Solution of generalized fractional reaction-diffusion equations

This paper deals with the investigation of a closed form solution of a generalized fractional reaction-diffusion equation. The solution of the proposed problem is developed in a compact form in terms of the H-function by the application of direct and inverse Laplace and Fourier transforms. Fractional order moments and the asymptotic expansion of the solution are also obtained.Comment: LaTeX, 18 pages, corrected typo

On the theory of superconductivity in ferromagnetic superconductors with triplet pairing

We point out that ferromagnetic superconductors with triplet pairing and strong spin-orbit coupling are even in the simplest case at least two-band superconductors. The Gor'kov type formalism for such superconductors is developed and the Ginzburg-Landau equations are derived. The dependence of the critical temperature on the concentration of ordinary point-like impurities is found. Its nonuniversality could serve as a qualitative measure of the two-band character of ferromagnetic superconductors. The problem of the upper critical field determination is also discussed.Comment: 8 pages, no figure; important changes with respect to the previous versions due to the correction of a mistake: in this new version, a more general form is considered for the order parameter (the two-components of the order parameter were considered before as equal, which is in general not true) ; submitted to Physical Review

Fractional reaction-diffusion equations

In a series of papers, Saxena, Mathai, and Haubold (2002, 2004a, 2004b) derived solutions of a number of fractional kinetic equations in terms of generalized Mittag-Leffler functions which provide the extension of the work of Haubold and Mathai (1995, 2000). The subject of the present paper is to investigate the solution of a fractional reaction-diffusion equation. The results derived are of general nature and include the results reported earlier by many authors, notably by Jespersen, Metzler, and Fogedby (1999) for anomalous diffusion and del-Castillo-Negrete, Carreras, and Lynch (2003) for reaction-diffusion systems with L\'evy flights. The solution has been developed in terms of the H-function in a compact form with the help of Laplace and Fourier transforms. Most of the results obtained are in a form suitable for numerical computation.Comment: LaTeX, 17 pages, corrected typo

Possible symmetries of the superconducting order parameter in a hexagonal ferromagnet

We study the order parameter symmetry in a hexagonal crystal with co-existing superconductivity and ferromagnetism. An experimental example is provided by carbon-based materials, such as graphite-sulfur composites, in which an evidence of such co-existence has been recently discovered. The presence of a non-zero magnetization in the normal phase brings about considerable changes in the symmetry classification of superconducting states, compared to the non-magnetic case.Comment: 4 pages, REVTe

Correlation between human ether-a-go-go-related gene channel inhibition and action potential prolongation

Background and Purpose: Human ether-a-go-go-related gene (hERG; Kv11.1) channel inhibition is a widely accepted predictor of cardiac arrhythmia. hERG channel inhibition alone is often insufficient to predict pro-arrhythmic drug effects. This study used a library of dofetilide derivatives to investigate the relationship between standard measures of hERG current block in an expression system and changes in action potential duration (APD) in human-induced pluripotent stem cell-derived cardiomyocytes (hiPSC-CMs). The interference from accompanying block of Cav1.2 and Nav1.5 channels was investigated along with an in silico AP model. Experimental Approach: Drug-induced changes in APD were assessed in hiPSC-CMs using voltage-sensitive dyes. The IC50 values for dofetilide and 13 derivatives on hERG current were estimated in an HEK293 expression system. The relative potency of each drug on APD was estimated by calculating the dose (D150) required to prolong the APD at 90% (APD90) repolarization by 50%. Key Results: The D150 in hiPSC-CMs was linearly correlated with IC50 of hERG current. In silico simulations supported this finding. Three derivatives inhibited hERG without prolonging APD, and these compounds also inhibited Cav1.2 and/or Nav1.5 in a channel state-dependent manner. Adding Cav1.2 and Nav1.2 block to the in silico model recapitulated the direction but not the extent of the APD change. Conclusions and Implications: Potency of hERG current inhibition correlates linearly with an index of APD in hiPSC-CMs. The compounds that do not correlate have additional effects including concomitant block of Cav1.2 and/or Nav1.5 channels. In silico simulations of hiPSC-CMs APs confirm the principle of the multiple ion channel effects

