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Irene Fonseca - Carnegie Mellon University. Pittsburgh, PA, US

Irene Fonseca

Professor | Carnegie Mellon University


Irene Fonseca's research focus is on training in applied mathematics at the broad interface between the physical sciences and engineering.


Irene Fonseca's primary focus is on research and training in applied mathematics at the broad interface between mathematics, the physical sciences and engineering. Irene's research program includes the mathematical study of shape memory alloys, ferroelectric, magnetic materials, composites, thin structures, phase transitions in fluids and solids, and the mathematical analysis of image segmentation, denoising, detexturing and recolorization in computer vision.

Areas of Expertise (5)



Business and Economics

Applied Mathematics

Shape Memory Alloys

Media Appearances (2)

SIAM: Irene Fonseca president of the Society for Industrial and Applied Mathematics – Pittsburgh,PA

Portuguese American Journal  online


Mathematician Irene Fonseca, 55, was elected president of the Society for Industrial and Applied Mathematics (SIAM) the world’s largest and most prestigious scientific society dedicated to applied mathematics.

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NSF Builds More Partnerships for International Research and Education

National Science Foundation  online


Science at the Triple Point Between Mathematics, Mechanics and Materials Science (Carnegie Mellon University) PIRE funding will enable PI Irene Fonseca and an international network of mathematicians from the United States, Belgium, United Kingdom, Germany and Italy to collaborate at the interface of mathematics and materials science and to develop sophisticated new methods for understanding the complexities of advanced materials. Graduate courses will be developed and U.S. students will strengthen their interdisciplinary and global research skills by conducting international research with multiple mentors and/or by participating in an international industrial research internship. Such international curriculum and student mobility will help internationalize U.S. institutions and place them in a vibrant international network of applied mathematicians.

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Irene Fonseca Publication Irene Fonseca Publication



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Irene Fonseca: Phase Separation in Heterogeneous Media Supercompatibility and the Design of Materials Irene Fonseca - Phase separation in heterogeneous media Irene Fonseca - 22 September 2016



Industry Expertise (3)



Writing and Editing

Accomplishments (1)

Senior Prize (professional)

International Society for the Interaction of Mechanics and Mathematics

Education (3)

University of Minnesota: M.S. 1983

University of Minnesota: Ph.D. 1985

University of Lisbon: Licenciatura, Mathematics 1980

Affiliations (5)

  • European Academy of Sciences : Fellow
  • American Mathematical Society : Fellow
  • SIAM : Fellow
  • American Association for the Advancement of Science (AAAS)
  • Association for Women in Mathematics (AWM)

Articles (5)

Higher order Ambrosio–Tortorelli scheme with non-negative spatially dependent parameters

Advances in Calculus of Variations

2023 The Ambrosio–Tortorelli approximation scheme with weighted underlying metric is investigated. It is shown that it Γ-converges to a Mumford–Shah image segmentation functional depending on the weight ωdx, where ω is a special function of bounded variation, and on its values at the jumps.

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Global and local energy minimizers for a nanowire growth model


2023 We consider a model for vapor–liquid–solid growth of nanowires proposed in the physical literature. Liquid drops are described as local or global volume-constrained minimizers of the capillarity energy outside a semi-infinite convex obstacle modeling the nanowire. We first address the existence of global minimizers and then, in the case of rotationally symmetric nanowires, we investigate how the presence of a sharp edge affects the shape of local minimizers and the validity of Young’s law.

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The mathematics of thin structures

Quarterly of Applied Mathematics

2022 This article offers various mathematical contributions to the behavior of thin films. The common thread is to view thin film behavior as the variational limit of a three-dimensional domain with a related behavior when the thickness of that domain vanishes. After a short review in Section 1 of the various regimes that can arise when such an asymptotic process is performed in the classical elastic case, giving rise to various well-known models in plate theory (membrane, bending, Von Karmann, etc…), the other sections address various extensions of those initial results.

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Domain Formation in Membranes Near the Onset of Instability

Journal of Nonlinear Science

2016 The formation of microdomains, also called rafts, in biomembranes can be attributed to the surface tension of the membrane. In order to model this phenomenon, a model involving a coupling between the local composition and the local curvature was proposed by Seul and Andelman in 1995. In addition to the familiar Cahn–Hilliard/Modica–Mortola energy, there are additional ‘forces’ that prevent large domains of homogeneous concentration.

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On the Motion of Curved Dislocations in Three Dimensions: Simplified Linearized Elasticity

SIAM Journal on Mathematical Analysis

2021 It is shown that in core-radius cutoff regularized simplified elasticity (where the elastic energy depends quadratically on the full displacement gradient rather than its symmetrized version), the force on a dislocation curve by the negative gradient of the elastic energy asymptotically approaches the mean curvature of the curve as the cutoff radius converges to zero.

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