Asymptotics, Numerics, Analysis
Research objectives and tasks
The proposal objectives are divided into the following sixteen tasks which are
grouped under four main themes; several of the tasks actually relate to more than one of the main themes. In particular, many of the tasks under A, B, and C have
a strong numerical component, which is in accordance with the Particpants' integrated modeling-analysis-numerics approach. Also extremely hard problems will be tackled where any progress could be considered a breakthrough.
A. Multiscale phenomena and limiting structures
- 1. Kinetic and relaxation methods for conservation laws and moment systems
(Derivation and validation of models using diffusive and hydrodynamic limits, ...)
- 2. Multiscale phenomena for charged particle systems
(Modeling, analysis and numerics of hybrid semiconductor and plasma models, ...)
- 3. Mass transportation and entropy methods
(Large-time asymptotics for kinetic and parabolic equations, ...)
- 4. Eulerian-Lagrangian methods
(Multiphase flows, particles and solids in fluids and sprays, ...)
- 5. Continuum and kinetic models of phase transitions
(Coagulation/fragmentation, Bose condensation, kinetic relations, ...)
- 6. Quantum evolution equations
(Hartree-Fock equation, Dirac equation, semiclassical/nonrelativistic limits, ...)
B. Collisional evolution equations
- 7. Transport and collisions
(Analysis of and numerics for the Boltzmann equation, traffic flow problems, ...)
- 8. Many-particle systems
(Asymptotic limits, derivation of: kinetic equations, fluid models, and nonlinear one-particle approximations, ...)
- 9. Collision and dispersive quantum models
(Derivation of "quantum Boltzmann" equations, electron-phonon interaction, weak coupling limits, interaction with random media, ...)
- 10. Kinetic models for granular media and materials
(Derivation, analysis and numerics for models with inelastic collisions and/or mean fields, thin film magnetism, ...)
C. Nonlinear waves and hyperbolic systems
- 11. Structural properties of hyperbolic systems
(Zero-viscosity limits, diffusive and dispersive effects, non-strict hyperbolicity, ...)
- 12. Stability of nonlinear waves and boundary layers
(Over-/undercompressible shock phenomena, discrete shock profiles, ...)
- 13. Hamilton-Jacobi equations and geometrical optics
(Thin film magnetism, mesh generation, pressureless gas, ...)
- 14. Fluid dynamics equations
(Navier-Stokes equation, rotating flows, atmospheric and oceanic flows, dynamo equations, ...)
D. Numerical methods and simulations
- 15. Numerical methods for balance laws and dispersive equations
(Central schemes, relaxation schemes, kinetic schemes, schemes for nonlinear Schrödinger eq., ...)
- 16. Computational singular (in)compressible flows
(Magneto-hydrodynamics, multiphase models, shallow water equation, semiconductor simulations, Euler equations, Navier-Stokes equations, ...)
Distribution of tasks, responsibilities, and collaboration in the network
Table 1 shows which of the teams work jointly on the tasks listed above and which Participant is responsible for monitoring and fostering work on each task.
Here, a cross "X" means that the team is working on that task; the sign "O" means that the team is responsible for that task.
Table 1 Distribution of tasks and responsibilities.
Schedule and milestones
In Table 2 we give a schedule of the most important goals (milestones) concerning the tasks listed above. Only selected results to be expected at the midterm review and
the end of the project are listed.
During the annual network conferences (usually lasting a full week) the responsible team for each task will report on progress. This will help to put in perspective the research accomplishments of the network and formulate appropriate future goals.
Table 2 Selected major milestones at the time of the Midterm Review and the FinalReport..
