A two-dimensional analytical solution is presented for stresses and displacements in an elastic curved beam forming incomplete ring frictionless unbonded contact with a rigid pin loaded by point force the presence of clearance. The circular modeled as thick ring, constrained at both ends plane stress state. displacement fields within are derived from biharmonic Airy function, according to Miche...

We investigate the asymptotic behaviour of the second-order correlation function of the characteristic polynomial of a Hermitian Wigner matrix at the edge of the spectrum. We show that the suitably rescaled second-order correlation function is asymptotically given by the Airy kernel, thereby generalizing the well-known result for the Gaussian Unitary Ensemble (GUE). Moreover, we obtain similar ...

We analyse new data for self-avoiding polygons (SAPs), on the square and triangular lattices, enumerated by both perimeter and area, providing evidence that the scaling function is the logarithm of an Airy function. The results imply universal amplitude combinations for all area moments and suggest that rooted SAPs may satisfy a q-algebraic functional equation. PACS numbers: 05.50+q, 02.10.AB, ...

We employ the Airy stress function to derive analytical solutions for plane strain static deformations of a functionally graded (FG) hollow circular cylinder with Young’s modulus E and Poisson’s ratio v taken to be functions of the radius r . For E1 and v1 power law functions of r , and for E1 an exponential but v1 an affine function of r , we derive explicit expressions for stresses and displa...

the major reason for the prediction of thermodynamic properties of mercury lies in the fact that itsintermolecular interactions highly depend on temperature and density. internal pressure is a good criterion toinvestigate the density dependence of the interatomic interactions. because its physical base is a forcetending to close together the molecules that is intermolecular interactions, and as...

We report a high power ultrafast Airy beam source producing femtosecond pulses at multi-gigahertz (GHz) repetition rate (RR). Based on intra-cavity cubic phase modulation of an optical parametric oscillator (OPO) designed in high harmonic cavity configuration synchronous to a femtosecond Yb-fiber laser operating at 78 MHz, we have produced ultrafast 2D Airy beam at multi-GHz repetition rate thr...

The Airy process τ → Aτ is characterized by its finite-dimensional distribution functions Pr (Aτ1 < ξ1, . . . , Aτm < ξm) . For m = 1 it is known that Pr (Aτ < ξ) is expressible in terms of a solution to Painlevé II. We show that each finite-dimensional distribution function is expressible in terms of a solution to a system of differential equations.

Computer algebra algorithms are developed for evaluating the coefficients in Airy-type asymptotic expansions that are obtained from integrals with a large parameter. The coefficients are defined from recursive schemes obtained from integration by parts. An application is given for the Weber parabolic cylinder function. 1991 Mathematics Subject Classification: 41A60, 33C10, 33C15, 33F05, 65D20.

ABSTRACT Modified Airy Function (MAF) method gives an approximate solution of the wave equation for planar waveguides with an arbitrary refractive index distribution. Unlike WKB method, the MAF solution does not diverge at the turning points and there is no need of connection formulae. Comparison with exact results for practical wave guides show that the errors in MAF solutions are small. Use o...

Graphene bilayers exhibit zero-energy flat bands at a discrete series of magic twist angles. In the absence intra-sublattice inter-layer hopping, states satisfy Dirac equation with non-abelian SU(2) gauge potential that cannot be diagonalized globally. We develop semiclassical WKB approximation scheme for this by introducing dimensionless Planck's constant proportional to angle, solving lineari...