Fourier spectral methods for fractional-in-space reaction-diffusion equations

Fractional differential equations are becoming increasingly used as a powerful modelling approach for understanding the many aspects of nonlocality and spatial heterogeneity. However, the numerical approximation of these models is computationally demanding and imposes a number of computational constraints. In this paper, we introduce Fourier spectral methods as an attractive and easy-to-code alternative for the integration of fractional-in-space reactiondiffusion equations. The main advantages of the proposed schemes is that they yield a fully diagonal representation of the fractional operator, with increased accuracy and efficiency when compared to low-order counterparts, and a completely straightforward extension to two and three spatial dimensions. Our approach is show-cased by solving several problems of practical interest, including the fractional Allen–Cahn, FitzHugh–Nagumo and Gray–Scott models,together with an analysis of the properties of these systems in terms of the fractional power of the underlying Laplacian operator

Fractional diffusion models of cardiac electrical propagation: role of structural heterogeneity in dispersion of repolarization

Structural heterogeneity constitutes one of the main substrates influencing impulse propagation in living tissues. In cardiac muscle, improved understanding on its role is key to advancing our interpretation of cell-to-cell coupling, and how tissue structure modulates electrical propagation and arrhythmogenesis in the intact and diseased heart. We propose fractional diffusion models as a novel mathematical description of structurally heterogeneous excitable media, as a mean of representing the modulation of the total electric field by the secondary electrical sources associated with tissue inhomogeneities. Our results, validated against in-vivo human recordings and experimental data of different animal species, indicate that structural heterogeneity underlies many relevant characteristics of cardiac propagation, including the shortening of action potential duration along the activation pathway, and the progressive modulation by premature beats of spatial patterns of dispersion of repolarization. The proposed approach may also have important implications in other research fields involving excitable complex media

Superconformal mechanics, black holes, and non-linear realizations

The OSp(2|2)-invariant planar dynamics of a D=4 superparticle near the horizon of a large mass extreme black hole is described by an N=2 superconformal mechanics, with the SO(2) charge being the superparticle's angular momentum. The {\it non-manifest} superconformal invariance of the superpotential term is shown to lead to a shift in the SO(2) charge by the value of its coefficient, which we identify as the orbital angular momentum. The full SU(1,1|2)-invariant dynamics is found from an extension to N=4 superconformal mechanics.Comment: 19 pages, plain latex file. Slightly shortened version, two references adde

A generic framework for context-sensitive analysis of modular programs

Context-sensitive analysis provides information which is potentially more accurate than that provided by context-free analysis. Such information can then be applied in order to validate/debug the program and/or to specialize the program obtaining important improvements. Unfortunately, context-sensitive analysis of modular programs poses important theoretical and practical problems. One solution, used in several proposals, is to resort to context-free analysis. Other proposals do address context-sensitive analysis, but are only applicable when the description domain used satisfies rather restrictive properties. In this paper, we argüe that a general framework for context-sensitive analysis of modular programs, Le., one that allows using all the domains which have proved useful in practice in the non-modular setting, is indeed feasible and very useful. Driven by our experience in the design and implementation of analysis and specialization techniques in the context of CiaoPP, the Ciao system preprocessor, in this paper we discuss a number of design goals for context-sensitive analysis of modular programs as well as the problems which arise in trying to meet these goals. We also provide a high-level description of a framework for analysis of modular programs which does substantially meet these objectives. This framework is generic in that it can be instantiated in different ways in order to adapt to different contexts. Finally, the behavior of the different instantiations w.r.t. the design goals that motivate our work is also discussed

Experimentally-calibrated population of models predicts and explains inter-subject variability in cardiac cellular\ud electrophysiology

Cellular and ionic causes of variability in the electrophysiological activity of hearts from individuals of the same species are unknown. However, improved understanding of this variability is key to enable prediction of the response of specific hearts to disease and therapies. Limitations of current mathematical modeling and experimental techniques hamper our ability to provide insight into variability. Here we describe a methodology to unravel the ionic determinants of inter-subject variability exhibited in experimental recordings, based on the construction and calibration of populations of models. We illustrate the methodology through its application to rabbit Purkinje preparations, due to their importance in arrhythmias and safety pharmacology assessment. We consider a set of equations describing the biophysical processes underlying rabbit Purkinje electrophysiology and we construct a population of over 10,000 models by randomly assigning specific parameter values corresponding to ionic current conductances and kinetics. We calibrate the model population by closely comparing simulation output and experimental recordings at three pacing frequencies. We show that 213 of the 10,000 candidate models are fully consistent with the experimental dataset. Ionic properties in the 213 models cover a wide range of values, including differences up to ±100% in several conductances. Partial correlation analysis shows that particular combinations of ionic properties determine the precise shape, amplitude and rate dependence of specific action potentials. Finally, we demonstrate that the population of models calibrated using data obtained under physiological conditions quantitatively predicts the action potential duration prolongation caused by exposure to four concentrations of the potassium channel blocker dofetilide

