Advanced topics in physics
A.A. 2023/2024
Obiettivi formativi
Knowledge of physical phenomena and methods, which are compulsory for the study of geophysics: gravitational field; dynamics of rigid bodies; oscillatory systems and wave phenomena; basic theory of electromagnetic fields. The discussion of these topics requires the knowledge of some mathematical concepts (differential operators, partial differential equations and basic methods for their analytical solution), which are introduced during the lectures.
Risultati apprendimento attesi
At the end of the course unit, the students will acquire:
1) Knowledge skills (ability to describe, in correct mathematical and physical terms, the motion of rigid bodies, the gravitational field, the behavior of oscillatory systems and wave phenomena, the propagation of electromagnetic waves; ability to solve problems, referred to these topics);
2) Communication skills (ability of exposing scientific topics, related to basic elements of mechanics and electrodynamics);
3) Learning skills (ability to read scientific papers and books to improve the knowledge on the topics introduced during the lectures).
1) Knowledge skills (ability to describe, in correct mathematical and physical terms, the motion of rigid bodies, the gravitational field, the behavior of oscillatory systems and wave phenomena, the propagation of electromagnetic waves; ability to solve problems, referred to these topics);
2) Communication skills (ability of exposing scientific topics, related to basic elements of mechanics and electrodynamics);
3) Learning skills (ability to read scientific papers and books to improve the knowledge on the topics introduced during the lectures).
Periodo: Secondo semestre
Modalità di valutazione: Esame
Giudizio di valutazione: voto verbalizzato in trentesimi
Corso singolo
Questo insegnamento può essere seguito come corso singolo.
Programma e organizzazione didattica
Edizione unica
Responsabile
Periodo
Secondo semestre
Programma
1) Gravitation: Gravitational acceleration and potential; Kepler's laws of planetary motion; Gravitational acceleration and the potential of a solid sphere; Laplace's equation is spherical polar coordinates; MacCullagh's formula for the gravitational potential.
2) Earth's rotation: Motion in a rotating coordinate system; The Coriolis and Eotvos effects; Precession and forced nutation of the Earth's rotation axis; The free Eulerian nutation of a rigid Earth; The Chandler wobble.
3) Gravity: The ellipticity of the Earth's figure; The geopotential; The equipotential surface of gravity; Gravity on the reference spheroid; Geocentric and geographic latitude; The geoid.
4) The tides: Origin of the lunar tide-raising forces; Tidal potential of the Moon; Tidal friction and deceleration of terrestrial and lunar rotations.
5) Seismic waves: Elasticity theory, stress and strain tensors, elasticity modulii and Poisson's ratio. Relations between elastic modulii; Lamé constants; The seismic wave equation; Three-dimensional propagation of P- and S- waves; Superficial waves; Absorption and Q factor of seismic waves; Free oscillations and standing waves. Case of 1D oscillation of a string; Free oscillations of the Earth; radial and toroidal modes. Seismometry and equation of the seismometer.
6) Waves and oscillations: Examples of oscillations in simple systems. Study of the resonance in a damped and forced oscillator. Other examples of wave: string waves, acoustic waves (velocity, brief description of music theory, notes, interval as ratio between different harmonics, etc..); waves in water; beats; transversal oscillations of a continuous string, wave equation, progressive waves, phase velocity, dispersion and group velocity; wave energy and intensity; reflection and transmission of waves. Fourier analysis of a periodic function.
7) Electromagnetic theory: Maxwell's equations in vacuum and in material; General properties, Energy, momentum and angular momentum carried by electromagnetic fields; plane waves; linear and circular polarization; electromagnetic waves in materials of geophysical interest, microscopic model of matter.
8) Geomagnetism: The dipole magnetic field and potential; Potential of the geomagnetic field; The Earth's dipole magnetic field; Secular variation; The origin of the internal field.
2) Earth's rotation: Motion in a rotating coordinate system; The Coriolis and Eotvos effects; Precession and forced nutation of the Earth's rotation axis; The free Eulerian nutation of a rigid Earth; The Chandler wobble.
