The seminar will take place on Monday, May 14, 2018 at 9:00 am in K4. Miroslav Tůma will conclude his lecture on “Combinatorial scientific computing and its problems”.

Abstract:

In this talk we would like to point out some relations between continuous modelling of problems in sciences and engineering and
underlying discrete algorithms. Without going into details we will mention some of these relations and show their use in contemporary computational mathematics.

The seminar will take place on Monday, April 30, 2018 at 9:00 am in K4. Ondrej Chrenko will conclude his lecture on “Hydrodynamic processes during formation of planetary systems”.

Abstract:

Planets form in protoplanetary disks which are rotating structures of gas and dust surrounding young stars. Before a protoplanetary disk disperses, the mass of gas dominates over the mass of solids and thus the evolution of the disk and planets is driven by hydrodynamic phenomena. Although this evolutionary stage does not last longer than several million years, it inevitably predetermines the properties of the emerging planetary system, i.e. the multiplicity of planets, their orbital configuration, distances from the central star, their masses and types (whether they become terrestrial or gas giants). Understanding the impact of hydrodynamic processes on planet formation can help us understand the great diversity among the observed extrasolar planetary systems.

First, I will demonstrate the variety of hydrodynamic processes in protoplanetary disks by reviewing several examples, e.g. instabilities leading to angular momentum transport, instabilities enhancing accretion of solids, and planet-disk interactions leading to planetary migration. Next, I will describe numerical solution of the fluid equations within the framework of so-called FARGO hydrodynamic codes (Masset 2000, Benítez-Llambay & Masset 2016) which are often used to study planet-disk interactions. I will present a recent 2D model focused on interactions of multiple planets with a gas disk and a coupled disk of pebbles (Chrenko et al. 2017). Finally, I will outline a more advanced 3D model which is currently under development and I will discuss the implementation of radiative diffusion and stellar irradiation.

The seminar will take place on Monday, April 16, 2018 at 9:00 am in K4. Ondrej Chrenko will continue with a second lecture on “Hydrodynamic processes during formation of planetary systems”.

Abstract:

Planets form in protoplanetary disks which are rotating structures of gas and dust surrounding young stars. Before a protoplanetary disk disperses, the mass of gas dominates over the mass of solids and thus the evolution of the disk and planets is driven by hydrodynamic phenomena. Although this evolutionary stage does not last longer than several million years, it inevitably predetermines the properties of the emerging planetary system, i.e. the multiplicity of planets, their orbital configuration, distances from the central star, their masses and types (whether they become terrestrial or gas giants). Understanding the impact of hydrodynamic processes on planet formation can help us understand the great diversity among the observed extrasolar planetary systems.

First, I will demonstrate the variety of hydrodynamic processes in protoplanetary disks by reviewing several examples, e.g. instabilities leading to angular momentum transport, instabilities enhancing accretion of solids, and planet-disk interactions leading to planetary migration. Next, I will describe numerical solution of the fluid equations within the framework of so-called FARGO hydrodynamic codes (Masset 2000, Benítez-Llambay & Masset 2016) which are often used to study planet-disk interactions. I will present a recent 2D model focused on interactions of multiple planets with a gas disk and a coupled disk of pebbles (Chrenko et al. 2017). Finally, I will outline a more advanced 3D model which is currently under development and I will discuss the implementation of radiative diffusion and stellar irradiation.

The seminar will take place on Monday, April 9, 2018 at 9:00 am in K4. Ondrej Chrenko will give a lecture “Hydrodynamic processes during formation of planetary systems”.

Abstract:

Planets form in protoplanetary disks which are rotating structures of gas and dust surrounding young stars. Before a protoplanetary disk disperses, the mass of gas dominates over the mass of solids and thus the evolution of the disk and planets is driven by hydrodynamic phenomena. Although this evolutionary stage does not last longer than several million years, it inevitably predetermines the properties of the emerging planetary system, i.e. the multiplicity of planets, their orbital configuration, distances from the central star, their masses and types (whether they become terrestrial or gas giants). Understanding the impact of hydrodynamic processes on planet formation can help us understand the great diversity among the observed extrasolar planetary systems.

First, I will demonstrate the variety of hydrodynamic processes in protoplanetary disks by reviewing several examples, e.g. instabilities leading to angular momentum transport, instabilities enhancing accretion of solids, and planet-disk interactions leading to planetary migration. Next, I will describe numerical solution of the fluid equations within the framework of so-called FARGO hydrodynamic codes (Masset 2000, Benítez-Llambay & Masset 2016) which are often used to study planet-disk interactions. I will present a recent 2D model focused on interactions of multiple planets with a gas disk and a coupled disk of pebbles (Chrenko et al. 2017). Finally, I will outline a more advanced 3D model which is currently under development and I will discuss the implementation of radiative diffusion and stellar irradiation.

The seminar will take place on Monday, March 19, 2018 at 9:00 am in K4. Erika Maringová will give a lecture “Up to the boundary Lipschitz regularity for variational problems”.

Abstract: We prove the existence of a regular solution to a wide class of convex, variational integrals. Via technique of construction of the barriers we show that the solution is Lipschitz up to the boundary. For the linear growth case [1], we identify the necessary and sufficient condition to existence of solution; in the case of superlinear growth [2], we provide the sufficient one. The result is not restricted to any geometrical assumption on the domain, only its regularity plays the role. The talk will be based on two works,

[1] L. Beck, M. Bulíček, and E. Maringová.  Globally Lipschitz minimizers for variational problems with linear growth, accepted to ESAIM: COCV in 2017.

[2] M. Bulíček, E. Maringová, B. Stroffolini and A. Verde. A boundary regularity result for minimizers of variational integrals with nonstandard growth, accepted to Nonlinear Analysis in 2018.

The seminar will take place on Monday, March 5, 2018 at 9:00 am in K4. Tomáš Los will give a lecture “On three-dimensional flows of internal pore pressure activated Bingham fluids”.

Abstract: We are concerned with a system of partial differential equations describing internal flows of homogeneous incompressible fluids of Bingham type with activated boundary conditions.The Bingham activation threshold depends on internal pore pressure in the material, which is governed by an advection-diffusion equation. This model may be suitable for description of certain class of granular water-saturated materials. By suitably extending recent approaches by Chupin and Math ́e and Bulíček and Málek (see also a closely related work by Maringova and Zabensky), we prove long time and large data existence of weak solutions.
This is a joint work with A. Abbatiello, J. Málek, and O. Souček.