A mixed finite element method for nearly incompressible multiple-network poroelasticity

In this paper, we present and analyze a new mixed finite element formulation of a general family of quasi-static multiple-network poroelasticity (MPET) equations. The MPET equations describe flow and deformation in an elastic porous medium that is permeated by multiple fluid networks of differing characteristics. As such, the MPET equations represent a generalization of Biot's equations, and numerical discretizations of the MPET equations face similar challenges. Here, we focus on the nearly incompressible case for which standard mixed finite element discretizations of the MPET equations perform poorly. Instead, we propose a new mixed finite element formulation based on introducing an additional total pressure variable. By presenting energy estimates for the continuous solutions and a priori error estimates for a family of compatible semi-discretizations, we show that this formulation is robust in the limits of incompressibility, vanishing storage coefficients, and vanishing transfer between networks. These theoretical results are corroborated by numerical experiments. Our primary interest in the MPET equations stems from the use of these equations in modelling interactions between biological fluids and tissues in physiological settings. So, we additionally present physiologically realistic numerical results for blood and tissue fluid flow interactions in the human brain

Parameter robust preconditioning by congruence for multiple-network poroelasticity

The mechanical behaviour of a poroelastic medium permeated by multiple interacting fluid networks can be described by a system of time-dependent partial differential equations known as the multiple-network poroelasticity (MPET) equations or multi-porosity/multi-permeability systems. These equations generalize Biot's equations, which describe the mechanics of the one-network case. The efficient numerical solution of the MPET equations is challenging, in part due to the complexity of the system and in part due to the presence of interacting parameter regimes. In this paper, we present a new strategy for efficiently and robustly solving the MPET equations numerically. In particular, we introduce a new approach to formulating finite element methods and associated preconditioners for the MPET equations. The approach is based on designing transformations of variables that simultaneously diagonalize (by congruence) the equations' key operators and subsequently constructing parameter-robust block-diagonal preconditioners for the transformed system. Our methodology is supported by theoretical considerations as well as by numerical results

Follow-up Studies of the Pulsating Magnetic White Dwarf SDSS J142625.71+575218.3

We present a follow-up analysis of the unique magnetic luminosity-variable carbon-atmosphere white dwarf SDSS J142625.71+575218.3. This includes the results of some 106.4 h of integrated light photometry which have revealed, among other things, the presence of a new periodicity at 319.720 s which is not harmonically related to the dominant oscillation (417.707 s) previously known in that star. Using our photometry and available spectroscopy, we consider the suggestion made by Montgomery et al. (2008) that the luminosity variations in SDSS J142625.71+575218.3 may not be caused by pulsational instabilities, but rather by photometric activity in a carbon-transferring analog of AM CVn. This includes a detailed search for possible radial velocity variations due to rapid orbital motion on the basis of MMT spectroscopy. At the end of the exercise, we unequivocally rule out the interacting binary hypothesis and conclude instead that, indeed, the luminosity variations are caused by g-mode pulsations as in other pulsating white dwarfs. This is in line with the preferred possibility put forward by Montgomery et al. (2008).Comment: 11 pages in emulateApJ, 12 figures, accepted for publication in Ap

Type Ia supernovae and the ^{12}C+^{12}C reaction rate

The experimental determination of the cross-section of the ^{12}C+^{12}C reaction has never been made at astrophysically relevant energies (E<2 MeV). The profusion of resonances throughout the measured energy range has led to speculation that there is an unknown resonance at E\sim1.5 MeV possibly as strong as the one measured for the resonance at 2.14 MeV. We study the implications that such a resonance would have for the physics of SNIa, paying special attention to the phases that go from the crossing of the ignition curve to the dynamical event. We use one-dimensional hydrostatic and hydrodynamic codes to follow the evolution of accreting white dwarfs until they grow close to the Chandrasekhar mass and explode as SNIa. In our simulations, we account for a low-energy resonance by exploring the parameter space allowed by experimental data. A change in the ^{12}C+^{12}C rate similar to the one explored here would have profound consequences for the physical conditions in the SNIa explosion, namely the central density, neutronization, thermal profile, mass of the convective core, location of the runaway hot spot, or time elapsed since crossing the ignition curve. For instance, with the largest resonance strength we use, the time elapsed since crossing the ignition curve to the supernova event is shorter by a factor ten than for models using the standard rate of ^{12}C+^{12}C, and the runaway temperature is reduced from \sim8.14\times10^{8} K to \sim4.26\times10^{8} K. On the other hand, a resonance at 1.5 MeV, with a strength ten thousand times smaller than the one measured at 2.14 MeV, but with an {\alpha}/p yield ratio substantially different from 1 would have a sizeable impact on the degree of neutronization of matter during carbon simmering. We conclude that a robust understanding of the links between SNIa properties and their progenitors will not be attained until the ^{12}C+^{12}C reaction rate is measured at energies \sim1.5 MeV.Comment: 15 pages, 6 tables, 10 figures, accepted for Astronomy and Astrophysic

Extended calibration range for prompt photon emission in ion beam irradiation

Monitoring the dose delivered during proton and carbon ion therapy is still a matter of research. Among the possible solutions, several exploit the measurement of the single photon emission from nuclear decays induced by the irradiation. To fully characterize such emission the detectors need development, since the energy spectrum spans the range above the MeV that is not traditionally used in medical applications. On the other hand, a deeper understanding of the reactions involving gamma production is needed in order to improve the physic models of Monte Carlo codes, relevant for an accurate prediction of the prompt-gamma energy spectrum.This paper describes a calibration technique tailored for the range of energy of interest and reanalyzes the data of the interaction of a 80MeV/u fully stripped carbon ion beam with a Poly-methyl methacrylate target. By adopting the FLUKA simulation with the appropriate calibration and resolution a significant improvement in the agreement between data and simulation is reported.Comment: 4 pages, 7 figures, Submitted to JINS

Measurement of secondary particle production induced by particle therapy ion beams impinging on a PMMA target

Particle therapy is a technique that uses accelerated charged ions for cancer treatment and combines a high irradiation precision with a high biological effectiveness in killing tumor cells [1]. Informations about the secondary particles emitted in the interaction of an ion beam with the patient during a treatment can be of great interest in order to monitor the dose deposition. For this purpose an experiment at the HIT (Heidelberg Ion-Beam Therapy Center) beam facility has been performed in order to measure fluxes and emission profiles of secondary particles produced in the interaction of therapeutic beams with a PMMA target. In this contribution some preliminary results about the emission profiles and the energy spectra of the detected secondaries will be presente