Fractional Hereditariness of Lipid Membranes: Instabilities and Linearized Evolution

In this work lipid ordering phase changes arising in planar membrane bilayers is investigated both accounting for elas- ticity alone and for effective viscoelastic response of such assemblies. The mechanical response of such membranes is studied by minimizing the Gibbs free energy which penalizes perturbations of the changes of areal stretch and their gradients only [1]. As material instabilities arise whenever areal stretches characterizing homogeneous configurations lie inside the spinoidal zone of the free energy density, bifurcations from such configurations are shown to occur as oscillatory perturbations of the in-plane displacement. Experimental observations [2] show a power-law in-plane viscous behavior of lipid structures allowing for an effective viscoelastic behavior of lipid membranes [3], which falls in the framework of Fractional Hereditariness. A suitable generalization of the variational principle invoked for the elasticity is applied in this case, and the corresponding Euler-Lagrange equation is found together with a set of bound- ary and initial conditions. Separation of variables allows for showing how Fractional Hereditariness owes bifurcated modes with a larger number of spatial oscillations than the corresponding elastic analog. Indeed, the available range of areal stresses for material instabilities is found to increase with respect to the purely elastic case. Nevertheless, the time evolution of the perturbations solving the Euler-Lagrange equation above exhibits time-decay and the large number of spatial oscillation slowly relaxes, thereby keeping the features of a long-tail type time-response.Comment: 21 pages, 11 figures, special issu

A mechanical picture of fractional-order Darcy equation

In this paper the authors show that fractional-order force-flux relations are obtained considering the flux of a viscous fluid across an elastic porous media. Indeed the one-dimensional fluid mass transport in an unbounded porous media with power-law variation of geometrical and physical properties yields a fractional-order relation among the ingoing flux and the applied pressure to the control section. As a power-law decay of the physical properties from the control section is considered, then the flux is related to a Caputo fractional derivative of the pressure of order 0 ≤ β≤1. If, instead, the physical properties of the media show a power-law increase from the control section, then flux is related to a fractional-order integral of order 0 ≤ β≤1. These two different behaviors may be related to different states of the mass flow across the porous media

Free energy and states of fractional-order hereditariness

Complex materials, often encountered in recent engineering and material sciences applications, show no complete separations between solid and fluid phases. This aspect is reflected in the continuous relaxation time spectra recorded in cyclic load tests. As a consequence the material free energy cannot be defined in a unique manner yielding a significative lack of knowledge of the maximum recoverable work that can extracted from the material. The non-uniqueness of the free energy function is removed in the paper for power-laws relaxation/creep function by using a recently proposed mechanical analogue to fractional-order hereditariness

Fractional order hereditariness of knee human ligament and tendon

Anterior Cruciate Ligament (ACL) is one of the four major ligaments in the knee, playing a critical role in stabilizing the joint. ACL is highly susceptible to injury, overall during sport activities, often precipitating catastrophic long-term joint outcomes. The ideal replacement graft for a torn ACL would restore native anatomy and function to the knee. Most commonly used autograft and allograft, including patellar tendon (P) and hamstring tendon (H) graft, or bioengineered synthetic grafts, may substantially alter the biomechanics of the knee, permitting a return to only moderate physical activities [1]. Main issues are the sub-optimal graft properties [2] and a still incomplete biomechanics characterization [1]. The goal of the present work is to fully characterize and compare the viscoelastic behavior of the ACL and natural/artificial grafts in order to highlight the differences that should be overcome to achieve a successful biomechanical performance and an ideal graft design

A population study of gaseous exoplanets

We present here the analysis of 30 gaseous extrasolar planets, with temperatures between 600 and 2400 K and radii between 0.35 and 1.9 $R_\mathrm{Jup}$. The quality of the HST/WFC3 spatially scanned data combined with our specialized analysis tools allow us to study the largest and most self-consistent sample of exoplanetary transmission spectra to date and examine the collective behavior of warm and hot gaseous planets rather than isolated case-studies. We define a new metric, the Atmospheric Detectability Index (ADI) to evaluate the statistical significance of an atmospheric detection and find statistically significant atmospheres around 16 planets out of the 30 analysed. For most of the Jupiters in our sample, we find the detectability of their atmospheres to be dependent on the planetary radius but not on the planetary mass. This indicates that planetary gravity plays a secondary role in the state of gaseous planetary atmospheres. We detect the presence of water vapour in all of the statistically detectable atmospheres, and we cannot rule out its presence in the atmospheres of the others. In addition, TiO and/or VO signatures are detected with 4$\sigma$ confidence in WASP-76 b, and they are most likely present in WASP-121 b. We find no correlation between expected signal-to-noise and atmospheric detectability for most targets. This has important implications for future large-scale surveys.Comment: 14 pages, 12 figures, 3 tables, published in A

Power-Laws hereditariness of biomimetic ceramics for cranioplasty neurosurgery

We discuss the hereditary behavior of hydroxyapatite-based composites used for cranioplasty surgery in the context of material isotropy. We classify mixtures of collagen and hydroxiapatite composites as biomimetic ceramic composites with hereditary properties modeled by fractional-order calculus. We assume isotropy of the biomimetic ceramic is assumed and provide thermodynamic of restrictions for the material parameters. We exploit the proposed formulation of the fractional-order isotropic hereditariness further by means of a novel mechanical hierarchy corresponding exactly to the three-dimensional fractional-order constitutive model introduced

A new dynamical modeling of the WASP-47 system with CHEOPS observations

Among the hundreds of known hot Jupiters (HJs), only five have been found to have companions on short-period orbits. Within this rare class of multiple planetary systems, the architecture of WASP-47 is unique, hosting an HJ (planet-b) with both an inner and an outer sub-Neptunian mass companion (-e and -d, respectively) as well as an additional non-transiting, long-period giant (-c). The small period ratio between planets -b and -d boosts the transit time variation (TTV) signal, making it possible to reliably measure the masses of these planets in synergy with the radial velocity (RV) technique. In this paper, we present new space- and ground-based photometric data of WASP-47b and WASP-47-d, including 11 unpublished light curves from the ESA mission CHaracterising ExOPlanet Satellite (CHEOPS). We analyzed the light curves in a homogeneous way together with all the publicly available data to carry out a global N-body dynamical modeling of the TTV and RV signals. We retrieved, among other parameters, a mass and density for planet -d of Md = 15.5 ± 0.8 M⊕ and ρd = 1.69 ± 0.22 g cm−3, which is in good agreement with the literature and consistent with a Neptune-like composition. For the inner planet (-e), we found a mass and density of Me = 9.0 ± 0.5 M⊕ and ρe = 8.1 ± 0.5 g cm−3, suggesting an Earth-like composition close to other ultra-hot planets at similar irradiation levels. Though this result is in agreement with previous RV plus TTV studies, it is not in agreement with the most recent RV analysis (at 2.8σ), which yielded a lower density compatible with a pure silicate composition. This discrepancy highlights the still unresolved issue of suspected systematic offsets between RV and TTV measurements. In this paper, we also significantly improve the orbital ephemerides of all transiting planets, which will be crucial for any future follow-up