4,925 research outputs found
Reduced Basis Approaches to Bifurcating Nonlinear Parametrized Partial Differential Equations
No full text
Driving bifurcating parametrized nonlinear PDEs by optimal control strategies: application to Navier-Stokes equations with model order reduction
Full text linkThis work deals with optimal control problems as a strategy to drive
bifurcating solution of nonlinear parametrized partial differential equations
towards a desired branch. Indeed, for these governing equations, multiple
solution configurations can arise from the same parametric instance. We thus
aim at describing how optimal control allows to change the solution profile and
the stability of state solution branches. First of all, a general framework for
nonlinear optimal control problem is presented in order to reconstruct each
branch of optimal solutions, discussing in detail the stability properties of
the obtained controlled solutions. Then, we apply the proposed framework to
several optimal control problems governed by bifurcating Navier-Stokes
equations in a sudden-expansion channel, describing the qualitative and
quantitative effect of the control over a pitchfork bifurcation, and commenting
in detail the stability eigenvalue analysis of the controlled state. Finally,
we propose reduced order modeling as a tool to efficiently and reliably solve
parametric stability analysis of such optimal control systems, which can be
challenging to perform with standard discretization techniques such as Finite
Element Method
Reduced order models for parametric bifurcation problems in nonlinear PDEs
Full text linkThis work is concerned with the analysis and the development of efficient Reduced Order Models (ROMs) for the numerical investigation of complex bifurcating phenomena held by nonlinear parametrized Partial Differential Equations (PDEs) in many physical contexts, from Continuum Mechanics to Quantum Mechanics passing through Fluid Dynamics. Indeed, the reconstruction of the bifurcation diagrams, which highlight the singularities of the equations and the possible coexisting states, requires a huge computational effort, especially in the multi-parameter context.
To overcome this issue, we developed a reduced order branch-wise algorithm for the efficient investigation of such complex behaviour, with a focus on the stability properties of the solutions. We applied our approach to the Von Kármán equations for buckling plates, the Gross-Pitaevskii equations in Bose-Einstein condensates, the Hyperelastic models for bending beams and the Navier-Stokes model for the flow in a channel.
Several issues and questions arise when dealing with the approximation and the reduction of bifurcating phenomena, we addressed them by considering new models and emerging methodologies. In particular, we developed a reduced order approach to deflated continuation method, to efficiently discover new solution branches. We proposed and discussed different Optimal Control Problems (OCPs) to steer the bifurcating behaviour towards desired states.
Finally, we exploited a Neural Network approach based on the Proper Orthogonal Decomposition (POD-NN), as an alternative to the Empirical Interpolation Method (EIM), to develop a reduced manifold based algorithm for the efficient detection of the bifurcation points
Optical coherence tomography diagnostic signs in posterior uveitis.
Full text linkA diagnostic sign refers to a quantifiable biological parameter that is measured and evaluated as an indicator of normal biological, pathogenic, or pharmacologic responses to a therapeutic intervention. When used in translational research discussions, the term itself often alludes to a signs used to accelerate or aid in diagnosis or monitoring and provide insight into "personalized" medicine. Many new diagnostic signs are being developed that involve imaging technology. Optical coherence tomography is an imaging technique that provides in vivo quasi-histological images of the ocular tissues and as such it's able to capture the structural and functional modifications that accompany inflammation and infection of the posterior part of the eye. From the hyperreflective inflammatory cells and deposits in the vitreous and on the hialoid, to the swollen photoreceptors bodies in multiple evanescent white dots syndrome, and from optical difference of the subretinal fluid compartments in Vogt-Koyanagi-Harada disease to the hyporeflective granulomas in the choroid, these tomographical signs can be validate to reach the status of biomarkers. Non-invasive imaging diagnostic signs of inflammation can be very useful to clinicians seeking to make a diagnosis and can represent a dataset for machine learning to offer a more empirical approach to the detection of posterior uveitis
An artificial neural network approach to bifurcating phenomena in computational fluid dynamics
No full textThis work deals with the investigation of bifurcating fluid phenomena using a reduced order modelling setting aided by artificial neural networks. We discuss the POD-NN approach dealing with non-smooth solutions set of nonlinear parametrized PDEs. Thus, we study the Navier-Stokes equations describing: (i) the Coanda effect in a channel, and (ii) the lid driven triangular cavity flow, in a physical/geometrical multi-parametrized setting, considering the effects of the domain's configuration on the position of the bifurcation points. Finally, we propose a reduced manifold-based bifurcation diagram for a non-intrusive recovery of the critical points evolution. Exploiting such detection tool, we are able to efficiently obtain information about the pattern flow behaviour, from symmetry breaking profiles to attaching/spreading vortices, even in the advection-dominated regime.MCS
Real Time Reduced Order Computational Mechanics Parametric PDEs Worked Out Problems
No full textThe book is made up by several worked out problems concerning the application of reduced order modeling to different parametric partial differential equations problems with an increasing degree of complexity.
This work is based on some experience acquired during lectures and exercises in classes taught at SISSA Mathematics Area in the Doctoral Programme “Mathematical Analysis, Modelling and Applications”, especially in computational mechanics classes, as well as regular courses previously taught at EPF Lausanne and during several summer and winter schools. The book is a companion for master and doctoral degree classes by allowing to go more deeply inside some partial differential equations worked out problems, examples and even exercises, but it is also addressed for researchers who are newcomers in computational mechanics with reduced order modeling.
In order to discuss computational results for the worked out problems presented in this booklet, we will rely on the RBniCS Project. The RBniCS Project contains an implementation in FEniCS of the reduced order modeling techniques (such as certified reduced basis method and Proper Orthogonal Decomposition-Galerkin methods) for parametric problems that will be introduced in this booklet
L’arredo liturgico medievale del San Francesco di Vetralla tra perduto e restauri
No full textIl saggio analizza il perduto arredo liturgico di XII-XIII secolo della chiesa di San Francesco a Vetralla, concentrandosi in particolare sulla testimonianza oggi più evidente: il pavimento marmoreo. Presso l'Archivio Centrale dello Stato di Roma sono stati rinvenuti inediti e interessanti documenti sul restauro della pavimentazione, che hanno permesso un'accurata e migliore analisi dello stesso. Studiati poi i pichi frammenti superstiti della recinzione liturgica, l'intervento è stato posto in relazione con la ristrutturazione dell'edificio e, soprattutto, con il contesto storico-politico dell'epoca e con il definirsi dei rapporti Roma-Viterbo. Si è, infine, valutato per il San Francesco il ruolo dei marmorari della bottega di Lorenzo nelle nuove dinamiche artistiche filo-romane del territorio nell'iniziale XIII secolo, momento in cui si è scelto di collocare la realizzazione del pavimento marmoreo
Francesco Scorza Barcellona o della passione agiografica
No full textL'autrice traccia, sul filo dei ricordi, il profilo scientifico ed umano di Francesco Scorza Barcellona ed introduce gli studi raccolti nel volume.The author traces, on the thread of memories, the scientific and human profile of Francesco Scorza Barcelona and introduces the studies collected in the book
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