Dynamically induced conformation depending on excited normal modes of fast oscillation

Abstract

We present dynamical effects on conformation in a simple bead-spring model consisting of three beads connected by two stiff springs. The conformation defined by the bending angle between the two springs is determined not only by a given potential energy function depending on the bending angle, but also by fast motion of the springs which constructs the effective potential. A conformation corresponding with a local minimum of the effective potential is hence called the dynamically induced conformation. We develop a theory to derive the effective potential using multiple-scale analysis and the averaging method. A remarkable consequence is that the effective potential depends on the excited normal modes of the springs and amount of the spring energy. Efficiency of the obtained effective potential is numerically verified.

Mode selectivity of dynamically induced conformation in many-body chainlike bead-spring models

“…The mode dependence of stabilization provides a sharp contrast with the Kapitza pendulum, since the oscillating external force always contributes to stabilize the inverted pendulum irrespective of the phase of the external force. This aspect motivates us to extend the previous analysis [20], which is restricted to three-body systems. The aim of this article is to answer the following questions in chainlike bead-spring models through the combination of the theory and numerical simulations: Is DIC ubiquitous?…”

“…This averaging also eliminates the N − 1 phases δ, but the N − 1 amplitudes w remain and may depend on the slow timescale t 1 . We then introduce a working hypothesis [20]…”

“…Excitation of the fast spring part induces additional effective forces on the conformation part, and the effective forces can modify the stability ruled by the bending potential. For instance, a local maximum of the bending potential can become a local minimum of the effective potential, as the spring energy increases [20]. The meaning of the dynamical stabilization is therefore the stabilization of a nonlocal-minimum point of the bending potential by exciting the spring part.…”

“…The meaning of the dynamical stabilization is therefore the stabilization of a nonlocal-minimum point of the bending potential by exciting the spring part. A dynamically stabilized conformation is called a dynamically induced conformation (DIC) [20].…”

“…The dynamical stabilization in the bead-spring model was first observed in numerical simulations without the bending potential [21] and then analyzed theoretically in the threebody model having a bending potential [20] with the aids of the multiple-scale analysis [22] and the averaging method [23][24][25]. A surprising result of the theory is that the stability of a conformation depends on the excited normal modes of the springs.…”