Search results for "Helmholtz"

Negative thermal expansion of quartz glass at low temperatures: An ab initio simulation study

2017

Abstract Using a mixed classical Molecular dynamics (MD)/ab initio simulation scheme combined with a quasi-harmonic approximation, we calculate the linear thermal expansion coefficient αL(T) in vitreous silica glasses. The systems are first cooled down by classical MD simulations. Then they are structurally relaxed by ab initio DFT calculations. The vibrational properties are calculated employing the frozen phonon method, and these results are finally used to calculate the Helmholtz free energy as a function of volume. In agreement with experiments, our simulations predict that αL(T) is negative at low temperatures up to T ≈ 150 K. In this low-temperature regime, the simulation results are …

On a topology optimization problem governed by two-dimensional Helmholtz equation

2015

The paper deals with a class of shape/topology optimization problems governed by the Helmholtz equation in 2D. To guarantee the existence of minimizers, the relaxation is necessary. Two numerical methods for solving such problems are proposed and theoretically justified: a direct discretization of the relaxed formulation and a level set parametrization of shapes by means of radial basis functions. Numerical experiments are given.

Integration of finite displacement interface element in reference and current configurations

2017

In the present paper the non-linear behaviour of a solid body with embedded cohesive interfaces is examined in a finite displacements context. The principal target is the formulation of a two dimensional interface finite element which is referred to a local reference frame, defined by normal and tangential unit vectors to the interface middle surface. All the geometric operators, such as the interface elongation and the reference frame, are computed as function of the actual nodal displacements. The constitutive cohesive law is defined in terms of Helmholtz free energy for unit undeformed interface surface and, in order to obtain the same nodal force vector and stiffness matrix by the two i…

Accurate expansion of cylindrical paraxial waves for its straightforward implementation in electromagnetic scattering

2017

Abstract The evaluation of vector wave fields can be accurately performed by means of diffraction integrals, differential equations and also series expansions. In this paper, a Bessel series expansion which basis relies on the exact solution of the Helmholtz equation in cylindrical coordinates is theoretically developed for the straightforward yet accurate description of low-numerical-aperture focal waves. The validity of this approach is confirmed by explicit application to Gaussian beams and apertured focused fields in the paraxial regime. Finally we discuss how our procedure can be favorably implemented in scattering problems.

Damage and plasticity at the interfaces in composite materials and structures

2009

Abstract The structural behavior at the interface between two surfaces of ductile, brittle or quasi-brittle materials is studied by a new analytical elastoplastic damaging model. The model is developed in the framework of a thermodynamically consistent theory. The Helmholtz free energy is written to predict the materials’ hardening or softening. An isotropic damage is considered and the possible effects of dilatancy are taken into account including non-associative flow rules. The interface laws are presented both in a rate and a discrete incremental form. The analytical formulation is then implemented into a finite element code and two structural members are studied to validate the model. T…

Controllability method for acoustic scattering with spectral elements

2007

We formulate the Helmholtz equation as an exact controllability problem for the time-dependent wave equation. The problem is then discretized in time domain with central finite difference scheme and in space domain with spectral elements. This approach leads to high accuracy in spatial discretization. Moreover, the spectral element method results in diagonal mass matrices, which makes the time integration of the wave equation highly efficient. After discretization, the exact controllability problem is reformulated as a least-squares problem, which is solved by the conjugate gradient method. We illustrate the method with some numerical experiments, which demonstrate the significant improveme…

A RADIATION CONDITION FOR UNIQUENESS IN A WAVE PROPAGATION PROBLEM FOR 2-D OPEN WAVEGUIDES

2009

We study the uniqueness of solutions of Helmholtz equation for a problem that concerns wave propagation in waveguides. The classical radiation condition does not apply to our problem because the inhomogeneity of the index of refraction extends to infinity in one direction. Also, because of the presence of a waveguide, some waves propagate in one direction with different propagation constants and without decaying in amplitude. Our main result provides an explicit condition for uniqueness which takes into account the physically significant components, corresponding to guided and non-guided waves; this condition reduces to the classical Sommerfeld-Rellich condition in the relevant cases. Final…

A method of variation of boundaries for waveguide grating couplers

2008

We describe a method for calculating the solution of the electromagnetic field in a non-rectilinear open waveguide by using a series expansion, starting from the field of a rectilinear waveguide. Our approach is based on a method of variation of boundaries. We prove that the obtained series expansion converges and we provide a radiation condition at infinity in such a way that the problem has a unique solution. Our approach can model several kinds of optical devices which are used in optical integrated circuits. Numerical examples will be shown for the case of finite aperiodic waveguide grating couplers.

Wave propagation in non rectilinear waveguides

2005

We present a mathematical framework for studying the problem of electromagnetic wave propagation in a 2-D or 3-D optical waveguide (optical fiber). We will consider both the case of a rectilinear waveguide and the one of a waveguide presenting imperfections, with applications to phenomenons of physical interest. Numerical examples will be given.

Measurements of aerosol size distributions with a pocket counter with variable expansion ratio

2008