# Publications

## Examples of NewFoS Research and Relevant Publications

### Wave Topology

The non-conventional topology of sound waves finds it roots in the phase of the waves. Phase control of acoustic waves through phononic crystals has been demonstrated. Our laboratories have achieved conventional coding of information in the phase of the acoustic waves Reference 1 and its application to conventional Boolean logic applications Reference 2. However, future applications of acoustic waves for parallel information processing requires that information be coded in the geometric phase associated with non-conventional topologies in wave-vector space. The amplitude of such a wave is supported by a manifold in wave vector space that exhibits a non-conventional topology, which manifests itself in the form of the accumulation of a geometric Berry phase along a closed path (non-zero Chern number). Such behavior has been achieved by considering by applying symmetry breaking stimuli or inserting within a medium symmetry braking elements. In the first case spatio-temporal external stimulus (electromagnetic, magnetic) can be used to break the time reversal symmetry of acoustic waves. For instance, we have created spatio-temporal modulated sound-supporting media by exploiting the giant photoelastic Reference 3. In that work, we have identified the non-conventional topology of bulk elastic waves in a time-dependent super-lattice as well as demonstrated the existence of bulk elastic waves with unidirectional backscattering-immune topological states. The bulk elastic wave function is supported in wave-number space by a Möbius strip-like manifold with non-conventional torsional topology. These topology protected bulk states exhibit unidirectional propagation and immunity to back scattering by defects. The concept of time-dependent materials that can break time reversal symmetry for bulk wave propagation may potentially serve as unique platforms to investigate a large variety of phenomena resulting from wave propagation with non-conventional topological states.

The second approach to achieving phononic crystals with topologically non-trivial bandgaps for both longitudinal and transverse polarizations relies on inclusions that break time-reversal symmetryReference 4. These inclusions result in protected one-way elastic edge waves. Gyroscopic inertial effects are used to break the time-reversal symmetry and realize the phononic analogue of the electronic quantum Hall effect. We have achieved Chern number of 1 and 2, indicating that these structures support single and multi-mode edge elastic waves immune to back-scattering. These robust one-way phononic waveguides could potentially lead to the design of a novel class of surface wave devices that are widely used in electronics, telecommunication and acoustic imaging.

### Acoustic and Mechanical Wave Duality

Chiral media are described within the Dirac formalism of relativistic wave mechanics. In this formalism, the wave function possesses a spinor-part that imparts a non-conventional topology to the wave-supporting manifold. This topology breaks the equivalence between the directions of propagation for sound waves. Some sound-supporting chiral media have been shown in our laboratories to lead to duality in the quantum-like statistics of sound wavesReference 1, Reference 2. Phonons are quanta of sound waves generally known to behave like bosons; hence, there is no restriction on the number of particles per state. In some of the more complex chiral media that we have investigated, the non-conventional spinor topology of the sound wave amplitude leads to an unusual constraint reminiscent of the no more than one “particle” in a state Pauli’s exclusion principle.

Critical developments in wave–particle duality in macroscopic systems, a phenomenon thought to be restricted to a peculiar microscale behavior, have been developed in our laboratories for 2-D hydrodynamic systemsReference 3. Bouncing drops of oil “walk” on an excitable liquid oil surface near a Faraday instability. Each droplet is accompanied by a surface wave that pilots its motion. Quantization emerges from the dynamic constraint imposed on the oil drop by its monochromatic pilot wave field. The droplet and the pilot wave interaction leads to classical phenomena that display the fundamentally probabilistic nature of quantum mechanical phenomena: single-particle diffraction, tunneling, singly and doubly quantized orbits, orbital level splitting, spin and multimodal statistics.

**Figure: **Bouncing drops of oil “walk” on an excitable liquid oil surface near a Faraday instability accompanied by a pilot wave leading to particle-wave duality behavior of the macroscopic system.

**Figure:** Schematic illustration of the torsional topology of the wave function in k space of a one-dimensional phononic crystal model co supporting rotational modes. The wave functions are represented in the form of two orthogonal vector fields (red and green) supported by a square cross section torus manifold possessing four 90^{0} twists. Parallel transport of the vector field on the manifold shows the topological properties of the wave function.

### Acoustic Wave Coherence

Phonon coherence processes in materials with highly nonlinear responses depend on the type of nonlinearity as well as its strength and order. Sound-supporting media offer a broad palette of nonlinear responses that include: (a) intrinsic nonlinearity of the constitutive materialsReference 1; (b) geometrical nonlinearity associated with Hertzian contact in granular mediaReference 2, Reference 3, or with rotational degrees-of-freedom in composite structuresReference 4; and (c) open system nonlinearity from exchanging matter or energy with an external reservoirReference 5. Wave decoherence caused by intrinsic phonon–phonon scattering in nonlinear media arises from multiple resonant processes leading to time-reversal symmetry breaking. Coherent wave structures such as solitary waves form in highly nonlinear, granular media. Bone is an open system chemo-mechanical composite system (a collagen matrix containing hydroxyapatite nano-plate crystals) and exhibits both rotational geometric nonlinearity and open system nonlinearity by exchanging physiological fluid with its environment.

**Figure: **microscale granular acoustic medium

**Figure:** One-dimensional granular medium (top). Granular crystals are known to be highly nonlinear and have a tunable dynamic response. They may serve as tunable acoustic diodes and switches, tunable acoustic filters; support nonlinear intrinsic energy localization (bottom), disorder induced localization, chaos and bifurcations, and localized defect states.

**Figure:** Hierarchical structure of dentine (or bone). Mineralized collagen fibril form one-dimensional non-linear phononic periodic structures. The open-system non-linearity results from exchange of physiological fluids via tubules.

### Wave Mixing

Emerging mixed-wave phenomena draw their characteristics from nonlinear interactions. These interactions exploit the magneto-elastic effect and/or the photo-elastic effect in inorganic media but also the mechano-transuction effect in biological media. While linearized interaction between elastic waves and spin waves in ferromagnetic media have been shown to lead to tunability of phononic crystalReference 1,Reference 2, higher level of control of the interaction of phonon and magnons (spin waves) can be achieve by exploiting resonances which depend on the transverse or longitudinal polarization of the elastic waveReference 3. This offers a unique mechanism of applying an external magnetic field to tune a mixed-wave system. The desired property of non-contact tunability of phononic structures can also be achieved by using the interaction between photons and phononsReference 4. Sound propagating in a biological tissue may interact with an intercellular signal such as a calcium wave through mechano-transductionReference 5 Reference 6. Recently, our researchers have shown these interactions may impart the calcium wave with non-conventional characteristics in the forms of unidirectional propagation and topological immunity to environmental cues[1].

- Effect of sound on gap-junction based intercellular signaling: Calcium waves under acoustic irradiation, P.A. Deymier, N. Swinteck, K. Runge, A. Deymier-Black and J.B. Hoying, Phys. Rev. E in review

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Figure: **phonon (blue)-spin wave (red) coupling through magneto-elastic effect.

**Video: **mechnotransduction of calcium wave in chain of endothelial cells.