Local Normal Mode Coupling and Energy Band Splitting in Elliptically Birefringent 1D Magnetophotonic Crystals

An analysis is presented of wave-vector dispersion in elliptically birefringent stratified magneto-optic media having one-dimensional periodicity. It is found that local normal-mode polarization-state differences between adjacent layers lead to mode coupling and impact the wave-vector dispersion and the character of the Bloch states of the system. This coupling produces extra terms in the dispersion relation not present in uniform circularly birefringent magneto-optic stratified media. Normal mode coupling lifts the degeneracy at frequency band cross-over points under certain conditions and induces a magnetization-dependent optical band gap. This study examines the conditions for band gap formation in the system. It shows that such a frequency-split can be characterized by a simple coupling parameter that depends on the relation between polarization states of local normal modes in adjacent layers. The character of the Bloch states and conditions for maximizing the strength of the band splitting in these systems are analyzed.Comment: 15 pages, 4 figure

The structure and composition statistics of 6A binary and ternary crystalline materials

The fundamental principles underlying the arrangement of elements into solid compounds with an enormous variety of crystal structures are still largely unknown. This study presents a general overview of the structure types appearing in an important subset of the solid compounds, i.e., binary and ternary compounds of the 6A column oxides, sulfides and selenides. It contains an analysis of these compounds, including the prevalence of various structure types, their symmetry properties, compositions, stoichiometries and unit cell sizes. It is found that these compound families include preferred stoichiometries and structure types that may reflect both their specific chemistry and research bias in the available empirical data. Identification of non-overlapping gaps and missing stoichiometries in these structure populations may be used as guidance in the search for new materials.Comment: 19 pages, 13 figure

Band structure and Bloch states in birefringent 1D magnetophotonic crystals: An analytical approach

An analytical formulation for the band structure and Bloch modes in elliptically birefringent magnetophotonic crystals is presented. The model incorporates both the effects of gyrotropy and linear birefringence generally present in magneto-optic thin film devices. Full analytical expressions are obtained for the dispersion relation and Bloch modes in a layered stack photonic crystal and their properties are analyzed. It is shown that other models recently discussed in the literature are contained as special limiting cases of the formulation presented herein

Quasi-Periodicity Under Mismatch Errors

Tracing regularities plays a key role in data analysis for various areas of science, including coding and automata theory, formal language theory, combinatorics, molecular biology and many others. Part of the scientific process is understanding and explaining these regularities. A common notion to describe regularity in a string T is a cover or quasi-period, which is a string C for which every letter of T lies within some occurrence of C. In many applications finding exact repetitions is not sufficient, due to the presence of errors. In this paper we initiate the study of quasi-periodicity persistence under mismatch errors, and our goal is to characterize situations where a given quasi-periodic string remains quasi-periodic even after substitution errors have been introduced to the string. Our study results in proving necessary conditions as well as a theorem stating sufficient conditions for quasi-periodicity persistence. As an application, we are able to close the gap in understanding the complexity of Approximate Cover Problem (ACP) relaxations studied by [Amir 2017a, Amir 2017b] and solve an open question

Groundwater-surface water exchange in the proglacial zone of retreating glaciers in SE Iceland

Groundwater-surface water exchange significantly impacts proglacial hydrology and ecology. This study applies a multidisciplinary approach to investigate groundwater-surface water exchange in the proglacial zones of two retreating glaciers in SE Iceland. Mapping of decadal changes in the extent of proglacial groundwater seeps in the large outwash plain of Skeiðarársandur has shown a 97% decline, as well as substantial falls in groundwater levels. Field and laboratory measurements suggested high spatial variability in hydraulic conductivity at the Skaftafellsjökull foreland. The highest hydraulic conductivity was measured in areas underlain by glaciofluvial deposits whilst the lowest hydraulic conductivities were associated with glacial tills and lacustrine deposits. Precipitation was identified as an important control on groundwater levels on various temporal scales. Automated monitoring of meltwater and groundwater levels also identified fluctuations in meltwater level as an important control on hydraulic heads, whose importance on groundwater levels has been observed during various flow regimes. The close connection between meltwater and groundwater levels suggest high meltwater-aquifer exchange. However, high meltwater-aquifer exchange is contested by significantly different geochemical and isotopic composition of groundwater and meltwater. Hydrogeological flux estimates suggest high spatial variability in groundwater seepage into the Instrumented Lake, which was attributed to the high variability in hydraulic conductivity around the lakeshores. These are also supported by high –resolution temperature mapping at the lake bed, which suggested that groundwater upwelling in the fine-grained lakeshore took place at discrete locations. This study suggests climate and glacier margin fluctuations as primary controls on proglacial groundwater-surface water exchange. It also highlights the importance of groundwater contributions to water quality and ecology, with groundwater-fed bodies possibly sustaining important ecological niches. However, proglacial groundwater-fed features are transient and are threatened by changes in precipitation and glacier retreat. Further declines in groundwater-fed hydrological systems are therefore projected to adversely impact proglacial groundwater-surface water interaction

Approximate Cover of Strings

Regularities in strings arise in various areas of science, including coding and automata theory, formal language theory, combinatorics, molecular biology and many others. A common notion to describe regularity in a string T is a cover, which is a string C for which every letter of T lies within some occurrence of C. The alignment of the cover repetitions in the given text is called a tiling. In many applications finding exact repetitions is not sufficient, due to the presence of errors. In this paper, we use a new approach for handling errors in coverable phenomena and define the approximate cover problem (ACP), in which we are given a text that is a sequence of some cover repetitions with possible mismatch errors, and we seek a string that covers the text with the minimum number of errors. We first show that the ACP is NP-hard, by studying the cover-size relaxation of the ACP, in which the requested size of the approximate cover is also given with the input string. We show this relaxation is already NP-hard. We also study another two relaxations of the ACP, which we call the partial-tiling relaxation of the ACP and the full-tiling relaxation of the ACP, in which a tiling of the requested cover is also given with the input string. A given full tiling retains all the occurrences of the cover before the errors, while in a partial tiling there can be additional occurrences of the cover that are not marked by the tiling. We show that the partial-tiling relaxation has a polynomial time complexity and give experimental evidence that the full-tiling also has polynomial time complexity. The study of these relaxations, besides shedding another light on the complexity of the ACP, also involves a deep understanding of the properties of covers, yielding some key lemmas and observations that may be helpful for a future study of regularities in the presence of errors