Design of Acoustic Cloak Using Generative Modeling and Gradient-Based Optimization

Metamaterials are engineered composites that can achieved electromagnetic and mechanical properties that do not exist in natural materials by rearranging their structures. Due to the complexity of the objective functions, it is difficult to find the globally optimized solutions in metameterial design. This talk outlines a gradient-based optimization with generative networks that can search for the globally optimized cloaking devices over a wide range of parameters. The GLO-Net[1] model was developed originally for one-dimensional nano-photonic metagratings is generalized in this work to design two-dimensional broadband acoustic cloaking devices by perturbing positions of each scatterer in planar configuration of cylindrical scatterers. Such optimized cloaking devices can efficiently suppress the total scattering cross section to the minimum at certain parameters over range of wavenumbers. During training each iteration, a generative model generates a batch of metamaterials and compute the total scattering cross section and its gradients using an in-house built multiple scattering MATLAB solver. To evaluate our approach, we compare our obtained results with fmincon in MATLAB. Reference: [1] Jiaqi Jiang and Jonathan A. Fan. Simulator-based training of generative neural networks for the inverse design of metasurfaces. Nanophotonics, 9(5):1059-1069, nov 2019.

Inverse metacluster design using generative modeling for minimal scattering response

Metamaterials are subwavelength-sized artificial structures with the ability to manipulate incident waves in such a way that affects how the energy propagates throughout the medium. In acoustics, particularly placed scattering elements can reduce the total scattering cross section (TSCS) response. We propose a method to inversely design acoustic metamaterial configurations using deep learning and generative modeling. Using our proprietary multiple scattering solver with MATLAB optimization toolbox, we generate a dataset of optimal configurations with minimized TSCS within a discrete range of wavenumbers. We use this dataset to train a Conditional Wasserstein Generative Adversarial Network (cWGAN) to generate similar metacluster designs corresponding to specified input TSCS. To improve the coordinate recognition ability of the cWGAN, we include the novel CoordConv layer in the generator and critic. After training, the cWGAN can produce a variety of optimal configurations given an expected TSCS. Evaluating TSCS of generated configurations shows that the model is capable of proposing scatterer configurations that are comparable or better than the dataset within the optimized range.

Selection rules for the S-Matrix bootstrap

We examine the space of allowed S-matrices on the Adler zeros' plane using the recently resurrected (numerical) S-matrix bootstrap program for pion scattering. Two physical quantities, an averaged total scattering cross-section, and an averaged entanglement power for the boundary S-matrices, are studied. Emerging linearity in the leading Regge trajectory is correlated with a reduction in both these quantities. We identify two potentially viable regions where the S-matrices give decent agreement with low energy S- and P-wave scattering lengths and have leading Regge trajectory compatible with experiments. We also study the line of minimum averaged total cross section in the Adler zeros' plane. The Lovelace-Shapiro model, which was a precursor to modern string theory, is given by a straight line in the Adler zeros' plane and, quite remarkably, we find that this line intersects the space of allowed S-matrices near both these regions.

The Gradient of Total Multiple Scattering Cross-Section and Its Application to Acoustic Cloaking

We derive a formula for the gradients of the total scattering cross-section (TSCS) with respect to positions of a set of cylindrical scatterers. The analytic form enhances modeling capability when combined with optimization algorithms and parallel computing. As application of the method, we consider a gradient-based minimization of TSCS for a set of cylindrical obstacles by incrementally repositioning them so that they eventually act as an effective cloaking device. The gradient-based optimization algorithm reduces the TSCS by evaluating its derivative with respect to the cylinder positions and then perturbatively optimizing the position of each cylinder in the cloaking device while taking into account acoustic multiple scattering between the cylinders. The method is illustrated for clusters of hard cylinders and sets of elastic thin shells in water.

Scattering and radiation of water waves by a submerged rigid disc in a two-layer fluid

Interaction of water waves with a horizontal rigid disc submerged in the lower layer of a two-layer fluid is studied in three dimensions using linear theory. The governing boundary value problem is reduced to a two-dimensional hypersingular integral equation. This integral equation is further reduced to a one-dimensional Fredholm integral equation of the second kind in terms of a newly defined function. The solution to the latter integral equation is used to compute the total scattering cross section and the hydrodynamic force for the scattering problem and the added mass and the damping coefficient for the radiation problem. Haskind relations connecting the solutions of the radiation and the scattering problems are also derived. The effects of variations of the submergence depth of the disc and the depth of the upper layer on different physical quantities are investigated. We observe amplification of the added mass and the damping coefficient, the total scattering cross section and the hydrodynamic force when the disc goes near the interface or when the height of the upper layer decreases. Known results for a horizontal disc submerged in a single-layer fluid of infinite depth are recovered from the present analysis.

Соударения медленных электронов с молекулами тимина

Using a hypocycloidal electron spectrometer, the total scattering cross section of slow (0–9 eV) electrons and the dissociative electron attachment cross section for thymine molecules in the gas phase were measured. The ionization cross section for a thymine molecule was studied in the energy range of 9–32 eV. Some features were found in the scattering cross section, caused by the formation and decay of short-lived states of the molecular negative ion. Three of them ( E = 0.32, 1.71, and 4.03 eV) relate to shape resonances; the others, which are observed for the first time, refer to the Feshbach resonances (or core-excited resonances). In the total dissociative attachment cross section in the energy range of E < 4 eV, a clear structure is observed due to the formation of a negative ion (T–H)^–, and a less intense structure associated with the total contribution of fragment thymine ions is found above 4 eV. The correlation of the features found in the total scattering cross section and in the dissociative attachment cross section is assessed. The absolute total scattering cross section was obtained by normalizing the measured curve to the theoretical calculation. In the total ionization cross section, features are observed that are associated both with the effect of the formation of fr-agment ions and with ionization due to the ejection of electrons from the orbitals of the outer shell of the molecule.

Relativistic quantum scattering yielded by Lorentz symmetry breaking effects

We investigate the scattering of a relativistic scalar quantum particle induced by a scattering-like potential that arises from the effects of the violation of the Lorentz symmetry. We then obtain the scattering phase shift caused by the influence of such a potential and use it to calculate the exact expressions for the scattering amplitude as well as for the total scattering cross-section through the optical theorem. In addition, we estimate an upper bound for the Lorentz symmetry violation parameters.