The doctorate council is made up of 25 Professors of the University of L’Aquila, and the coordinator is Prof. Davide Gabrielli.
The program aims at training students to get a deep knowledge of the theoretical features of a mathematical subject
and to develop a qualified preparation to apply mathematical models in a diversified range of scientific areas.
The doctorate is one of the programmes of the INdAMDPCOFUND2015


Group theoretical approach for symmetric encryption
Speakers: AragonaCivino, 10 hours
Program: Gruppi di permutazione ed in particolare gruppi primitivi, accenno alla classificazione dei gruppi primitivi finiti di O’NanScott, crittografia simmetrica e cifrari a blocchi, gruppi generati dalle funzioni di cifratura di un crittosistema simmetrico, attacchi algebrici su cifrari a blocchi, attacchi di imprimitività, studio del gruppo G(SPN) generato dalle funzioni di cifratura di un SPN, condizioni per cui G(SPN) sia primitivo e condizioni per cui G(SPN) sia l’alterno.
Selected topics in kinetic theory of gases
Speaker: Colangeli, 10 hours
Program: The course will cover a selection of topics of classical kinetic theory of gases: phase space and Lioville’s theorem; hard spheres and mean free path; BBGKY hierarchy; Boltzmann equation for hard spheres; Noncutoff potentials and grazing collisions; FokkerPlanck equation; Htheorem and irreversibility; ChapmanEnskog expansion; Kac ring model.
Bibliography: Carlo Cercignani, The Boltzmann Equation and Its Applications, Springer (1988)
Title: Variational derivation of continuum mechanics equationsProfessor: Francesco dell’Isola and/or Luca Placidi
Aim: The aim of this short course is to introduce the students to the variational methods that are used in continuum mechanics. Static and dynamic cases will be analyzed. The mathematical derivations will be done on the basis of assumptions that are formulated on the form of the action functional. In the static case, the action is reduced to the total energy functional and a method to derive its form from a discrete model is also sketched.
Duration: 10 hours divided into 5 lectures
Topics: The subjects developed during the course will be a suitable selection of the following ones: 3D continuum elastodynamic model derivations for the standard and for the strain gradient case. EulerBernoulli beam theory derived from an Action principle as well as from a discrete model. Continuum equations for materials with band gap for the 3D and for the 1D cases. The choice may depend on the interests of the students
MODELS: Standard and strain gradient elastic materials. Euler beams. Materials with band gap.METHODS: Variational methods. Heuristic homogenization procedure.
Program: A possible effective program may be the following:
LECTURE 1: It is shown in details the case of 3D continuum elastodynamic case for the standard.
LECTURE 2: It is shown in details the case of 3D continuum elastodynamic case for the strain gradient case.
LECTURE 3: Standard EulerBernoulli beam theory will be derived from an action.
LECTURE 4: Standard EulerBernoulli beam theory will be derived from a discrete model.
LECTURE 5: The derivation of the continuum equations for materials with band gap for the 3D and for the 1D cases will be shown.
Bibliography: Some basic reference texts are the following:
dell'Isola Francesco, PLACIDI L (2011). Variational principles are a powerful tool also for formulating field theories. In: FRANCESCO DELL'ISOLA, SERGEY GAVRILYUK. (a cura di): FRANCESCO DELL'ISOLA, SERGEY GAVRILYUK, CISM Courses and Lectures. Variational Models and Methods in Solid and Fluid Mechanics. CISM INTERNATIONAL CENTRE FOR MECHANICAL SCIENCES, vol. 535, p. 116, Wien, New York:SpringerWienNewYork, ISBN: 9783709109823, ISSN: 02541971
N. Auffray, F. dell'Isola, V. Eremeyev, A. Madeo, PLACIDI L, G. Rosi (2014). Least action principle for second gradient continua and capillary fluids: a Lagrangian approach following Piola's point of view. In: (a cura di): U.Andreaus, F. dell’Isola, R. Esposito, S. Forest, G. Maier, and U. Perego, The complete works of Gabrio Piola, volume I. Advanced Structured Materials. ADVANCED STRUCTURED MATERIALS, vol. 38, Springer Verlag, ISSN: 18698433, doi: 10.1007/9783319002637_4
El Sherbiny Mohammed, Placidi L (2018). Discrete and continuous aspects of some metamaterial elastic structures with band gaps. ARCHIVE OF APPLIED MECHANICS, vol. 18, p. 17251742, ISSN: 09391533, doi: 10.1007/s0041901813991
Turco E., Golaszewski M., Giorgio I., Placidi L (2017). Can a henckytype model predict the mechanical behaviour of pantographic lattices?. In: (a cura di): Sofonea M., dell'Isola F., Steigmann D., Mathematical Modelling in Solid Mechanics. ADVANCED STRUCTURED MATERIALS, vol. 69, p. 285311, Singapore:Springer Nature, ISBN: 9789811037634, ISSN: 18698433, doi: 10.1007/9789811037641_18
Differential forms and application in geometry and physics
At a first glance, differential forms (also known as covectors) might seem as just a technical tool. Locally, 1dimensional differential forms look just as the dual of vectors, which everybody is familiar with. However, differential forms capture some very deep global geometric and topologic properties of the space they are attached to. Therefore, differential forms led to the discovery of a vast number of new results in area such as differntial, symplectic, contact and algebraic geometry, algebraic topology, classical and quantum mechanics, just to name a few. The course will be an introduction into differential forms.
Prerequisites: We will assume knowledge only in calculus in Rn (differentiation and integration). However, it would also be desirable, but not compulsory, some basic knowledge in: smooth manifolds, algebraic topology and differential geometry of surfaces.
References: M. do Carmo, Differential forms and applications, Springer1991 J. M. Lee, Introduction to Smooth Manifolds, Springer 2006 R. Bott and L. W. Tu, Differential Forms in Algebraic Topology, Srpinger 1982
Students have access to a wide variety of computing equipment in the DISIM department. They have access to various scientific laboratories among which we mention the High Performance Parallel Computing (HPPC) with the supercalculator Caliban with a computing power of about 2.5 teraflops. They also have access to databases as ARXIV, ALL, EBSCO, DOAJ, virtual Emeroteca Caspur, JCR, JSTOR, AMS/Mathschinet, Numdam, PUBMET, Science Direct, Scopus, Springer Link, WILEY on line library, ISI web of knolewdge, Web of Science.
c/o DISIM, via Vetoio
67100 L'Aquila (AQ), Italy
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