The equations describing engineering and real-life models are usually derived in an approximated way. Thus, in most cases it is necessary to deal with equations containing some kind of perturbation. In this paper we consider fractional dfferential equations and study the eects on the continuous and numerical solution, of perturbations on the given function, over long-time intervals. Some bounds on the global error are also determined.

Recently, an algorithm for coupling a Finite Volume (FV) method, that discretize the Navier-Stokes equations on block structured Eulerian grids, with the weakly-compressible Lagrangian Smoothed Particle Hydrodynamics (SPH) was presented in [16]. The algorithm takes advantage of the SPH method to discretize flow regions close to free-surfaces and of the FV method to resolve the bulk flow and the wall regions. The continuity between the two solutions is guaranteed by overlapping zones. Here we extend the algorithm by adding the possibility to have: 1) net mass transfer between the SPH and FV sub-domains; 2) free-surface across the overlapping region. In this context, particle generation at common boundaries is required to prevent depletion or clustering of particles. This operation is not trivial, because consistency between the Lagrangian and Eulerian description of the flow must be retained to ensure mass conservation. We propose here a new coupling paradigm that extends the algorithm developed in [16] and renders it suitable to test cases where vorticity and free surface significantly pass from one domain to the other. On the SPH side, a novel technique for the creation/deletion of particle was developed. On the FV side, the information recovered from the SPH solver are exploited to improve free surface prediction in a fashion that resemble the Particle Level-Set algorithms. The combination of the two new features was tested and validated in a number of test cases where both vorticity and front evolution are important. Convergence and robustness of the algorithm are shown.

The understanding of the performance of a propeller in realistic operative conditions is nowadays a key issue for improving design techniques, guaranteeing safety and continuity of operation at sea, and reducing maintenance costs. In this paper, a summary of the recent research carried out at CNR-INSEAN devoted to the analysis of propeller loads in realistic operative scenarios, with particular emphasis on the in-plane loads, is presented. In particular, the experimental results carried out on a free running maneuvering model equipped with a novel force transducer are discussed and supported by CFD (Computational Fluid Dynamics) analysis and the use of a simplified propeller model, based on Blade Element Momentum Theory, with the aim of achieving a deeper understanding of the mechanisms that govern the functioning of the propeller in off-design. Moreover, the analysis includes the scaling factors that can be used to obtain a prediction from model measurements, the propeller radial force being the primary cause of failures of the shaft bearings. In particular, the analysis highlighted that cavitation at full scale can cause the increment of in-plane loads by about 20% with respect to a non-cavitating case, that that in-plane loads could be more sensitive to cavitation than thrust and torque, and that Reynolds number effect is negligible. For the analysis of cavitation, an alternative version of the BEMT solver, improved with cavitation linear theory, was developed.

In this note we prove a modular variable Orlicz inequality for the local maximal operator. This result generalizes several Orlicz and variable exponent modular inequalities that have appeared previously in the literature.

We present a Python open-source package called Visbrain that offers a coherent visualization suite for multi-modal brain data (intracranial and scalp EEG, MEG, structural and functional MRI). The current version of Visbrain is essentially articulated around four modules dedicated to 1) 3D visualization of functional and/or connectivity results (Brain), 2) polysomnographic data visualization and sleep analysis (Sleep, [1]), 3) data mining and basic plotting functions (Signal), 4) topographic representation (Topo). We also included functions for page layout and export of paper-ready high-quality figure. Those modules come with a modular and powerful graphical user interfaces built with PyQt. Each module has been developed in collaboration with neuroscientists and experts in the field and provides a comprehensive set of functionalities. Visbrain is developed on top of VisPy [2], a Python package providing high performance 2D and 3D visualization by leveraging the computational power of the graphic card. This package is available on Github and comes with an extensive documentation, examples and datasets (see http://visbrain.org).

