We develop a selfconsistent solution of the Schrödinger and Poisson equations in semiconductor heterostructures with arbitrary doping profiles and layer geometries. An algorithm for this nonlinear problem is presented in a multiband k ·P framework for the electronic band structure using the finite element method. The discretized functional integrals associated with the Schrödinger and Poisson e...

We study the dynamical equations of nonlinear inductor-capacitor circuits. We present a novel Lagrangian description of the dynamics and provide a variational interpretation, which is based on the maximum principle of optimal control theory. This gives rise to an alternative method for deriving the dynamic equations. We show how this generalized Lagrangian description is related to generalized ...

The calculus of variations is an important tool in the study of boundary value problems for differential systems. A development of this approach, called the control variational method, is based on the use of the optimal control theory, especially of the Pontryagin maximum principle. In this presentation, we review the results established in the literature on the control variational method and i...

In this paper, a numerical solution based on Haar wavelet quasilinearization (HWQ) is used for finding the solution of nonlinear Euler-Lagrange equations which arise from the problems in calculus of variations. Some examples of variational problems are given and outcomes compared with exact solutions to demonstrate the accuracy and efficiency of the method.

 (i) ∂v ∂t + divx (v ⊗ v) +∇xp = ν∆xv + f ∀(x, t) ∈ Ω× (0, T ) , (ii) divx v = 0 ∀(x, t) ∈ Ω× (0, T ) , (iii) v = 0 ∀(x, t) ∈ ∂Ω × (0, T ) , (iv) v(x, 0) = v0(x) ∀x ∈ Ω . Here v = v(x, t) : Ω× (0, T ) → R is an unknown velocity, p = p(x, t) : Ω× (0, T ) → R is an unknown pressure, associated with v, ν > 0 is a given constant viscosity, f : Ω× (0, T ) → R is a given force field and v0 : Ω → R N...