On the analysis of mixed-index time fractional differential equation systems

In this paper we study the class of mixed-index time fractional differential equations in which different components of the problem have different time fractional derivatives on the left hand side. We prove a theorem on the solution of the linear system of equations, which collapses to the well-known Mittag-Leffler solution in the case the indices are the same, and also generalises the solution of the so-called linear sequential class of time fractional problems. We also investigate the asymptotic stability properties of this class of problems using Laplace transforms and show how Laplace transforms can be used to write solutions as linear combinations of generalised Mittag-Leffler functions in some cases. Finally we illustrate our results with some numerical simulations.Comment: 21 pages, 6 figures (some are made up of sub-figures - there are 15 figures or sub-figures

Vectorised simulations for stochastic differential equations

Often when solving stochastic differential equations numerically, many simulations must be generated. For example, this approach is required when computing the statistics of the numerical solution, or when verifying the strong order of convergence of a numerical method (when a range of step sizes is also required). Such computational effort can be very slow, and this paper discusses an approach to vectorise the simulation calculations and hence produce an efficient implementation. The numerical simulations here were performed in MATLAB but the techniques are equally applicable in a high performance computing environment using, for example, Fortran 90

DBI Galileon and Late time acceleration of the universe

We consider 1+3 dimensional maximally symmetric Minkowski brane embedded in a 1+4 dimensional maximally symmetric Minkowski background. The resulting 1+3 dimensional effective field theory is of DBI (Dirac-Born-Infeld) Galileon type. We use this model to study the late time acceleration of the universe. We study the deviation of the model from the concordance \Lambda CDM behaviour. Finally we put constraints on the model parameters using various observational data.Comment: 16 pages, 7 eps figures, Latex Style, new references added, corrected missing reference

Population of human ventricular cell models calibrated with in vivo measurements unravels ionic mechanisms of cardiac alternans

Cardiac alternansis an important risk factor in cardiac physiology, and is related to the initiation of many pathophysiological conditions. However, the mechanisms underlying the generation of alternans remain unclear. In this study, we used a population of computational human ventricle models based onthe O’Hara model [1] to explore the effect of 11 key factors experimentally reported to be related to alternans. In vivo experimental datasets coming from patients undergoing cardiac surgery were used in the calibration of our in silico population of models. The calibrated models in the population were divided into two groups (Normal and Alternans) depending on alternans occurrence. Our results showed that there were significant differences in the following 5 ionic currents between the two groups: fast sodium current, sodium calcium exchanger current, sodium potassium pump current, sarcoplasmic reticulum (SR) calcium release flux and SR calcium reuptake flux. Further analysis indicated that fast sodium current and SR calcium uptake were the two most significant currents that contributed to voltage and calcium alternans generation, respectively

Chronology Protection in Galileon Models and Massive Gravity

Galileon models are a class of effective field theories that have recently received much attention. They arise in the decoupling limit of theories of massive gravity, and in some cases they have been treated in their own right as scalar field theories with a specific nonlinearly realized global symmetry (Galilean transformation). It is well known that in the presence of a source, these Galileon theories admit superluminal propagating solutions, implying that as quantum field theories they must admit a different notion of causality than standard local Lorentz invariant theories. We show that in these theories it is easy to construct closed timelike curves (CTCs) within the {\it naive} regime of validity of the effective field theory. However, on closer inspection we see that the CTCs could never arise since the Galileon inevitably becomes infinitely strongly coupled at the onset of the formation of a CTC. This implies an infinite amount of backreaction, first on the background for the Galileon field, signaling the break down of the effective field theory, and subsequently on the spacetime geometry, forbidding the formation of the CTC. Furthermore the background solution required to create CTCs becomes unstable with an arbitrarily fast decay time. Thus Galileon theories satisfy a direct analogue of Hawking's chronology protection conjecture.Comment: 34 pages, no figure

Supernova Brightening from Chameleon-Photon Mixing

Measurements of standard candles and measurements of standard rulers give an inconsistent picture of the history of the universe. This discrepancy can be explained if photon number is not conserved as computations of the luminosity distance must be modified. I show that photon number is not conserved when photons mix with chameleons in the presence of a magnetic field. The strong magnetic fields in a supernova mean that the probability of a photon converting into a chameleon in the interior of the supernova is high, this results in a large flux of chameleons at the surface of the supernova. Chameleons and photons also mix as a result of the intergalactic magnetic field. These two effects combined cause the image of the supernova to be brightened resulting in a model which fits both observations of standard candles and observations of standard rulers.Comment: 17 pages, 3 figure

Simple non-mydriatic retinal photography is feasible and demonstrates retinal microvascular dilation in Chronic Obstructive Pulmonary Disease (COPD).

BACKGROUND: Chronic Obstructive Pulmonary Disease (COPD) is associated with an increased risk of myocardial infarction and stroke but it remains unclear how to identify microvascular changes in this population. OBJECTIVES: We hypothesized that simple non-mydriatic retinal photography is feasible and can be used to assess microvascular damage in COPD. METHODS: Novel Vascular Manifestations of COPD was a prospective study comparing smokers with and without COPD, matched for age. Non-mydriatic, retinal fundus photographs were assessed using semi-automated software. RESULTS: Retinal images from 24 COPD and 22 control participants were compared. Cases were of similar age to controls (65.2 vs. 63.1 years, p = 0.38), had significantly lower Forced Expiratory Volume in one second (FEV1) (53.4 vs 100.1% predicted; p < 0.001) and smoked more than controls (41.7 vs. 29.6 pack years; p = 0.04). COPD participants had wider mean arteriolar (155.6 ±15 uM vs. controls [142.2 ± 12 uM]; p = 0.002) and venular diameters (216.8 ±20.7 uM vs. [201.3± 19.1 uM]; p = 0.012). Differences in retinal vessel caliber were independent of confounders, odds ratios (OR) = 1.08 (95% confidence intervals [CI] = 1.02, 1.13; p = 0.007) and OR = 1.05 (CI = 1.01, 1.09; p = 0.011) per uM increase in arteriolar and venular diameter respectively. FEV1 remained significantly associated with retinal vessel dilatation r = -0.39 (p = 0.02). CONCLUSIONS: Non-mydriatic retinal imaging is easily facilitated. We found significant arteriole and venous dilation in COPD compared to age-matched smokers without COPD associated with lung function independent of standard cardiovascular risk factors. Retinal microvascular changes are known to be strongly associated with future vascular events and retinal photography offers potential to identify this risk. TRIAL REGISTRATION: clinicaltrials.gov NCT02060292

Constraining symmetron fields with atom interferometry

We apply the new constraints from atom-interferometry searches for screening mechanisms to the symmetron model, finding that these experiments exclude a previously unexplored region of the parameter space. We discuss the possibility of networks of domain walls forming in the vacuum chamber, and how this could be used to discriminate between models of screening