The containment of the invasive species is a widespread problem in the environmental management, with a significant economic impact. We analyze an optimal control model which aims to find the best temporal resource allocation strategy for the removal of an invasive species. We study the existence and uniqueness of the optimal solution when both initial and final conditions on the state variable are fixed. We derive and alternative optimality system in the state and control variables and we use the phase-space analysis to provide qualitative insights into the system dynamics and to analyze the behavior of the optimal solution. Finally, we find the expression of the optimal solution for the free terminal time problem. We apply these techniques to two case studies: the case of feral cats population in Australia, where we assume a logistic growth; the control of wild-boars populations in Italy, where we include an Allee effect in the population growth. This work has been carried out within the H2020 project 'ECOPOTENTIAL: Improving Future Ecosystem Benefits Through Earth Observations'. The project has received funding from the European Union's Horizon 2020 research and innovation programme under grant agreement No 641762. References [1] Baker, C. M., F. Diele, D. Lacitignola, C. Marangi, A. Martiradonna (2017). Optimal control of invasive species through a dynamical systems approach, Discrete and Continuous Dynamical System, under review. [2] Baker, C.M., M. Bode (2013). Spatial control of invasive species in conservation landscapes, Comput. Manag. Sci., 10, 331-351. [3] Lenhart, S., J.T. Workman (2007). Optimal control applied to biological models, Chapman & Hall/CRC, London.

This BMC special issue collects a selection of eleven revised and extended papers presented at, or originated from, the 2015 and 2016 editions of the international meeting on Computational Intelligence methods for Bioinformatics and Biostatistics, CIBB2015 and CIBB2016, respectively.

Selection of papers from BBCC2017

The definition of the Simon tensor, originally given only in Kerr spacetime and associated with the static family of observers, is generalized to any spacetime and to any possible observer family. Such generalization is obtained by a standard '3 + 1' splitting of the Bianchi identities, which are rewritten here as a 'balance equation' between various spatial fields, associated with the kinematical properties of the observer congruence and representing the spacetime curvature.

The (first-order) gravitational self-force correction to the spin-orbit precession of a spinning compact body along a slightly eccentric orbit around a Schwarzschild black hole is computed through the ninth postNewtonian order and to second order in the eccentricity, improving recent results by Kavanagh et al. [Phys. Rev. D 96, 064012 (2017)]. We show that our higher-accurate theoretical estimates of the spin precession exhibits an improved agreement with corresponding numerical self-force data. We convert our new theoretical results into its corresponding effective-one-body counterpart, thereby determining several new post-Newtonian terms in the gyrogravitomagnetic ratio g(S*).

In general relativity (GR), linearized gravitational waves propagating in empty Minkowski spacetime along a fixed spatial direction have the property that the wave front is the Euclidean plane. Beyond the linear regime, exact plane waves in GR have been studied theoretically for a long time and many exact vacuum solutions of the gravitational field equations are known that represent plane gravitational waves. These have parallel rays and uniform wave fronts. It turns out, however, that GR also admits exact solutions representing gravitational waves propagating along a fixed direction that are nonplanar. The wave front is then nonuniform and the bundle of rays is twisted. We find a class of solutions representing nonplanar unidirectional gravitational waves and study some of the properties of these twisted waves.

We study the metric perturbations induced by a classical spinning particle moving along a circular orbit on a Schwarzschild background, limiting the analysis to effects which are first order in spin. The particle is assumed to move on the equatorial plane and has its spin aligned with the z axis. The metric perturbations are obtained by using two different approaches, i.e., by working in two different gauges: the Regge-Wheeler gauge (using the Regge-Wheeler-Zerilli formalism) and a radiation gauge (using the Teukolsky formalism). We then compute the linear-in-spin contribution to the first-order self-force contribution to Detweiler's redshift invariant up to the 8.5 post-Newtonian order. We check that our result is the same in both gauges, as appropriate for a gauge-invariant quantity, and agrees with the currently known 3.5 post-Newtonian results.

