my picture

Ahmad Zareei
Postdoctoral Fellow in Applied Mathematics,
School of Engineering and Applied Sciences,
Harvard University, Cambridge, MA


Press Appearance:

American Scientist

American Scientist
Our research of ocean cloaking on American Scientist cover photo!

Metamaterials:

Cloaking Waves in Shallow Water Cloaking water waves in shallow water
A major obstacle in designing a perfect cloak for objects in shallow-water waves is that the linear transformation media scheme (also known as transformation optics) requires spatial variations of two independent medium properties. In the Maxwell’s equation and for the well-studied problem of electromagnetic cloaking, these two properties are permittivity and permeability. Designing an anisotropic material with both variable permittivity and variable permeability, while challenging, is achievable. On the other hand, for long gravity waves, whose governing equation maps one-to-one to the single polarization Maxwell’s equations, the two required spatially variable properties are the water depth and the gravitational acceleration; in this case changing the gravitational acceleration is simply impossible. Here we present a nonlinear transformation that only requires the change in one of the medium properties, which, in the case of shallow-water waves, is the water depth, while keeping the gravitational acceleration constant. This transformation keeps the governing equation perfectly intact and, if the cloak is large enough, asymptotically satisfies the necessary boundary conditions. [PDF]
  • A. Zareei & M.-R. Alam, Perfect cloaking in shallow water waves via nonlinear medium transformation, Journal of Fluid Mechanics, 778, pp 273-287, [PDF]
Broadband Flexural Cloaking Broadband Cloaking of Flexural Waves
The governing equation for elastic waves in flexural plates is not form invariant, and hence designing a cloak for such waves faces a major challenge. Here, we present the design of a perfect broadband cloak for flexural waves through the use of a nonlinear transformation in the region of the cloak and by matching term by term the original and transformed equations and also assuming a prestressed material with body forces. For a readily achievable flexural cloak in a physical setting, we further present an approximate adoption of our perfect cloak under more restrictive physical constraints. Through direct simulation of the governing equations, we show that this cloak, as well, maintains a consistently high cloaking efficiency over a broad range of frequencies. The methodology developed here may be used for steering waves and designing cloaks in other physical systems with non-form-invariant governing equations. [PDF]
  • A. Zareei & M.-R. Alam, Broadband Cloaking of Flexural Waves,, Physical Review E, 95.6, pp 063002, [PDF, arXiv.org]
  • A. Darabi, A. Zareei, M.-R. Alam & M. Leamy, 2018. Experimental Demonstration of an Ultra Broadband Nonlinear Transformation Cloak for Flexural Waves, Physical Review Letters, 121(17), p.174301. [PDF]
Continuous Profile Flexural GRIN Lens Continuous Profile Flexural GRIN Lens
A significant challenge in flexural wave energy harvesting is the design of an aberration-free lens capable of finely focusing waves over a broad frequency range. To date, flexural lenses have been created using discrete inclusions, voids, or stubs, often in a periodic arrangement, to focus waves via scattering. These structures are narrowband either because scattering is efficient over a small frequency range, or the arrangements exploit Bragg scattering bandgaps, which themselves are narrowband. In addition, current lens designs are based on a single frequency and approximate the necessary refractive index profile discretely, introducing aberrations and frequency-dependent focal points. Here, we design a flexural GRIN lens in a thin plate by smoothly varying the plate’s rigidity, and thus its refractive index. Our lens (i) is broadband, since the design does not depend on frequency and does not require bandgaps, (ii) has a fixed focal point over a wide range of frequencies, and (iii) is theoretically capable of zero-aberration focusing. We numerically explore our Continuous Profile GRIN lens (CP-GRIN lens) and then experimentally validate an implemented design. Furthermore, we use a piezoelectric energy harvester disk, located at the first focus of the CP-GRIN, to document improvements in power gain. [PDF]
  • A. Zareei, A. Darabi, M. Leamy & M.-R. Alam, Continuous Profile Flexural GRIN Lens: Focusing and Harvesting Flexural Waves, Applied Physics Letters 112, 023901 (2018), [PDF]
  • A. Darabi, A. Zareei, M.-R. Alam & M. Leamy, Broadband Bending of Flexural Waves: Acoustic Shapes and Patterns, Scientific Reports, 8 (1), 11219, (2018), [PDF]
Carpet Cloak Cloaking by a Floating Thin Plate
An alternative way of cloaking is to use an engineered elastic buoyant carpet placed on water around the object. The carpet will effectively bend the wave rays around the object and shield the object from impinging waves. The method can potentially open up a new avenue in the protection of ocean objects, particularly offshore structures, from the action of oceanic waves hence reducing load on such structures. [PDF]
  • A. Zareei & M.-R. Alam, Cloaking by a Floating Thin Plate, IWWWFB (2016), [PDF]
  • A. Zareei, T. Iida & M.-R. Alam, Claking via Buoyant Elastic Carpet, in preparation for Journal of Fluid Mechanics

