Search

In this paper, we deal with the existence and multiplicity of solutions for perturbed Schrödinger equation with electromagnetic fields and critical nonlinearity in RN: -ε²ΔAu(x) + V(x)u(x) = |u|2*-2u + h(x, |u|²)u for all x ∈ RN, where ∇Au(x) := (∇ + iA(x))u, V(x) is a nonnegative potential. By using Lions' second concentration compactness principle and concentration compactness principle at infinity to prove that the (PS)c condition holds locally and by variational method, we show that this equation has at least one solution provided that ε < ε, for any m ∈ N, it has m pairs of solutions if ε < εm, where ε and εm are sufficiently small positive numbers. [ABSTRACT FROM AUTHOR]

This paper focuses on mathematical models describing the mechanical behavior of ferromagnetic materials under magnetization. Through combination of the electromagnetic field theory with the theory of elastic mechanics, several nonlinear systems of fourth-order partial differential equations were deduced. By making further assumption, the first-order approximation of the above equations was established, of which the solutions are good enough for engineering application. [ABSTRACT FROM AUTHOR]

In this paper, we deal with the existence and multiplicity of solutions for perturbed Schrödinger equation with electromagnetic fields and critical nonlinearity in RN: -ε²ΔAu(x) + V(x)u(x) = |u|2*-2u + h(x, |u|²)u for all x ∈ RN, where ∇Au(x) := (∇ + iA(x))u, V(x) is a nonnegative potential. By using Lions' second concentration compactness principle and concentration compactness principle at infinity to prove that the (PS)c condition holds locally and by variational method, we show that this equation has at least one solution provided that ε < ε, for any m ∈ N, it has m pairs of solutions if ε < εm, where ε and εm are sufficiently small positive numbers. [ABSTRACT FROM AUTHOR]

A transient three-dimensional coupled numerical model has been established to clarify the influence of the external transverse static magnetic field (TSMF) on droplet evolution behaviors during the electroslag remelting (ESR) process with an alternating current (50 Hz). The development of the electromagnetic field code and the calculation procedure showed that the periodic inverse Lorentz force (50 Hz) could be fully coupled with the volume of fluid model in each iteration when an external TSMF of 0.05 T is superimposed. The droplet evolution behaviors with and without the external TSMF were demonstrated and analyzed. The numerical results showed that the huge periodic inverse Lorentz force could smash the droplet neck into numerous smaller droplets during the ESR process with the external TSMF; simultaneously, the interfacial area and falling time could be increased, indicating that the purification efficiency could be expected to improve. [ABSTRACT FROM AUTHOR]

A micromorphic continuum model is exploited to derive the governing equations for the electromagnetoelastic field superposed to a ferroelectric configuration of polarizable dielectrics. The microcontinuum structure accounts for charge microdensity to obtain dipole and quadrupole densities and their evolution equations. These quantities enter as arguments of the constitutive tensors, besides the microstrain measures. A strain-free polarized initial state is considered, and a set of non-linear equations is derived for the superposed field. These equations are linearized to show a simple relation between microstrain and incremental polarization. The case of micropolar continua is analyzed to compare the present model with the formulation of the same problem, obtained in the past on the basis of a continuum theory of electrodynamics. [ABSTRACT FROM AUTHOR]

A technique is proposed for mathematical and numerical modeling of thermomechanical processes in electrically conductive bodies subjected to an external electromagnetic field. The initial relations for the determination of the electromagnetic field are the Maxwell equations. The stress and strain states of the body are described using the equations of nonisothermal elastoplasticity. The model takes into account the coupling of the electromagnetic and thermal fields. All physical and mechanical parameters of the material depend on temperature. The process of high-temperature induction treatment of a ferromagnetic cylinder is considered as an example [ABSTRACT FROM AUTHOR]