Conformal symmetry transformations and nonlinear Maxwell equations

We make use of the conformal compactification of Minkowski spacetime $M^{\#}$ to explore a way of describing general, nonlinear Maxwell fields with conformal symmetry. We distinguish the inverse Minkowski spacetime $[M^{\#}]^{-1}$ obtained via conformal inversion, so as to discuss a doubled compactified spacetime on which Maxwell fields may be defined. Identifying $M^{\#}$ with the projective light cone in $(4+2)$-dimensional spacetime, we write two independent conformal-invariant functionals of the $6$-dimensional Maxwellian field strength tensors -- one bilinear, the other trilinear in the field strengths -- which are to enter general nonlinear constitutive equations. We also make some remarks regarding the dimensional reduction procedure as we consider its generalization from linear to general nonlinear theories.Comment: 12 pages, Based on a talk by the first author at the International Conference in Mathematics in honor of Prof. M. Norbert Hounkonnou (October 29-30, 2016, Cotonou, Benin). To be published in the Proceedings, Springer 201

Some Variations on Maxwell's Equations

In the first sections of this article, we discuss two variations on Maxwell's equations that have been introduced in earlier work--a class of nonlinear Maxwell theories with well-defined Galilean limits (and correspondingly generalized Yang-Mills equations), and a linear modification motivated by the coupling of the electromagnetic potential with a certain nonlinear Schroedinger equation. In the final section, revisiting an old idea of Lorentz, we write Maxwell's equations for a theory in which the electrostatic force of repulsion between like charges differs fundamentally in magnitude from the electrostatic force of attraction between unlike charges. We elaborate on Lorentz' description by means of electric and magnetic field strengths, whose governing equations separate into two fully relativistic Maxwell systems--one describing ordinary electromagnetism, and the other describing a universally attractive or repulsive long-range force. If such a force cannot be ruled out {\it a priori} by known physical principles, its magnitude should be determined or bounded experimentally. Were it to exist, interesting possibilities go beyond Lorentz' early conjecture of a relation to (Newtonian) gravity.Comment: 26 pages, submitted to a volume in preparation to honor Gerard Emch v. 2: discussion revised, factors of 4\pi corrected in some equation

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Time-domain numerical simulations of multiple scattering to extract elastic effective wavenumbers

Elastic wave propagation is studied in a heterogeneous 2-D medium consisting of an elastic matrix containing randomly distributed circular elastic inclusions. The aim of this study is to determine the effective wavenumbers when the incident wavelength is similar to the radius of the inclusions. A purely numerical methodology is presented, with which the limitations usually associated with low scatterer concentrations can be avoided. The elastodynamic equations are integrated by a fourth-order time-domain numerical scheme. An immersed interface method is used to accurately discretize the interfaces on a Cartesian grid. The effective field is extracted from the simulated data, and signal-processing tools are used to obtain the complex effective wavenumbers. The numerical reference solution thus-obtained can be used to check the validity of multiple scattering analytical models. The method is applied to the case of concrete. A parametric study is performed on longitudinal and transverse incident plane waves at various scatterers concentrations. The phase velocities and attenuations determined numerically are compared with predictions obtained with multiple scattering models, such as the Independent Scattering Approximation model, the Waterman-Truell model, and the more recent Conoir-Norris model.Comment: Waves in Random and Complex Media (2012) XX

Estimating the carbon content of the deep mantle with Icelandic melt inclusions

Earth’s carbon budget is central to our understanding of the long-term co-evolution of life and the planet. Direct observations of surface reservoirs allow for the detailed quantification of their carbon content. However, the carbon content of Earth’s deep interior remains poorly constrained. Here we study olivine-hosted melt inclusions from two Icelandic eruptions, with those from the Miðfell eruption allowing us to investigate the carbon content of the deep mantle. Comparison with the previously studied Borgarhraun eruption highlights the presence of deep, plume-sourced mantle material within the Miðfell source region. Miðfell contains trace element-depleted melt inclusions undersaturated in CO2, which have high CO2/Ba (= 396 ± 48) and CO2/Nb (= 1832 ± 316), though some inclusions preserve even greater relative carbon enrichment. These observations allow us to reconstruct the CO2 content of the bulk Miðfell source as being > 690 ppm. By identifying that Miðfell is a mixture of depleted and deep mantle components, we can estimate a CO2 content for the deep mantle component of 1350 ± 350 ppm; a concentration that is over ten times higher than depleted MORB mantle estimates. Assuming that the deep mantle component identified in Miðfell is representative of a global reservoir, then with our new CO2 estimate and by considering a range of representative mantle fractions for this reservoir, we calculate that it contains up to 14 times more carbon than that of the atmosphere, oceans, and crust combined. Our result of elevated CO2/Ba and CO2/Nb ratios, and carbon enrichment support geochemical bulk Earth carbon models that call for the presence of carbon-rich deep mantle domains to balance Earth’s relatively carbon-poor upper mantle and surface environment

