Inertial Motions of a Rigid Body with a cavity filled with a viscous liquid

We study inertial motions of the coupled system, S, constituted by a rigid body containing a cavity that is completely filled with a viscous liquid. We show that for data of arbitrary size (initial kinetic energy and total angular momentum) every weak solution (a la Leray-Hopf) converges, as time goes to infinity, to a uniform rotation, thus proving a famous "conjecture" of Zhukovskii. Moreover we show that, in a wide range of initial data, this rotation must occur along the central axis of inertia of S that has the largest moment of inertia. Furthermore, necessary and sufficient conditions for the rigorous nonlinear stability of permanent rotations are provided, which improve and/or generalize results previously given by other authors under different types of approximation of the original equations and/or suitable symmetry assumptions on the shape of the cavity. Finally, we present a number of results obtained by a targeted numerical simulation that, on the one hand, complement the analytical findings, whereas, on the other hand, point out new features that the analysis is yet not able to catch, and, as such, lay the foundation for interesting and challenging future investigation.Comment: Some of the main results proved in this paper were previously announced in Comptes Rendus Mecanique, Vol. 341, 760--765 (2013

A Lagrange multiplier method for a Stokes-Biot fluid-poroelastic structure interaction model

We study a finite element computational model for solving the coupled problem arising in the interaction between a free fluid and a fluid in a poroelastic medium. The free fluid is governed by the Stokes equations, while the flow in the poroelastic medium is modeled using the Biot poroelasticity system. Equilibrium and kinematic conditions are imposed on the interface. A mixed Darcy formulation is employed, resulting in continuity of flux condition of essential type. A Lagrange multiplier method is employed to impose weakly this condition. A stability and error analysis is performed for the semi-discrete continuous-in-time and the fully discrete formulations. A series of numerical experiments is presented to confirm the theoretical convergence rates and to study the applicability of the method to modeling physical phenomena and the sensitivity of the model with respect to its parameters

Partitioning strategies for the interaction of a fluid with a poroelastic material based on a Nitsche's coupling approach

We develop a computational model to study the interaction of a fluid with a poroelastic material. The coupling of Stokes and Biot equations represents a prototype problem for these phenomena, which feature multiple facets. On one hand it shares common traits with fluid-structure interaction. On the other hand it resembles the Stokes-Darcy coupling. For these reasons, the numerical simulation of the Stokes-Biot coupled system is a challenging task. The need of large memory storage and the difficulty to characterize appropriate solvers and related preconditioners are typical shortcomings of classical discretization methods applied to this problem. The application of loosely coupled time advancing schemes mitigates these issues because it allows to solve each equation of the system independently with respect to the others. In this work we develop and thoroughly analyze a loosely coupled scheme for Stokes-Biot equations. The scheme is based on Nitsche's method for enforcing interface conditions. Once the interface operators corresponding to the interface conditions have been defined, time lagging allows us to build up a loosely coupled scheme with good stability properties. The stability of the scheme is guaranteed provided that appropriate stabilization operators are introduced into the variational formulation of each subproblem. The error of the resulting method is also analyzed, showing that splitting the equations pollutes the optimal approximation properties of the underlying discretization schemes. In order to restore good approximation properties, while maintaining the computational efficiency of the loosely coupled approach, we consider the application of the loosely coupled scheme as a preconditioner for the monolithic approach. Both theoretical insight and numerical results confirm that this is a promising way to develop efficient solvers for the problem at hand

Contract agreements via logic

We relate two contract models: one based on event structures and game theory, and the other one based on logic. In particular, we show that the notions of agreement and winning strategies in the game-theoretic model are related to that of provability in the logical model.Comment: In Proceedings ICE 2013, arXiv:1310.401

A computational study of cancer hyperthermia based on vascular magnetic nanoconstructs

The application of hyperthermia to cancer treatment is studied using a novel model arising from the fundamental principles of flow, mass and heat transport in biological tissues. The model is defined at the scale of the tumour microenvironment and an advanced computational scheme called the embedded multiscale method is adopted to solve the governing equations. More precisely, this approach involves modelling capillaries as one-dimensional channels carrying flow, and special mathematical operators are used to model their interaction with the surrounding tissue. The proposed computational scheme is used to analyse hyperthermic treatment of cancer based on systemically injected vascular magnetic nanoconstructs carrying super-paramagnetic iron oxide nanoparticles. An alternating magnetic field is used to excite the nanoconstructs and generate localized heat within the tissue. The proposed model is particularly adequate for this application, since it has a unique capability of incorporating microvasculature configurations based on physiological data combined with coupled capillary flow, interstitial filtration and heat transfer. A virtual tumour model is initialized and the spatio-temporal distribution of nanoconstructs in the vascular network is analysed. In particular, for a reference iron oxide concentration, temperature maps of several different hypothesized treatments are generated in the virtual tumour model. The observations of the current study might in future guide the design of more efficient treatments for cancer hyperthermia

A Deep Learning approach to Reduced Order Modelling of Parameter Dependent Partial Differential Equations

Within the framework of parameter dependent PDEs, we develop a constructive approach based on Deep Neural Networks for the efficient approximation of the parameter-to-solution map. The research is motivated by the limitations and drawbacks of state-of-the-art algorithms, such as the Reduced Basis method, when addressing problems that show a slow decay in the Kolmogorov n-width. Our work is based on the use of deep autoencoders, which we employ for encoding and decoding a high fidelity approximation of the solution manifold. In order to fully exploit the approximation capabilities of neural networks, we consider a nonlinear version of the Kolmogorov n-width over which we base the concept of a minimal latent dimension. We show that this minimal dimension is intimately related to the topological properties of the solution manifold, and we provide some theoretical results with particular emphasis on second order elliptic PDEs. Finally, we report numerical experiments where we compare the proposed approach with classical POD-Galerkin reduced order models. In particular, we consider parametrized advection-diffusion PDEs, and we test the methodology in the presence of strong transport fields, singular terms and stochastic coefficients

A Semantic-Based Framework for Summarization and Page Segmentation in Web Mining

This chapter addresses two crucial issues that arise when one applies Web-mining techniques for extracting relevant information. The first one is the acquisition of useful knowledge from textual data; the second issue stems from the fact that a web page often proposes a considerable amount of \u2018noise\u2019 with respect to the sections that are truly informative for the user's purposes. The novelty contribution of this work lies in a framework that can tackle both these tasks at the same time, supporting text summarization and page segmentation. The approach achieves this goal by exploiting semantic networks to map natural language into an abstract representation, which eventually supports the identification of the topics addressed in a text source. A heuristic algorithm uses the abstract representation to highlight the relevant segments of text in the original document. The verification of the approach effectiveness involved a publicly available benchmark, the DUC 2002 dataset, and satisfactory results confirmed the method effectiveness

An approximate randomization-based neural network with dedicated digital architecture for energy-constrained devices

Variable energy constraints affect the implementations of neural networks on battery-operated embedded systems. This paper describes a learning algorithm for randomization-based neural networks with hard-limit activation functions. The approach adopts a novel cost function that balances accuracy and network complexity during training. From an energyspecific perspective, the new learning strategy allows to adjust, dynamically and in real time, the number of operations during the network’s forward phase. The proposed learning scheme leads to efficient predictors supported by digital architectures. The resulting digital architecture can switch to approximate computing at run time, in compliance with the available energy budget. Experiments on 10 real-world prediction testbeds confirmed the effectiveness of the learning scheme. Additional tests on limited-resource devices supported the implementation efficiency of the overall design approac