Training nonlinear elastic functions: nonmonotonic, sequence dependent and bifurcating

Control of Nonlinear Bifurcating Systems

{ Bifurcation analysis provides a methodology for the study of the changes of stability behavior of nonlinear and parameter dependent systems. The inception of bifurcations is associated with systems exhibiting critical modes. Consequently, stabilization of critical systems can be considered as control of the underlying bifurcations. Based on bifurcation equations and the center manifold theore...

Sequence-dependent elastic properties of DNA.

Harmonic elastic constants of 3-11 bp duplex DNA fragments were evaluated using four 5 ns unrestrained molecular dynamics simulation trajectories of 17 bp duplexes with explicit inclusion of solvent and counterions. All simulations were carried out with the Cornell et al. force-field and particle mesh Ewald method for long-range electrostatic interactions. The elastic constants including anisot...

The Computation of One-Parameter Families of Bifurcating Elastic Surfaces

We consider the problem of constructing the middle surface of a deformed elastic shell from its first and second fundamental forms, âαβ and b̂αβ . The undeformed shell is a spherical cap of radius R and thickness h with an angular width 2θ0 where 0 < θ0 < π/2. The cap is subjected to a constant uniform load λ and is simply supported at its edge. We seek to compute the one–parameter families of b...

Size-dependent nonlinear elastic scaling of multiwalled carbon nanotubes.

We characterize through large-scale simulations the nonlinear elastic response of multiwalled carbon nanotubes (MWCNTs) in torsion and bending. We identify a unified law consisting of two distinct power law regimes in the energy-deformation relation. This law encapsulates the complex mechanics of rippling and is described in terms of elastic constants, a critical length scale, and an anharmonic...

Nonlinear Elastic