Global existence of Dirac-wave maps with curvature term on expanding spacetimes.
Ontology highlight
ABSTRACT:
SUBMITTER: Branding V
PROVIDER: S-EPMC6190925 | biostudies-other | 2018
REPOSITORIES: biostudies-other
Publications
Global existence of Dirac-wave maps with curvature term on expanding spacetimes.
Branding Volker V Kröncke Klaus K
Calculus of variations and partial differential equations 20180720 5
We prove the global existence of Dirac-wave maps with curvature term with small initial data on globally hyperbolic manifolds of arbitrary dimension which satisfy a suitable growth condition. In addition, we also prove a global existence result for wave maps under similar assumptions. ...[more]
Similar Datasets
Project description:The curvature of the sea wave was tested as a parameter for estimating wave direction in the search for better results in estimates of wave direction in shallow waters, where waves of different sizes, frequencies and directions intersect and it is difficult to characterize. We used numerical simulations of the sea surface to determine wave direction calculated from the curvature of the waves. Using 1000 numerical simulations, the statistical variability of the wave direction was determined. The results showed good performance by the curvature parameter for estimating wave direction. Accuracy in the estimates was improved by including wave slope parameters in addition to curvature. The results indicate that the curvature is a promising technique to estimate wave directions.•In this study, the accuracy and precision of curvature parameters to measure wave direction are analyzed using a model simulation that generates 1000 wave records with directional resolution.•The model allows the simultaneous simulation of time-series wave properties such as sea surface elevation, slope and curvature and they were used to analyze the variability of estimated directions.•The simultaneous acquisition of slope and curvature parameters can contribute to estimates wave direction, thus increasing accuracy and precision of results.
| S-EPMC4929270 | biostudies-literature
Project description:The first objective of this paper is to prove the existence and uniqueness of global solutions for a Kirchhoff-type wave equation with nonlinear dissipation of the form Ku'' + M(|A (1/2) u|(2))Au + g(u') = 0 under suitable assumptions on K, A, M(·), and g(·). Next, we derive decay estimates of the energy under some growth conditions on the nonlinear dissipation g. Lastly, numerical simulations in order to verify the analytical results are given.
| S-EPMC3996994 | biostudies-other
Project description:Post-graphene organic Dirac (PGOD) materials are ordered two-dimensional networks of triply bonded sp 2 carbon nodes spaced by ?-conjugated linkers. PGOD materials are natural chemical extensions of graphene that promise to have an enhanced range of properties and applications. Experimentally realised molecules based on two PGOD nodes exhibit a bi-stable closed-shell/multi-radical character that can be understood through competing Lewis resonance forms. Here, following the same rationale, we predict that similar states should be accessible in PGOD materials, which we confirm using accurate density functional theory calculations. Although for graphene the semimetallic state is always dominant, for PGOD materials this state becomes marginally meta-stable relative to open-shell multi-radical and/or closed-shell states that are stabilised through symmetry breaking, in line with analogous molecular systems. These latter states are semiconducting, increasing the potential use of PGOD materials as highly tuneable platforms for future organic nano-electronics and spintronics.
| S-EPMC5717056 | biostudies-literature
Project description:Colossal negative magnetoresistance is a well-known phenomenon, notably observed in hole-doped ferromagnetic manganites. It remains a major research topic due to its potential in technological applications. In contrast, topological semimetals show large but positive magnetoresistance, originated from the high-mobility charge carriers. Here, we show that in the highly electron-doped region, the Dirac semimetal CeSbTe demonstrates similar properties as the manganites. CeSb0.11Te1.90 hosts multiple charge density wave modulation vectors and has a complex magnetic phase diagram. We confirm that this compound is an antiferromagnetic Dirac semimetal. Despite having a metallic Fermi surface, the electronic transport properties are semiconductor-like and deviate from known theoretical models. An external magnetic field induces a semiconductor metal-like transition, which results in a colossal negative magnetoresistance. Moreover, signatures of the coupling between the charge density wave and a spin modulation are observed in resistivity. This spin modulation also produces a giant anomalous Hall response.
