39,923 research outputs found
Computation of the Modes of Elliptic Waveguides with a Curvilinear 2D Frequency-Domain Finite-Difference Approach
A scalar Frequency-Domain Finite-Difference approach to the mode computation of elliptic waveguides is presented. The use of an elliptic cylindrical grid allows us to take exactly into account the curved boundary of the structure and a single mesh has been used both for TE and TM modes. As a consequence, a high accuracy is obtained with a reduced computational burden, since the resulting matrix is highly sparse
Semi-analytic method for slow light photonic crystal waveguide design
We present a semi-analytic method to calculate the dispersion curves and the
group velocity of photonic crystal waveguide modes in two-dimensional
geometries. We model the waveguide as a homogenous strip, surrounded by
photonic crystal acting as diffracting mirrors. Following conventional
guided-wave optics, the properties of the photonic crystal waveguide may be
calculated from the phase upon propagation over the strip and the phase upon
reflection. The cases of interest require a theory including the specular order
and one other diffracted reflected order. The computational advantages let us
scan a large parameter space, allowing us to find novel types of solutions.Comment: Accepted by Photonics and Nanostructures - Fundamentals and
Application
A dissipative algorithm for wave-like equations in the characteristic formulation
We present a dissipative algorithm for solving nonlinear wave-like equations
when the initial data is specified on characteristic surfaces. The dissipative
properties built in this algorithm make it particularly useful when studying
the highly nonlinear regime where previous methods have failed to give a stable
evolution in three dimensions. The algorithm presented in this work is directly
applicable to hyperbolic systems proper of Electromagnetism, Yang-Mills and
General Relativity theories. We carry out an analysis of the stability of the
algorithm and test its properties with linear waves propagating on a Minkowski
background and the scattering off a Scwharszchild black hole in General
Relativity.Comment: 23 pages, 7 figure
Residual-based stabilization of the finite element approximation to the acoustic perturbation equations for low Mach number aeroacoustics
This is the peer reviewed version of the following article: [Guasch, O., Sánchez-Martín, P., Pont, A., Baiges, J., and Codina, R. (2016) Residual-based stabilization of the finite element approximation to the acoustic perturbation equations for low Mach number aeroacoustics. Int. J. Numer. Meth. Fluids, 82: 839–857. doi: 10.1002/fld.4243], which has been published in final form at http://onlinelibrary.wiley.com/doi/10.1002/fld.4243/abstract. This article may be used for non-commercial purposes in accordance with Wiley Terms and Conditions for Self-Archiving.The acoustic perturbation equations (APE) are suitable to predict aerodynamic noise in the presence of a non-uniform mean flow. As for any hybrid computational aeroacoustics approach, a first computational fluid dynamics simulation is carried out from which the mean flow characteristics and acoustic sources are obtained. In a second step, the APE are solved to get the acoustic pressure and particle velocity fields. However, resorting to the finite element method (FEM) for that purpose is not straightforward. Whereas mixed finite elements satisfying an appropriate inf–sup compatibility condition can be built in the case of no mean flow, that is, for the standard wave equation in mixed form, these are difficult to implement and their good performance is yet to be checked for more complex wave operators. As a consequence, strong simplifying assumptions are usually considered when solving the APE with FEM. It is possible to avoid them by resorting to stabilized formulations. In this work, a residual-based stabilized FEM is presented for the APE at low Mach numbers, which allows one to deal with the APE convective and reaction terms in its full extent. The key of the approach resides in the design of the matrix of stabilization parameters. The performance of the formulation and the contributions of the different terms in the equations are tested for an acoustic pulse propagating in sheared-solenoidal mean flow, and for the aeolian tone generated by flow past a two-dimensional cylinder.Peer ReviewedPostprint (author's final draft
Static non-reciprocity in mechanical metamaterials
Reciprocity is a fundamental principle governing various physical systems,
which ensures that the transfer function between any two points in space is
identical, regardless of geometrical or material asymmetries. Breaking this
transmission symmetry offers enhanced control over signal transport, isolation
and source protection. So far, devices that break reciprocity have been mostly
considered in dynamic systems, for electromagnetic, acoustic and mechanical
wave propagation associated with spatio-temporal variations. Here we show that
it is possible to strongly break reciprocity in static systems, realizing
mechanical metamaterials that, by combining large nonlinearities with suitable
geometrical asymmetries, and possibly topological features, exhibit vastly
different output displacements under excitation from different sides, as well
as one-way displacement amplification. In addition to extending non-reciprocity
and isolation to statics, our work sheds new light on the understanding of
energy propagation in non-linear materials with asymmetric crystalline
structures and topological properties, opening avenues for energy absorption,
conversion and harvesting, soft robotics, prosthetics and optomechanics.Comment: 19 pages, 3 figures, Supplementary information (11 pages and 5
figures
Adaptive Energy Preserving Methods for Partial Differential Equations
A method for constructing first integral preserving numerical schemes for
time-dependent partial differential equations on non-uniform grids is
presented. The method can be used with both finite difference and partition of
unity approaches, thereby also including finite element approaches. The schemes
are then extended to accommodate -, - and -adaptivity. The method is
applied to the Korteweg-de Vries equation and the Sine-Gordon equation and
results from numerical experiments are presented.Comment: 27 pages; some changes to notation and figure
Interaction for the trapped fermi gas from a unitary transformation of the exact two-body spectrum
We study systems of few two-component fermions interacting in a Harmonic
Oscillator trap. The fermion-fermion interaction is generated in a finite basis
with a unitary transformation of the exact two-body spectrum given by the Busch
formula. The few-body Schr\"odinger equation is solved with the formalism of
the No-Core Shell Model. We present results for a system of three fermions
interacting at unitarity as well as for finite values of the S-wave scattering
length and effective range . Unitary systems with four and five
fermions are also considered. We show that the many-body energies obtained in
this approach are in excellent agreement with exact solutions for the
three-body problem, and results obtained by other methods in the other cases.Comment: 9 pages, 6 figures. Accepted for publication in Eur. Phys. J.
- …