On the nature of turbulence

A mechanism for the generation of turbulence and related phenomena in dissipative systems is proposed.The research was supported by the Netherlands Organisation for the Advancement of Pure Research (Z.W.O.).     

Brownian local time and quantum mechanics

LetV be any (sufficiently regular) attractive potential in one and two dimensions. We make rigorous an argument of M. Kac [1], relating the recurrence of the Brownian motion to the existence of at least one bound state for the quantum HamiltonianH = –(/2)+ V.     

Some rigorous results on the Sherrington-Kirkpatrick spin glass model

We prove that in the high temperature regime (T/J>1) the deviation of the total free energy of the Sherrington-Kirkpatrick (S-K) spin glass model from the easily computed log Av(Z _N ({J})) converges in distribution, asN , to a (shifted) Gaussian variable. Some weak results about the low temperature regime are also obtained.Dedicated to Walter Thirring on his 60^th birthdayResearch supported in part by the NSF grant PHY-8605164. Present address: Courant Institute of Mathematical Sciences, 251 Mercer St., New York, NY 10012, USAResearch supported in part by the NSF grant DMR 86-12369On leave from Institut des Hautes Etudes Scientifiques, Bures-Sur-Yvette, France     

Kramers-Wannier dualities via symmetries

Kramers-Wannier dualities in lattice models are intimately connected with symmetries. We show that they can be found directly and explicitly from the symmetry transformations of the boundary states in the underlying conformal field theory. Intriguingly, the only models with a self-duality transformation turn out to be those with an auto-orbifold property.     

Competition between supernucleation and plasticization in the crystallization and rheological behavior of PCL/CNT‐based nanocomposites and nanohybrids

PCL was blended with pristine multiwalled carbon nanotubes (MWCNT) and with a nanohybrid obtained from the same MWCNT but grafted with low molecular weight PCL, employing concentrations of 0.25 to 5 wt % of MWCNT and MWCNT‐g‐PCL. Excellent CNT dispersion was found in all samples leading to supernucleation of both nanofiller types. Nanohybrids with 1 wt % or less MWCNTs crystallize faster than nanocomposites (due to supernucleation), while the trend eventually reverses at higher nanotubes content (because of plasticization). Rheological results show that yield‐like behavior develops in both nanocomposites, even for the minimum content of carbon nanotubes. In addition, the MWCNT‐g‐PCL family, when compared with the neat polymer, exhibits lower values of viscosity and modulus in oscillatory shear, and higher compliance in creep. These rheological differences are discussed in terms of the plasticization effect caused by the existence of low molecular weight free and grafted PCL chains in the nanohybrids. © 2017 Wiley Periodicals, Inc. J. Polym. Sci., Part B: Polym. Phys. 2017 , 55, 1310–1325     

Automorphism modular invariants of current algebras

We consider those two-dimensional rational conformal field theories (RCFTs) whose chiral algebras, when maximally extended, are isomorphic to the current algebra formed from some untwisted affine Lie algebra at fixed level. In this case the partition function is specified by an automorphism of the fusion ring and corresponding symmetry of the Kac-Peterson modular matrices. We classify all such partition functions when the underlying finite-dimensional Lie algebra is simple. This gives all possible spectra for this class of RCFTs. While accomplishing this, we also find the primary fields with second smallest quantum dimension.Supported in part by NSERC.     

Statistical mechanics of vortices in an inviscid two-dimensional fluid

In this paper we study rigorously the statistical mechanics of a gas of vortices in the thermodynamic limit. In this limit, no negative temperature states are found to exist.Work supported in part by NSF Grant MCS 78-02721