## Presentation

The Ph.D. Course in Mathematical Models for Engineering, Electromagnetics and Nanosciences is aimed at preparing young graduated students to perform theoretical and applied research in the fields of Mathematics, Electromagnetics and Material Sciences. The program aims also at the development of scientific interaction between mathematics and applications.

Indeed mathematical modeling is actively employed in methods and problems studied in all curricula; for instance, we recall mathematical modeling of electrical conduction in biological materials with micro-structure, and the study of propagation of electromagnetic non-uniform waves in lossy media. On the other hand electromagnetics and materials science share the interest in innovative materials and systems (artificial materials, metamaterials, composites, nanostructured materials and components, photonic crystals, plasmonics, biological systems). The investigation of new materials can be carried out through the interaction of the electromagnetic radiation (in a wide spectral range, from the far infrared to the x-rays) and matter, by means of advanced optical and electronic spectroscopies, also making ise of synchrotron raxiation. In fact, electromagnetics and materials science share many techniques for analysis, simulation and characterization of the properties of such materials and systems, while the interest in their construction is specific to materials science.

GENERAL EDUCATIONAL LINES:

At the beginning of each academic year, in the first two years, the student submits a study program which must be approved by the Faculty of the Doctorate. Usually three courses in advanced institutional subjects will be followed in the first year, and chosen among the ones selected by the Board, and two more advanced courses will be chosen by the student. The courses will be taught by Professors from the University "La Sapienza" or from other Italian or foreign Universities or Research Centers. As a rule the student is expected to follow other educational activities besides the courses: short courses, seminars held by Italian and foreign experts active in the field, also chosen in the professional and nonacademic environment.

The Board may accept as equivalent to the requirements above other educational experiences obtained in Italian or foreign Universities or Research Centers.

At the end of each course, the student must pass a short oral exam according to the formats and directives determined by the Faculty.

The third year of the PhD program is mainly devoted to the preparation of the final dissertation.

The students are expected to take part in Congresses and Schools and to attend laboratories and scientific centers in which they can further their own research. The purpose of this is to encourage them to reach an active role in their research groups.

More in detail the objectives of each curriculum are as follows.

MATHEMATICS FOR ENGINEERING:

As far as the curriculum in Mathematics for Engineering is concerned, the most important aim of this Doctoral Program is to provide an intense mathematical preparation for young people coming from scientific and technological backgrounds (like those in Engineering, Economy, Statistics, Biology, Chemistry, Physics) and, at the same time, to provide young mathematicians with an opening to new problems originating in applications of Mathematics. To this end the Doctorate offers short courses relevant to mathematical modeling in industrial production or in biomedical innovation. Research may be concerned both with the development of theoretical methods aimed at tackling real problems, and with innovative application of such methods. The students are encouraged to write a dissertation dealing with problems coming from the real world, since an applied mathematician should be able to communicate with nonacademic agencies with an interest in technology. The student is also encouraged to pursue experiences of research in other Italian or foreign Universities or Research centers, and internships with companies interested in the use of mathematical methods and models.

ELECTROMAGNETICS:

The curriculum in Electromagnetics expects to include the students in research groups of the Departments that support scientifically the Ph.D. course. Such groups perform research in Electromagnetics at a high and internationally recognized level. The Ph.D. students are individually assigned a specific research topic for the course, during which they get acquainted with the many and rapidly evolving techniques adopted in the study of different problems under the guidance of supervisors. Several lines of research are available, concerning the frequency spectrum between industrial and optical frequencies of electromagnetic waves, the technologies of Physics, the analysis of materials by means of acoustic, electromagnetic, electro-optical, nuclear, optical and thermal techniques.

MATERIALS SCIENCE:

Main objective of the curriculum in Materials Science is the training of Philosophy Doctors expert in the field of new advanced materials and nanosciences. In the last few years, material science has developed worldwide, owing to the huge interest in materials with peculiar properties, suited for the most varied applications, ranging from electronics to sensors and devices, from the chemical to the physical sciences and to the biological applications, from building to motor or aviation industry, just to quote a few significant examples. It is therefore important to train researchers possessing a good balance of base knowledge and applicative skills, as it is nowadays required from industries and enterprises operating with everyday more advanced technologies, with a constant innovation perspective, and by the international research institutions. Materials science, with particular attention to the development of advanced materials on the nanometric scale, is present in different fields, such as chemistry, physics, chemical-physics of hybrid organic-inorganic systems, electronics, applied mathematics, crystallography. The research groups mainly based in the Physics and Chemistry Departments of the "La Sapienza" University of Rome boast several high scientific skills at the international level in such fields, and the participation of Ph.D. students in these experimental groups constitutes one of the main issues of their education, through exploitation of advanced on-campus laboratpries and large research infrastructures, like synchrotron radiation.

