Christian Cherubini

SECOND ORDER SCALAR INVARIANTS OF THE RIEMANN TENSOR: APPLICATIONS TO BLACK HOLE SPACETIMES

We discuss the Kretschmann, Chern–Pontryagin and Euler invariants among the second order scalar invariants of the Riemann tensor in any spacetime in the Newman–Penrose formalism and in the framework of gravitoelectromagnetism, using the Kerr–Newman geometry as an example. An analogy with electromagnetic invariants leads to the definition of regions of gravitoelectric or gravitomagnetic dominance.

Mathematical modelling of active contraction in isolated cardiomyocytes

We investigate the interaction of intracellular calcium spatio-temporal variations with the self-sustained contractions in cardiac myocytes. A consistent mathematical model is presented considering a hyperelastic description of the passive mechanical properties of the cell, combined with an active-strain framework to explain the active shortening of myocytes and its coupling with cytosolic and sarcoplasmic calcium dynamics. A finite element method based on a Taylor-Hood discretization is employed to approximate the nonlinear elasticity equations, whereas the calcium concentration and mechanical activation variables are discretized by piecewise linear finite elements. Several numerical tests illustrate the ability of the model in predicting key experimentally established characteristics including: (i) calcium propagation patterns and contractility, (ii) the influence of boundary conditions and cell shape on the onset of structural and active anisotropy and (iii) the high localized stress distributions at the focal adhesions. Besides, they also highlight the potential of the method in elucidating some important subcellular mechanisms affecting, e.g. cardiac repolarization.

On the electrical intestine turbulence induced by temperature changes

Paralytic ileus is a temporary syndrome with impairment of peristalsis and no passage of food through the intestine. Although improvements in supportive measures have been achieved, no therapy useful to specifically reduce or eliminate the motility disorder underlying postoperative ileus has been developed yet. In this paper, we draw a plausible, physiologically fine-tuned scenario, which explains a possible cause of paralytic ileus. To this aim we extend the existing 1D intestinal electrophysiological Aliev-Richards-Wikswo ionic model based on a double-layered structure in two and three dimensions. Thermal coupling is introduced here to study the influence of temperature gradients on intestine tissue which is an important external factor during surgery. Numerical simulations present electrical spiral waves similar to those experimentally observed already in the heart, brain and many other excitable tissues. This fact seems to suggest that such peculiar patterns, here electrically and thermally induced, may play an important role in clinically experienced disorders of the intestine, then requiring future experimental analyses in the search for possible implications for medical and physiological practice and bioengineering.

Wave-train-induced termination of weakly anchored vortices in excitable media.

A free vortex in excitable media can be displaced and removed by a wave train. However, simple physical arguments suggest that vortices anchored to large inexcitable obstacles cannot be removed similarly. We show that unpinning of vortices attached to obstacles smaller than the core radius of the free vortex is possible through pacing. The wave-train frequency necessary for unpinning increases with the obstacle size and we present a geometric explanation of this dependence. Our model-independent results suggest that decreasing excitability of the medium can facilitate pacing-induced removal of vortices in cardiac tissue.

Mechanistic insights into hypothermic ventricular fibrillation: the role of temperature and tissue size

AIMS Hypothermia is well known to be pro-arrhythmic, yet it has beneficial effects as a resuscitation therapy and valuable during intracardiac surgeries. Therefore, we aim to study the mechanisms that induce fibrillation during hypothermia. A better understanding of the complex spatiotemporal dynamics of heart tissue as a function of temperature will be useful in managing the benefits and risks of hypothermia. METHODS AND RESULTS We perform two-dimensional numerical simulations by using a minimal model of cardiac action potential propagation fine-tuned on experimental measurements. The model includes thermal factors acting on the ionic currents and the gating variables to correctly reproduce experimentally recorded restitution curves at different temperatures. Simulations are implemented using WebGL, which allows long simulations to be performed as they run close to real time. We describe (i) why fibrillation is easier to induce at low temperatures, (ii) that there is a minimum size required for fibrillation that depends on temperature, (iii) why the frequency of fibrillation decreases with decreasing temperature, and (iv) that regional cooling may be an anti-arrhythmic therapy for small tissue sizes however it may be pro-arrhythmic for large tissue sizes. CONCLUSION Using a mathematical cardiac cell model, we are able to reproduce experimental observations, quantitative experimental results, and discuss possible mechanisms and implications of electrophysiological changes during hypothermia.

Vacuum C metric and the gravitational stark effect

We study the vacuum C-metric and its physical interpretation in terms of the exterior spacetime of a uniformly accelerating spherically - symmetric gravitational source. Wave phenomena on the linearized C-metric background are investigated. It is shown that the scalar perturbations of the linearized C-metric correspond to the gravitational Stark effect. This effect is studied in connection with the Pioneer anomaly.

Massless field perturbations and gravitomagnetism in the Kerr-Taub-NUT spacetime

A single master equation is given describing spin

Circular holonomy in the Taub-NUT spacetime

sl~2

Excised acoustic black holes : The scattering problem in the time domain

test fields that are gauge- and tetrad-invariant perturbations of the Kerr-Taub-NUT (Newman-Unti-Tamburino) spacetime representing a source with a mass M, gravitomagnetic monopole moment

Teukolsky Master Equation : de Rham Wave Equation for Gravitational and Electromagnetic Fields in Vacuum

\ensuremath{-}\mathcal{l},