|A: Multiscale phenomena and limiting structures||Large-time asymptotics using entropy methods; analysis of hybrid semiconductor models; analysis of Hartree-Fock type models.||Analysis of Dirac equations; kinetic relations to phase transition problems|
|Coagulation-fragmentation: Description of the gelation profile and new numerical methods for computing the gelation time||applications to combustion|
|application of Sobolev inequalities to large
- time asyptotics of non
- homogeneous kinetic equations
|B: Collisional evolution equations||Analysis of Boltzmann equation and traffic flow problems; derivation and analysis of "quantum Boltzmann" equations||Derivation of granular media models incorporating inelastic collisions|
|C: Nonlinear waves and hyperbolic systems||Zero-viscosity limit of hyperbolic systems; stability of nonlinear waves||Analysis of Hamilton
- Jacobi equations; derivation and analysis of rotating flow models
|D: Numerical methods and simulations||Relaxation schemes for balance laws||Semiconductor simulations for hybrid models|
|Convergence of Godunov scheme (small BV solutions for general hyperbolic systems)||Existence for partial viscosity (small BV solutions for general hyperbolic systems)|
|Study of multiresolution schemes for stiff problems||comparison with finite volume methods|
|Analysis of spectral discretisation of nonlinear Schrödinger equations|
Organization and management
Remark 1 : SC <-> TC Note that SC and TC ares a priori disjunct. Any shift of money thus has to be decided first by the TC, independly of the SC. Hense the "network management commitee" and the "training management commitee" are in check and balance concerning the main deliverable, the training months. Only in the exceptional case when the TC proposes a shift of training money between teams, the head of the TC becomes a member of the SC for deciding the matter.
Remark 2 : ATO The CO or the SIC can summom up the ATO at any time, also by means of telecommunication and bring any issue of the vote of ATO which decides by absolute 2/3 majority (10 TOs vote in favour of the proposition). This way, a 2/3 vote of ATO overrules any other decision process.
Research Effort of the Participants
Table 3 : Professional research effort on the network project
4 Organisation and Management
The following management structure, as sketched in the additional graphic, takes into account the particularly high training need. The committees are supported by 2 advisory boards which are not directly involved in management tasks : the Scientfic Advisory Board (SAB) for scientific and the Industrial Advisory Board (IAB) for industry related aspects.
· Coordinator (CO) and Scientist-in-charge (SiC)
The CO is responsible for all management tasks according to the RTN rules. The SiC, his equal partner, is the main responsible for the scientific orientation and quality of the network. The SiC is also the interface to the SAB : he stays in continuous contact with its members and he summons up the SAB whenever appropriate.
· Steering Committee (SC) (6 (7) members)
The SC is involved in all major decisions in the management of the network. The SC consists of the CO (head) and the SiC, as well as two senior members of the two former TMR networks. For decisions on training matters, the head of the TC is added to the SC, thus forming the 7 member SC+. % The SC mainly works by e-mail, phone, meetings as well as by a "common workspace" in the network homepage. "Video conferences" will be performed (on an experimental basis).
· Training Committee (TC) (8 members)
The TC assists TOs (= "Scientists-in-charge-of-the-work") and CO in all training aspects and helps actively the groups in finding young researchers, e.g. in advertisement of open positions.The TC systematically monitors the Pre/Postdoc hiring both for the quality and orientation of the training. In case a team does not fullfill its contractual duty in delivering the training months, the TC can suggest training budget shifts between groups. Once the TC has voted such a proposition, it sends it to the SC, which discusses it together with the head of the TC (=SC+). The SC+ then decides by simple majority vote.The TC is also in charge of coordinating the training events like summer/winter schools (cf Sec 5)
· Assembly of Team Organizers (ATO) (15 members)
The TOs are the principal partners of the CO in the organization of the network. The CO stays in permanent contact by e-mail with the TOs who act also on behalf of their satellites. At least once a year the CO summons a personal meeting of the ATO (or replacements of their choice.)
In order to disseminate abilities in research project management, additional training months have been allocated to the coordinating team. About 8 months of training will be partly dedicated to enable young scientists to help the CO in the scientific coordination, also for the annual reports, midterm review, etc. Female candidates or candidates from the "less experienced" satellites (Poland, Prague, Israel) will be preferred, appointment upon information of the TC, as usual.
· IT and e-publishing Committee (ITEC) (8 members)
In comparison to the proposal a new committee has been created which is in charge of tasks like the quite complex HYKE webpage containing "work spaces" (a forum/archive for each committee) and state-of-the-art preprint server. This committee includes 8 members, both network scientists with good IT knowledge and technal staff at the groups A1 and F2. It is led by the Paris groups F1 and F2, who were mentioned for these tasks already in the proposal. The internet domain www.hyke.org for HYKE has been reserved.
The following mechanisms will be used to monitor and report progress: