A Generalization of Abel Inversion to non axisymmetric density distribution

Abel Inversion is currently used in laser-plasma studies in order to estimate the electronic density $n_e$ from the phase-shift map $\delta \phi$ obtained via interferometry. The main limitation of the Abel method is due to the assumption of axial symmetry of the electronic density, which is often hardly fulfilled. In this paper we present an improvement to the Abel inversion technique in which the axial symmetry condition is relaxed by means of a truncated Legendre Polinomial expansion in the azimutal angle. With the help of simulated interferograms, we will show that the generalized Abel inversion generates accurate densities maps when applied to non axisymmetric density sources

Competing mechanisms of stress-assisted diffusivity and stretch-activated currents in cardiac electromechanics

We numerically investigate the role of mechanical stress in modifying the conductivity properties of the cardiac tissue and its impact in computational models for cardiac electromechanics. We follow a theoretical framework recently proposed in [Cherubini, Filippi, Gizzi, Ruiz-Baier, JTB 2017], in the context of general reaction-diffusion-mechanics systems using multiphysics continuum mechanics and finite elasticity. In the present study, the adapted models are compared against preliminary experimental data of pig right ventricle fluorescence optical mapping. These data contribute to the characterization of the observed inhomogeneity and anisotropy properties that result from mechanical deformation. Our novel approach simultaneously incorporates two mechanisms for mechano-electric feedback (MEF): stretch-activated currents (SAC) and stress-assisted diffusion (SAD); and we also identify their influence into the nonlinear spatiotemporal dynamics. It is found that i) only specific combinations of the two MEF effects allow proper conduction velocity measurement; ii) expected heterogeneities and anisotropies are obtained via the novel stress-assisted diffusion mechanisms; iii) spiral wave meandering and drifting is highly mediated by the applied mechanical loading. We provide an analysis of the intrinsic structure of the nonlinear coupling using computational tests, conducted using a finite element method. In particular, we compare static and dynamic deformation regimes in the onset of cardiac arrhythmias and address other potential biomedical applications

Statistical characterization of the anisotropic strain energy in soft materials with distributed fibers

We discuss analytical and numerical tools for the statistical characterization of the anisotropic strain energy density of soft hyperelastic materials embedded with fibers. We consider spatially distributed orientations of fibers following a tridimensional or a planar architecture. We restrict our analysis to material models dependent on the fourth pseudo-invariant I4 of the Cauchy-Green tensor, and to exponential forms of the fiber strain energy function Ψaniso. Under different loading conditions, we derive the closed-form expression of the probability density function for I4 and Ψaniso. In view of bypassing the cumbersome extension-contraction switch, commonly adopted for shutting down the contribution of contracted fibers in models based on generalized structure tensors, for significant loading conditions we identify analytically the support of the fibers in pure extension. For uniaxial loadings, the availability of the probability distribution function and the knowledge of the support of the fibers in extension yield to the analytical expression of average and variance of I4 and Ψaniso, and to the direct definition of the average second Piola-Kirchhoff stress tensor. For generalized loadings, the dependence of I4 on the spatial orientation of the fibers can be analyzed through angle plane diagrams. Angle plane diagrams facilitate the assessment of the influence of the pure extension condition on the definition of the stable support of fibers for the statistics related to the anisotropic strain energy density. © 2015 Elsevier Ltd. All rights reserved

Role of laser contrast and foil thickness in target normal sheath acceleration

In this paper we present an experimental investigation of laser driven light-ion acceleration using the ILIL laser at an intensity of 2×1019 W/cm2. In the experiment we focused our attention on the identification of the role of target thickness and resistivity in the fast electron transport and in the acceleration process. Here we describe the experimental results concerning the effect of laser contrast in the laser–target interaction regime. We also show preliminary results on ion acceleration which provide information about the role of bulk target ions and surface ions and target dielectric properties in the acceleration process

Application of novel techniques for interferogram analysis to laser-plasma femtosecond probing

Recently, two novel techniques for the extraction of the phase-shift map (Tomassini {\it et.~al.}, Applied Optics {\bf 40} 35 (2001)) and the electronic density map estimation (Tomassini P. and Giulietti A., Optics Communication {\bf 199}, pp 143-148 (2001)) have been proposed. In this paper we apply both methods to a sample laser-plasma interferogram obtained with femtoseconds probe pulse, in an experimental setup devoted to laser particle acceleration studies.Comment: Submitted to Laser and Particle Beam

Optical diagnostics for density measurement in high-quality laser-plasma electron accelerators

Implementation of laser-plasma-based acceleration stages in user-oriented facilities requires the definition and deployment of appropriate diagnostic methodologies to monitor and control the acceleration process. An overview is given here of optical diagnostics for density measurement in laser-plasma acceleration stages, with emphasis on well-established and easily implemented approaches. Diagnostics for both neutral gas and free-electron number density are considered, highlighting real-time measurement capabilities. Optical interferometry, in its various configurations, from standard two-arm to more advanced common-path designs, is discussed, along with spectroscopic techniques such as Stark broadening and Raman scattering. A critical analysis of the diagnostics presented is given concerning their implementation in laser-plasma acceleration stages for the production of high-quality GeV electron bunches

A space-fractional bidomain framework for cardiac electrophysiology: 1D alternans dynamics

Cardiac electrophysiology modeling deals with a complex network of excitable cells forming an intricate syncytium: the heart. The electrical activity of the heart shows recurrent spatial patterns of activation, known as cardiac alternans, featuring multiscale emerging behavior. On these grounds, we propose a novel mathematical formulation for cardiac electrophysiology modeling and simulation incorporating spatially non-local couplings within a physiological reaction–diffusion scenario. In particular, we formulate, a space-fractional electrophysiological framework, extending and generalizing similar works conducted for the monodomain model. We characterize one-dimensional excitation patterns by performing an extended numerical analysis encompassing a broad spectrum of space-fractional derivative powers and various intra- and extracellular conductivity combinations. Our numerical study demonstrates that (i) symmetric properties occur in the conductivity parameters’ space following the proposed theoretical framework, (ii) the degree of non-local coupling affects the onset and evolution of discordant alternans dynamics, and (iii) the theoretical framework fully recovers classical formulations and is amenable for parametric tuning relying on experimental conduction velocity and action potential morphology.ELKARTEK KK-2020/0000