This paper discusses light propagation in N-layered turbid media. The hybrid diffusion-P3 equation is solved for an N-layered finite or infinite turbid medium in the steady-state domain for one point source using the extrapolated boundary condition. The Fourier transform formalism is applied to derive the analytical solutions of the fluence rate in Fourier space. Two inverse Fourier transform m...

Two-dimensional magnetic skyrmions are particle-like domains in thin films. The kinetic property of at finite temperature is well described by the Thiele equation, including a stochastic field and mass. This study examines validity constant-mass approximation comparing Fourier spectrum Brownian motions equation Landau–Lifshitz–Gilbert equation. Then, expression diffusion flow derived from four-...

where Î denotes the Fourier transform, and ω denotes frequency. Proof 1 Taking the Fourier transform of the Heat Equation: { ∂tu(t, x) = ∆u(t, x) x ∈ R u(0, x) = I(x) t = 0 yields: ∂tû(t, ω) = (iω) · (iω)û(t, ω) = −|ω|û(t, ω), where û(t, ω) is the Fourier transform of u. Solving this differential equation yields û(t, ω) = e−|ω| 2tÎ(ω). We note that a = 0 when I ∈ L since Î(0) = ∫ R2 I(x) dx is ...

In this paper, to solve a linear one-dimensional Volterra  integral equation of the second kind. For this purpose using the equation form, we have defined a linear transformation and by using it's conjugate and reproducing kernel functions, we obtain a basis for the functions space.Then we obtain the solution of  integral equation in terms of the basis functions. The examples presented in this ...

We adapt methodology of statistical mechanics and quantum field theory to approximate solutions to an arbitrary order ordinary differential equation boundary value problem by a second-order equation. In particular, we study equations involving the derivative of a double-well potential such as u− u3 or − u + 2u3. Using momentum (Fourier) space variables we average over short length scales and de...

ABSTRACT In this paper, we propose a new numerical method for solving a rib waveguide TE-mode problem. In the proposed method, the cross-section of the waveguide is divided into several regions and the refractive index profile and field distribution in each region are expanded into Fourier cosine series, and then are substituted in the wave equation. A second-order differential matrix equation ...

In this paper, we derive a multi-symplectic Fourier pseudospectral scheme for the Kawahara equation with special attention to the relationship between the spectral differentiationmatrix and discrete Fourier transform. The relationship is crucial for implementing the scheme efficiently. By using the relationship, we can apply the Fast Fourier transform to solve the Kawahara equation. The effecti...