3) Gravity: The ellipticity of the Earth's figure; The geopotential; The equipotential surface of gravity; Gravity on the reference spheroid; Geocentric and geographic latitude; The geoid.
4) The tides: Origin of the lunar tide-raising forces; Tidal potential of the Moon; Tidal friction and deceleration of terrestrial and lunar rotations.
5) Seismic waves: Elasticity theory, stress and strain tensors, elasticity modulii and Poisson's ratio. Relations between elastic modulii; Lamé constants; The seismic wave equation; Three-dimensional propagation of P- and S- waves; Superficial waves; Absorption and Q factor of seismic waves; Free oscillations and standing waves. Case of 1D oscillation of a string; Free oscillations of the Earth; radial and toroidal modes. Seismometry and equation of the seismometer.
6) Waves and oscillations: Examples of oscillations in simple systems. Study of the resonance in a damped and forced oscillator. Other examples of wave: string waves, acoustic waves (velocity, brief description of music theory, notes, interval as ratio between different harmonics, etc..); waves in water; beats; transversal oscillations of a continuous string, wave equation, progressive waves, phase velocity, dispersion and group velocity; wave energy and intensity; reflection and transmission of waves. Fourier analysis of a periodic function.
7) Electromagnetic theory: Maxwell's equations in vacuum and in material; General properties, Energy, momentum and angular momentum carried by electromagnetic fields; plane waves; linear and circular polarization; electromagnetic waves in materials of geophysical interest, microscopic model of matter.
8) Geomagnetism: The dipole magnetic field and potential; Potential of the geomagnetic field; The Earth's dipole magnetic field; Secular variation; The origin of the internal field.
Prerequisiti
Basic knowledge of mechanics (kinematics and dynamics of a point body), geometrical optics, electrical and magnetic fields.
Metodi didattici
The course units will be organized with frontal lectures (4 cfu, corresponding to 32 hours) and exercises (2 cfu, corresponding to 24 hours). Tutorial activity to support students with a weak basic knowledge of physics and mathematics will be possible and activated, if necessary.
Materiale di riferimento
Notes supplied by the teacher, available on Ariel.
Suggested textbooks:
a) "Fundamentals of Geophysics", di W. Lowrie, Cambridge University Press
b) "A Student's Guide to Geophysical Equations", W. Lowrie, Cambridge
Suggested textbooks:
a) "Fundamentals of Geophysics", di W. Lowrie, Cambridge University Press
b) "A Student's Guide to Geophysical Equations", W. Lowrie, Cambridge
Modalità di verifica dell’apprendimento e criteri di valutazione
The examination consists in an oral exam, aimed to verify that the student has reached the objectives of the course. This may consists of an exposition of the main physical concepts and of the matemathical model of the different topics discussed in the course, and of the ability of solving simple problems, where the acquired knowledgements are applied.
FIS/01 - FISICA SPERIMENTALE
FIS/02 - FISICA TEORICA, MODELLI E METODI MATEMATICI
FIS/03 - FISICA DELLA MATERIA
FIS/04 - FISICA NUCLEARE E SUBNUCLEARE
FIS/05 - ASTRONOMIA E ASTROFISICA
FIS/07 - FISICA APPLICATA (A BENI CULTURALI, AMBIENTALI, BIOLOGIA E MEDICINA)
FIS/02 - FISICA TEORICA, MODELLI E METODI MATEMATICI
FIS/03 - FISICA DELLA MATERIA
FIS/04 - FISICA NUCLEARE E SUBNUCLEARE
FIS/05 - ASTRONOMIA E ASTROFISICA
FIS/07 - FISICA APPLICATA (A BENI CULTURALI, AMBIENTALI, BIOLOGIA E MEDICINA)
Esercitazioni pratiche con elementi di teoria: 24 ore
Lezioni: 32 ore
Lezioni: 32 ore
Docente:
Piovella Nicola Umberto Cesare
Siti didattici
Docente/i
Ricevimento:
mercoledì 15.30-17.30
5 piano, edificio LITA stanza A/5/C1