In this article, we suggest simple alternatives to the methods recently used by Jain and Sebastian [ J. Phys. Chem. B 2016 , 120 , 3988 ] and Chechkin et al. [ Phys. Rev. X 2017 , 7 , 021002 ] to treat a model of non-Gaussian Brownian diffusion based on the dynamics of a particle governed by Ornstein-Uhlenbeck modulated white noise. In addition to substantiating these authors' earlier findings (which show that a particle can execute a simple random walk even when the distribution of its displacements deviates from Gaussianity), our approach identifies another process, two-state white noise, that exhibits the same "anomalous" Brownian behavior. Indeed, we find that the modulation of white noise by any stochastic process whose time correlation function decays exponentially is likely to behave similarly, suggesting that the occurrence of such behavior can be widespread and commonplace.

Breakup of liquid drops occurs in several natural and industrial settings. Fully resolved Volume of Fluid based simulations presented in this study reveal the complete flow physics and droplet dynamics that lead to the breakup of a drop in a particular mode. We have investigated the effects of density ratio and Reynolds number on the dynamics of drop deformation and subsequent breakup. A density ratio-Weber number phase plot is presented that indicates the variation in the deformation of the drop at various density ratios and Weber numbers. We show that the breakup dynamics of the droplets at low density ratios is significantly different to that observed at high density ratios. We also study the temporal characteristics of the droplet deformation and motion.

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Recent work by Cerasoli et al (2018 Phys. Rev. E 98 042149) on a two-dimensional model of biased Brownian gyrators driven in part by temperature differences along distinct Cartesian axes, x and y, has revealed interesting asymmetries in the steady-state distribution of particle positions. These asymmetries are said to be reminiscent of the more conventional asymmetries associated with the fluctuation theorems of far-from-equilibrium thermodynamics. In the present paper, working within a path integral formalism, we derive the exact time-dependent propagator of this same 2D dual-temperature system, and show that it does in fact also satisfy several conventional fluctuation theorems, including the Crooks relation, the Jarzynski equality, the detailed fluctuation theorem, and the integral fluctuation theorem. For these theorems to be satisfied, however, we find that a parameter that we identify as an ‘effective temperature’ must bear a definite relation to the two temperatures that control particle dynamics in the x and y directions. This effective temperature turns out to be the harmonic mean of two analogous temperatures introduced by Cerasoli et al.