A
handbook of
Gamma-convergence
Course
`From Discrete Systems to Continuum Problems' (Würzburg 2012)
- LECTURE NOTES (will be update as I find
mistakes/misprints)
Mini-course
`Homogenization
of Lattice systems' (INdAM, Rome 2005) - LECTURE NOTES
Course
`From Discrete Systems to Continuous Variational Problems' (Utah 2005)
- LECTURE NOTES
Research
areas: Calculus
of Variations, Gamma-convergence, Homogenization, Discrete Variational
Problems, Fracture Mechanics, Image Processing, Geometric Measure
Theory
Previous positions:
Associate
Professor at SISSA, Trieste
1995-2000
Associate
Professor at the University of Brescia, 1992-1995
`Ricercatore'
at the University of Brescia, 1988-1992
(`Servizio
civile', 1986-1988)
Contract
Professor at the University of Udine, 1985-1986
`Perfezionando'(Ph
D, adviser E. De Giorgi)
at Scuola Normale Superiore, Pisa,
1983-1985
`Laurea'
in Mathematics at the University of Pisa, 1983
Visiting positions:
Tata Institute
of Fundamental Research, Bangalore, India (1994, 2004), Max-Planck
Institute for Mathematics in the Sciences, Leipzig (1998),
University
of Minnesota, Dept.
Aerospace Engr. Mech. (1998), CalTech, Pasadena (1998, 2003,2004),
Centre Emile Borel, Paris (1998), Carnegie-Mellon
University, Pittsburgh (1999, 2003), Isaac
Newton Institute, Cambridge (1999), University Paris
VI and XIII (2000, 2001 and 2002), Stanford University (Timoshenko
Visiting Scholar 2004)
Ph.D. Theses (Adviser)
R.
Alicandro. Approximation of Free-Discontinuity Problems (SISSA,
1999)
M.S.
Gelli. Variational Limits of Discrete Systems (SISSA, 1999)
N.
Ansini. Homogenization Problems for Multi-dimensional and
Multi-scale
Structures (SISSA, 2000)
M.Cicalese.
Multi-scale analysis for variational problems arising from discrete
systems
(University of Naples `Federico II', 2003)
C.I Zeppieri
Multi-scale analysis via Gamma-convergence (Universita' di Roma La
Sapienza, 2006)
L.Sigalotti. In progress. (Universita' di Roma La Sapienza)
M.Maslennikov. In progress.
(Universita' di Roma La Sapienza)
I also had the pleasure of collaborating to the following
theses:
M.
Solci A Variational Model for Phase Separation (PAVIA 2003,
adviser
E.Vitali).
Editorial Board:
Networks and Heterogeneous Media
Encyclopedia of Mathematical Physics
Some
Publications (see also my web page at Scuola
Normale Superiore, Pisa)
Books and Lecture
Notes
A. Braides.
An
Introduction to Homogenization and Gamma-convergence.
In: G. Allaire, A. Braides, G. Buttazzo, A.
Defranceschi,
L.V. Gibiansky.
School
on Homogenization. Lecture Notes of the Courses held at ICTP,
Trieste,
4--17 September 1993
A. Braides and A.
Defranceschi.
Homogenization
of Multiple Integrals
Oxford University
Press, Oxford, 1998.
A. Braides.
Approximation
of Free-Discontinuity Problems
Lecture Notes
in Mathematics No. 1694, Springer Verlag, Berlin, 1998.
A. Braides and M.S. Gelli.
From
Discrete
to Continuum: a Variational Approach.
Lecture Notes. SISSA, Trieste, 2000.(file
pdf)
A. Braides
Gamma-convergence
for Beginners.
Oxford
University
Press, 2002
A. Braides
From
discrete
to continuous variational problems: an introduction .
Lecture Notes. School on Homogenization Techniques and Asymptotic
Methods
for Problems with Multiple Scales.
Torino, September 2001
appeared as part of
A. Braides and M.S. Gelli.
From discrete systems to continuous variational problems: an
introduction.
Topics on concentration phenomena and problems with multiple scales,
3--77, Lect. Notes Unione Mat. Ital., 2, Springer, Berlin, 2006.
A. Braides
A handbook of Gamma-convergence
in Handbook of Differential
Equations. Stationary Partial Differential Equations, Volume 3 (M.
Chipot and P. Quittner, eds.) Elsevier 2006.
Editorial Activity
Topics
on concentration phenomena and problems with multiple
scales. Edited by Andrea Braides and Valeria Chiadò Piat.
Lecture Notes of the Unione Matematica Italiana, 2. Springer-Verlag,
Berlin, 2006. xii+316
Editorial Board. Encyclopedia
of Mathematical Physics. Elsevier, 2006
Recent Papers
A. Braides and A. Piatnitski.
Variational problems
with
percolation: dilute spin systems at zero temperature
Preprint 2011
A. Braides, A. Causin and M. Solci.
Interfacial energies
on
quasicrystals
Preprint 2011.
