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.

We generalize to the Kerr spacetime existing self-force results on tidal invariants for particles moving along circular orbits around a Schwarzschild black hole. We obtain linear-in-mass-ratio (conservative) corrections to the quadratic and cubic electric-type invariants and the quadratic magnetic-type invariant in series of the rotation parameter up to the fourth order and through the ninth and eighth post-Newtonian orders, respectively. We then analytically compute the associated eigenvalues of both electric and magnetic tidal tensors.

Twisted gravitational waves (TGWs) are nonplanar unidirectional Ricci-flat solutions of general relativity. Thus far only TGWs of Petrov type II are implicitly known that depend on a solution of a partial differential equation and have wave fronts with negative Gaussian curvature. A special Petrov type D class of such solutions that depends on an arbitrary function is explicitly studied in this paper and its Killing vectors are worked out. Moreover, we concentrate on two solutions of this class, namely, the Harrison solution and a simpler solution we call the w-metric and determine their Penrose plane-wave limits. The corresponding transition from a nonplanar TGW to a plane gravitational wave is elucidated.

We generalize to Kerr spacetime previous gravitational self-force results on gyroscope precession along circular orbits in the Schwarzschild spacetime. In particular we present high order post-Newtonian expansions for the gauge invariant precession function along circular geodesics valid for an arbitrary Kerr spin parameter and show agreement between these results and those derived from the full post-Newtonian conservative dynamics. Finally we present strong field numerical data for a range of the Kerr spin parameter, showing agreement with the gravitational self-force-post-Newtonian results, and the expected lightring divergent behavior. These results provide useful testing benchmarks for self-force calculations in Kerr spacetime, and provide an avenue for translating self-force data into the spin-spin coupling in effective-one-body models.

We perform direct numerical simulations of three-dimensional Rayleigh-Taylor turbulence with a nonuniform singular initial temperature background. In such conditions, the mixing layer evolves under the driving of a varying effective At wood number; the long-time growth is still self-similar, but no longer proportional to t(2) and depends on the singularity exponent c of the initial profile Delta T proportional to z(c). We show that universality is recovered when looking at the efficiency, defined as the ratio of the variation rates of the kinetic energy over the heat flux. A closure model is proposed that is able to reproduce analytically the time evolution of the mean temperature profiles, in excellent agreement with the numerical results. Finally, we reinterpret our findings in the light of spontaneous stochasticity where the growth of the mixing layer is mapped into the propagation of a wave of turbulent fluctuations on a rough background.

We present a boundary condition scheme for the lattice Boltzmann method that has significantly improved stability for modeling turbulent flows while maintaining excellent parallel scalability. Simulations of a three-dimensional lid-driven cavity flow are found to be stable up to the unprecedented Reynolds number Re = 5 x 10(4) for this setup. Excellent agreement with energy balance equations, computational and experimental results are shown. We quantify rises in the production of turbulence and turbulent drag, and determine peak locations of turbulent production.

We propose a mesoscopic model of binary fluid mixtures with tunable viscosity ratio based on a two-range pseudopotential lattice Boltzmann method, for the simulation of soft flowing systems. In addition to the short-range repulsive interaction between species in the classical single-range model, a competing mechanism between the short-range attractive and midrange repulsive interactions is imposed within each species. Besides extending the range of attainable surface tension as compared with the single-range model, the proposed scheme is also shown to achieve a positive disjoining pressure, independently of the viscosity ratio. The latter property is crucial for many microfluidic applications involving a collection of disperse droplets with a different viscosity from that of the continuum phase. As a preliminary application, the relative effective viscosity of a pressure-driven emulsion in a planar channel is computed.

The recognition of spatial patterns within agricultural fields, presenting similar yield potential areas, stable through time, is very important for optimizing agricultural practices. This study proposes the evaluation of different clustering methodologies applied to multispectral satellite time series for retrieving temporally stable (constant) patterns in agricultural fields, related to within-field yield spatial distribution. The ability of different clustering procedures for the recognition and mapping of constant patterns in fields of cereal crops was assessed. Crop vigor patterns, considered to be related to soils characteristics, and possibly indicative of yield potential, were derived by applying the different clustering algorithms to time series of Landsat images acquired on 94 agricultural fields near Rome (Italy). Two different approaches were applied and validated using Landsat 7 and 8 archived imagery. The first approach automatically extracts and calculates for each field of interest (FOI) the Normalized Difference Vegetation Index (NDVI), then exploits the standard K-means clustering algorithm to derive constant patterns at the field level. The second approach applies novel clustering procedures directly to spectral reflectance time series, in particular: (1) standard K-means; (2) functional K-means; (3) multivariate functional principal components clustering analysis; (4) hierarchical clustering. The different approaches were validated through cluster accuracy estimates on a reference set of FOIs for which yield maps were available for some years. Results show that multivariate functional principal components clustering, with an a priori determination of the optimal number of classes for each FOI, provides a better accuracy than those of standard clustering algorithms. The proposed novel functional clustering methodologies are effective and efficient for constant pattern retrieval and can be used for a sustainable management of agricultural fields, depending on farming systems and environmental conditions in different regions.

