Unstable fingering patterns of Hele-Shaw flows as a dispersionless limit of the Kortweg-de vries hierarchy

We show that unstable fingering patterns of two-dimensional flows of viscous fluids with open boundary are described by a dispersionless limit of the Korteweg-de Vries hierarchy. In this framework, the fingering instability is linked to a known instability leading to regularized shock solutions for nonlinear waves, in dispersive media. The integrable structure of the flow suggests a dispersive regularization of the finite-time singularities.     

Integrable structure of interface dynamics

We establish the equivalence of 2D contour dynamics to the dispersionless limit of the integrable Toda hierarchy constrained by a string equation. Remarkably, the same hierarchy underlies 2D quantum gravity.     

Molekularstruktur der vernetzten Polymeren

Ohne Zusammenfassung     

Single-particle density matrix of a one-dimensional system of spin 1/2 Fermi particles

Institute of Chemical Physics, USSR Academy of Sciences. Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 85, No. 3, pp. 443–449, December, 1990.     

Hydrodynamic characteristics of branched polystyrenes with varying content of a highly branched fraction

The branched polymers containing different amounts of the highly branched fraction are synthesized by the radical copolymerization of styrene and divinylbenzene under conditions of the reversible inhibition by 2,2,6,6-tetramethylpiperidine-1-oxyl. The branched polystyrenes are studied by size-exclusion chromatography combined with static light scattering, viscometry, and pulsed-field gradient nuclear magnetic resonance. The branched polymers prepared by living radical polymerization (in the presence of 2,2,6,6-tetramethylpiperidine-1-oxyl) feature reduced intrinsic viscosities and increased self-diffusion coefficients compared with their linear analogs. As the content of the highly branched fraction in the synthesized polymers grows, the Zimm contraction factor in toluene solution decreases to g′ = 0.13. The Kuhn-Mark-Houwink parameters for these polymers in toluene solution (a = 0.43) confirm the nonlinear architecture of macromolecules.     

Asymmetric six-vertex model and the classical Ruijsenaars–Schneider system of particles

We discuss the correspondence between models solved by the Bethe ansatz and classical integrable systems of the Calogero type. We illustrate the correspondence by the simplest example of the inhomogeneous asymmetric six-vertex model parameterized by trigonometric (hyperbolic) functions.     

Threshold Collision Energy of the QCD Phase Diagram Tricritical Endpoint

Using the most advanced formulation of the hadron resonance gas model we analyze the two sets of irregularities found at chemical freeze-out of central nuclear-nuclear collisions at the center of mass energies 3.8–4.9 GeV and 7.6–9.2 GeV. In addition to previously reported irregularities at the collision energies 4.9 and 9.2 GeV we found sharp peaks of baryonic charge density. Also we analyze the collision energy dependence of the modified Wroblewski factor and the strangeness suppression factor. Based on the thermostatic properties of the mixed phase of a 1st order phase transition and the ones of the Hagedorn mass spectrum we explain, respectively, the reason of observed chemical equilibration of strangeness at the collision energy 4.9 GeV and above 8.7 GeV. It is argued that the both sets of irregularities possibly evidence for two phase transitions, namely, the 1st order transition at lower energy range and the 2nd order transition at higher one. In combination with a recent analysis of the light nuclei number fluctuations we conclude that the center of mass collision energy range 8.8–9.2 GeV may be in the nearest vicinity of the QCD tricritical endpoint. The properties of the phase existing between two phase transitions are revealed and discussed.