk transition kernel, starting from either the Bernoulli measure $\nu_{\rho}$ or the equilibrium measure $\mu_{\rho}$, where $\rho\in(0,1)$ is the density of 1's. We consider the annealed Lyapunov exponents, that is, the exponential growth rates of the successive moments of $u$. We show that if the random walk transition kernel has zero mean and finite variance, then these exponents are trivial for $1\leq d\leq4$, but display an interesting dependence on the diffusion constant $\kappa$ for $d\geq 5$, with qualitatively different behavior in different dimensions. In earlier work we considered the case where $\xi$ is a field of independent simple random walks in a Poisson equilibrium, respectively, a symmetric exclusion process in a Bernoulli equilibrium, which are both reversible dynamics. In the present work a main obstacle is the nonreversibility of the voter model dynamics, since this precludes the application of spectral techniques. The duality with coalescing random walks is key to our analysis, and leads to a representation formula for the Lyapunov exponents that allows for the application of large deviation estimates.Comment: Published in at http://dx.doi.org/10.1214/10-AOP535 the Annals of Probability (http://www.imstat.org/aop/) by the Institute of Mathematical Statistics (http://www.imstat.org

Synthesis of polyethers of hexafluorobenzene and hexafluoropentanediol

Two new polyethers, poly /hexafluoropentamethylene tetrafluoro-p-phenylene ether/ and a completely hydroxyl-terminated polyether, is prepared by reactions of hexafluorobenzene with hexafluoropentanediol. The polyethers can be prepared as low molecular weight oils, as intermediate molecular weight waxes, or as high molecular weight elastomers

Hypocretin-1 receptors regulate the reinforcing and reward-enhancing effects of cocaine: pharmacological and behavioral genetics evidence.

Considerable evidence suggests that transmission at hypocretin-1 (orexin-1) receptors (Hcrt-R1) plays an important role in the reinstatement of extinguished cocaine-seeking behaviors in rodents. However, far less is known about the role for hypocretin transmission in regulating ongoing cocaine-taking behavior. Here, we investigated the effects of the selective Hcrt-R1 antagonist SB-334867 on cocaine intake, as measured by intravenous (IV) cocaine self-administration in rats. The stimulatory effects of cocaine on brain reward systems contribute to the establishment and maintenance of cocaine-taking behaviors. Therefore, we also assessed the effects of SB-334867 on the reward-enhancing properties of cocaine, as measured by cocaine-induced lowering of intracranial self-stimulation (ICSS) thresholds. Finally, to definitively establish a role for Hcrt-R1 in regulating cocaine intake, we assessed IV cocaine self-administration in Hcrt-R1 knockout mice. We found that SB-334867 (1-4 mg/kg) dose-dependently decreased cocaine (0.5 mg/kg/infusion) self-administration in rats but did not alter responding for food rewards under the same schedule of reinforcement. This suggests that SB-334867 decreased cocaine reinforcement without negatively impacting operant performance. SB-334867 (1-4 mg/kg) also dose-dependently attenuated the stimulatory effects of cocaine (10 mg/kg) on brain reward systems, as measured by reversal of cocaine-induced lowering of ICSS thresholds in rats. Finally, we found that Hcrt-R1 knockout mice self-administered far less cocaine than wildtype mice across the entire dose-response function. These data demonstrate that Hcrt-R1 play an important role in regulating the reinforcing and reward-enhancing properties of cocaine and suggest that hypocretin transmission is likely essential for establishing and maintaining the cocaine habit in human addicts

Stretched Exponential Relaxation in the Biased Random Voter Model

We study the relaxation properties of the voter model with i.i.d. random bias. We prove under mild condions that the disorder-averaged relaxation of this biased random voter model is faster than a stretched exponential with exponent $d/(d+\alpha)$, where $0<\alpha\le 2$ depends on the transition rates of the non-biased voter model. Under an additional assumption, we show that the above upper bound is optimal. The main ingredient of our proof is a result of Donsker and Varadhan (1979).Comment: 14 pages, AMS-LaTe

Democratic Transition and Electoral Choice: The Legacy of One-Party Rule in Hungary and Poland

Why did reforming Eastern European countries adopt the electoral systems they did? Why, for example, did Poland adopt proportional representation while Hungary adopted a system of fairly strict majority rule? Often, the expectation is that new democracies will adopt electoral systems characterized by proportional representation rather than majority rule. This expectation is based on two (unwarranted) assumptions: (1) that proportional representation is better able to produce political stability and (2) that incumbent reformers care more about stability than about their own political power. Because it is reliant on these assumptions, the prevailing literature is unable to explain Hungary’s adoption of majority rule; it is also unable to explain the degree of proportional representation agreed upon in the process of democratic transition. In this paper, I present a formal model of regime transition that explains the electoral systems that emerged from democratic transition in Poland, Hungary, and Czechoslovakia. Aside from explaining Hungary’s majoritarian outcome, the model holds without reference to the efficacy of proportional representation. It also makes simpler assumptions about the behavior of parties to constitutional negotiation