We introduce the generalized Airy-Gauss (AiG) beams and analyze their propagation through optical systems described by ABCD matrices with complex elements in general. The transverse mathematical structure of the AiG beams is form-invariant under paraxial transformations. The conditions for square integrability of the beams are studied in detail. The model of the AiG beam describes in a more rea...

We evaluate the partition functions in the neighbourhood of catastrophes by saddle point integration and express them in terms of generalized Airy functions.

We explore an application of the Physics-Informed Neural Networks (PINNs) in conjunction with Airy stress functions and Fourier series to find optimal solutions a few reference biharmonic problems elasticity elastic plate theory. Biharmonic relations are fourth-order partial differential equations (PDEs) that challenging solve using classical numerical methods have not been addressed PINNs. Our...

Abstract The geometrically nonlinear vibrations of simply supported double-layer graphene sheet systems under in-plane magnetic field are considered in the presented manuscript. interaction between layers is taken into account due to van der Waals forces. investigation based on nonlocal elasticity theory, Kirchhoff plate theory and von Kármán theory. effect Lorentz force Maxwell’s equations. go...

In this article we propose and analyze a Virtual Element Method (VEM) to approximate the isolated solutions of von Kármán equations, which describe deformation very thin elastic plates. We consider variational formulation in terms two variables: transverse displacement plate Airy stress function. The VEM scheme is conforming H 2 for both variables has advantages supporting general polygonal mes...