The early life microbiota protects neonatal mice from pathological small intestinal epithelial cell shedding

The early life gut microbiota plays a crucial role in regulating and maintaining the intestinal barrier, with disturbances in these communities linked to dysregulated renewal and replenishment of intestinal epithelial cells. Here we sought to determine pathological cell shedding outcomes throughout the postnatal developmental period, and which host and microbial factors mediate these responses. Surprisingly, neonatal mice (Day 14 and 21) were highly refractory to induction of cell shedding after intraperitoneal administration of liposaccharide (LPS), with Day 29 mice showing strong pathological responses, more similar to those observed in adult mice. These differential responses were not linked to defects in the cellular mechanisms and pathways known to regulate cell shedding responses. When we profiled microbiota and metabolites, we observed significant alterations. Neonatal mice had high relative abundances of Streptococcus, Escherichia, and Enterococcus and increased primary bile acids. In contrast, older mice were dominated by Candidatus Arthromitus, Alistipes, and Lachnoclostridium, and had increased concentrations of SCFAs and methyamines. Antibiotic treatment of neonates restored LPS-induced small intestinal cell shedding, whereas adult fecal microbiota transplant alone had no effect. Our findings further support the importance of the early life window for microbiota-epithelial interactions in the presence of inflammatory stimuli and highlights areas for further investigation

Outcomes following autologous hematopoietic stem cell transplant for patients with relapsed Wilms' tumor: a CIBMTR retrospective analysis.

Despite the marked improvement in the overall survival (OS) for patients diagnosed with Wilms' tumor (WT), the outcomes for those who experience relapse have remained disappointing. We describe the outcomes of 253 patients with relapsed WT who received high-dose chemotherapy (HDT) followed by autologous hematopoietic stem cell transplant (HCT) between 1990 and 2013, and were reported to the Center for International Blood and Marrow Transplantation Research. The 5-year estimates for event-free survival (EFS) and OS were 36% (95% confidence interval (CI); 29-43%) and 45% (95 CI; 38-51%), respectively. Relapse of primary disease was the cause of death in 81% of the population. EFS, OS, relapse and transplant-related mortality showed no significant differences when broken down by disease status at transplant, time from diagnosis to transplant, year of transplant or conditioning regimen. Our data suggest that HDT followed by autologous HCT for relapsed WT is well tolerated and outcomes are similar to those reported in the literature. As attempts to conduct a randomized trial comparing maintenance chemotherapy with consolidation versus HDT followed by stem cell transplant have failed, one should balance the potential benefits with the yet unknown long-term risks. As disease recurrence continues to be the most common cause of death, future research should focus on the development of consolidation therapies for those patients achieving complete response to therapy

The physiological bases of hidden noise-induced hearing loss: protocol for a functional neuroimaging study

Background: Rodent studies indicate that noise exposure can cause permanent damage to synapses between inner hair cells and high-threshold auditory nerve fibers, without permanently altering threshold sensitivity. These demonstrations of what is commonly known as “hidden hearing loss” have been confirmed in several rodent species, but the implications for human hearing are unclear. Objective: Our Medical Research Council (MRC) funded programme aims to address this unanswered question, by investigating functional consequences of the damage to the human peripheral and central auditory nervous system that results from cumulative lifetime noise exposure. Behavioral and neuroimaging techniques are being used in a series of parallel studies aimed at detecting hidden hearing loss in humans. The planned neuroimaging study aims to (1) identify central auditory biomarkers associated with hidden hearing loss, (2) investigate if there are any additive contributions from tinnitus or diminished sound tolerance, which are often comorbid with hearing problems, and (3) explore the relation between subcortical functional Magnetic Resonance Imaging (fMRI) measures and the auditory brainstem response (ABR). Methods: Individuals aged 25 to 40 years with pure tone hearing thresholds ≤ 20 dB HL over the range 500 Hz to 8 kHz and no contraindications for MRI or signs of ear disease will be recruited into the study. Lifetime noise exposure will be estimated using an in-depth structured interview. Auditory responses throughout the central auditory system will be recorded using ABR and fMRI. Analyses will focus predominantly on correlations between lifetime noise exposure and auditory response characteristics. Results: This article reports the study protocol. The programme grant was awarded in July 2013. Enrollment for the study described in this protocol commenced in February 2017 and was completed in December 2017. Results are expected in 2018. Conclusions: This challenging and comprehensive study will have the potential to impact diagnostic procedures for hidden hearing loss, enabling early identification of noise-induced auditory damage via the detection of changes in central auditory processing. Consequently, this will generate the opportunity to give personalized advice regarding provision of ear defense and monitoring of further damage, thus reducing the incidence of noise-induced hearing loss