# Presentation: 558731

## Experimental studies of nanoscale energy localization in periodic condensed matter systemsA. J. Sievers, LASSP, Cornell University, DMR-0301035

- Bright and dark envelope solitons are a characteristic signature of continuous nonlinear systems. Both bright and dark traveling, locked, intrinsic localized modes (ILMs) have now been generated in a discrete system, i.e., in the acoustic spectrum of a small nonlinear micromechanical cantilever array.
- Placing the uniform driver frequency above the plane wave spectrum of this array produces a stationary ILM while placing it in the finite gaps between the plane wave modes generates ILMs that have a well defined round trip time. These same dynamical properties may be expected to occur in other small nonlinear systems such as NEMS arrays or the vibrations  of quantum dots.

- Experimental observations of two kinds of nonlinear
- localized excitations for a MEMS array displayed as cantilever site vs time. Dark regions correspond to highly excited cantilevers. (a) Stationary ILM. White horizontal lines are images of stationary cantilevers. (b) A traveling ILM that is reflected at the boundaries.

**Notes:**
It has been known for some time that nonlinearity and discreteness play important roles in many branches of condensed matter physics as evidenced by the appearance of domain walls, kinks and solitons. A recent discovery is that localized dynamical energy in a perfect nonlinear lattice can be stabilized by the lattice discreteness. Intrinsic localized modes (ILMs) are the resulting signature. Their energy profiles resemble those of localized modes at defects in a harmonic lattice but, like solitons, they can move. These localized excitations act like particles and interact strongly at short distances, unlike traditional solitons which simply pass through each other. ILMs have been observed in macroscopic arrays as diverse as coupled Josephson junctions, optical waveguides, two-dimensional nonlinear photonic crystals and micromechanical cantilevers. Such dynamically driven localized modes are providing a new window into the underlying simplicity of nonequilibrium dynamics. Because of the ease of sample fabrication with silicon technology and the intuitive optical visualization techniques we have developed, our experimental studies are able to demonstrate the general nature and properties of dynamical energy localization while at the same time providing new information on ILM generation, locking, pinning, and interaction with impurities. 
Our experimental investigation of the dynamics of a small micromechanical cantilever array in the presence of a continuous, locking driver has produced surprising results. With sufficient driving amplitude, and with its frequency strategically located in the plane wave acoustic spectrum either bright or dark running ILMs can be generated. We find that the running, locked ILM is a property of a small array since a sufficient frequency interval between the plane wave modes is required to stabilize its very precise round trip time; however, simulations show that if the array has an insufficient number of elements such smoothly running excitations are suppressed. 
Since the appearance of locked running ILMs depends on discreteness, nonlinearity, the mode density, and the balancing of nonlinearity against the dispersion, the same dynamical properties may be expected to occur in other small discrete nonlinearly coupled systems such as for NEMS arrays, BEC in optical lattices, and the vibrations of quantum dots.

## Experimental studies of nanoscale energy localization in periodic condensed matter systemsA. J. Sievers, LASSP, Cornell University, DMR-0301035

- Two undergraduates (Michael Gerrity, Hovig Charchaflian),  two graduate students (Bruce Hubbard, Jonathan Wrubel), one postdoc (M. Sato) and one research associate (N. Agladze) contributed to this research.

- Experimental studies of nanoscale energy localization in periodic condensed matter systemsA. J. Sievers, LASSP, Cornell University, DMR-0301035

**Broader impact:**
- The localization of energy observed for our nonlinear periodic cantilevers should also be relevant to some modern engineering problems, such as the vibration-induced fatigue failure of jet engine rotor blades. The large and localized vibrational blade amplitudes under forced response that are observed to appear at some rotational speeds are not predicted for a tuned linear system and have been described in terms of variations in blade geometry. From our work it is clear that even a bladed disk containing homogeneous blades of exactly the same geometry can give rise to large amplitude localized vibrations simply because each perfect nonlinear blade is coupled to its neighbors.

- REU student learning how to use our ZEMAX EE ray tracing program

**Notes:**
The localization of energy observed for our nonlinear periodic cantilevers should also be relevant to some modern engineering problems. The vibration-induced fatigue failure of jet engine rotor blades is such a case. This complex system problem can be traced back to the observed fluttering of bladed disks as a function of revolution speed, a fundamental vibrational problem that has been studied intensely for 35 years. The large and localized vibrational blade amplitudes under forced response that are observed to appear at some speeds are not predicted for a tuned linear system. These observations have been described repeatedly in terms of variations in blade geometry and/or blade homogeneity and the task of controlling and predicting the vibrational amplitudes of mistuned bladed disks remains an active engineering research area. From our work it is clear that even a bladed disk containing homogeneous blades of exactly the same geometry and composition can, given the right conditions, undergo a modulational instability at certain rotational speeds that would give rise to large amplitude localized vibrations simply because each perfect nonlinear blade is coupled to its neighbors.