Density Fluctuation Mediated Superconductivity

We conpare predictions of the mean-field theory of supercnductivity for metallic systems on the border of a density instability for cubic and tetragonal lattices. The calculations are based on a parametrisation of an effective interaction arising from the exchange of density fluctuations and assume that a single band is relevant for superconductivity. The results show that for comparable model parameters, desnity fluctuation mediated pairing is more robust in quasi-two dimensions than in three dimensions, and that the robustness of pairing increases gradually as one goes from a cubic to a more and more anisotropic tetragonal structure. We also find that the robustness of density fluctuation mediated pairing can depend sensitively on the incipient ordering wavevector. We discuss the similarities and differences between the mean-field theories of superconductivity for density and magnetically mediated pairing

Magnetism, Critical Fluctuations and Susceptibility Renormalization in Pd

Some of the most popular ways to treat quantum critical materials, that is, materials close to a magnetic instability, are based on the Landau functional. The central quantity of such approaches is the average magnitude of spin fluctuations, which is very difficult to measure experimentally or compute directly from the first principles. We calculate the parameters of the Landau functional for Pd and use these to connect the critical fluctuations beyond the local-density approximation and the band structure.Comment: Replaced with the revised version accepted for publication. References updated, errors corrected, other change

Pressure-dependence of electron-phonon coupling and the superconducting phase in hcp Fe - a linear response study

A recent experiment by Shimizu et al. has provided evidence of a superconducting phase in hcp Fe under pressure. To study the pressure-dependence of this superconducting phase we have calculated the phonon frequencies and the electron-phonon coupling in hcp Fe as a function of the lattice parameter, using the linear response (LR) scheme and the full potential linear muffin-tin orbital (FP-LMTO) method. Calculated phonon spectra and the Eliashberg functions $\alpha^2 F$ indicate that conventional s-wave electron-phonon coupling can definitely account for the appearance of the superconducting phase in hcp Fe. However, the observed change in the transition temperature with increasing pressure is far too rapid compared with the calculated results. For comparison with the linear response results, we have computed the electron-phonon coupling also by using the rigid muffin-tin (RMT) approximation. From both the LR and the RMT results it appears that electron-phonon interaction alone cannot explain the small range of volume over which superconductivity is observed. It is shown that ferromagnetic/antiferromagnetic spin fluctuations as well as scattering from magnetic impurities (spin-ordered clusters) can account for the observed values of the transition temperatures but cannot substantially improve the agreeemnt between the calculated and observed presure/volume range of the superconducting phase. A simplified treatment of p-wave pairing leads to extremely small ($\leq 10^{-2}$ K) transition temperatures. Thus our calculations seem to rule out both $s$- and $p$- wave superconductivity in hcp Fe.Comment: 12 pages, submitted to PR

The Dependence of the Superconducting Transition Temperature of Organic Molecular Crystals on Intrinsically Non-Magnetic Disorder: a Signature of either Unconventional Superconductivity or Novel Local Magnetic Moment Formation

