Fall 2017 - wiki.math.ntnu.no

Time/place: Friday 15th of December 2017, 14:15-15:00, room 656
Speaker: Tatsuo Iguchi (Keio/Bordeaux) Title: Initial value problem to a shallow water model with a floating solid body
Abstract: In this talk we are concerned with the well-posedness of the initial value problem to a shallow water model for two-dimensional water waves with a floating solid body. We consider three cases: the body is fixed, the motion of the body is prescribed, and the body moves freely according to Newton's laws. The difficulty of the analysis comes from the fact that we have to treat the contact points, where the water, the air, and the solid body meet. This model yields a new type of free boundary problems for a quasilinear hyperbolic system. We will report that the initial value problem to this model is in fact well-posed. This result is based on the joint research with David Lannes at University of Bordeaux.

Time/place: Friday 15th of December 2017, 14:15-15:00, room 656

Speaker: Tatsuo Iguchi (Keio/Bordeaux)
Title: Initial value problem to a shallow water model with a floating solid body

Abstract: In this talk we are concerned with the well-posedness of the initial value problem to a shallow water model for two-dimensional water waves with a floating solid body. We consider three cases: the body is fixed, the motion of the body is prescribed, and the body moves freely according to Newton's laws. The difficulty of the analysis comes from the fact that we have to treat the contact points, where the water, the air, and the solid body meet. This model yields a new type of free boundary problems for a quasilinear hyperbolic system. We will report that the initial value problem to this model is in fact well-posed.
This result is based on the joint research with David Lannes at University of Bordeaux.

Time/place: Friday 24th of November 2017, 14:15-15:00, room 656
Speaker: Per Kristian Hove (NTNU) Title: The Idun cluster and other available computing resources
Abstract: We will give a hands-on demonstration of how to use NTNU's Idun cluster, and have a look at the differences between the cluster and the department's own computing resources and discuss which resources are most suitable for the different types of computations. We will also briefly touch upon options for parallelizing your computations.

Time/place: Monday 13th of November 2017, 11:15-12:00, room S21
Speaker: Evgeniy Lokharu (Linköping/Lund) Title: Small-amplitude steady water waves with vorticity
Abstract: We consider the nonlinear problem of steady gravity-driven waves on the free surface of a two-dimensional flow of an incompressible fluid. We neglect the surface tension and assume a flow to be rotational and also allow interior stagnation points. In the talk we will discuss a recent progress in the theory of small-amplitude steady water waves with vorticity. Such waves are small perturbations of uniform streams with a several counter-currents. In contrast to the irrotational case of zero vorticity, when only Stokes and Solitary waves exist, the class of small-amplitude waves with vorticity includes multi-modal and non-symmetric waves and, possibly, waves with even more complicated geometry. The talk will be based on a joint work with Vladimir Kozlov from Linköping University.

Time/place: Monday 13th of November 2017, 11:15-12:00, room S21

Speaker: Evgeniy Lokharu (Linköping/Lund)
Title: Small-amplitude steady water waves with vorticity

Abstract: We consider the nonlinear problem of steady gravity-driven waves on the free surface of a two-dimensional flow of an incompressible fluid. We neglect the surface tension and assume a flow to be rotational and also allow interior stagnation points. In the talk we will discuss a recent progress in the theory of small-amplitude steady water waves with vorticity. Such waves are small perturbations of uniform streams with a several counter-currents. In contrast to the irrotational case of zero vorticity, when only Stokes and Solitary waves exist, the class of small-amplitude waves with vorticity includes multi-modal and non-symmetric waves and, possibly, waves with even more complicated geometry.

The talk will be based on a joint work with Vladimir Kozlov from Linköping University.

Time/place: Friday, 3rd of November, 14:15-15:00, room 656
Speaker: Dietmar Hömberg (NTNU/TU Berlin) Title: From dilatometer experiments to distortion compensation – optimal control problems related to solid-solid phase transitions
Abstract: In the first part of my talk I will discuss the question of how to measure a phase transition. This brings us to the dilatometer experiment in which the temperature in one point and the overall length change of a specimen is measured during controlled cooling. I will present a simple dilatometer model and show that it allows for a unique identification of the evolution of two product phases growing at the expense of one parent phase. Numerical experiments confirm this result for the case of fast cooling. In the case of slow cooling an additional measurement of the electric power for counter heating could help to improve the results. In the second part of my talk I will discuss the compensation of unwanted workpiece deformations by changing the phase mixture in a two phase material. The problem can be formulated as an optimal shape design problem for the interface between the two subdomains. I will reformulate the problem using a phase field relaxation, present a well-posedness result, show some numerical simulations and conclude with some future research topics.

