Wave propagation in complex coordinates

ArticleWe give an interpretation for the use of complex spatial coordinates in electromagnetism, in terms of a family of closely related inhomogeneous media. Using this understanding we find that the phenomenon of reflection can be related to branch cuts in the wave that originate from poles of ϵ (z) at complex positions. Demanding that these branch cuts disappear, we derive a new large family of inhomogeneous media that are reflectionless for a single angle of incidence. Extending this property to all angles of incidence leads us to a generalized form of the Poschl Teller potentials that in general include regions of loss and gain. We conclude by analyzing our findings within the phase integral (WKB) method, and find another very large family of isotropic planar media that from one side have a transmission of unity and reflection of zero, for all angles of incidence.SARH and TGP acknowledge financial support from EPSRC program grant EP/I034548/1

Perfect transmission through disordered media

This is the author accepted manuscript. The final version is available from American Physical Society via the DOI in this record.The transmission of a wave through a randomly chosen `pile of plates' typically decreases expo- nentially with the number of plates, a phenomenon closely related to Anderson localisation. In ap- parent contradiction we construct disordered planar permittivity pro les which are complex-valued (i.e. have reactive and dissipative properties) that appear to vary randomly with position, yet are one-way re ectionless for all angles of incidence and exhibit a transmission coe cient of unity. In addition to these complex-valued 'random' planar permittivity pro les, we construct a family of real-valued, two-way re ectionless and perfectly transmitting disordered permittivity pro les that function only for a single angle of incidence and a narrow frequency range.C. G. K. acknowledges financial support from the EPSRC Centre for Doctoral Training in Electromagnetic Metamaterials Grant No. EP/L015331/1. S. A. R. H. acknowledges financial support from EPSRC program Grant No. EP/I034548/1, the Royal Society, and TATA. T. G. P. acknowledges financial support from EPSRC program Grant No. EP/I034548/1. The authors acknowledge useful discussions about localization in disordered media with J. Bertolotti

Relationship between caries in primary teeth and defects in permanent teeth

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Electromagnetic interactions in a pair of coupled split-ring resonators

This is the author accepted manuscript. The final version is available from American Physical Society via the DOI in this record.Split-ring Resonators (SRRs) are a fundamental building block of many electromagnetic metamaterials. Typically the response of a metamaterial is assumed to be independent of inter-element interactions in the material. We show that SRRs in close proximity to each other exhibit a rich coupling that involves both electric and magnetic interactions. We study experimentally and computationally the strength and nature of the coupling between two identical SRRs as a function of their separation and relative orientation. We characterise the electric and magnetic couplings and find that, when SRRs are close enough to be in each other's near-field, the electric and magnetic couplings may either reinforce each other or act in opposition. At larger separations retardation effects become important.We acknowledge financial support from the Engineering and Physical Sciences Research Council (EPSRC) of the United Kingdom, via the EPSRC Centre for Doctoral Training in Metamaterials (Grant No. EP/L015331/1)

A review of the importance of the Caribbean region in Oligo-Miocene low latitude planktonic foraminiferal biostratigraphy and the implications for modern biogeochronological schemes

Planktonic foraminifera are widely used in marine biostratigraphy thanks to their small size, limited stratigraphic range and abundance in oceanic sediments. The utility of planktonic foraminifera in biostratigraphy was first fully recognised within the Caribbean region during the middle of the 20th century. The area was critical for the subsequent development of the low latitude biostratigraphic schemes and remains fundamental for modern day biogeochronologies. This study presents a historical review of the Oligo-Miocene component of these biostratigraphic schemes, including the first proposed scheme of Cushman and Stainforth (1945) and the subsequent development. The work of Hans Bolli and Walter Blow is particularly highlighted due to their heavy influence on modern day biostratigraphy, including these authors initially recognising the biostratigraphic utility of a number of bioevents still applied today. These Caribbean-centric schemes are correlated to the modern-day low latitude biogeochronology of Wade et al. (2011), with this synthesis highlighting that a number of bioevents (e.g. Top Paragloborotalia kugleri and Top Catapsydrax dissimilis) have been applied consistently since their initial recognition. This in turn allows the recognisability of these bioevents to be deduced based on how consistently applied each datum has been. In addition, the range charts of six studies focusing heavily on the Caribbean have been reassessed to determine whether there is potential to apply a given bioevent, and the original author merely did not recognise the biostratigraphic utility of the species or favoured another bioevent. In considering this historical review, a number of amendments to Wade et al. (2011) and future priorities to planktonic foraminifera biogeochronologies are suggested. Most notably, the re-introduction of Base Globigerinatella insueta as a primary bioevent due to the historical biostratigraphic importance of this species. This event now defines early Miocene Subzone M3b (Gt. insueta/Ct. dissimilis PRZ) dividing Zone M3 into an upper Subzone M3b (Base Gt. insueta) and lower Subzone M3a (Base Globigerinatella sp.). Finally, the Miocene to Recent timescale of Wade et al. (2011) has been recalibrated following more recent updates to the magnetostratigraphy (Kochhann et al., 2016; Ogg et al., 2016; Drury et al., 2017; Beddow et al., 2018) and cyclostratigraphy (Wilkens et al., 2017). The overall effect on the planktonic foraminifera biogeochronology is minor but our results become the suggested biostratigraphic framework for the low latitudes

