# Research Seminar Series

### Applied Mathematics Seminars

## Applied Mathematics Seminars: A mean field approach to the quasineutral limit for the Vlasov-Poisson equation

27 October 2017 14:00 in *CM219*

The Vlasov-Poisson system is a kinetic equation that models collisionless plasma. A plasma has a characteristic scale called the Debye length, which is typically much shorter than the scale of observation. In this case the plasma is called ‘quasineutral’. This motivates studying the limit in which the ratio between the Debye length and the observation scale tends to zero. Under this scaling, the formal limit of the Vlasov-Poisson system is the Kinetic Isothermal Euler system. The Vlasov-Poisson system itself can formally be derived as the limit of a system of ODEs describing the dynamics of a system of N interacting particles, as the number of particles approaches infinity. The rigorous justification of this mean field limit remains an open problem. In this talk I will present recent joint work with Mikaela Iacobelli, in which we derive the Kinetic Isothermal Euler system from a regularised particle model. Our approach uses a combined mean field and quasineutral limit.

Contact david.bourne@durham.ac.uk for more information

This seminar series is the continuation of the Numerical Analysis Seminar series that ran until August 2016. This change of name reflects the broader interests of the Applied Mathematics group (note that the Mathematical and Theoretical Particle Physics group also has a seminar series).

### Arithmetic Study Group

## Applied Mathematics Seminars: A mean field approach to the quasineutral limit for the Vlasov-Poisson equation

27 October 2017 14:00 in *CM219*

The Vlasov-Poisson system is a kinetic equation that models collisionless plasma. A plasma has a characteristic scale called the Debye length, which is typically much shorter than the scale of observation. In this case the plasma is called ‘quasineutral’. This motivates studying the limit in which the ratio between the Debye length and the observation scale tends to zero. Under this scaling, the formal limit of the Vlasov-Poisson system is the Kinetic Isothermal Euler system. The Vlasov-Poisson system itself can formally be derived as the limit of a system of ODEs describing the dynamics of a system of N interacting particles, as the number of particles approaches infinity. The rigorous justification of this mean field limit remains an open problem. In this talk I will present recent joint work with Mikaela Iacobelli, in which we derive the Kinetic Isothermal Euler system from a regularised particle model. Our approach uses a combined mean field and quasineutral limit.

Contact david.bourne@durham.ac.uk for more information

This seminar series is the continuation of the Numerical Analysis Seminar series that ran until August 2016. This change of name reflects the broader interests of the Applied Mathematics group (note that the Mathematical and Theoretical Particle Physics group also has a seminar series).

### Centre for Particle Theory Colloquia

## Applied Mathematics Seminars: A mean field approach to the quasineutral limit for the Vlasov-Poisson equation

27 October 2017 14:00 in *CM219*

The Vlasov-Poisson system is a kinetic equation that models collisionless plasma. A plasma has a characteristic scale called the Debye length, which is typically much shorter than the scale of observation. In this case the plasma is called ‘quasineutral’. This motivates studying the limit in which the ratio between the Debye length and the observation scale tends to zero. Under this scaling, the formal limit of the Vlasov-Poisson system is the Kinetic Isothermal Euler system. The Vlasov-Poisson system itself can formally be derived as the limit of a system of ODEs describing the dynamics of a system of N interacting particles, as the number of particles approaches infinity. The rigorous justification of this mean field limit remains an open problem. In this talk I will present recent joint work with Mikaela Iacobelli, in which we derive the Kinetic Isothermal Euler system from a regularised particle model. Our approach uses a combined mean field and quasineutral limit.

Contact david.bourne@durham.ac.uk for more information

This seminar series is the continuation of the Numerical Analysis Seminar series that ran until August 2016. This change of name reflects the broader interests of the Applied Mathematics group (note that the Mathematical and Theoretical Particle Physics group also has a seminar series).

### Computing Seminars/Talks

27 October 2017 14:00 in *CM219*

Contact david.bourne@durham.ac.uk for more information

### CPT Student Seminar

27 October 2017 14:00 in *CM219*

Contact david.bourne@durham.ac.uk for more information

### Departmental Research Colloquium

27 October 2017 14:00 in *CM219*

Contact david.bourne@durham.ac.uk for more information

### Distinguished Lectures and Public Lectures

27 October 2017 14:00 in *CM219*

Contact david.bourne@durham.ac.uk for more information

### Geometry and Topology Seminar

27 October 2017 14:00 in *CM219*

Contact david.bourne@durham.ac.uk for more information

### Informal HEP Journal club

27 October 2017 14:00 in *CM219*

Contact david.bourne@durham.ac.uk for more information

### Maths HEP Lunchtime Seminars

27 October 2017 14:00 in *CM219*

Contact david.bourne@durham.ac.uk for more information

### Pure Maths Colloquium

27 October 2017 14:00 in *CM219*

Contact david.bourne@durham.ac.uk for more information

### Statistics Seminars

27 October 2017 14:00 in *CM219*

Contact david.bourne@durham.ac.uk for more information

### Stats4Grads

27 October 2017 14:00 in *CM219*

Contact david.bourne@durham.ac.uk for more information

Information about seminars for the current academic year. For information on previous years' seminars please see the seminar archives pages.