The energy content of (exact) electromagnetic and gravitational plane waves is studied in terms of super-energy tensors (the Bel, Bel-Robinson and the-less familiar-Chevreton tensors) and natural observers. Starting from the case of single waves, the more interesting situation of colliding waves is then discussed, where the nonlinearities of the Einstein's theory play an important role. The causality properties of the super-momentum four vectors associated with each of these tensors are also investigated when passing from the single-wave regions to the interaction region.

Twisted gravitational waves (TGWs) are nonplanar waves with twisted rays that move along a fixed direction in space. We study further the physical characteristics of a recent class of Ricci-flat solutions of general relativity representing TGWs with wave fronts that have negative Gaussian curvature. In particular, we investigate the influence of TGWs on the polarization of test electromagnetic waves and on the motion of classical spinning test particles in such radiation fields. To distinguish the polarization effects of twisted waves from plane waves, we examine the theoretical possibility of existence of spin-twist coupling and show that this interaction is generally consistent with our results.

We study trapped surfaces from the point of view of local isometric embedding into 3D Riemannian manifolds. When a two-surface is embedded into 3D Euclidean space, the problem of finding all surfaces applicable upon it gives rise to a non-linear partial differential equation of the Monge-Ampere type, first discovered by Darboux, and later reformulated by Weingarten. Even today, this problem remains very difficult, despite some remarkable results. We find an original way of generalizing the Darboux technique, which leads to a coupled set of six non-linear partial differential equations. For the 3-manifolds occurring in Friedmann-(Lemaitre)-Robertson-Walker cosmologies, we show that the local isometric embedding of trapped surfaces into them can be proved by solving just one non-linear equation. Such an equation is here solved for the three kinds of Friedmann model associated with positive, zero, negative curvature of spatial sections, respectively.

We compute the rotations, during a scattering encounter, of the spins of two gravitationally interacting particles at second order in the gravitational constant (second post-Minkowskian order). Following a strategy introduced by us D. Bini and T. Damour, Phys. Rev. D 96, 104038 2017 PRVDAQ 10.1103/PhysRevD.96.104038, we transcribe our result into a correspondingly improved knowledge of the spin-orbit sector of the effective one-body (EOB) Hamiltonian description of the dynamics of spinning binary systems. We indicate ways of resumming our results for defining improved versions of spinning EOB codes which might help in providing a better analytical description of the dynamics of coalescing spinning binary black holes.

We investigate the hyperbolic scattering of test particles, spinning test particles, and particles with spin-induced quadrupolar structure by a Kerr black hole in the ultrarelativistic regime. We also study how the features of the scattering process modify if the source of the background gravitational field is endowed with a nonzero mass quadrupole moment as described by the (approximate) Hartle-Thorne solution. We compute the scattering angle either in closed analytical form, when possible, or as a power series of the (dimensionless) inverse impact parameter. It is a function of the parameters characterizing the source (intrinsic angular momentum and mass quadrupole moment) as well as the scattered body (spin and polarizability constant). Measuring the scattering angle thus provides useful information to determine the nature of the two components of the binary system undergoing high-energy scattering processes.

We compute gravitational self-force (conservative) corrections to tidal invariants for spinning particles moving along circular orbits in a Schwarzschild spacetime. In particular, we consider the square and the cube of the gravitoelectric quadrupolar tidal tensor and the square of the gravitomagnetic quadrupolar tidal tensor. Our results are accurate to first order in spin and through the 9.5 post-Newtonian order. We also compute the associated electric-type and magnetic-type eigenvalues.

We study tidal effects induced by a particle moving along a slightly eccentric equatorial orbit in a Schwarzschild spacetime within the gravitational self-force framework. We compute the first-order (conservative) corrections in the mass ratio to the eigenvalues of the electric-type and magnetic-type tidal tensors up to the second order in eccentricity and through the 9.5 post-Newtonian order. Previous results on circular orbits are thus generalized and recovered in a proper limit.