Bounds on Plasma Instability Growth Rates

Shape-dependent bounds on cell growth rates

I consider how cell shape and environmental geometry affect the rate of nutrient capture and the consequent maximum growth rate of a cell, focusing on rod-like species like E. coli. Simple modeling immediately implies that it is the elongated profiles of such cells that allows for them to grow – as observed – at exponential rates in nutrient-rich media. Growth is strongly suppressed when nutrie...

Extremal Bounds on Drift Wave Growth Rates and Transport

Eigenmodes and growth rates of relativistic current filamentation instability in a collisional plasma.

I theoretically found eigenmodes and growth rates of relativistic current filamentation instability in collisional regimes, deriving a generalized dispersion relation from self-consistent beam-Maxwell equations. For symmetrically counterstreaming, fully relativistic electron currents, the collisional coupling between electrons and ions creates the unstable modes of growing oscillation and wave,...

Upper bounds on oarsening rates

Upper bounds on mixing rates

We prove upper bounds on the rate, called ”mixing rate”, at which the von Neumann entropy of the expected density operator of a given ensemble of states changes under nonlocal unitary evolution. For an ensemble consisting of two states, with probabilities of p and 1 − p, we prove that the mixing rate is bounded above by 4 √ p(1− p) for any Hamiltonian of norm 1. For a general ensemble of states...