Natalia Ernst | Searcharxiv

arXiv2020

Intensification of tilted atmospheric vortices by asymmetric diabatic heating

Päschke et al. (JFM, 701, 137--170 (2012)) studied the nonlinear dynamics of strongly tilted vortices subject to asymmetric diabatic heating by asymptotic methods. They found, \ia, that an azimuthal Fourier mode~1 heating pattern can intensify or attenuate such a vortex depending on the relative orientation of tilt and heating asymmetries. The theory originally addressed the gradient wind regime which, asymptotically speaking, corresponds to vortex Rossby numbers of order unity in the limit. Formally, this restricts the applicability of the theory to rather weak vortices in the near equatorial region. It is shown below that said theory is, in contrast, uniformly valid for vanishing Coriolis parameter and thus applicable to vortices up to low hurricane strengths. In addition, the paper presents an extended discussion of the asymptotics as regards their physical interpretation and their implications for the overall vortex dynamics. The paper's second contribution is a series of three-dimensional numerical simulations examining the effect of different orientations of dipolar heat release on idealized tropical cyclones. Comparisons with numerical solutions of the asymptotic equations yield evidence that supports the original predictions. In addition, the influence of asymmetric diabatic heat release on the time evolution of centerline tilt is analysed further, and a steering mechanism based on the orientation of the heating dipole is revealed.

physics.flu-dyn↗

arXiv2017

A fuzzy-set theoretical framework for computing exit rates of rare events in potential-driven diffusion processes

This article is about molecular simulation. However, the theoretical results apply for general overdamped Langevin dynamics simulations. Molecular simulation is often used for determining the stability of a complex (e.g., ligand-receptor). The stability can be measured by computing the expected holding time of the complex before its dissociation. This dissociation can be seen as an exit event from a certain part S of the conformational state space. Determining exit rates (i.e, for SDE-based simulations exiting from a given starting set S) for a stochastic process in which the exit event occurs very rarely is obviously hard to solve by straight forward simulation methods. Finding a low variance procedure for computing rare event statistics is still an open problem. Imagine now, e.g., a simulation of a diffusion process. As long as the time-dependent state trajectory is inside the starting set S, no information is gained about the rare event statistics. Only at that point of time, when the process leaves the starting set, a piece of information about the exit rate is collected. If S, however, is a fuzzy set given by a membership function, then there might be additional information of the kind "the process is about to leave the set". However, how to define an exit rate from a fuzzy set?

math.DS↗