The Ph.D. Course in Mathematical Models for Engineering, Electromagnetism and Nanosciences aims at preparing young graduate students to perform theoretical and applied research in the fields of Mathematics, Electromagnetism and Material Sciences. The program also aims at the development of scientific interaction between mathematics and applications. Indeed, mathematics is actively employed in research themes and methods of both electromagnetism and materials science, in terms of modelling, analysis and simulation; as examples, we recall the applications to electrical conduction in biological materials with micro-structure, the study of propagation of electromagnetic non-uniform waves in lossy media, symmetry rupture in chiral materials, and multi-scale characterization techniques, such as those based on spectroscopy. 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 different spectral ranges) and matter, by means of advanced optical and electronic spectroscopy. In addition, 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 more specific to materials science.
ORGANIZATION
- The PhD Course has three curricula (Mathematics for Engineering, Electromagnetism and Materials Science). Each curriculum has a supervisor: he/she is a Faculty Board member who supports the Coordinator and the Board in didactic aspects such as, for instance, details on the courses’ program, referee proposals, proposals and interactions with defense committees.
- The PhD Course has a Quality Committee, composed by six members of the Faculty Board, which supports the Coordinator and the Board in internal (Sapienza) and external (Ministry) assessment and evaluation procedures.
- The Board has approved the establishment of an Advisory Board, whose members are currently being selected.
Also with the aim of performing a revision of the PhD programs and goals, the Board has planned a consultation with potentially interested external parties. The consultation will be carried out through a questionnaire.
GENERAL EDUCATIONAL LINES
At the beginning of each Academic Year, for the first two years, the PhD student presents a study plan which must be approved by the PhD Board. PhD student are required to follow two/three courses during the first year and one course during the second year. The courses will be held by professors from Sapienza or from other institutions or by foreign professors visiting Italy. PhD students are also asked to follow the mini-courses and the series of seminars of interest to their curriculum, held by Italian and foreign experts who work in specific fields, also coming from the productive and professional world. The Academic Board can acknowledge the equivalence of training experiences carried out at other universities or research institutes, also abroad. At the end of each course, PhD students are required to take a verification with the Lecturer. The third year of the PhD cycle is mainly dedicated to the preparation of the final dissertation.
PhD students are expected to take part in Congresses and Schools and to attend laboratories and scientific centers in which they can develop their own research or follow related research programs. The goal is to encourage them to reach an active role in their research groups. PhD students also carry personal study and research activities in dedicated offices and in SBAI libraries, as well as laboratory activities.
Details on the objectives of each curriculum follow.
MATHEMATICS FOR ENGINEERING
The main goals of the “Mathematics for Engineering” curriculum are to give a solid mathematical preparation to young researchers coming from scientific and technological backgrounds, at the same time supplying young mathematicians with an opening to new problems originating from applications and from industry. Scientific interests are indeed mainly concerned with qualitative, quantitative and numerical analysis, as well as to validation, of deterministic and stochastic mathematical models which are being developed to solve concrete problems in Physics, Chemistry, Biology, and Engineering. This program takes advantage from a sinergy with the various expertises within the Board.
In view of the above, research programs may be concerned both with the development of theoretical methods related to existing problems and with innovative applications of such methods to a particular scientific or technological topic. We refer in particular to differential models in fluid dynamics, electromagnetism, materials science, population dynamics, trafic flows, as well as to numerical, computational, algebraic and geometrical methods for data analysis. Finally, we believe that an applied mathematician should be given the ability to interact outside of academia: hence, we encourage research on problems brought from external parties and we support research periods not only in other universities, both also in research institutions and companies interested in developing, analysing and using mathematical models and methods.
ELECTROMAGNETISM
The "Electromagnetism" curriculum aims at directly involving students into the research groups collaborating with the Departments of the Doctorate Board members. Students are individually assigned a specific research topic for their doctorate. The research areas include (not limited to) the analysis of the spectrum of electromagnetic waves (ranging from industrial to optical frequencies) and physical technologies, including the analysis of materials and the linear and nonlinear interaction between electromagnetic field and matter. The materials of interest are mainly those identified as innovative, such as artificial, composite, nanostructured materials, metamaterials, photonic crystals, plasmonic structures, but also organic materials and biological tissues.
The curriculum in Electromagnetism also includes the development and application of advanced methodologies based on microscopy (electron, X-ray, scanning probe microscopies), diffraction (electron and X-ray), spectroscopy, and multiscale chemistry (from the macroscopic to the atomic scale). The understanding of phenomena at the nanometric and atomic scale also benefits from theoretical study using atomistic simulation approaches. In the highly interdisciplinary perspective that characterizes the entire doctoral course, applications vary, e.g., from materials science to energy, microelectronics, the biomedical sector, and cultural heritage.
MATERIALS SCIENCE
The main objective of the “Materials Science” curriculum is the training of Philosophy Doctors expert in the field of new advanced materials and nanosciences. In the last few years, materials science has developed worldwide, owing to a huge interest in materials with peculiar properties, suited for the most varied applications, ranging from energy storage/conversion to electronics, sensors and devices, from chemical and physical sciences to biological applications, from environmental sustainability to building, motor and aviation industries, 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 companies and enterprises operating with everyday more advanced technologies, towards 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, and crystallography. The research groups, mainly based in the Physics and Chemistry Departments of Sapienza University of Rome, boast several remarkable 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 aspects of their education.
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