Together with Dr. Yuri Braiman and Professor F. Family, I am developing new mathematical approaches to the study of nonlinear friction in arrays of coupled oscillators. This research is also related to the dynamics of Josephson junction and Laser arrays.
Friction between materials is of fundamental importance for many applications in pure and applied sciences. Understanding basic mechanisms occurring at the interface of two materials brought into close contact is significant for a wide range of technological applications, from adhesion to wear and lubrication. A characteristic feature of friction is that it extends from macroscopic to microscopic length scales (nanoscales) and is related to a rich variety of phenomena such as earthquakes, avalanches, and nanotribology.
The limit of small velocities leads to a special type of dynamics called stick-slip motion which is of particular interest for many applications. We have identified universal mechanisms involving saddle node bifurcations in coupled nonlinear oscillators for such stick-slip motion, and we are now studying the influence of thermal noise and quenched randomness on the dynamics. We are finding that the nonlinear dynamics can lead to both a dramatic increase in the friction coefficient, and under suitable conditions to noise induced lubrication.
Y.Braiman, F.Family and G.Hentschel, Low Voltage Dynamics in Parallel Arrays of Josephson Junctions. Applied Physics Letters 68, 3180 (1996)
Y.Braiman, F.Family and G.Hentschel, Array Enhanced Frinction in the Periodic Stick-Slip Motion of Nonlinear Oscillators. Phys. Rev. E53,R3305 (1996)
F. Family. Y. Braiman and H.G.E. Hentschel, Nonlineartity and Hopping Mechanism for Stick-Slip Dynamics}. Julich Workshop on Friction, Arching and Contact Dynamics (1996).
Y.Braiman, F.Family and G.Hentschel, Nonlinear Friction in the Periodic Stick-Slip Motion of Coupled Oscillators}. Phys. Rev. B55, 5491 (1997).
M.N. Popescu, Y. Braiman, F. Family and H.G.E. Hentschel, Quenched Disorder-Induced Enhancement of Chaotic Diffusion. Phys. Rev. E58, R4057 (1998).
H.G.E. Hentschel, Y.Braiman and F.Family, Friction Selection in Nonlinear Particle Arrays. Phys. Rev. Lett. 83, 104 (1999).
Y.Braiman, F.Family, H.G.E. Hentschel and J. Krim, Tuning Friction with Noise and Disorder. Phys. Rev. E59, R4737 (1999).
