The theory of complex variables is used to solve analytically the transcendental equation which defines the position, as a function of time, in an inverse-distance-squared force field, and thereby the desired solution is reduced to elementary quadrature.

An analytical solution is developed to quantify a site-specific fluorophore lifetime perturbation that occurs, for example, when the local metabolic status is different from that of surrounding tissue. This solution may be used when fluorophores are distributed throughout a highly turbid media and the site of interest is embedded many mean scattering distances from the source and the detector. ...

A generalized harmonic balance method is used to calculate the periodic solutions of a nonlinear oscillator with discontinuities for which the elastic force term is proportional to sgn(x). This method is a modification of the generalized harmonic balance method in which analytical approximate solutions have rational form. This approach gives us not only a truly periodic solution but also the fr...

Treating a boundary value problem in analytical fluid dynamics, translation of 2D steady Navier-Stokes equations to ordinary differential form leads to a second order equation of Riccati type. In the case of a compressible fluid with constant kinematic viscosity along streamlines, it is possible to find an exact solution of the differential problem by rational combination of Airy’s functions an...

Micro channel gas flows are of importance in a range Micro Electro Mechanical Systems (MEMS). Due to the confined geometry of the channel, the mean free path of the gas can be comparable to the characteristic length of the micro channel, leading to slip-like flow behavior and strong diffusion-enhanced transport of mass and momentum. The Extended Navier Stokes Equations (ENSE) have successfully ...

We construct the solutions to the strong shock wave problem with generalized geometries in nonideal magnetogasdynamics. Here, it is assumed that the density ahead of the shock front varies according to a power of distance from the source of the disturbance. Also, an analytical expression for the total energy carried by the wavemotion in non-ideal medium under the influence of magnetic field is ...

Exact analytical solutions of boundary layer flows along a vertical porous plate with uniform suction are derived and presented in this paper. The solutions concern the Blasius, Sakiadis, and Blasius-Sakiadis flows with buoyancy forces combined with either MHD Lorentz or EMHD Lorentz forces. In addition, some exact solutions are presented specifically for water in the temperature range of 0◦C ≤...

In this paper we will study the non-linear oscillation of a conservative system having inertia and static non-linearities. By combining the linearization of the governing equation with the method of harmonic balance, we investigate analytical approximate solutions for the non-linear oscillations of the system. Unlike the classical harmonic balance method, linearization is performed prior to pro...

Presented in this paper is a rigorous solution of the conventional Terzaghi one-dimensional consolidation under haversine cyclic loading with any rest period. The clay deposit is either permeable at both top and bottom or permeable at the top and impermeable at the bottom. This exact analytical solution was achieved using Fourier harmonic analysis for the periodic function representing the rate...