@article { refId0,
	title = {On the genesis of directional friction through bristle-like mediating elements},
	journal = {ESAIM: COCV},
	volume = {23},
	number = {3},
	year = {2017},
	pages = {1023-1046},
	abstract = {<p>We propose an explanation of the genesis of directional dry friction, as emergent property of the oscillations produced in a bristle-like mediating element by the interaction with microscale fluctuations on the surface. Mathematically, we extend a convergence result by Mielke, for Prandtl{\textendash}Tomlinson-like systems, considering also non-homothetic scalings of a wiggly potential. This allows us to apply the result to some simple mechanical models, that exemplify the interaction of a bristle with a surface having small fluctuations. We find that the resulting friction is the product of two factors: a geometric one, depending on the bristle angle and on the fluctuation profile, and a energetic one, proportional to the normal force exchanged between the bristle-like element and the surface. Finally, we apply our result to discuss the with the nap/against the nap asymmetry.</p>},
	doi = {10.1051/cocv/2017030},
	url = {https://doi.org/10.1051/cocv/2017030},
	author = {Paolo Gidoni and Antonio DeSimone}
}
@article {Fonda2016,
	title = {Generalizing the Poincar{\'e}{\textendash}Miranda theorem: the avoiding cones condition},
	journal = {Annali di Matematica Pura ed Applicata (1923 -)},
	volume = {195},
	number = {4},
	year = {2016},
	month = {Aug},
	pages = {1347{\textendash}1371},
	abstract = {<p>After proposing a variant of the Poincar{\'e}{\textendash}Bohl theorem, we extend the Poincar{\'e}{\textendash}Miranda theorem in several directions, by introducing an avoiding cones condition. We are thus able to deal with functions defined on various types of convex domains, and situations where the topological degree may be different from \$\$\backslashpm \$\${\textpm}1. An illustrative application is provided for the study of functionals having degenerate multi-saddle points.</p>},
	issn = {1618-1891},
	doi = {10.1007/s10231-015-0519-6},
	url = {https://doi.org/10.1007/s10231-015-0519-6},
	author = {Alessandro Fonda and Paolo Gidoni}
}