Origin of symbol-using systems: speech, but not sign, without the semantic urge

Natural language—spoken and signed—is a multichannel phenomenon, involving facial and body expression, and voice and visual intonation that is often used in the service of a social urge to communicate meaning. Given that iconicity seems easier and less abstract than making arbitrary connections between sound and meaning, iconicity and gesture have often been invoked in the origin of language alongside the urge to convey meaning. To get a fresh perspective, we critically distinguish the origin of a system capable of evolution from the subsequent evolution that system becomes capable of. Human language arose on a substrate of a system already capable of Darwinian evolution; the genetically supported uniquely human ability to learn a language reflects a key contact point between Darwinian evolution and language. Though implemented in brains generated by DNA symbols coding for protein meaning, the second higher-level symbol-using system of language now operates in a world mostly decoupled from Darwinian evolutionary constraints. Examination of Darwinian evolution of vocal learning in other animals suggests that the initial fixation of a key prerequisite to language into the human genome may actually have required initially side-stepping not only iconicity, but the urge to mean itself. If sign languages came later, they would not have faced this constraint

Presymptomatic risk assessment for chronic non-communicable diseases

The prevalence of common chronic non-communicable diseases (CNCDs) far overshadows the prevalence of both monogenic and infectious diseases combined. All CNCDs, also called complex genetic diseases, have a heritable genetic component that can be used for pre-symptomatic risk assessment. Common single nucleotide polymorphisms (SNPs) that tag risk haplotypes across the genome currently account for a non-trivial portion of the germ-line genetic risk and we will likely continue to identify the remaining missing heritability in the form of rare variants, copy number variants and epigenetic modifications. Here, we describe a novel measure for calculating the lifetime risk of a disease, called the genetic composite index (GCI), and demonstrate its predictive value as a clinical classifier. The GCI only considers summary statistics of the effects of genetic variation and hence does not require the results of large-scale studies simultaneously assessing multiple risk factors. Combining GCI scores with environmental risk information provides an additional tool for clinical decision-making. The GCI can be populated with heritable risk information of any type, and thus represents a framework for CNCD pre-symptomatic risk assessment that can be populated as additional risk information is identified through next-generation technologies.Comment: Plos ONE paper. Previous version was withdrawn to be updated by the journal's pdf versio

Rupture by damage accumulation in rocks

The deformation of rocks is associated with microcracks nucleation and propagation, i.e. damage. The accumulation of damage and its spatial localization lead to the creation of a macroscale discontinuity, so-called "fault" in geological terms, and to the failure of the material, i.e. a dramatic decrease of the mechanical properties as strength and modulus. The damage process can be studied both statically by direct observation of thin sections and dynamically by recording acoustic waves emitted by crack propagation (acoustic emission). Here we first review such observations concerning geological objects over scales ranging from the laboratory sample scale (dm) to seismically active faults (km), including cliffs and rock masses (Dm, hm). These observations reveal complex patterns in both space (fractal properties of damage structures as roughness and gouge), time (clustering, particular trends when the failure approaches) and energy domains (power-law distributions of energy release bursts). We use a numerical model based on progressive damage within an elastic interaction framework which allows us to simulate these observations. This study shows that the failure in rocks can be the result of damage accumulation