Image-based blood flow estimation using a semi-analytical solution to the advection–diffusion equation in cylindrical domains

Instantaneous Bethe–salpeter Equation: (semi-)analytical Solution

The Bethe–Salpeter equation for bound states of a fermion–antifermion pair in the instantaneous approximation for the involved interaction kernel is converted into an equivalent matrix eigenvalue problem with explicitly (algebraically) given matrices. PACS numbers : 11.10.St, 03.65.Ge ∗ E-mail address : [email protected] ‡ E-mail address : [email protected] † E-mail address : franz.schoebe...

An Analytical Solution of the Generalized Equation of Energy Transport in One-dimensional Semi-infinite Domains

This paper presents an integral solution of the generalized one-dimensional equation of energy transport with the convective term. The solution of the problem has been achieved by the use of a novel technique that involves generalized derivatives (in particular, derivatives of noninteger orders). Confluent hypergeometric functions, known as Whittaker’s functions, appear in the course of the sol...

A Semi-Analytical Method for the Solution of Helmholtz Equation

This note is concerned with a semi-analytical method for the solution of 2-D Helmholtz equation in unit square. The method uses orthogonal functions to project the problem down to finite dimensional space. After the projection, the problem simplifies to that of obtaining solutions for second order constant coefficient differential equations which can be done analytically. Numerical results indi...

Semi-analytical Solution of Dirac equation in Schwarzschild Geometry

A Semi-analytical Solution for Flexural Vibration of Micro Beams Based on the Strain Gradient Theory

In this paper, the flexural free vibrations of three dimensional micro beams are investigated based on strain gradient theory. The most general form of the strain gradient theory which contains five higher-order material constants has been applied to the micro beam to take the small-scale effects into account. Having considered the Euler-Bernoulli beam model, governing equations of motion are w...