Speaker: **Charlotte Perrin**

Title: **Macroscopic systems with maximum packing constraint**

Abstract:

This talk addresses the mathematical analysis of fluid models including a maximum packing constraint. These equations arise naturally for instance in the modeling of mixtures like suspensions. I will present recent results on two classes of PDEs systems which correspond to two modeling approaches: the “soft” approach based on compressible equations with singular constitutive laws (pressure and/or viscosities) close to the maximal constraint; and the “hard” approach based on a free boundary problem between a congested domain with incompressible dynamics and a free domain with compressible dynamics.

]]>Speaker: **Radomír Chabiniok**

Title: **Cardiac modeling in clinical practice: Physiology, biophysics & patient-specific management**

Abstract:

Biophysical modeling of cardiovascular system has been a very active research field in the past decades [1]. A number of sophisticated models based on physiological and physical assumptions have been created. A diligent work on mathematical analysis of complex problems, creation of efficient numerical schemes and development of computational resources allowed to conduct some significant model-validation studies. Efficient data assimilation techniques allowed to incorporate clinical data to extend the information included in the data but without modeling not accessible, and to increase the predictive capabilities of the models. Translating existing models into clinical practice is the next, and ultimately crucial step.

This task strongly depends on the interaction between clinical and modeling teams. While the clinical team characterizes the problem typically by targeting an important component in diagnosis or decision making for optimal management of a given patient the modeling team contributes by proposing the most suitable techniques to address the given question. The modeling ingredients selected must be compatible with the accuracy requested in the given problem, and the modeling framework must be in line with the time-constraint given by the clinical question. This talk will demonstrate a few examples of clinical modeling topics run between the research group M?DISIM of Inria Saclay Ile-de-France and various clinical partners.

First, the clinical application of modeling for monitoring purposes in patients under general anesthesia or at intensive care units will be presented. A direct collaboration with the Department of Anesthesia, Lariboisiere hospital in Paris, France, with two anesthetists directly included in the Inria modeling team (A. le Gall, MD full-time during his 3-year PhD project, and F. Vallee, MD, half-time) allows to advance this research towards first proof-of-concept works.

Secondly, augmenting the interpretation of clinical exams will be demonstrated on single- ventricle patients in an early-stage heart failure (HF). Such patients undergo a combined cardiovascular magnetic resonance (CMR) and heart catheterisation exam under pharmacological stress. Even such a complex data acquisition may not, however, uncover the underlying major component of their HF. Modeling shows a greatly promising tool to assist in refining the diagnosis the step prior to target the optimal treatment option. This project is pursued in the collaboration of Inria with Biomedical engineering department directly incorporated within St Thomas’ Hospital, King’s College of London, UK. A regular weekly work of an Inria researcher at St Thomas’ hospital and additional visits of a PhD candidate in the Inria lab is another example of a mode of function? of such a translational interdisciplinary research.

Finally, the problem of the optimal timing for a valve replacement therapy in patients with chronically overloaded ventricle will be discussed. It represents an example of addressing a question whether to and when to perform the intervention, and ultimately leads to a need to extend the modeling framework to capture the long-term progress of the pathology. This project is a part of an Associated research team? ToFMOD between Inria and University of Texas Southwestern Medical Center Dallas, with additional contributing partners being King’s College London, Institute for Clinical and Experimental Medicine (IKEM) and Czech Technical University in Prague. The decision was taken to confront and extend the existing long-term models with the patients with repaired Tetralogy of Fallot (rToF) as: 1) ToF is the most common complex congenital heart disease; 2) rToF patients are being followed with regular CMRs every 2-5 years (i.e. the longitudinal data of changes of the heart dilatation prior to intervention, an reverse- remodel-shrinking afterwards are possible to obtain). We believe that the knowledge gathered from the specific congenital heart disease cohort might be in addition to directly impacting the management of rToF patients partially applied in other more common acquired diseases.

All together, such presented modes of interdisciplinary work might lead to increasing a number of successful clinical applications of modelling with the ultimate goal in advancing healthcare.

Inria, M?DISIM research team, Paris-Saclay University, France

LMS, Ecole Polytechnique, CNRS, Paris-Saclay University, France

School of Biomedical Engineering and Imaging Sciences, St Thomas’ Hospital, King’s College London, UK

Literature: [1] R. Chabiniok et al.: Multi-physics and multiscale modelling, data?model fusion and integration of organ physiology in the clinic: ventricular cardiac mechanics, Interface Focus 6, 2016

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Speaker: **Ondřej Pejcha**

Title: **Catastrophic interactions of binary stars and the associated transients**

Abstract:

In this project, we plan to employ two numerical methods not commonly used in this subfield of astronomy. First, we will use low-Mach number (magneto)-hydrodynamics, which filters out sound waves in order to not be limited by the CFL condition. We will need to include realistic equation of state, energy transport by radiative diffusion, cylindrical or custom coordinates to capture non-spherical objects, complicated boundary conditions (stellar surface and excised cores of the stars), and eventually magnetic fields. Small regions of the domain might become supersonic. On the other hand, we will likely not need adaptive mesh refinement, nuclear burning or radiation transport beyond simple diffusion/conduction.

