THE ENERGY ASPECT OF THE RECIPROCAL INTERACTIONS OF PAIRS OF TWO DIFFERENT VIBRATION MODES OF A CLAMPED ANNULAR PLATE

The standardized mutual active and reactive sound power of a clamped plate, representing the energy aspect of the reciprocal interactions of two different in vacuo modes, has been computed. It was assumed that the vibrations are axisymmetric, elastic and time harmonic, the plate's transverse deflection is small as compared with the plate's size, and that the vibration velocity is small as compared with the acoustic wavenumber generated. The Kirchhoff-Love theory of a perfectly elastic plate was used. The integral formulae for the mutual sound power were transformed into their Hankel representations which made possible their subsequent computation. A closed path integral was used to express the integral in its Hankel representation to compute the mutual active sound power. The asymptotic stationary phase method was used to compute the two magnitudes, i.e., the mutual active and reactive sound power. The results obtained are the asymptotic formulae valid for the acoustically fast waves. The oscillating as well as the non-oscillating terms have been identified in the formulae to make possible their further separate analysis. The availability of the asymptotic formulae makes possible some fast numerical computations of the mutual sound power. Moreover, the formulae presented herein, together with those for the individual modes known from the literature, make a complete basis for further computations of the total sound power of the plate's damped and forced vibrations in fluid.     

Gold particle interaction in regular arrays probed by surface enhanced Raman scattering

Lithographically designed two-dimensional arrays consisting of gold nanoparticles deposited on a smooth gold film are used as substrate to examine the SERS effect of the trans-1,2-bis (4-pyridyl) ethylene molecule. These arrays display two plasmon bands instead of the single one observed for the same arrays of particles but deposited on indium tin oxide coated glass. Laser excitation within the short wavelength band does not bring about any SERS spectrum, while excitation within the long wavelength band yields SERS spectra with a gain per molecule rising up to 10(8). The simultaneous investigation of extinction and Raman spectra of arrays exhibiting various topography parameters enables us to suggest an interpretation for both the occurrence of the two plasmon resonances and for the high Raman enhancement. We suggest to assign the short wavelength band to a plasmon wave propagating at the gold glass interface and the long wavelength one to an air/gold surface plasmon mode modified by particle-particle interaction.     

Beyond generative models: superfast traversal,optimization, novelty,exploration and discovery (STONED) algorithm for molecules using SELFIES

Inverse design allows the generation of molecules with desirable physical quantities using property optimization. Deep generative models have recently been applied to tackle inverse design, as they possess the ability to optimize molecular properties directly through structure modification using gradients. While the ability to carry out direct property optimizations is promising, the use of generative deep learning models to solve practical problems requires large amounts of data and is very time-consuming. In this work, we propose STONED – a simple and efficient algorithm to perform interpolation and exploration in the chemical space, comparable to deep generative models. STONED bypasses the need for large amounts of data and training times by using string modifications in the SELFIES molecular representation. First, we achieve non-trivial performance on typical benchmarks for generative models without any training. Additionally, we demonstrate applications in high-throughput virtual screening for the design of drugs, photovoltaics, and the construction of chemical paths, allowing for both property and structure-based interpolation in the chemical space. Overall, we anticipate our results to be a stepping stone for developing more sophisticated inverse design models and benchmarking tools, ultimately helping generative models achieve wider adoption.

Interpolation and exploration within the chemical space for inverse design.     

Gårding's Theory of Hyperbolic Polynomials

This paper presents a simple, self‐contained account of Gårding's theory of hyperbolic polynomials, together with a recent convexity result of Bauschke‐Güler‐Lewis‐Sendov and an inequality of Gurvits. This account begins by establishing some new results. The first concerns the existence of a pointwise arrangement of the eigenvalues so that they become global real analytic functions. The second asserts that the associated “branches” are independent of the choice of hyperbolic direction. © 2013 Wiley Periodicals, Inc.