Nonaffine lattice dynamics with the Ewald method reveals strongly nonaffine elasticity of α-quartz

Nonaffine rubber elasticity for stiff polymer networks.

We present a theory for the elasticity of cross-linked stiff polymer networks. Stiff polymers, unlike their flexible counterparts, are highly anisotropic elastic objects. Similar to mechanical beams, stiff polymers easily deform in bending, while they are much stiffer with respect to tensile forces ("stretching"). Unlike in previous approaches, where network elasticity is derived from the stret...

Adaptive Tracking Control for Nonaffine Nonlinear Systems With Zero Dynamics

A direct adaptive neural network tracking control scheme is presented for a class of nonaffine nonlinear systems with zero dynamics. The method does not assume boundedness on the time derivative of a control effectiveness term. Parameters in neural networks are updated using a gradient descent method which designed in order to minimize a quadratic cost function of the error between the unknown ...

Nonaffine correlations in random elastic media.

Materials characterized by spatially homogeneous elastic moduli undergo affine distortions when subjected to external stress at their boundaries, i.e., their displacements from a uniform reference state grow linearly with position , and their strains are spatially constant. Many materials, including all macroscopically isotropic amorphous ones, have elastic moduli that vary randomly with positi...

Non-gatherable Triples for Nonaffine Root Systems

This paper contains a complete description of minimal non-gatherable triangle triples in the lambda-sequences for the classical root systems, F4 and E6. Such sequences are associated with reduced decompositions (words) in affine and non-affine Weyl groups. The existence of the non-gatherable triples is a combinatorial obstacle for using the technique of intertwiners for an explicit description ...

Adaptive Control of Nonaffine Systems with Applications to Flight Control