The Height of Chromospheric Loops in an Emerging Flux Region

Context. The chromospheric layer observable with the He I 10830 {\AA} triplet is strongly warped. The analysis of the magnetic morphology of this layer therefore requires a reliable technique to determine the height at which the He I absorption takes place. Aims. The He I absorption signature connecting two pores of opposite polarity in an emerging flux region is investigated. This signature is suggestive of a loop system connecting the two pores. We aim to show that limits can be set on the height of this chromospheric loop system. Methods. The increasing anisotropy in the illumination of a thin, magnetic structure intensifies the linear polarization signal observed in the He I triplet with height. This signal is altered by the Hanle effect. We apply an inversion technique incorporating the joint action of the Hanle and Zeeman effects, with the absorption layer height being one of the free parameters. Results. The observed linear polarization signal can be explained only if the loop apex is higher than \approx5 Mm. Best agreement with the observations is achieved for a height of 6.3 Mm. Conclusions. The strength of the linear polarization signal in the loop apex is inconsistent with the assumption of a He I absorption layer at a constant height level. The determined height supports the earlier conclusion that dark He 10830 {\AA} filaments in emerging flux regions trace emerging loops.Comment: 7 pages, 4 figure

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

Melting curve of 4^4He: no sign of the supersolid transition down to 10 mK

We have measured the melting curve of $^4$He in the temperature range from 10 to 400 mK with the accuracy of about 0.5 $\mu$bar. Crystals of different quality show the expected $T^4$-dependence in the range from 80 to 400 mK without any sign of the supersolid transition, and the coefficient is in excellent agreement with available data on the sound velocity in liquid $^4$He and on the Debye temperature of solid $^4$He. Below 80 mK we have observed a small deviation from $T^4$-dependence which however cannot be attributed to the supersolid transition because instead of decrease the entropy of the solid rather remains constant, about $2.5\times10^{-6}$ $R$Comment: 4 pages, 2 figures, published in Physical Review Letter

Observations of solar scattering polarization at high spatial resolution

The weak, turbulent magnetic fields that supposedly permeate most of the solar photosphere are difficult to observe, because the Zeeman effect is virtually blind to them. The Hanle effect, acting on the scattering polarization in suitable lines, can in principle be used as a diagnostic for these fields. However, the prediction that the majority of the weak, turbulent field resides in intergranular lanes also poses significant challenges to scattering polarization observations because high spatial resolution is usually difficult to attain. We aim to measure the difference in scattering polarization between granules and intergranules. We present the respective center-to-limb variations, which may serve as input for future models. We perform full Stokes filter polarimetry at different solar limb positions with the CN band filter of the Hinode-SOT Broadband Filter Imager, which represents the first scattering polarization observations with sufficient spatial resolution to discern the granulation. Hinode-SOT offers unprecedented spatial resolution in combination with high polarimetric sensitivity. The CN band is known to have a significant scattering polarization signal, and is sensitive to the Hanle effect. We extend the instrumental polarization calibration routine to the observing wavelength, and correct for various systematic effects. The scattering polarization for granules (i.e., regions brighter than the median intensity of non-magnetic pixels) is significantly larger than for intergranules. We derive that the intergranules (i.e., the remaining non-magnetic pixels) exhibit (9.8 \pm 3.0)% less scattering polarization for 0.2<u<0.3, although systematic effects cannot be completely excluded. These observations constrain MHD models in combination with (polarized) radiative transfer in terms of CN band line formation, radiation anisotropy, and magnetic fields.Comment: Accepted for publication in A&

Underground Neutrino Detectors for Particle and Astroparticle Science: the Giant Liquid Argon Charge Imaging ExpeRiment (GLACIER)

The current focus of the CERN program is the Large Hadron Collider (LHC), however, CERN is engaged in long baseline neutrino physics with the CNGS project and supports T2K as recognized CERN RE13, and for good reasons: a number of observed phenomena in high-energy physics and cosmology lack their resolution within the Standard Model of particle physics; these puzzles include the origin of neutrino masses, CP-violation in the leptonic sector, and baryon asymmetry of the Universe. They will only partially be addressed at LHC. A positive measurement of $\sin^22\theta_{13}>0.01$ would certainly give a tremendous boost to neutrino physics by opening the possibility to study CP violation in the lepton sector and the determination of the neutrino mass hierarchy with upgraded conventional super-beams. These experiments (so called ``Phase II'') require, in addition to an upgraded beam power, next generation very massive neutrino detectors with excellent energy resolution and high detection efficiency in a wide neutrino energy range, to cover 1st and 2nd oscillation maxima, and excellent particle identification and $\pi^0$ background suppression. Two generations of large water Cherenkov detectors at Kamioka (Kamiokande and Super-Kamiokande) have been extremely successful. And there are good reasons to consider a third generation water Cherenkov detector with an order of magnitude larger mass than Super-Kamiokande for both non-accelerator (proton decay, supernovae, ...) and accelerator-based physics. On the other hand, a very massive underground liquid Argon detector of about 100 kton could represent a credible alternative for the precision measurements of ``Phase II'' and aim at significantly new results in neutrino astroparticle and non-accelerator-based particle physics (e.g. proton decay).Comment: 31 pages, 14 figure