John W. Miles

Bio: John W. Miles is an academic researcher. The author has contributed to research in topics: Integral transform. The author has an hindex of 1, co-authored 1 publications receiving 21 citations.

Sumudu transform and the solution of integral equation of convolution type

Abstract: The convolution theorem for the Sumudu transform of a function which can be expressed as a polynomial or a convergent infinite series is proved and its applicability demonstrated in solving convolution type integral equations.

Application of Sumudu transform to partial differential equations

Abstract: The Sumudu transform of partial derivatives is derived, and its applicability demonstrated using three different partial differential equations.

Further Properties of the Sumudu Transform and Its Applications.

Abstract: This note discusses the general properties of the Sumudu transform and the Sumudu transform of special functions. For any function f (t) with corresponding Sumudu transform F (u), the effect of shifting the parameter t in f (t) by τ on the Sumudu transform F (u) is found. Also obtained are the effect of the multiplication of any function f (t) by a power of t and the division of the function f (t) by t on the Sumudu transform F (u). For any periodic function f (t) with periodicity T > 0 the Sumudu transform is easily derived. Illustrations are provided with Abel's integral equation, an integro-differential equation, a dynamic system with delayed time signals and a differential dynamic system.

Stagnation points and bifurcation in 3‐D mountain airflow

Abstract: The effect of non-linearity on the formation of mountain-wave induced stagnation points is examined using the scaling laws for ideal hydrostatic flow and a series of runs with decelerating winds in a numerical model. In the limit of small deceleration rate (i.e., near steady state) runs with a variety of mountain heights and widths give similar results; i.e., the speed extrema values in the 3-D wave fields collapse onto “universal curves”. For a Gaussian hill with circular contours, stagnation first occurs at a point above the lee slope. This result contradicts the result of linear theory that stagnation begins on the windward slope. The critical value of ĥfor stagnation above a Gaussian hill is ĥ crit = 1.1 ± 0.1. For a 3/2-power hill, the critical height is slightly higher, ĥ crit = 1.2 ± 0.2. These values are significantly larger than the value for a ridge (ĥ crit = 0.85), due to dispersion of wave energy aloft. The application of Sheppard's rule and the vorticity near the stagnation point are discussed. As expected from linear theory, the presence of positive windshear suppresses stagnation aloft. With Richardson number = 20 for example, stagnation first begins at the ground at a value of ĥ= 1.6 ± 0.2. When a stagnation point first forms aloft in the unsheared case, the flow field begins to evolve in the time domain and the scaling laws are violated. We interpret these events as a wave-breaking induced bifurcation which leads to stagnation on the windward slope and the formation of a wake. DOI: 10.1034/j.1600-0870.1993.00003.x

Transient bending waves in plates studied by hologram interferometry

Abstract: Propagating bending waves are studied in plates made of aluminum and wood. The waves are generated by the impact of a ballistic pendulum. Hologram interferometry, with a double pulsed ruby laser as the light source, is used to record the out of plane motion of the waves. Elliptic-like fringes visualize differences in wave speed for different directions in the anisotropic plate and circular ones are obtained for the isotropic plate. The experimental data for the isotropic plate compare favorably with analytical results derived from the Kirchhoff-plate equation with a point impact of finite duration. A similarity variable is found when starting conditions are modeled as a Dirac pulse in space and time, that brings new understanding to the importance of specific parameters for wave propagation in plates. A formal solution is obtained for a point force with an arbitrary time dependence. For times much larger than the contact time, the plate deflection is shown to be identical to that from a Dirac pulse applied at the mean contact time. A method for determining material parameters, and the mean contact time, from the interferograms is hence developed.