Topics in contact Hamiltonian systems:analytical and numerical perspectives

The work of this thesis explores contact Hamiltonian systems as ageometrical setting to study physical systems with dissipation. Unlikesymplectic dynamical systems, contact Hamiltonian systems do notconserve energy, allowing the description of systems with differenttypes of dissipation and forcing. The thesis is divided into threeparts: the first part provides background knowledge on contactmanifolds and introduces contact Hamiltonian systems with examples.The second part focuses on numerical methods for contact Hamiltoniansystems, including geometry preserving integrators and deep learningtechniques. The third part presents analytical results: thecomputation of the Baker-Campbell-Hausdorff formula for certainalgebras and the study of symmetry and integrability in contactHamiltonian systems. The thesis builds on previously published workand includes unpublished work in progress

On the quantum entanglement: a geometrical perspective.

Nella tesi viene affrontato il problema dell'entanglement da un punto di vista geometrico, usando sia la geometria differenziale che la geometria algebrica. Particolare attenzione viene data al problema della separabilità: ovvero il distinguere se uno stato è entangled o separabile. Nel primo capitolo si introduce il formalismo geometrico che verrà usato per analizzare la struttura della meccanica quantistica e dell'entanglement: vengono presentati elementi di geometria differenziale complessa, geometria proiettiva e geometria algebrica. Nel secondo capitolo, dopo un breve riepilogo sulla meccanica quantistica, vengono usati gli strumenti introdotti nel capitolo precedente per costruirne ed analizzarne la struttura differenziale. Nel terzo capitolo l'entanglement viene studiato con alcuni esempi ed applicazioni con metodo tradizionale, dopo di che anche gli aspetti geometrici vengono analizzati. Infine, nell'ultimo capitolo viene proposto un nuovo approccio di tipo algebrico derivato dalla dualità di Schur - Weyl

New Directions for Contact Integrators

Contact integrators are a family of geometric numerical schemes which guarantee the conservation of the contact structure. In this work we review the construction of both the variational and Hamiltonian versions of these methods. We illustrate some of the advantages of geometric integration in the dissipative setting by focusing on models inspired by recent studies in celestial mechanics and cosmology.Comment: To appear as Chapter 24 in GSI 2021, Springer LNCS 1282

Geometric Numerical Integration of Liénard Systems via a Contact Hamiltonian Approach

Starting from a contact Hamiltonian description of Li\'enard systems, we introduce a new family of explicit geometric integrators for these nonlinear dynamical systems. Focusing on the paradigmatic example of the van der Pol oscillator, we demonstrate that these integrators are particularly stable and preserve the qualitative features of the dynamics, even for relatively large values of the time step and in the stiff regime

Numerical integration in celestial mechanics:A case for contact geometry

Several dynamical systems of interest in Celestial Mechanics can be written in the form of a Newton equation with time-dependent damping, linear in the velocities. For instance, the modified Kepler problem, the spin–orbit model and the Lane–Emden equation all belong to such class. In this work, we start an investigation of these models from the point of view of contact geometry. In particular, we focus on the (contact) Hamiltonisation of these models and on the construction of the corresponding geometric integrators

Peri-operative red blood cell transfusion in neonates and infants: NEonate and Children audiT of Anaesthesia pRactice IN Europe: A prospective European multicentre observational study

BACKGROUND: Little is known about current clinical practice concerning peri-operative red blood cell transfusion in neonates and small infants. Guidelines suggest transfusions based on haemoglobin thresholds ranging from 8.5 to 12 g dl-1, distinguishing between children from birth to day 7 (week 1), from day 8 to day 14 (week 2) or from day 15 (≥week 3) onwards. OBJECTIVE: To observe peri-operative red blood cell transfusion practice according to guidelines in relation to patient outcome. DESIGN: A multicentre observational study. SETTING: The NEonate-Children sTudy of Anaesthesia pRactice IN Europe (NECTARINE) trial recruited patients up to 60 weeks' postmenstrual age undergoing anaesthesia for surgical or diagnostic procedures from 165 centres in 31 European countries between March 2016 and January 2017. PATIENTS: The data included 5609 patients undergoing 6542 procedures. Inclusion criteria was a peri-operative red blood cell transfusion. MAIN OUTCOME MEASURES: The primary endpoint was the haemoglobin level triggering a transfusion for neonates in week 1, week 2 and week 3. Secondary endpoints were transfusion volumes, 'delta haemoglobin' (preprocedure - transfusion-triggering) and 30-day and 90-day morbidity and mortality. RESULTS: Peri-operative red blood cell transfusions were recorded during 447 procedures (6.9%). The median haemoglobin levels triggering a transfusion were 9.6 [IQR 8.7 to 10.9] g dl-1 for neonates in week 1, 9.6 [7.7 to 10.4] g dl-1 in week 2 and 8.0 [7.3 to 9.0] g dl-1 in week 3. The median transfusion volume was 17.1 [11.1 to 26.4] ml kg-1 with a median delta haemoglobin of 1.8 [0.0 to 3.6] g dl-1. Thirty-day morbidity was 47.8% with an overall mortality of 11.3%. CONCLUSIONS: Results indicate lower transfusion-triggering haemoglobin thresholds in clinical practice than suggested by current guidelines. The high morbidity and mortality of this NECTARINE sub-cohort calls for investigative action and evidence-based guidelines addressing peri-operative red blood cell transfusions strategies. TRIAL REGISTRATION: ClinicalTrials.gov, identifier: NCT02350348

Support Code for Geometric numerical integration of Lìenard systems via a contact Hamiltonian approach

This is the support Code for Geometric numerical integration of Lìenard systems via a contact Hamiltonian approach

Simulation code for Bravetti, Seri, Vermeeren, Zadra: "Numerical integration in celestial mechanics: a case for contact geometry"

Support material for Bravetti, Seri, Vermeeren, Zadra: "Numerical integration in celestial mechanics: a case for contact geometry