01320nas a2200133   4500008004100000245008300041210006900124300001400193490000700207520089100214100001801105700002201123856004101145       2017                        eng d00aOn the genesis of directional friction through bristle-like mediating elements0 agenesis of directional friction through bristlelike mediating el  a1023-10460 v233 a<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–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>1 aGidoni, Paolo1 aDeSimone, Antonio  uhttps://doi.org/10.1051/cocv/201703000945nas a2200157   4500008004100000022001400041245007900055210007200134260000800206300001600214490000800230520046300238100002200701700001800723856004600741       2016                        eng d  a1618-189100aGeneralizing the Poincaré–Miranda theorem: the avoiding cones condition0 aGeneralizing the Poincaré–Miranda theorem the avoiding cones con  cAug  a1347–13710 v1953 a<p>After proposing a variant of the Poincaré–Bohl theorem, we extend the Poincaré–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 \$\$±1. An illustrative application is provided for the study of functionals having degenerate multi-saddle points.</p>1 aFonda, Alessandro1 aGidoni, Paolo  uhttps://doi.org/10.1007/s10231-015-0519-6