Time/place: Friday, 3rd of November, 14:15-15:00, room 656

Speaker: Dietmar Hömberg (NTNU/TU Berlin)
Title: From dilatometer experiments to distortion compensation – optimal control problems related to solid-solid phase transitions

Abstract: In the first part of my talk I will discuss the question of how to measure a phase transition. This brings us to the dilatometer experiment in which the temperature in one point and the overall length change of a specimen is measured during controlled cooling. I will present a simple dilatometer model and show that it allows for a unique identification of the evolution of two product phases growing at the expense of one parent phase. Numerical experiments confirm this result for the case of fast cooling. In the case of slow cooling an additional measurement of the electric power for counter heating could help to improve the results.

In the second part of my talk I will discuss the compensation of unwanted workpiece deformations by changing the phase mixture in a two phase material. The problem can be formulated as an optimal shape design problem for the interface between the two subdomains. I will reformulate the problem using a phase field relaxation, present a well-posedness result, show some numerical simulations and conclude with some future research topics.

Time/place: Friday 15th of September 2017, 14:15-15:00, room 656
Speaker: Juan Manfredi (University of Pittsburgh) Title: Analysis and Probability of the p-Laplacian
Abstract: We will present an overview of the theory of asymptotic mean values for p-harmonic functions, the theory of tug-of-war processes, and their relationship.

Time/place: Thursday 31st of August 2017, 10:15-11:00, room 1329
Speaker: Boris Andreianov (Université de Tours) Title: Conservation Laws with Point Constraints: Analysis, Approximation, Modeling of Road and Pedestrian Traffic
In the past ten years, the standard Lighthill-Whitham-Richards (LWR) model of road traffic was enriched with the feature of point constraint on the flux in order to model paytolls, traffic lights, construction sites etc. Non-local variants of such models were recently proposed by M.D. Rosini et al., with the aim to reproduce capacity drop and self-organization phenomena proper to real pedestrian and traffic flows at exits. Their theoretical study falls into the framework of discontinuous-flux conservation laws. The coupling induced by non-locality is resolved via splitting of fixed-point arguments. Simple convergent finite volume numerical schemes are proposed and their ability to reproduce e.g. the Faster Is Slower feature and the Braess paradox is demonstrated. Most recent developments tend towards extension of the analysis to the "second-order" Aw-Rascle-Zhang (ARZ) model of road traffic. We achieve partial existence results based on wave-front tracking and on a careful use of renormalization and entropy dissipation properties for ARZ. Based on a series of joint works with C. Donadello, U. Razafison, M.D. Rosini.

Time/place: Thursday 31st of August 2017, 10:15-11:00, room 1329

Speaker: Boris Andreianov (Université de Tours)
Title: Conservation Laws with Point Constraints: Analysis, Approximation, Modeling of Road and Pedestrian Traffic

In the past ten years, the standard Lighthill-Whitham-Richards (LWR) model of road traffic was enriched with the feature of point constraint on the flux in order to model paytolls, traffic lights, construction sites etc.
Non-local variants of such models were recently proposed by M.D. Rosini et al., with the aim to reproduce capacity drop and self-organization phenomena proper to real pedestrian and traffic flows at exits. Their theoretical study falls into the framework of discontinuous-flux conservation laws. The coupling induced by non-locality is resolved via splitting of fixed-point arguments. Simple convergent finite volume numerical schemes are proposed and their ability to reproduce e.g. the Faster Is Slower feature and the Braess paradox is demonstrated.
Most recent developments tend towards extension of the analysis to the "second-order" Aw-Rascle-Zhang (ARZ) model of road traffic. We achieve partial existence results based on wave-front tracking and on a careful use of renormalization and entropy dissipation properties for ARZ.
Based on a series of joint works with C. Donadello, U. Razafison, M.D. Rosini.