Modelling optical emission of Ultra-luminous X-ray Sources accreting above the Eddington limit

We study the evolution of binary systems of Ultra-luminous X-ray sources and compute their optical emission assuming accretion onto a black hole via a non standard, advection-dominated slim disc with an outflow. We consider systems with black holes of $20M_{\odot}$ and $100M_{\odot}$, and donor masses between $8M_{\odot}$ and $25M_{\odot}$. Super-critical accretion has considerable effects on the optical emission. The irradiating flux in presence of an outflow remains considerably stronger than that produced by a standard disc. However, at very high accretion rates the contribution of X-ray irradiation becomes progressively less important in comparison with the intrinsic flux emitted from the disc. After Main Sequence the evolutionary tracks of the optical counterpart on the colour-magnitude diagram are markely different from those computed for Eddington-limited accretion. Systems with stellar-mass black holes and $12-20 M_{\odot}$ donors accreting supercritically are characterized by blue colors (F450W -- F555W $\simeq - 0.2 : +0.1$) and high luminosity ($M_{V} \simeq - 4 : - 6.5$). Systems with more massive black holes accreting supercritically from evolved donors of similar mass have comparable colours but can reach $M_V \simeq - 8$. We apply our model to NGC 1313 X-2 and NGC 4559 X-7. Both sources are well represented by a system accreting above Eddington from a massive evolved donor. For NGC 1313 X-2 the agreement is for a $\sim 20M_{\odot}$ black hole, while NGC4559 X-7 requires a significantly more massive black hole.Comment: 13 pages, 15 figures, Accepted for publication in MNRAS; Acknowledgments adde

Maximal tori of monodromy groups of FF-isocrystals and an application to abelian varieties

Let $X_0$ be a smooth geometrically connected variety defined over a finite field $\mathbb F_q$ and let $\mathcal E_0^{\dagger}$ be an irreducible overconvergent $F$-isocrystal on $X_0$. We show that if a subobject of minimal slope of the underlying convergent F-isocrystal $\mathcal E_0$ admits a non-zero morphism to $\mathcal O_{X_0}$ as convergent isocrystal, then $\mathcal E_0^{\dagger}$ is isomorphic to $\mathcal O^{\dagger}_{X_0}$ as overconvergent isocrystal. This proves a special case of a conjecture of Kedlaya. The key ingredient in the proof is the study of the monodromy group of $\mathcal E_0^{\dagger}$ and the subgroup defined by $\mathcal E_0$. The new input in this setting is that the subgroup contains a maximal torus of the entire monodromy group. This is a consequence of the existence of a Frobenius torus of maximal dimension. As an application, we prove a finiteness result for the torsion points of abelian varieties, which extends the previous theorem of Lang-N\'eron and answers positively a question of Esnault.Comment: 16 pages; minor edit

Mechanics and polarity in cell motility

The motility of a fish keratocyte on a flat substrate exhibits two distinct regimes: the non-migrating and the migrating one. In both configurations the shape is fixed in time and, when the cell is moving, the velocity is constant in magnitude and direction. Transition from a stable configuration to the other one can be produced by a mechanical or chemotactic perturbation. In order to point out the mechanical nature of such a bistable behaviour, we focus on the actin dynamics inside the cell using a minimal mathematical model. While the protein diffusion, recruitment and segregation govern the polarization process, we show that the free actin mass balance, driven by diffusion, and the polymerized actin retrograde flow, regulated by the active stress, are sufficient ingredients to account for the motile bistability. The length and velocity of the cell are predicted on the basis of the parameters of the substrate and of the cell itself. The key physical ingredient of the theory is the exchange among actin phases at the edges of the cell, that plays a central role both in kinematics and in dynamics

Force traction microscopy: An inverse problem with pointwise observations

Force Traction Microscopy is an inversion method that allows to obtain the stress field applied by a living cell on the environment on the basis of a pointwise knowledge of the displacement produced by the cell itself. This classical biophysical problem, usually addressed in terms of Green functions, can be alternatively tackled using a variational framework and then a finite elements discretization. In such a case, a variation of the error functional under suitable regularization is operated in view of its minimization. This setting naturally suggests the introduction of a new equation, based on the adjoint operator of the elasticity problem. In this paper we illustrate the rigorous theory of the two-dimensional and three dimensional problem, involving in the former case a distributed control and in the latter case a surface control. The pointwise observations require to exploit the theory of elasticity extended to forcing terms that are Borel measure

Behavior of cell aggregates under force-controlled compression

In this paper we study the mechanical behavior of multicellular aggregates under compressive loads and subsequent releases. Some analytical properties of the solution are discussed and numerical results are presented for a compressive test under constant force imposed on a cylindrical specimen. The case of a cycle of compressions at constant force and releases is also considered. We show that a steady state configuration able to bear the load is achieved. The analytical determination of the steady state value allows to obtain mechanical parameters of the cellular structure that are not estimable from creep tests at constant stres

Effective governing equations for poroelastic growing media

A new mathematical model is developed for the macroscopic behaviour of a porous, linear elastic solid, saturated with a slowly flowing incompressible, viscous fluid, with surface accretion of the solid phase. The derivation uses a formal two-scale asymptotic expansion to exploit the well-separated length scales of the material: the pores are small compared to the macroscale, with a spatially periodic microstructure. Surface accretion occurs at the interface between the solid and fluid phases, resulting in growth of the solid phase through mass exchange from the fluid at a prescribed rate (and vice versa). The averaging derives a new poroelastic model, which reduces to the classical result of Burridge and Keller in the limit of no growth. The new model is of relevance to a large range of applications including packed snow, tissue growth, biofilms and subsurface rocks or soils