Patterns in high-frequency FX data: Discovery of 12 empirical scaling laws

We have discovered 12 independent new empirical scaling laws in foreign exchange data-series that hold for close to three orders of magnitude and across 13 currency exchange rates. Our statistical analysis crucially depends on an event-based approach that measures the relationship between different types of events. The scaling laws give an accurate estimation of the length of the price-curve coastline, which turns out to be surprisingly long. The new laws substantially extend the catalogue of stylised facts and sharply constrain the space of possible theoretical explanations of the market mechanisms.

Fabrication and spectral characterization of the porous dielectric THz waveguides using microstructured molding technique

We report two novel fabrication techniques, as well as spectral transmission and propagation loss measurements of the subwavelength plastic wires with highly porous (up to 86%) and non-porous transverse geometries. The two fabrication techniques we describe are based on the microstructured molding approach. In one technique the mold is made completely from silica by stacking and fusing silica capillaries to the bottom of a silica ampoule. The melted material is then poured into the silica mold to cast the microstructured preform. Another approach uses microstructured mold made of plastic which is co-drawn with a cast preform. Material of the mold is then dissolved after fiber drawing. We also describe a novel THz-TDS setup with an easily adjustable optical path length, designed to perform cutback measurements using THz fibers of up to 50 cm in length. We find that while both porous and non-porous subwavelength fibers of the same outside diameter have low propagation losses (alpha leg 0.02cm-1), however, the porous fibers exhibit a much wider spectral transmission window and enable transmission at higher frequencies compared to the non-porous fibers. We then show that the typical bell-shaped transmission spectra of the subwavelengths fibers can be very well explained by the onset of material absorption loss at higher frequencies due to strong confinement of the modal fields in the material region of the fiber, as well as strong coupling loss at lower frequencies due to mismatch of the modal field diameter and a size of the gaussian-like beam of a THz source.

The collapse transition on superhydrophobic surfaces

We investigate the transition between the Cassie-Baxter and Wenzel states of a slowly evaporating, micron-scale drop on a superhydrophobic surface. In two dimensions analytical results show that there are two collapse mechanisms. For long posts the drop collapses when it is able to overcome the free energy barrier presented by the hydrophobic posts. For short posts, as the drop loses volume, its curvature increases allowing it to touch the surface below the posts. We emphasise the importance of the contact line retreating across the surface as the drop becomes smaller: this often preempts the collapse. In a quasi-three dimensional simulation we find similar behaviour, with the additional feature that the drop can de-pin from all but the peripheral posts, so that its base resembles an inverted bowl.