As is the case every academic year, the Center organizes a series of seminars,
given by faculty members of the University of Patras, visiting faculty
from other universities and graduate students who wish to present informally
results related to their Master's or Ph. D. thesis' work. The speakers
generally come from different disciplines and are asked to present their
work in a way that would be understandable to a rather broad scientific
audience. The only requirement is that their topic be relevant to a problem
in the area of Nonlinear Systems, which is of mathematical, physical, biological,
technological, economic or social interest.
If there is sufficient interest, the lectures will be given in English!
The Mathematics Department, and in particular the Division of Applied Analysis
is organizing this semester a series of seminars which are of particular
interest to those working with nonlinear differential equations.
10:00 - 11:30: Room 342 Math/Biol build.
Prof. Giorgio Turchetti, Dept of Physics, University of Bologna
Mathematical Models in Biology: Immune System and Aging
Biological systems exhibit many space-time scales. Large scale models
are based on population dynamics and the influence of environment
is described by deterministic or stochastic forcing terms. In the case
of the immune system the evolution of the virgin and memory T lymphocytes
is considered under the action of a chronic antigenic stress. The main
properties of the proposed Langevin equation and of the related Ulembeck
process are outlined.
The model describes the decrease of the virgin T cell compartment and
provides survival curves, assuming that the compartment depletion is a
mortality marker. A microscopic model for the clonal expansion under
the action of the acute antigenic attack and chronic stress is outlined.
12:00 - 1:30: Room 342 Math/biol build.
Prof. N. Buric , Dept. of Physics, University of Beograd
Phenomenological Model of Immune Response to Immunogenic Tumors
Immune response constitutes a set of complicated processes in a quite
complex system. Extreme complexity of the system, and quite partial knowledge
of the basic reactions and processes involved, justifies a phenomenological
approach to the modeling of the systems dynamics. We proposed and analyzed a model of the immune response to immunogenic tumor which has quite simple
formulation and could have sufficiently complicated dynamics. The model
gives consistent predictions for the values of the relevant parameters
estimated from real data.
7:00 - 8:30 p.m. Room 235 Math/Biol. build.
Prof. Giorgio Turchetti, Dept of Physics, University of Bologna
Geometrical Aspects in Intense Particle Beam Dynamics
High intensity accelerators are facing new applications for neutron
spectroscopy, wastes transmutation and inertial fusion. Mathematical modeling
is based on Hamiltonian dynamics, however the relevance of Coulomb
interactions requires a statistical approach. Neglecting the collisions,
the Poisson-Vlasov equations describe the evolution of
the system and some analytic solutions such as KV are known. The mathematical
properties of the envelope equations, they satisfy, are outlined.
Given the self consistent electric field, the single particle dynamics
is investigated by the frequency analysis. The resonance structure is found
and the chaotic regions appear to be enhanced by the presence of
mismatch oscillations and lattice non linearities. Comparison with the simulations
is discussed.
10:00 - 11:30: Room 235 Math/Biol build.
Prof. N. Buric, Dept. of Physics, University of Beograd
Self-Similarity and Transport in 2 Degree of Freedom Hamiltonian
Systems
The phase portrait of a typical Hamiltonian dynamical system is a
complicated fractal with strong evidence of self-similarity. This fractal structure
is responsible for the difficulties in the development of a computationally effective theory of transport in the phase
space. However, the self-similarity
of such fractals could be used to encode them in terms of continuous
and smooth functions. This is the basic idea in the method of modular smoothing.
We illustrate the method by discussing its applications for
the calculations of KAM tori, critical functions and actions of periodic
orbits.
The exact times of forthcoming seminars will be announced by e-mail to all persons whose address is in the current C.R.A.N.S list of e-mail addresses. If you wish to have your address added to this list, please send a message to bountis@math.upatras.gr.