arXiv subjects

J. L. Aragon

Publications and source records attributed to J. L. Aragon.

5 recordsLinked to original sources

arXiv2018

Clifford Algebra with Mathematica

The Clifford algebra of a n-dimensional Euclidean vector space provides a general language comprising vectors, complex numbers, quaternions, Grassman algebra, Pauli and Dirac matrices. In this work, we present an introduction to the main ideas of Clifford algebra, with the main goal to develop a package for Clifford algebra calculations for the computer algebra program Mathematica. The Clifford algebra package is thus a powerful tool since it allows the manipulation of all Clifford mathematical objects. The package also provides a visualization tool for elements of Clifford Algebra in the 3-dimensional space. clifford.m is available from github.com/jlaragonvera/Geometric-Algebra

math-ph↗

arXiv2007

Strong far field coherent scattering of ultraviolet radiation by holococcolithophores

By considering the structure of holococcoliths (calcite plates that cover holococcolithophores, a haploid phase of the coccolithophore life cycle) as a photonic structure, we apply a discrete dipolar approximation to study the light backscattering properties of these algae. We show that some holococcolith structures have the ability to scatter the ultraviolet (UV) radiation. This property may represent an advantage for holococcolithophores possessing it, by allowing them to live higher in the water column than other coccolithophores.

physics.bio-ph↗

arXiv2007

Conformal mapping of ultrasonic crystals: confining ultrasound and cochlear-like wave guiding

Conformal mapping of a slab of a two-dimensional ultrasonic crystal generate a closed geometrical arrangement of ultrasonic scatterers with appealing acoustic properties. This acoustic shell is able to confine ultrasonic modes. Some of these internal resonances can be induced from an external wave source. The mapping of a linear defect produces a wave-guide that exhibits a spatial-frequency selection analogous to that characteristic of a synthetic "cochlea". Both, experimental and theoretical results are reported here.

physics.flu-dyn↗

arXiv2005

Confinement of hydrodynamic modes on a free surface and their quantum analogs

A subtle procedure to confine hydrodynamic modes on the free surface of a fluid is presented here. The experiment consists of a square vessel with an immersed square central well vibrating vertically so that the surface waves generated by the meniscus at the vessel boundary interfere with the bound states of the well. This is a classical analogy of a quantum well where some fundamental phenomena, such as bonding of states and interference between free waves and bound states, can be visualized and controlled. The above mentioned interference leads to a novel hydrodynamic transition from quasiperiodic to periodic patterns. Tight binding numerical calculations are performed here to show that our results could be transferred to design quantum confinements exhibiting electronic quasiperiodic surface states and their rational approximants for the first time.

physics.flu-dyn↗

arXiv2002

Quasiperiodic extended Bloch states in a surface wave experiment

Bloch-like surface waves associated with a quasiperiodic structure are observed for the first time in a classic wave propagation experiment which consists of pulse propagation with a shallow fluid covering a quasiperiodically drilled bottom. We show that a transversal pulse propagates as a plane wave with quasiperiodic modulation, displaying the characteristic undulatory propagation in this quasiperiodic systems and reinforcing the idea that analogous concepts to Bloch functions can be applied to quasicrystals under certain circumstances.

cond-mat.mtrl-sci↗