PHYSICS OF LIQUIDS

Course objectives

GENERAL OBJECTIVES: The course in Physics of Liquids aims to provide the necessary knowledge to understand the disordered state of matter. Emphasis will be directed toward the connection between the inter-particle interaction potential and the resulting equilibrium structure. The themes of short-range ordering and of the dynamics in the fluid and glass phases will be studied in depth. At the end of the course, students will develop quantitative reasoning skills and analytical abilities useful for studying, modelling and understanding phenomena related to disordered soft matter. SPECIFIC OBJECTIVES: A - Knowledge and understanding OF 1) To know the theory of classical fluids, from mean field models, to integral theories and perturbative approaches. OF 2) To understand the physical basis of the integral closures. OF 3) To know how to extract structural and dynamical quantities from the scattering of X rays and neutrons. OF 4) Know how to go from a microscopic theory to a hydrodynamic theory. B - Application skills OF 5) To be able to compute the cluster integrals that compose the virial coefficient for simple interaction potentials. OF 6) To be able to solve the equations governing the structure of a fluid in the presence of external fields. OF 7) To be able to apply perturbative techniques … C - Autonomy of judgment OF 8) To be able to understand the results of experiments and simualtions on simple and complex liquids. OF 9) To be able to integrate the knowledge acquired in order to choose the best closure relations for a particular problem. D - Communication skills OF 10) To know how to communicate the results of experiments and simulations on simple liquids. E - Ability to learn OF 11) Have the ability to consult and understand books and articles in order to gain a deeper knowledge of the topics discussed during the course.

Channel 1
JOHN RUSSO Lecturers' profile

Program - Frequency - Exams

Course program
Review of thermodynamics and statistical mechanics concepts (2 hrs) Simple and complex liquids (4 hrs) Van der Waals equation (4 hrs) Pair correlation function (6 hrs) Elastic scattering (4 hrs) Ornstein-Zernike equation (6 hrs) Closures from functional derivatives (6 hrs) Percus-Yevick solution for hard spheres and Baxter model (4 hrs) Perturbation theories (4 hrs) Correlation functions in time and space (2 hrs) Introduction to Dynamics (2 hrs) Diffusion and velocity auto-correlation function (4 hrs) Mori-Zwanzig projection operator formalism (4 hrs) Hydrodynamics and dynamic structure factors (4 hrs) Le equazioni di Navier Stokes (4 ore)
Prerequisites
It is good to have knowledge of Statistical mechanics: *) temporal and ensemble averages *) canonical and grand-canonical ensemble Mathematical Methods: *) complex analysis *) Cauchy integral representations *) Fourier Transforms
Books
Text #1: "Theory of Simple Liquids" by Hansen and McDonald, Associated Press Text #2: “A concise course on the Theory of classical Liquids” by A. Santos, Springer
Teaching mode
The format of the course consists of lectures at the blackboard and computer demonstrations of programs to compute functional minimization and numerical simulations.
Frequency
Frontal lectures.
Exam mode
The final grading will be based on an oral exam of about 1h, that consists of a discussion on the topics covered during the course. In order to pass the oral exam, the student must be able to present an argument, to do a demonstration, or repeat a calculation discussed during the course and to apply the methods that she/he learned to examples and situations similar to those already discussed. For the evaluation the following points will be considered: - accuracy of the concepts laid out; - clarity and accuracy of the exposition; - ability to analytically develop the theory.
Lesson mode
The format of the course consists of lectures at the blackboard and computer demonstrations of programs to compute functional minimization and numerical simulations.
JOHN RUSSO Lecturers' profile

Program - Frequency - Exams

Course program
Review of thermodynamics and statistical mechanics concepts (2 hrs) Simple and complex liquids (4 hrs) Van der Waals equation (4 hrs) Pair correlation function (6 hrs) Elastic scattering (4 hrs) Ornstein-Zernike equation (6 hrs) Closures from functional derivatives (6 hrs) Percus-Yevick solution for hard spheres and Baxter model (4 hrs) Perturbation theories (4 hrs) Correlation functions in time and space (2 hrs) Introduction to Dynamics (2 hrs) Diffusion and velocity auto-correlation function (4 hrs) Mori-Zwanzig projection operator formalism (4 hrs) Hydrodynamics and dynamic structure factors (4 hrs) Le equazioni di Navier Stokes (4 ore)
Prerequisites
It is good to have knowledge of Statistical mechanics: *) temporal and ensemble averages *) canonical and grand-canonical ensemble Mathematical Methods: *) complex analysis *) Cauchy integral representations *) Fourier Transforms
Books
Text #1: "Theory of Simple Liquids" by Hansen and McDonald, Associated Press Text #2: “A concise course on the Theory of classical Liquids” by A. Santos, Springer
Teaching mode
The format of the course consists of lectures at the blackboard and computer demonstrations of programs to compute functional minimization and numerical simulations.
Frequency
Frontal lectures.
Exam mode
The final grading will be based on an oral exam of about 1h, that consists of a discussion on the topics covered during the course. In order to pass the oral exam, the student must be able to present an argument, to do a demonstration, or repeat a calculation discussed during the course and to apply the methods that she/he learned to examples and situations similar to those already discussed. For the evaluation the following points will be considered: - accuracy of the concepts laid out; - clarity and accuracy of the exposition; - ability to analytically develop the theory.
Lesson mode
The format of the course consists of lectures at the blackboard and computer demonstrations of programs to compute functional minimization and numerical simulations.
  • Lesson code1044819
  • Academic year2025/2026
  • CoursePhysics
  • CurriculumCondensed matter physics: Theory and experiment (Percorso valido anche per coloro che partecipano al percorso internazionale italo-francese-portoghese-canadese finalizzato al conseguimento del titolo multiplo)
  • Year1st year
  • Semester2nd semester
  • SSDFIS/03
  • CFU6