Indeed mathematical modeling is actively employed in methods and problems studied in all curricula; for instance, we recall mathematical modeling of electrical conduction in biological materials with micro-structure, and the study of propagation of electromagnetic non-uniform waves in lossy media. On the other hand electromagnetics and materials science share the interest in innovative materials and systems (artificial materials, metamaterials, composites, nanostructured materials and components, photonic crystals, plasmonics, biological systems). The investigation of new materials can be carried out through the interaction of the electromagnetic radiation (in a wide spectral range, from the far infrared to the x-rays) and matter, by means of advanced optical and electronic spectroscopies, also making ise of synchrotron raxiation. In fact, electromagnetics and materials science share many techniques for analysis, simulation and characterization of the properties of such materials and systems, while the interest in their construction is specific to materials science.

GENERAL EDUCATIONAL LINES:

At the beginning of each academic year, in the first two years, the student submits a study program which must be approved by the Faculty of the Doctorate. Usually three courses in advanced institutional subjects will be followed in the first year, and chosen among the ones selected by the Board, and two more advanced courses will be chosen by the student. The courses will be taught by Professors from the University "La Sapienza" or from other Italian or foreign Universities or Research Centers. As a rule the student is expected to follow other educational activities besides the courses: short courses, seminars held by Italian and foreign experts active in the field, also chosen in the professional and nonacademic environment.

The Board may accept as equivalent to the requirements above other educational experiences obtained in Italian or foreign Universities or Research Centers.

At the end of each course, the student must pass a short oral exam according to the formats and directives determined by the Faculty.

The third year of the PhD program is mainly devoted to the preparation of the final dissertation.

The students are expected to take part in Congresses and Schools and to attend laboratories and scientific centers in which they can further their own research. The purpose of this is to encourage them to reach an active role in their research groups.

More in detail the objectives of each curriculum are as follows.

MATHEMATICS FOR ENGINEERING:

As far as the curriculum in Mathematics for Engineering is concerned, the most important aim of this Doctoral Program is to provide an intense mathematical preparation for young people coming from scientific and technological backgrounds (like those in Engineering, Economy, Statistics, Biology, Chemistry, Physics) and, at the same time, to provide young mathematicians with an opening to new problems originating in applications of Mathematics. To this end the Doctorate offers short courses relevant to mathematical modeling in industrial production or in biomedical innovation. Research may be concerned both with the development of theoretical methods aimed at tackling real problems, and with innovative application of such methods. The students are encouraged to write a dissertation dealing with problems coming from the real world, since an applied mathematician should be able to communicate with nonacademic agencies with an interest in technology. The student is also encouraged to pursue experiences of research in other Italian or foreign Universities or Research centers, and internships with companies interested in the use of mathematical methods and models.

ELECTROMAGNETICS:

The curriculum in Electromagnetics expects to include the students in research groups of the Departments that support scientifically the Ph.D. course. Such groups perform research in Electromagnetics at a high and internationally recognized level. The Ph.D. students are individually assigned a specific research topic for the course, during which they get acquainted with the many and rapidly evolving techniques adopted in the study of different problems under the guidance of supervisors. Several lines of research are available, concerning the frequency spectrum between industrial and optical frequencies of electromagnetic waves, the technologies of Physics, the analysis of materials by means of acoustic, electromagnetic, electro-optical, nuclear, optical and thermal techniques.

MATERIALS SCIENCE:

Main objective of the curriculum in Materials Science is the training of Philosophy Doctors expert in the field of new advanced materials and nanosciences. In the last few years, material science has developed worldwide, owing to the huge interest in materials with peculiar properties, suited for the most varied applications, ranging from electronics to sensors and devices, from the chemical to the physical sciences and to the biological applications, from building to motor or aviation industry, just to quote a few significant examples. It is therefore important to train researchers possessing a good balance of base knowledge and applicative skills, as it is nowadays required from industries and enterprises operating with everyday more advanced technologies, with a constant innovation perspective, and by the international research institutions. Materials science, with particular attention to the development of advanced materials on the nanometric scale, is present in different fields, such as chemistry, physics, chemical-physics of hybrid organic-inorganic systems, electronics, applied mathematics, crystallography. The research groups mainly based in the Physics and Chemistry Departments of the "La Sapienza" University of Rome boast several high scientific skills at the international level in such fields, and the participation of Ph.D. students in these experimental groups constitutes one of the main issues of their education, through exploitation of advanced on-campus laboratpries and large research infrastructures, like synchrotron radiation.

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