A. Braides and N.K. Yip.
A quantitative
description
of mesh dependence for the discretization of singularly perturbed
non-convex problems.
Preprint 2011.
<>A. Braides, A. Defranceschi and E. Vitali.
A compactness result
for a
second-order variational discrete model
M2AN, to appear
A. Braides and A. Piatnitski
Homogenization of
surface
and length energies for spin systems.
Preprint, 2010
A. Braides and M. Solci.
Interfacial
energies on Penrose lattices.
M3AS, 21 (2011), 1193-1210
A. Braides and C. Larsen.
$\Gamma$-convergence
for stable states and local minimizers.
Ann. SNS Pisa, (2011)
A. Braides and L.Sigalotti.
Models of
defects
in atomistic systems.
Calc. Var. Partial Diff. Eq., 41 (2011), 71-109
A. Braides, M.S. Gelli, and M. Novaga.
Motion
and
pinning of discrete interfaces.
Arch. Ration. Mech. Anal., 95 (2010), 469-498.
A. Braides, M. Briane, and J.
Casado
Diaz.
Homogenization
of non-uniformly bounded periodic diffusion energies in dimension two.
Nonlinearity 22 (2009), 1459-148
A. Braides, G. Riey, and M.
Solci.
Homogenization
of Penrose tilings.
C.R. Acad. Sci., Ser. I 347 (2009), 697-700
A. Braides - C.I. Zeppieri
Multiscale
analysis of a prototypical model for the interaction between
microstructure and surface energy
Interfaces Free Bound. 11 (2009), 61--118.
A. Braides, M. Maslennikov,
and L.
Sigalotti.
Homogenization
by blow-up.
Applicable Anal. 87 (2008), 1341--1356.
R. Alicandro - A.
Braides -
M. Cicalese
Continuum
limits of discrete thin films with superlinear growth densities
Calc. Var. Partial Diff. Eq. 33 (2008), 267--297
A. Braides and L. Sigalotti.
Asymptotic
analysis of periodically-perforated nonlinear media at and close to the
critical exponent.
C.R. Acad. Sci. Paris 346 (2008), 363--367.
A.
Braides - L. Truskinovsky
Asymptotic
expansions by Gamma-convergence
Cont. Mech. Therm. 20 (2008), 21--62
A.Braides - G. Riey
A
variational
model in image processing with focal points
ESAIM: M2AN 42 (2008) 729--748
A. Braides and V.
Chiado' Piat
Non convex
homogenization problems for singular structures
Network and Heterogenous
Media 3 (2008), 489-508
A. Braides and A. Piatnitski.
Overall properties of a
discrete
membrane
with randomly distributed defects
Arch. Ration. Mech. Anal. 189 (2008), 301--323
A. Braides - A. Gloria
Exact
bounds on the effective behaviour of a conducting `discrete'
polycrystal
Multiscale Modeling and Simulation 6 (2007), 1198-1216
A. Braides - M. Solci - E.
Vitali
A
derivation of linear elastic energies from pair-interaction atomistic
systems
Network and Heterogenous Media 2 (2007), 551-567
A. Braides - A. Chambolle -
M.
Solci
A
relaxation
result for energies defined on pairs set-function and
applications
ESAIM:COCV 13 (2007), 717-734
A. Braides - C. I. Zeppieri
A
note
on equi-integrability in dimension reduction problems
Calc. Var. Partial Differential Equations 29 (2007),
231-238
A. Braides - M. Briane
Homogenization
of non-linear variational problems with thin low-conducting layers.
Appl. Math. Optim. 55 (2007), no. 1, 1--29
A. Braides and M. Cicalese.
Surface energies in
nonconvex
discrete
systems.
M3AS 17 (2007) 985-1037
R. Alicandro, A. Braides
and
M. Cicalese
Phase and
anti-phase boundaries in binary discrete systems: a
variational viewpoint.
Netw. Heterog. Media 1 (2006), no. 1, 85--107
N.
Ansini - A. Braides - V. Valente
Multi-Scale
Analysis by G-convergence of a Shell-Membrane Transition.
SIAM J. Math. Anal. 38 (2006), no. 3, 944--976
A. Braides and V. Chiado' Piat
Another
brick in the wall.
Variational problems in materials science, 13--24, Progr. Nonlinear
Differential Equations Appl., 68, Birkhäuser, Basel, 2006
A.
Braides, A.J. Lew and M. Ortiz.
Effective cohesive behavior
of
layers
of interatomic planes.
Arch. Ration. Mech. Anal. 180 (2006), no. 2, 151--182
A. Braides and R. March
Approximation by
$\Gamma$-convergence of a curvature-depending functional
in
Visual Reconstruction.
Comm. Pure Appl. Math. 59 (2006), no. 1, 71--121
Complete
List of Publications (as of June 2011)
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