Mathematical challenges in sustainable electric network managementsystems, BCAM-BX Workshop, Bilbo, November 2010

Applied Mathematics and Energy Generation

and Management.

Math & Energy

Enrike ZuazuaBCAM & Ikerbasque

BCAM

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Launched in September 1st, 2008:

• To perform research in the frontiers of mathematics

• To train and attract talented scientists

• To interact with industry

• To contribute to disseminating mathematics within society

• To strengthen the Basque science and technology system andbecome a relevant node in the international mathematics researchnetwork.

To irrigate Basque society and knowledge and R+D system withMathematics: R+D+M

Ruper Ordorika / Bernardo Atxaga: 37 Galdera Mugaz Bestalde Du-dan Kontaktu Bakarrari

37 Questions to my only contact beyond frontiers

Esaidan, zoriontsuak al zarete mugaz bestaldeko biztanleak?

Tell me, are you happy the inhabitants of beyond frontiers?

Mugaz bestaldean, ba al dago marrubirik? Arrain abisalek ba al duteaurresentipenik eguzkiaz?

Beyond frontiers, are there strawberries? Do abyssal fishes have aperception of sun?

ENERGY

We all have the perception of sun as the main source of energy.

But modern life relies on many other sources:

• water

• electricity

• oil

• gas

• ...

And this implies important challenges at different levels:

• Production/Transformation

• Management

• Distribution

• ...

Our needs are increasing. Our planet is growing in population andinhabitants have higher and higher needs.

Our needs are also changing.

This raises a key and difficult challenge: Sustainability!

More and more resources and efforts are being invested on renewableenergy research.

MATHEMATICS

And what can maths do?

To provide:

• models

• analytical understanding

• algorithms

• numerical simulations.

The laws of nature are but the mathematical thoughts of God.

Euclid (of Alexandria): 300 BC

Mathematical modeling: Numbers, symbols, need to be integrated inharmony into coherent models/systems to mimic, reproduce naturaland technological phenomena and interactions.

Analytical understanding: Mathematical analysis of these modelsallows a better understanding of their inner mechanisms, to foreseetheir potential evolution. It is the tool to design and create newstructures, new engines.

Isaac Newton (1642 -1727); Albert Einstein (1879 - 1955)

Algorithms: The human spoken language that computers under-stand.

Numerical simulations:

Math + Computers = the new paradigm of science.

An this has been ongoing since ever!

Pythagoras of Samos (570- 495 BC)

Research = To fail better. (Samuel Beckett ( 1906 – 1989))

Mathematics, and mathematical community evolve continuously, tobring light to increasingly complex scenarios and challenges.

WHAT KIND OF MATHEMATICS?

Capable of dealing with fluctuations, randomness, uncertainty...

From the provider to the customer

Of multi-scale nature

Complex modeling : multi-math.

Multi-math = multi-physics: Capturing the energy of waves andtides....

MATHEMATICS IN BCAM

Coordinated by E. Zuazua

Partial Differential Equations = The models of continuum mechanics:

• Elastic structures

• Fluid Mechanics

and, in general, of industrial processes.

Relevant in:

• Oil recovery

• Chemical refinement processes

• Gas and water transportation

• Electrical networks

A model for the evolution of an oil-slick by averaging Navier-Stokesequations:

Control Theory : The science of control and communication in ani-mals and machines.

Norbert Wiener (1894–1964) in “Cybernetics”, 1948.

Multi-scale control of a gas network

Multiplicity of control problems

Numerics.

F. Palacios (Stanford U.), C. Castro (UPM, Madrid); A. Bueno (Ox-ford U.), E. Z. (BCAM & Ikerbasque)

Putting these pieces together:

• Current joint work with the team leaded by S. Rementeria andI. Garabieta (Arteche Group) on the development of numericalmethods and algorithms for computing temperature on electricalnetworks.

• European Research Council Advanced Grant (ERC) 246775 - NU-

MERIWAVES : New analytical and numerical methods in

wave propagation

Coordinated by U. Ayesta

Networks are ubiquitous and the need of dealing with their design andoptimization is dramatically increasing.

Optimization, Operational research, graph theory, combinatorics, stochas-tic modeling and analysis, queuing theory are some of the tools fromapplied mathematics that are required for an optimal design of thesenetworks making a compromise, a trade-off, between different rele-vant requirements:

• Maximal speed

• Minimal energy consumption

Coordinated by E. Akhmatskaya

Multiscale computing:

The need of computational sciences is rapidly and endless increasingin alternative & renewable energies research

A present challenge is to develop robust and scalable algorithmsadapted to massively parallel architectures.

New technologies for solar energy:

One of the main potential applications:

Solar power, as a source of renewable, nonpolluting energy, requiresof going beyond the current crystalline silicon technology towardsorganic polymer-based photovoltaics solar cells.

Mathematical biology : project leaded by Philipp Getto

Biology is also energy driven.

DEB (dynamic energy budget) modeling of energy management pro-ceseses of individuals as it changes through life history with applica-tions to biotechnology, human health, global change,...

Our research refers in particular to:

• Fish cannibalism (pike, perch)

• Daphnia consuming Algae

Coordinated by J. Ph. Lessard

Computational Mathematics aims to develop the methods and al-gorithms needed to translate mathematical understanding intocomputer algorithms and, in this manner, to help solving increas-ingly complex problems.

Often complex problems have intricate solutions, evolving in time inan unexpected manner, experiencing bifurcations, branching phenom-ena. Building numerical methods capable of capturing this compli-cated topological properties is a challenge.

This occurs for instance in the context of delay equations. Delaymay drastically change the dynamical properties of systems. And,of course, delay does play a role in many issues related to energymanagement.

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Coordinated by C. Mora-Corral

Materials are also energy driven. Their configurations are nothazardous but rather driven and determined by precise laws of min-imization of energy. This is true for homogeneous elastic materials,but also for new composite materials, in the context of viscoelasticity,thermoelasticity, etc.

The mathematical theory of the Calculus of Variations explains howand why minimizers are reached and how they look. It also explainsimportant phenomena such as: cavitation, fracture, fatigue and

damage.

Also intimately related to the theory of optimization and optimal

design that, mimicking the dynamics in nature navigates in complexsurfaces searching for the minima.

Joint initiative BCAM-Baltogar

To be initiated in january 2011 .... in collaboration with Baltogarteam: A. Moreno, J. I. Antolın,...

to develop an Innovative CFD Platform for the Design and Op-

timization of High Performance Turbomachinery.

Bukatzen....

all these problems are difficult, important and complex, and the workplan ambitious... but do not forget...

Any intelligent fool can make things bigger, more complex, and moreviolent. It takes a touch of genius - and a lot of courage - to movein the opposite direction.

(Albert Einstein)

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