Second task aims to build moving-mesh radiation-hydrodynamics in 2D and 3D to study aspherical shock collisions and instabilities. The idea is to combine many essentially 1D Lagrangian spherical cones with transverse fluxes. For radiation, flux-limited diffusion will be sufficient (implicit update to explicit hydrodynamics), but detailed microphysics is important: realistic equation of state, opacities, and potential complications like small chemical reaction networks and growth of dust.

]]>*Speaker*: **Petr Zeman**

*Title*: **Vysokoteplotní chování nových tenkovrstvých materiálů**

*Abstract*:

Pokrok v oblasti nových technologií je úzce spojen s vývojem nových pokročilých materiálů. Pro vysokoteplotní aplikace jsou klíčové materiály, které jsou schopny odolávat nejen vysokým teplotám, ale i současnému vlivu okolního prostředí. Důležitou roli v tomto ohledu sehrávají vysokoteplotní tenkovrstvé materiály schopné modifikovat a ochránit povrch základního materiálu.

Přednáška uvede posluchače do problematiky vysokoteplotních materiálů s důrazem na tenkovrstvé materiály a metody charakterizace jejich vysokoteplotního chování. Významná pozornost bude věnována studiu oxidační odolnosti a teplotní stability struktury, složení a vlastností nových tenkovrstvých materiálů na bázi multiprvkových neoxidových a oxidových keramik a kovových skel připravených na pracovišti přednášejícího.

*Speaker*: **Eduard Rohan**

*Title*: **Homogenization of hierarchically arranged porous media **

*Abstract*:

The talk is aimed as an itroduction to the homogenization-based modelling of the so-called double-porosity media. Two situations can be distinguished: A) media described by the Biot-Darcy system of equations with highly heterogeneous permeability coefficients and other poroelastic coefficients, or B) media constituted by nested periodic structures. We focus on the second type of porous media formed by a microporous elastic skeleton with mesoscopic channels (cracks, or fissures). At the microscale level, the linearized fluid-structure interaction problem is treated, so that the first level of homogenization leads to the Biot continuum model describing the mesoscopic matrix coupled with the Stokes flow in the channels. The second step of the homogenization leads to a macroscopic model describing flow at the micro and meso-scopic pores coupled with the overall equilibrium equation respecting the hierarchical structure of the two-phase medium. Applications in the tissue perfusion modelling are shown.

Junior researchers will present their works. Program of the seminar can be found here: UNCE_MathMAC-Seminar_2018-12 (clickable on the page of this post)

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*Speaker:* **Michal Pavelka**

*Title:* **Geometric mechanics and thermodynamics of non-Newtonian fluids**

*Abstract:*

A fluid is non-Newtonian when it exhibits behavior outside of the scope of Navier-Stokes equations. Such behavior is usually caused by some microstructure affecting the overall motion. The equations can be split into reversible and irreversible part. The reversible part is mechanics, and is thus Hamiltonian and generated by a Poisson bracket. The irreversible part is generated by a dissipation potential driving the evolution towards equilibrium (GENERIC framework). It will be shown how to construct the Poisson brackets by means of differential geometry and Lie groups (semidirect product) and how to build a dissipation potential. This is a joint work with Petr Pelech, Karel Tůma and Josef Málek.

]]>*Speaker*: **Miroslav Bulíček**

*Title*: **Well posedness of nonlinear parabolic systems beyond natural duality**

*Abstract*:

We develop a methodology for proving well-posedness in optimal regularity spaces for a wide class of nonlinear parabolic initial-boundary value systems, where the standard monotone operator theory fails, namely for the situation when the nonlinear elliptic operator is monotone and has linear growth at infinity. The existence, uniqueness and regularity results by now are standard whenever the right hand side belongs to the corresponding negative Sobolev space. However, even if the formal a priori estimates are available, the existence and the uniqueness results was essentially missing. We overcome the related crucial difficulty, namely lack of the standard duality pairing, by resorting to proper weighted spaces and consequently provide existence, uniqueness and optimal regularity. As a consequence, we also obtain the uniqueness result for parabolic systems when the right hand side is just a Radon measure.

**Title**: Finite amplitude stability of internal steady flows of the Giesekus viscoelastic rate-type fluid

**Abstract**: We investigate the finite amplitude stability of internal steady flows of viscoelastic fluids described by the Giesekus model. The flow stability is investigated using a Lyapunov functional that is constructed on the basis of thermodynamical arguments. Using the functional, we derive bounds on the Reynolds and Weissenberg number that guarantee the unconditional asymptotic stability of the corresponding flow. Further, the functional allows one to explicitly analyse the role of elasticity in the onset of instability, which is a problem related to the elastic turbulence. The application of the theoretical results is documented in the finite amplitude stability analysis of Taylor–Couette flow of the Giesekus fluid.

This is a joint work with V. Průša and K. Tůma.

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