Geophysical Fluid Dynamics:

Interaction between topographic features and internal waves Interaction between topographic features and internal waves
Interaction of stratified flows with the solid bottom boundary is a main source for generation of internal waves. This interaction can lead to generation of near-inertial internal waves which appear as a prominent peak in the internal wave spectrum. In some specific occasions, if the bottom topography wavenumber is an integer coefficient of the wavenumber of incident internal wave, the interaction could lead to generation of high wavenumer internal waves which are potentially susceptible to breaking. Here we show that the distribution of energy of internal gravity waves over a patch of seabed corrugations strongly depends on the distance of the patch to adjacent seafloor features located downstream of the patch.[PDF]
  • F. Karimpour, A. Zareei, J. Choufag & M.-R. Alam Sensitivity of internal wave energy distribution over seabed corrugations to adjacent seabed feature , Journal of Fluid Mechanics, 824, pp 74-96, [PDF, arXiv.org]
Instability internal waves Inherently Unstable Internal Waves due to Resonant Harmonic Generation
Here we show that there exist internal gravity waves that are inherently unstable, that is, they cannot exist in nature for a long time. The instability mechanism is a one-way (irreversible) harmonic-generation resonance that permanently transfers the energy of an internal wave to its higher harmonics. We show that, in fact, there are a countably infinite number of such unstable waves. For the harmonic-generation resonance to take place, nonlinear terms in the free surface boundary condition play a pivotal role, and the instability does not occur in a linearly-stratified fluid if a simplified boundary condition such as a rigid lid or a linearized boundary condition is employed. Harmonic-generation resonance presented here also provides a mechanism for the transfer of internal wave energy to the higher-frequency part of the spectrum where internal waves are more prone to breaking, hence losing energy to turbulence and heat and contributing to oceanic mixing. [PDF]
  • Y. Liang, A. Zareei & M.-R. Alam, Inherently unstable internal gravit waves due to resonant harmonic generation, Journal of Fluid Mechanics, 811, pp 400-420, [PDF]

Hydrodynamic Quantum Analogs:

Euler-Schrodinger Transformation Euler-Schrodinger Transformation
Peculiar micro-scale quantum behaviors has been observed experimentally in the hydrodynamics of a bouncing droplet on a vibrant fluid bath. Supported by recent experiments, we have been recently working on a mathematical map between Schrodinger equation describing quantum systems and Euler’s equation describing classical small scale water waves. We are excited to investigate the implication, potentials, and limits of this fundamental transformation to (i) find a physical understanding of quantum behaviors observed in micro-scale fluid systems, (ii) potentially develop an equivalent hydrodynamic setups for quantum experiments and vice versa, and (iii) investigate possibility of a hydrodynamic quantum computer for solving complex problems.

Microfluidics and Active Matter:

Micro-Swimmers at Low Reynolds number:
Motion at low Reynolds number is impossible with periodic wave motions due to time symmetry of equations; an asymmetric wave-like motion can generate locomotion. We have created an artificial mechanisms that mimic the locomotory functions of nematodes with efficient viscous pumping. We show that the blade not only induces a flow structure similar to that of the worm, but also mixes the surrounding fluid by generating a circulatory flow. [PDF]
  • A. Zareei, M.A. Jalali, M. Saadat & M.-R. Alam, Digitized Gait of C. Elegans generate propulsion and mixing, Physical Review Applied, 11.1 (2019): 014065, [PDF]


410 Pierce Hall, Harvard University, Cambridge, MA, 02138 ahmad@g.harvard.edu