arXiv subjects

Ron Maimon

Publications and source records attributed to Ron Maimon.

3 recordsLinked to original sources

arXiv2005

Computational Theory of Biological Function I

This series presents an approach to mathematical biology which makes precise the function of biological molecules. Because biological systems compute, the theory is a general purpose computer language. I build a language for efficiently representing the function of protein-like molecules in a cell. The first paper only presents the kinematic part of the formalism, but this is already useful for representing large-scale protein networks. The full formalism allows us to investigate the properties of protein interaction models, ultimately yielding an estimate of the random-access memory of the proteins, a measure of their capacity for computation.

q-bio.MN↗

arXiv2003

One-Way Hysteresis in the Depinning Transition

We identify a mechanism for a type of hysteresis which we predict to occur in a variety of depinning transitions. We show that the phenomenon of one-way hysteresis is generic to stress-overshoot models of the depinning transition, and we show how to calculate the size of the hysteresis gap exactly in a large class of models. Unlike thermodynamic phase transitions, the dynamic phase transition is still {\em continuous} despite the presence of hysteresis because the terms which produce the hysteresis are renormalization group irrelevant. We discuss the experimental and numerical signatures of one-way hysteresis, which includes microscopic nucleation.

cond-mat.dis-nn↗

arXiv2001

First passage time exponent for higher-order random walks:Using Levy flights

We present a heuristic derivation of the first passage time exponent for the integral of a random walk [Y. G. Sinai, Theor. Math. Phys. {\bf 90}, 219 (1992)]. Building on this derivation, we construct an estimation scheme to understand the first passage time exponent for the integral of the integral of a random walk, which is numerically observed to be $0.220\pm0.001$. We discuss the implications of this estimation scheme for the $n{\rm th}$ integral of a random walk. For completeness, we also address the $n=\infty$ case. Finally, we explore an application of these processes to an extended, elastic object being pulled through a random potential by a uniform applied force. In so doing, we demonstrate a time reparameterization freedom in the Langevin equation that maps nonlinear stochastic processes into linear ones.

cond-mat.stat-mech↗