Stochastic processes are the formal representation of real systems whose evolution in time or space can be assumed as random. This contribution summarizes the necessary mathematical background material on the topic, including terminology and notation. It also illustrates the Markov property (or "lack of memory") of stochastic processes and shows examples of the main Markov processes, that are particularly relevant in applications. Indications are also given on the techniques for the numerical investigation of such processes. Extensive references for both advanced theory and biological/biochemical applications are provided.

The threat, impact and management problems associated with alien plant invasions are increasingly becoming a major issue in environmental conservation. Invasive species cause significant damages, and high associated costs. Controlling them cost-effectively is an ongoing challenge, and mathematical models and optimizations are becoming increasingly popular as a tool to assist managers. The aim of this study is to develop a modelling approach for the optimal spatiotemporal control of invasive species in natural protected areas of high conservation value. Typically, control programs are either distributed uniformly across an area, or applied with a given fixed intensity, although there is no guarantee that such a strategy would be cost-effective at the conservation asset. The proposed approach, based on diffusion equations, is spatially explicit, and includes a functional response (Holling type II) which models the control rate as a function of the invasive species density. We apply a budget constraint to the control program and search for the optimal effort allocation for the minimisation of the invasive species density. Remote sensing derived input layers and expert knowledge have been assimilated in the model to estimate the initial species distribution and its habitat suitability, empirically extracted by a land cover map of the study area. Both the initial density map and the land cover map have been generated by using very high resolution satellite images and validated by means of ground truth data. The approach has been applied to the Alta Murgia National Park, where the EU LIFE Alta Murgia Project is underway with the aim to eradicate Ailanthus altissima, one of the most invasive alien plant species in Europe. The Alta Murgia National Park is one of the study site of the on-going H2020 project ECOPOTENTIAL which aims at the integration of modelling tools and Earth Observations for a sustainable management of protected areas. The H2020 project 'ECOPOTENTIAL: Improving Future Ecosystem Benefits Through Earth Observations' (http://www.ecopotential-project.eu) has received funding from the European Union's Horizon 2020 research and innovation programme under grant agreement No 641762. All ground data regarding Ailanthus altissima (Mill.) Swingle presence and distribution are from the EU LIFE Alta Murgia Project (LIFE12 BIO/IT/000213 titled "Eradication of the invasive exotic plant species Ailanthus altissima from the Alta Murgia National Park" funded by the LIFE+ financial instrument of the European Commission).

We propose a novel in silico model for computing drug release from multi-layer capsules. The diffusion problem in such heterogeneous layer-by-layer composite medium is described by a system of coupled partial differential equations, which we solve analytically using separation of variables. In addition to the conventional partitioning and mass transfer interlayer conditions, we consider a surface finite mass transfer resistance, which corresponds to the case of a coated capsule. The drug concentration in the core and through all the layers, as well as in the external release medium, is given in terms of a Fourier series that we compute numerically to describe and characterize the drug release mechanism.

The nucleotides ATP and ADP regulate many aspects of endothelial cell (EC) biology, including intracellular calcium concentrations, focal adhesion activation, cytoskeletal organization, and cellular motility. In vivo, ECs are constantly under flow, and the concentration of ATP/ADP on the EC surface is determined by the combined effects of nucleotide convective and diffusive transport as well as hydrolysis by ectonucleotidases on the EC surface. In addition, experiments have demonstrated that flow induces ATP release from the cells. Previous computational models have incorporated the above effects and thus described nucleotide concentration at the EC surface. However, it remains unclear what physical processes are responsible for nucleotide regulation. While some EC responses to flow have been shown to be directly driven by shear stress, others appear to also involve a non-negligible contribution of transport. In the present work, we develop a mathematical model and perform numerical simulations to investigate the relative contributions of shear stress and transport to nucleotide concentration at the EC surface. Because in vitro experiments are performed by using confluent cells in some cases and subconfluent cells in other cases, we also investigate the effect of cell density on the results. The outcomes of the simulations demonstrate a complex interplay between shear stress and transport such that transport has a significant contribution at certain shear stress values but not at others. The effect of transport on nucleotide concentration increases with cell density. The present findings enhance our understanding of the mechanisms that govern the regulation at the EC surface under flow. The implications of these findings for downstream responses such as cellular motility merit future investigation.

