The rupture of a polymer chain maintained at temperature T under fixed tension is prototypical to a wide array of systems failing under constant external stress and random perturbations. Past research focused on analytic and numerical studies of the mean rate of collapse of such a chain. Surprisingly, an analytic calculation of the probability distribution function (PDF) of collapse rates appears to be lacking. Since rare events of rapid collapse can be important and even catastrophic, we present here a theory of this distribution, with a stress on its tail of fast rates. We show that the tail of the PDF is a power law with a universal exponent that is theoretically determined. Extensive numerics validate the offered theory. Lessons pertaining to other problems of the same type are drawn.

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Using 2D Molecular Dynamics simulation, the equilibrium and dynamical properties of a gravitationally equilibrated Yukawa liquid are investigated. We observe that due to asymmetry introduced in one direction by gravity, several interesting features arise. For example, for a given value of coupling parameter Γ, screening parameter κ, and according to a chosen value of gravitational force g (say in y-direction), the system is seen to exhibit super-, sub- or normal diffusion. Interestingly, x-averaged density profiles, unlike a barotropic fluid, acquires sharp, free surface with scale free linear y-dependence. As can be expected for a system with macroscopic gradients, self-diffusion calculated from Green-Kubo’s formalism does not agree with that obtained from Einstein-Smoluchowski diffusion. A 2D angular-radial pair correlation function g(r, θ) clearly indicates asymmetric features induced by gravity. We observe that due to compression in y-direction, though in liquid state for all values of gravity considered, the transverse mode is found to predominant as compared to the longitudinal mode, leading to a novel Anisotropic Solid-like Yukawa liquid.

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Turbulence is one of the outstanding open problems. Fluid flow past an obstacle is simplest of all paradigms to understand the transition to turbulence. For Navier-Stokes liquids, a transition to turbulence is fully governed by Reynolds number (Re). Using classical molecular dynamics simulation of particles interacting via a Yukawa-type interaction, it is demonstrated unequivocally that for a given Re, the transition from laminar to turbulent flow is controlled by strength and range of inter-particle potential. For a wide range of inter-particle interaction strengths and ranges, our simulation data are seen to collapse onto a universal Strouhal-Reynolds curve with new asymptotic values for a range of Re, 2 ≤ Re ≤ 35. From the emergence of vortex street structures behind the obstacle, it is evident that the onset of turbulence is possible at low Re in Yukawa liquids. Growth rates of the instability are obtained using atomistic calculations and are observed to increase quadratically with low values of Re.