We give a theoretical analysis of published experimental studies of the effects of impurities and disorder on the superconducting transition temperature, T_c, of the organic molecular crystals kappa-ET_2X and beta-ET_2X (where ET is bis(ethylenedithio)tetrathiafulvalene and X is an anion eg I_3). The Abrikosov-Gorkov (AG) formula describes the suppression of T_c both by magnetic impurities in singlet superconductors, including s-wave superconductors and by non-magnetic impurities in a non-s-wave superconductor. We show that various sources of disorder lead to the suppression of T_c as described by the AG formula. This is confirmed by the excellent fit to the data, the fact that these materials are in the clean limit and the excellent agreement between the value of the interlayer hopping integral, t_perp, calculated from this fit and the value of t_perp found from angular-dependant magnetoresistance and quantum oscillation experiments. If the disorder is, as seems most likely, non-magnetic then the pairing state cannot be s-wave. We show that the cooling rate dependence of the magnetisation is inconsistent with paramagnetic impurities. Triplet pairing is ruled out by several experiments. If the disorder is non-magnetic then this implies that l>=2, in which case Occam's razor suggests that d-wave pairing is realised. Given the proximity of these materials to an antiferromagnetic Mott transition, it is possible that the disorder leads to the formation of local magnetic moments via some novel mechanism. Thus we conclude that either kappa-ET_2X and beta-ET_2X are d-wave superconductors or else they display a novel mechanism for the formation of localised moments. We suggest systematic experiments to differentiate between these scenarios.Comment: 18 pages, 5 figure

The global, regional, and national burden of inflammatory bowel disease in 195 countries and territories, 1990-2017 : a systematic analysis for the Global Burden of Disease Study 2017

Background The burden of inflammatory bowel disease (IBD) is rising globally, with substantial variation in levels and trends of disease in different countries and regions. Understanding these geographical differences is crucial for formulating effective strategies for preventing and treating IBD. We report the prevalence, mortality, and overall burden of IBD in 195 countries and territories between 1990 and 2017, based on data from the Global Burden of Diseases, Injuries, and Risk Factors Study (GBD) 2017. Methods We modelled mortality due to IBD using a standard Cause of Death Ensemble model including data mainly from vital registrations. To estimate the non-fatal burden, we used data presented in primary studies, hospital discharges, and claims data, and used DisMod-MR 2.1, a Bayesian meta-regression tool, to ensure consistency between measures. Mortality, prevalence, years of life lost (YLLs) due to premature death, years lived with disability (YLDs), and disability-adjusted life-years (DALYs) were estimated. All of the estimates were reported as numbers and rates per 100 000 population, with 95% uncertainty intervals (UI). Findings In 2017, there were 6.8 million (95% UI 6.4-7.3) cases of IBD globally. The age-standardised prevalence rate increased from 79.5 (75.9-83.5) per 100 000 population in 1990 to 84.3 (79.2-89.9) per 100 000 population in 2017. The age-standardised death rate decreased from 0.61 (0.55-0.69) per 100 000 population in 1990 to 0.51 (0.42-0.54) per 100 000 population in 2017. At the GBD regional level, the highest age-standardised prevalence rate in 2017 occurred in high-income North America (422.0 [398.7-446.1] per 100 000) and the lowest age-standardised prevalence rates were observed in the Caribbean (6.7 [6.3-7.2] per 100 000 population). High Sociodemographic Index (SDI) locations had the highest age-standardised prevalence rate, while low SDI regions had the lowest age-standardised prevalence rate. At the national level, the USA had the highest age-standardised prevalence rate (464.5 [438.6-490.9] per 100 000 population), followed by the UK (449.6 [420.6-481.6] per 100 000). Vanuatu had the highest age-standardised death rate in 2017 (1.8 [0.8-3.2] per 100 000 population) and Singapore had the lowest (0.08 [0.06-0.14] per 100 000 population). The total YLDs attributed to IBD almost doubled over the study period, from 0.56 million (0.39-0.77) in 1990 to 1.02 million (0.71-1.38) in 2017. The age-standardised rate of DALYs decreased from 26.5 (21.0-33.0) per 100 000 population in 1990 to 23.2 (19.1-27.8) per 100 000 population in 2017. Interpretation The prevalence of IBD increased substantially in many regions from 1990 to 2017, which might pose a substantial social and economic burden on governments and health systems in the coming years. Our findings can be useful for policy makers developing strategies to tackle IBD, including the education of specialised personnel to address the burden of this complex disease. Copyright (C) 2019 The Author(s). Published by Elsevier Ltd. This is an Open Access article under the CC BY 4.0 license.Peer reviewe