| S-EPMC10575584 | biostudies-literature
Project description:Robust laser sources are a fundamental building block for contemporary information technologies. Originating from condensed-matter physics, the concept of topology has recently entered the realm of optics, offering fundamentally new design principles for lasers with enhanced robustness. In analogy to the well-known Majorana fermions in topological superconductors, Dirac-vortex states have recently been investigated in passive photonic systems and are now considered as a promising candidate for robust lasers. Here, we experimentally realize the topological Dirac-vortex microcavity lasers in InAs/InGaAs quantum-dot materials monolithically grown on a silicon substrate. We observe room-temperature continuous-wave linearly polarized vertical laser emission at a telecom wavelength. We confirm that the wavelength of the Dirac-vortex laser is topologically robust against variations in the cavity size, and its free spectral range defies the universal inverse scaling law with the cavity size. These lasers will play an important role in CMOS-compatible photonic and optoelectronic systems on a chip.
| S-EPMC10593858 | biostudies-literature
Project description:In recent years, photonics has proven itself as an excellent platform for emulation of relativistic phenomena. Here, we show an example of relativistic-like trapping in photonic system that realizes Dirac-like dispersion with spatially inhomogeneous mass term. The modes trapped by such cavities, their energy levels, and corresponding orbitals are then characterized through optical imaging in real and momentum space. The fabricated cavities host a hierarchy of photonic modes with distinct radiation profiles directly analogous to various atomic orbitals endowed with unique characteristics, such as pseudo-particle-hall symmetry and spin degeneracy, and they carry topological charge which gives rise to radiative profiles with angular momentum. We demonstrate that these modes can be directionally excited by pseudo-spin-polarized boundary states. In addition to the fundamental interest in the structure of these pseudo-relativistic orbitals, the proposed system offers a route for designing new types of nanophotonic devices, spin-full resonators and topological light sources compatible with integrated photonics platforms.
| S-EPMC10032596 | biostudies-literature
Project description:Research in global change ecology relies heavily on global climatic grids derived from estimates of air temperature in open areas at around 2 m above the ground. These climatic grids do not reflect conditions below vegetation canopies and near the ground surface, where critical ecosystem functions occur and most terrestrial species reside. Here, we provide global maps of soil temperature and bioclimatic variables at a 1-km2 resolution for 0-5 and 5-15 cm soil depth. These maps were created by calculating the difference (i.e. offset) between in situ soil temperature measurements, based on time series from over 1200 1-km2 pixels (summarized from 8519 unique temperature sensors) across all the world's major terrestrial biomes, and coarse-grained air temperature estimates from ERA5-Land (an atmospheric reanalysis by the European Centre for Medium-Range Weather Forecasts). We show that mean annual soil temperature differs markedly from the corresponding gridded air temperature, by up to 10°C (mean = 3.0 ± 2.1°C), with substantial variation across biomes and seasons. Over the year, soils in cold and/or dry biomes are substantially warmer (+3.6 ± 2.3°C) than gridded air temperature, whereas soils in warm and humid environments are on average slightly cooler (-0.7 ± 2.3°C). The observed substantial and biome-specific offsets emphasize that the projected impacts of climate and climate change on near-surface biodiversity and ecosystem functioning are inaccurately assessed when air rather than soil temperature is used, especially in cold environments. The global soil-related bioclimatic variables provided here are an important step forward for any application in ecology and related disciplines. Nevertheless, we highlight the need to fill remaining geographic gaps by collecting more in situ measurements of microclimate conditions to further enhance the spatiotemporal resolution of global soil temperature products for ecological applications.