We present a general mechanistic model of mass diffusion for a composite sphere placed in a large ambient medium. The multi-layer problem is described by a system of diffusion equations coupled via interlayer boundary conditions such as those imposing a finite mass resistance at the extemal surface of the sphere. While the work is applicable to the generic problem of heat or mass transfer in a multi-layer sphere, the analysis and results are presented in the context of drug kinetics for desorbing and absorbing spherical microcapsules. We derive an analytical solution for the concentration in the sphere and in the surrounding medium that avoids any artificial truncation at a finite distance. The closed-form solution in each concentric layer is expressed in terms of a suitably-defined inverse Laplace transform that can be evaluated numerically. Concentration profiles and drug mass curves in the spherical layers and in the external environment are presented and the dependency of the solution on the mass transfer coefficient at the surface of the sphere analyzed.

In this study, we designed a novel drug-eluting coating for vascular implants consisting of a core coating of the anti-proliferative drug docetaxel ( DTX) and a shell coating of the platelet glycoprotein IIb/IIIa receptor monoclonal antibody SZ-21. The core/shell structure was sprayed onto the surface of 316L stainless steel stents using a coaxial electrospray process with the aim of creating a coating that exhibited a differential release of the two drugs. The prepared stents displayed a uniform coating consisting of nano/micro particles. In vitro drug release experiments were performed, and we demonstrated that a biphasic mathematical model was capable of capturing the data, indicating that the release of the two drugs conformed to a diffusion-controlled release system. We demonstrated that our coating was capable of inhibiting the adhesion and activation of platelets, as well as the proliferation and migration of smooth muscle cells ( SMCs), indicating its good biocompatibility and anti-proliferation qualities. In an in vivo porcine coronary artery model, the SZ-21/DTX drug-loaded hydrophobic core/hydrophilic shell particle coating stents were observed to promote re-endothelialization and inhibit neointimal hyperplasia. This core/shell particle-coated stent may serve as part of a new strategy for the differential release of different functional drugs to sequentially target thrombosis and in-stent restenosis during the vascular repair process and ensure rapid re-endothelialization in the field of cardiovascular disease.

The topic of controlled drug release has received much attention in recent years, for example in the design of tablets and in local drug delivery devices such as stents, transdermal patches and orthopaedic implants. In recent years, we have developed a series of models for such devices to describe drug release from a polymeric platform and transport in surrounding biological tissues. These works have culminated in the development of a mathematical model that demonstrates agreement with in-vivo drug release and tissue uptake data, for the case of a drug-eluting stent. If, on the one hand, these fully coupled models are indeed necessary to understand the spatio-temporal drug concentration in the surrounding environment, on the other hand it is clear that device manufacturers cannot intervene on the underlying biology. What they can control, however, are the properties of the polymeric platform to ensure the desired drug release profile is achieved. Indeed, the release profile is known to be a key predictor of device performance. Therefore, in the present work we focus instead primarily on the properties of the drug-containing coating. We consider two particular aspects of the drug coating design. Firstly, the delivery of two therapeutic agents, what we refer to as dual drug delivery. Depending on the particular application in question, it may be desirable for the drugs to be released at similar rates, or perhaps one of the drugs released rapidly with the other being eluted over a longer period of time. In the case of drug-eluting stents, for example, devices which release an anti-proliferative and a 'pro-healing' drug have been proposed, whilst a combination of the two has also been suggested. Secondly, motivated by today's advances in micro and nanotechnology, we propose variable porosity multi-layer coatings as an additional means of controlling the dual drug delivery. In this talk we present our mathematical model of dual drug delivery from a durable polymer coated device. We demonstrate how the release rate of each drug may in principle be controlled by varying the underlying microstructure of polymer coating or by changing the initial loading configuration of the two drugs . Our results show the role of the relevant material parameters used to tailor the release curves to a given application.

Many drugs currently on the market or in development are poorly water-soluble. This presents a serious challenge to the pharmaceutical industry because orally delivered drugs that are poorly soluble tend to pass through the gastrointestinal tract before they can fully dissolve, leading to poor drug bioavailability. One strategy to improve drug solubility is to use a solid dispersion. A solid dispersion typically consists of a hydrophobic drug embedded in a hydrophilic polymer matrix. When the dispersion dissolves in the stomach, drug-polymer interactions maintain the drug at supersaturated levels, thereby accelerating drug dissolution. Unfortunately, despite extensive research, the dissolution behaviour of solid dispersions is only partially understood. This makes the design of successful solid dispersions a somewhat hit and miss affair. Clearly, the construction of reliable mathematical models that capture the key interactions between the drug, polymer and solvent molecules in a dissolving solid dispersion would greatly assist with their rational design. In this presentation, we develop mathematical models describing the storage and dissolution of solid dispersions. The models consist of coupled systems of nonlinear partial differential equations. We then analyze in detail a particular problem describing a solid dispersion in storage. The drug-polymer interaction in the dispersion is modelled using Flory-Huggins theory , and we use the model to identify regimes in the model parameter space that lead to stable, metastable and unstable storage behaviour (phase separation).We illustrate the various phenomena arising using numerical simulations.