The sequential regularization method is a reformulation of the unsteady Navier– Stokes equations from the viewpoint of constrained dynamical systems or the approximate Helmholtz– Hodge projection. In this paper we study the long time behavior of the sequential regularization formulation. We give a uniform-in-time estimate between the solution of the reformulated system and that of the Navier–St...

Abstract-In this work, cut-off frequencies of propagation of electromagnetic waves in a hexagonal waveguide are calculated using twodimensional (2-D) finite element method. The numerical approach is a standard one and involves six finite elements. A new type of hexagonal waveguide structure for the simple homogeneous dielectric case has been considered. The starting point is Maxwell’s equations...

background : effects of electromagnetic fields on healing have been investigated for centuries. substantial data indicates that exposure to electromagnetic field can lead to enhanced healing in both soft and hard tissues. helmholtz coil is a device that generates pulsed electromagnetic fields. objective : in this study, a pair of helmholtz coils for enhancing the healing process in periodontiti...

We study the time-harmonic Galbrun equation describing propagation of sound in presence a steady background flow. With additional rotational and gravitational terms these equations are also fundamental helio- asteroseismology as model for stellar oscillations. For simple damping we prove well-posedness equations, i.e., uniqueness, existence, stability solutions under mild conditions on paramete...

We derive and analyze new boundary element (BE) based finite element discretizations of potential-type, Helmholtz and Maxwell equations on arbitrary polygonal and polyhedral meshes. The starting point of this discretization technique is the symmetric BE Domain Decomposition Method (DDM), where the subdomains are the finite elements. This can be interpreted as a local Trefftz method that uses PD...

Sound waves along a rigid axisymmetric tube with a variable cross-section are considered. The governing Helmholtz equation is solved using power-series expansions in a stretched radial coordinate, leading to a hierarchy of one-dimensional ordinary differential equations in the longitudinal direction. The lowest approximation for axisymmetric motion turns out to be Webster’s horn equation. Fourt...

Acoustic waves in a rigid axisymmetric tube with a variable cross-section are considered. The governing Helmholtz equation is solved using Neumann series (expansions in Bessel functions of various orders) with a stretched radial coordinate, leading to a hierarchy of one-dimensional ordinary differential equations in the longitudinal direction. The lowest approximation for axisymmetric motion in...

In this paper, we consider near cloaking for the full Maxwell equations. We extend the method of [5, 6], where the quasi-static limit case and the Helmholtz equation are considered, to electromagnetic scattering problems. We construct very effective near cloaking structures for the electromagnetic scattering problem at a fixed frequency. These new structures are, before using the transformation...

We investigate the dispersive properties of evolution equations on waveguides with a non flat shape. More precisely we consider an operator H = −∆x −∆y + V (x, y) with Dirichled boundary condition on an unbounded domain Ω, and we introduce the notion of a repulsive waveguide along the direction of the first group of variables x. If Ω is a repulsive waveguide, we prove a sharp estimate for the H...

Abstract. We investigate the use of compactly supported divergence-free wavelets for the representation of solutions of the Navier-Stokes equations. After reviewing the theoretical construction of divergence-free wavelet vectors, we present in detail the bases and corresponding fast algorithms for two and three-dimensional incompressible flows. We also propose a new method to practically comput...