Conventional microparticle transports by light or sound are realized along a straight line. Recently, this limit has been overcome in optics as the growing up of the self-accelerating Airy beams, which are featured by many peculiar properties, e.g., bending propagation, diffraction-free and self-healing. However, the bending angles of Airy beams are rather small since they are only paraxial sol...

We report on an approach to generate non-diffractive and non-dispersive Airy3 bullets with enhanced spatio-temporal energy confinement. By appropriately reshaping the initial spectral components in the Fourier domain, the resulting optical bullets show a significant enhancement of their central lobe intensity while exhibiting a reduced spatio-temporal outspread of the surrounding sub...

Negative propagation is an unusual effect concerning the local sign change in the Poynting vector components of an optical beam under free propagation. We report this effect for finite-energy Airy beams in a subwavelength nonparaxial regime. This effect is due to a coupling process between propagating and evanescent plane waves forming the beam in the spectral domain and it is demonstrated for ...

Abstract In this note, we formulate a new linear operator given by Airy functions of the first type in complex domain. We aim to study view geometric function theory based on subordination and superordination concepts. The is suggested define class normalized (the univalent functions) calling difference formula. As result, formula joining modified different classes analytic open unit disk.

In last passage percolation models lying in the Kardar–Parisi–Zhang universality class, maximizing paths that travel over distances of order $n$ accrue energy fluctuates on scale $n^{1/3}$; and these deviate from linear interpolation their endpoints $n^{2/3}$. These energies may be viewed via a coordinate system respects scalings. What emerges by doing so is indexed $x,y\in \mathbb{R}$ $s,t\in ...

Abstract We consider properties of semi-classical orthogonal polynomials with respect to the generalised Airy weight ω <mml:mo stret...

Let jν,k denote the k-th positive zero of the Bessel function Jν(x). In this paper, we prove that for ν > 0 and k = 1, 2, 3, . . . , ν − ak 21/3 ν < jν,k < ν − ak 21/3 ν + 3 20 ak 21/3 ν1/3 . These bounds coincide with the first few terms of the well-known asymptotic expansion jν,k ∼ ν − ak 21/3 ν + 3 20 ak 21/3 ν1/3 + · · · as ν →∞, k being fixed, where ak is the k-th negative zero of the Airy...

An analytical method to find the flow generated by the basic singularities of Stokes flow in a wedge of arbitrary angle is presented. Specifically, we solve a biharmonic equation for the stream function of the flow generated by a point stresslet singularity and satisfying no-slip boundary conditions on the two walls of the wedge. The method, which is readily adapted to any other singularity typ...