in this paper, we present an efficient method for determining the solution of the stochastic second kind volterra integral equations (svie) by using the taylor expansion method. this method transforms the svie to a linear stochastic ordinary differential equation which needs specified boundary conditions. for determining boundary conditions, we use the integration technique. this technique give...

3 The permittivity of space-time is a metric on u(1). 8 3.1 Electrostatics. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8 3.1.1 The electric field. . . . . . . . . . . . . . . . . . . . . . . . 8 3.1.2 The dielectric displacement. . . . . . . . . . . . . . . . . . 8 3.1.3 The dielectric operator and the dielectric coefficient. . . . 9 3.1.4 The dielectric coefficient. . . . . . . ...

The problem of Bloch electrons in two dimensions subject to magnetic and intense electric fields is investigated. Magnetic translations, electric evolution and energy translation operators are used to specify the solutions of the Schrödinger equation. For rational values of the magnetic flux quanta per unit cell and commensurate orientations of the electric field relative to the original lattic...

in this paper, numerical investigation of a flat passive micromixer with heterogeneous surface properties that the flow through it, is driven by the electroosmotic flow have been presented. the governing equations, which consist of a laplace equation for the distribution of external electric potential, a poisson equation for the distribution of electric double layer potential, modified navier-s...

The four most important factors that govern the return stroke evolution can be identified as: (i) electric field due to charge distributed along the channel, (ii) transient enhancement of conductance by several orders at the bridging regime (iii) the non-linear increase in channel conductance at the propagating current front and (iv) the associated dynamic electromagnetic field which support th...

In this paper atmospheric electric field distribution is determined in the vicinity of the Franklin’s lightning protection rod top which is modeled by half-spherical ending. Special emphasis is given to determination of critical atmospheric electric field that leads to break-down at the top of the rod. For the values of external atmospheric electric field that overcome critical value at the rod...