Active interfaces, a universal approach
This thesis proposes and characterises a stochastic model of an active interface within the framework of statistical mechanics. Statistical methods have indeed proven successful in probing the dynamics of kinetically roughened interfaces, producing results which ﬁll a wide, 40 year long literature. The principle of universality, according to which large scales and long times screen a system intimate details, provides a mean to systematise such knowledge: many growing interfaces, for instance, are described by the same equation—the Kardar-ParisiZhang (KPZ) equation. To what extent living interfaces ﬁt into the picture is still an open question, a question this thesis attempts to answer by drawing inspiration from the membrane of moving cells. Here, the aforementioned universality principle can be used as a road roller to pave our way into the crowded and highly dynamic environment of the cell membrane. The hope is that of smoothening all—and only—the irrelevant asperities, minor attributes whose account does yield an insight nowhere near the eﬀort they require. The result of our crude approximation, that is the model presented in the thesis, can be thoroughly analysed with numerical and analytical methods: its main features turn out to match qualitatively those of actual membranes. In addition, the model allows for a rigorous derivation of the ﬁeld equations which govern its large scales and long times properties. Scaling arguments then show that these equations include all the relevant ingredients, so as to corroborate the crude approximations made at the beginning. The model presented can thus be concluded to be a reasonable candidate for the universal description of active interfaces and reveal the signature features that can be looked for in experiments.