In this paper, we prove the local well-posedness of the Ericksen-Leslie system, and the global well-posednss for small initial data under the physical constrain condition on the Leslie coefficients, which ensures that the energy of the system is dissipated. Instead of the GinzburgLandau approximation, we construct an approximate system with the dissipated energy based on a new formulation of th...

The phase angle of the cantilever oscillation in tapping mode scanning force microscopy can be related to the energy dissipated per oscillation period through an analytical model that assumes a sinusoidal movement of the cantilever @J. Tamayo and R. Garcı́a, Appl. Phys. Lett. 73, 2926 ~1998!; J. P. Cleveland, B. Anczykowski, E. Schmid, and V. Elings, Appl. Phys. Lett. 72, 2613 ~1998!#. In this w...

In this paper, we study the role of boundary conditions on the optimal shape of a dyadic tree in which flows a Newtonian fluid. Our optimization problem consists in finding the shape of the tree that minimizes the viscous energy dissipated by the fluid with a constrained volume, under the assumption that the total flow of the fluid is conserved throughout the structure. These hypotheses model s...

Internal tides have been implicated as a major source of mechanical energy for mixing in the ocean interior. Indeed, microstructure and tracer measurements have indicated that enhanced turbulence levels occur near topography where internal tides are generated. However, the details of the energy budget and the mechanisms by which energy is transferred from the internal tide to turbulence have be...

A short-term flow, kind of softening of soil during cyclic loading, makes a perceivable impact on strain progression in saturated soil during cyclic loading. A short-term flow developed during cyclic mobility of soil can be seen from the stress-strain relationship observed during cyclic triaxial tests. After few cycles of loading soil starts to exhibit very low stiffness at the beginning of a l...

The instantaneous displacement, velocity and acceleration of a cantilever tip impacting onto a graphite surface are reconstructed. The total dissipated energy and the dissipated energy per cycle of each excited flexural mode during the tip interaction is retrieved. The tip dynamics evolution is studied by wavelet analysis techniques that have general relevance for multi-mode atomic force micros...