| S-EPMC9303923 | biostudies-literature
Project description:This review provides a summary of the global epidemiology of inflammatory bowel diseases (IBD). It is now clear that IBD is increasing worldwide and has become a global emergence disease. IBD, which includes Crohn's disease (CD) and ulcerative colitis (UC), has been considered a problem in industrial-urbanized societies and attributed largely to a Westernized lifestyle and other associated environmental factors. Its incidence and prevalence in developing countries is steadily rising and has been attributed to the rapid modernization and Westernization of the population. There is a need to reconcile the most appropriate treatment for these patient populations from the perspectives of both disease presentation and cost. In the West, biological agents are the fastest-growing segment of the prescription drug market. These agents cost thousands of dollars per patient per year. The healthcare systems, and certainly the patients, in developing countries will struggle to afford such expensive treatments. The need for biological therapy will inevitably increase dramatically, and the pharmaceutical industry, healthcare providers, patient advocate groups, governments and non-governmental organizations should come to a consensus on how to handle this problem. The evidence that IBD is now affecting a much younger population presents an additional concern. Meta-analyses conducted in patients acquiring IBD at a young age also reveals a trend for their increased risk of developing colorectal cancer (CRC), since the cumulative incidence rates of CRC in IBD-patients diagnosed in childhood are higher than those observed in adults. In addition, IBD-associated CRC has a worse prognosis than sporadic CRC, even when the stage at diagnosis is taken into account. This is consistent with additional evidence that IBD negatively impacts CRC survival. A continuing increase in IBD incidence worldwide associated with childhood-onset of IBD coupled with the diseases' longevity and an increase in oncologic transformation suggest a rising disease burden, morbidity, and healthcare costs. IBD and its associated neoplastic transformation appear inevitable, which may significantly impact pediatric gastroenterology and adult CRC care. Due to an infrastructure gap in terms of access to care between developed vs. developing nations and the uneven representation of IBD across socioeconomic strata, a plan is needed in the developing world regarding how to address this emerging problem.
| S-EPMC4020403 | biostudies-other
Project description:The leishmaniases are vector-borne diseases that have a broad global distribution throughout much of the Americas, Africa, and Asia. Despite representing a significant public health burden, our understanding of the global distribution of the leishmaniases remains vague, reliant upon expert opinion and limited to poor spatial resolution. A global assessment of the consensus of evidence for leishmaniasis was performed at a sub-national level by aggregating information from a variety of sources. A database of records of cutaneous and visceral leishmaniasis occurrence was compiled from published literature, online reports, strain archives, and GenBank accessions. These, with a suite of biologically relevant environmental covariates, were used in a boosted regression tree modelling framework to generate global environmental risk maps for the leishmaniases. These high-resolution evidence-based maps can help direct future surveillance activities, identify areas to target for disease control and inform future burden estimation efforts.
| S-EPMC4103681 | biostudies-literature
Project description:PurposeTo quantify the abnormal corneal thinning and posterior surface steepening that is observed in keratoconus with an Ectasia Index.MethodsOptical coherence tomography (OCT) was used to image the corneas of normal individuals and patients with varying stages of keratoconus (manifest, subclinical, and forme fruste). Maps of corneal pachymetry and posterior surface mean curvature were generated, and an Ectasia Index was calculated by multiplying Gaussian fits obtained from the two types of maps. Repeated five-fold cross-validation was used to evaluate the ability of the Ectasia Index to differentiate between normal and keratoconic eyes. The classification performance of the Ectasia Index was compared to minimum pachymetry and maximum posterior mean curvature.ResultsThirty-two eyes from 16 normal individuals, 89 eyes from 63 patients with manifest keratoconus, 16 eyes from 15 patients with subclinical keratoconus, and 26 eyes from 26 patients with forme fruste keratoconus were included in the study. During cross-validation, 100% of the eyes with manifest (89 of 89) and subclinical (16 of 16) keratoconus were correctly classified by the Ectasia Index. The average classification accuracy for the forme fruste keratoconus group was 63 ± 21% (16.4 of 26). The specificity for the normal group was 91 ± 10% (29.1 of 32). The Ectasia Index had a higher sensitivity for keratoconus detection and similar specificity in comparison to minimum pachymetry and maximum posterior mean curvature.ConclusionsThe Ectasia Index could be a valuable additional metric for clinicians to consider when screening for keratoconus. [J Refract Surg. 2022;38(8):502-510.].
| S-EPMC10311947 | biostudies-literature