Seminars 2006
Seminarios del Grupo M.S.M.I.
Lunes 13 de Noviembre de 2006
The ECMI Educational Programme Mathematics in Industry
Università di Milano and ADAMSS Institute Milan
Abstract
Mathematics, as the language of the sciences, has
always played an important role in technology, and now
is applied also to a variety of problems in commerce
and the environment. European industry is increasingly
becoming dependent on high technology and the need for
mathematical expertise in both research and development
can only grow. More and more companies recognise that
mathematical/computer simulations may replace
experiments in their product design to give both
reduced costs and flexibility. These new demands on
mathematics have stimulated academic interest in
Industrial Mathematics and many mathematical groups
worldwide are committed to interaction with industry
as part of their research activities. In 1986, ten of
these groups in Europe founded ECMI with the intention
of offering their collective knowledge and expertise to
European Industry. No single European country is likely
to have sufficient expertise of mathematical knowledge
to cover all possible applications of interest to
industry, whereas ECMI can provide a comprehensive
coverage of mathematical skills and their diverse
applications. The ECMI Master Programme on Mathematics
in Industry aims at educating industrial mathematicians
to meet the growing demand for such experts. In modern
industry, mathematical methods play an increasingly
important role in research and development, production,
distribution and management. These methods come not
only from classical applied mathematics (mathematical
physics, numerical mathematics, probability theory and
statistics), but also involve e.g. operations research,
control theory, signal processing and cryptography.
Furthermore, mathematicians are more and more involved
in the formulation, analysis and evaluation of
mathematical models. Teaching centres in various
European countries are providing various educational
activities for this need, in addition to organising a
twoyear educational programme on Mathematics for
Industry designed to provide new recruits for industry.
El Seminario tendrá lugar a las 15:00 horas en la Sala
2.1.D04 (Edificio Sabatini) Universidad Carlos III.
Curso de Modelización en la Ciencia y en la Industria.
Noviembre de 2006.
Stochastic Processes in Agents Based Models
Università di Milano and ADAMSS Institute Milan
Abstract
Particular attention is being paid these days to the
mathematical modelling of the social behaviour of
individuals in a biological population. On one hand,
there is an intrinsic interest in population dynamics
of herds, and, on the other hand, agent based models
are being used in complex optimization problems (ACO's,
i.e. Ant Colony Optimization). Further
decentralized/parallel computing is exploiting the
capabilities of discretization of nonlinear
reactiondiffusion systems by means of stochastic
interacting particle systems. These systems lead to
selforganization phenomena exhibiting interesting
spatial patterns. As a working example, an interacting
particle system modelling the social behaviour of ants
is proposed. It consists of a system of stochastic
differential equations driven by social
aggregating/repelling ``forces". Specific reference
will be made to the species ``Polyergus Rufescens" that
has been observed in nature. Extensions to models of
nucleation and growth, chemotaxis, such as angiogenesis
related to tumor growth, will be presented. In these
models, the so called organization process is driven by
an underlying field that is strongly coupled with the
spatial structure of the population of interacting
individuals/agents/cells. Suitable ``laws of large
numbers" are shown to imply convergence of the
empirical spatial distributions of interacting
individuals to nonlinear reactiondiffusion equations,
as the total number of individuals becomes sufficiently
large.
Los contenidos y fechas del curso están en el siguiente
fichero
pdf
Seminarios del Grupo M.S.M.I.
Miércoles 20 de Septiembre de 2006
Negative Differential Conductance, Bistability, and
ElectricField Domains in QuantumCascade Structures
Paul Drude Institute for Solid State Electronics,
Berlin
Abstract
In undoped quantumcascade structures (QCSs), negative
differential conductance (NDC) and bistable behavior is
observed in the currentdensityelectricfield (jF)
characteristics. While the jF characteristic of a QCS
with a single period exhibits NDC without bistability,
NDC and a bistable behavior are observed for a QCS with
20 periods of the same design. Calculations using a
scatteringrate model neglecting any field
inhomogeneities show that the interplay of resonant
tunneling between the states in the QCS with resonant
scattering of longitudinal optical phonons can lead to
NDC in both structures. The currentvoltage
characteristics of doped QCSs exhibit current plateaus
with discontinuities for voltages below the lasing
threshold. The number of current discontinuities is
correlated with the number of periods of the QCS,
suggesting the formation of electricfield domains that
span the entire structure. In addition to this global
fielddomain formation typical for conventional
superlattices, there is also a local fielddomain
formation within each period of the QCS. A
selfconsistent calculation of the conduction band
profile and corresponding electronic wave functions
shows that the low and highfield domains are related
to resonant tunneling between different states in the
active region and injector of the cascade structure.
El Seminario tendrá lugar a las 15:00 horas en la Sala
2.1.D04 (Edificio Sabatini) Universidad Carlos III.
Seminarios del Grupo M.S.M.I.
Miércoles 5 de Abril de 2006
An ODE Model of the Motion of Pelagic Fish
Center for Nonlinear Science and Department of
Mathematics University of California, Santa Barbara
Abstract
A system of ordinary differential equations (ODEs) is
derived from a discrete system of Vicsek, Czirók et
al., describing the motion of a school of fish. Classes
of linear and periodic solutions of the ODEs are found
and their stability explored. The existence of toroidal
solutions is also proven. Applications of the model to
the migration of the capelin, a pelagic fish that
undertakes an extensive migration in the North
Atlantic, are dissussed and simulation presented.
El Seminario tendrá lugar a las 15:30 horas en la Sala
2.1.D04 (Edificio Sabatini) Universidad Carlos III.


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