Video: Waves propagating from an initial source, two Gaussian pulses,  after encountering a time interface split into forward and backward propagating waves. The backward propagating waves reconstruct to create the image of the source at a later time. There is no energy exchange at the time interface, i.e., it is energy conserving.  

Using nonlocal interactions in phononic crystals allows for bandstructure customization. The proposed mechanism introduces carefully tailored nonlocal interactions at the temporal interface, thus transitioning from a material with local interactions only, to a material with nonlocal interactions with stationary inflection points in the dispersion curve. This causes the propagating wave-packet to stop at a desired location in space without scattering and diffusing (or spreading), i.e., the wave is frozen.

Fractional derivatives are being widely used in the constitutive laws for the modeling of complex materials to explain anomalous phenomena. However, these fractional calculus based models are assumed apriori and their coefficients are determined by fitting experimental data. There is a lack of explanation about why these fractional derivatives appear or how are they connected to the material microstructure. Our work establishes this exact connection: we show that, a two-phase heterogenous medium governed by classical elasticity at the microscale and with power-law autocovariance of the phase distribution gives an effective macroscopic constitutive law that involves fractional Laplacian operators. 

We provide a powerful analytical inverse design principle to customize the first 2 bands of the dispersion relation by employing non-local interactions in phononic crystals.

The need to tailor materials with complex valued effective uniaxial permittivity tensor (characterized by transverse and axial components) has become increasingly important in practical electromagnetic applications, for e.g., hyperbolic metamaterials have gained widespread interest due to their use in resolving subwavelength objects, optical negative refraction, and spontaneous emission engineering. Realistic hyperbolic metamaterials have loss (non-zero imaginary part of permittivity) which needs to be accounted for device-level accurate predictions. This is exactly the regime that our work addresses by proposing improved numerically conjectured bounds on the range of complex permittivity values, and bounds correlating the trans. and axial components of the uniaxial complex effective permittivity tensor of a quasistatic two-phase composite.

Geometry optimization of a water molecule using finite element method for  density functional theory