L3 - CUPGE - Physics and Mathematics

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Introduction to the synthesis of chemical elements in the Universe (Big Bang, stars)

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This optional course introduces the physics concepts used in Nanoscience and Nanotechnology. It will allow students to better understand the particular phenomena related to the nanometric scale. It also includes an introduction to the 4 microscopies that allow to observe and measure at this scale: AFM, STM, SEM, TEM

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This optional course focuses on solving physics problems on a computer. It includes the use of the Python language for scientific programming with a special focus on visualization and animation. It offers an introduction to the possibilities offered by numerical physics through different simulations (FDTD simulation of the propagation of a 1D electromagnetic wave, etc.)

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The course aims to give a first general introduction of physics to the biological sciences and to put in context the use of modern physics concepts, methods and approaches to describe biological systems and their complexity from the molecular to the cellular scale. It is thus necessary to understand the central role of physics for a century now to learn today the principles of organization and dynamics of living and complex matter (from the cell to populations of individuals). At the same time it is necessary to understand that biological systems represent a new opportunity for physicists to learn more about the complexity of living matter and its capacity for self-organization, regulation and control with a view also to new biomimetic applications.

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This UE represents the natural continuation of the UEs of classical Newtonian mechanics.

In the first part of the course, we deal with Classical Mechanics starting from the principle of least action to arrive at two new formulations: the Lagrangian formalism and the Hamiltonian formalism. We study the link between physical symmetries and conservation laws (E. Noether's theorem) and we introduce Poisson's brackets which allow us to write the classical laws of temporal evolution of physical quantities in a form which already prefigures those of quantum mechanics.

In the second part of the course, starting from the examination of the experimental limits of classical mechanics, a new theory of mechanics is introduced: Quantum Mechanics. It is a theory that is conceptually completely different from the previous classical theories, based on a description of physical phenomena in terms of probabilities and therefore no longer deterministic. It is a radical change of paradigm that has shaken up the physics of the last century and has allowed a deeper understanding of physical nature, with fundamental and practical consequences that have radically changed the life of humanity (atomic physics, chemistry, nuclear energy, transistors, LASERS, to name but a few). 

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In a first part: to deepen the basic notions of differential calculus seen in L2.

In a second part: introduce the qualitative study of differential equations.

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This course is a continuation of the courses on electromagnetism and waves given in L2.

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Practical work in various fields of physics.

The topics covered include the study of mechanical and electrical oscillating systems (simple pendulum, torsion pendulum, coupled pendulums, RLC circuit, inductively coupled circuits), acoustic waves, some notions of wave optics (diffraction and interference), the practical application of electronic circuits for the study of components or electrical systems (diodes, LEDs and photodiodes, transmission line) and the study of some properties of matter (magnetism, photoelectric effect, Faraday effect).

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This first module of Fluid Mechanics aims to provide basic elements on the behavior of industrial fluids (air, water, hydraulic fluid) in order to dimension simple systems involving fluid in static or dynamic (flow rates, pressure, speed, pressure drops,...). Emphasis is placed on the study and design of hydraulic installations.

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This module is an introduction to the concepts and methods of statistical physics of equilibrium systems with a bottom-up approach: starting with examples and then giving the general principles. It draws heavily on the course by Harvey Gould and Jan Tobochnik. A historical introduction to the construction of the theory of Brownian motion constitutes the last chapter of the course.

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The course builds on the knowledge acquired in L1 and L2 to acquire the basics of special relativity (1/3 of the EU) and to offer students a brief introduction to subatomic particle physics (2/3 of the EU). It will thus allow to master an introduction to the description of the intimate structure of matter. After having developed the tools of special relativity necessary to the continuation of the course, we will detail both the study of atomic nuclei (nuclear physics) and that of "elementary" particles (subatomic physics proper). A first description of the standard model of particle physics and of the basic concepts of nuclear physics will be given.

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The practical work of wave optics studies the phenomena of interference using the Michelson and Fabry-Perot interferometers as an application of a high resolution spectroscopy. (Practical work on Michelson interferometer and Fabry-Perot interferometer)

The phenomena of interference are also recorded in holographic plates for the restitution and the study of holograms (TP holography)

The polarization of light is studied and is used to study birefringent materials (e.g. calcite), liquid crystals, isotropic materials placed under stress (induced birefringence)... (TP birefringence)

The emission of electromagnetic waves by heated bodies is studied in the black body practical exercises. The temperature of different hot bodies is determined with a pyrometer, a spectroscopy and an infrared camera (for the human body for example).

Lasers are also studied, their emission, their longitudinal and transverse modes either on a "fixed" cavity or on an open and adjustable cavity. (TP HeNe laser I and II)

The speed of propagation of an electromagnetic wave modulated in intensity is measured through a measurement of phase shift of its modulation induced by its propagation. (TP speed of light)

Objects are analyzed by Fourier optics which, after filtering, allows certain details to appear or disappear. The study is also compared to digital Fourier filtering (TP strioscopy)

Finally, the property of certain substances, subjected to a magnetic field, to deviate the plane of polarization of the light passing through them is being studied in the Faraday effect TP.

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This course aims at introducing the basics of physical hydrodynamics. The kinematic aspects are treated in a first step: Euler and Lagrange formalism, analysis of the motion of an element of fluid volume, introduction of the current and potential velocity functions, and applications to different types of flows. In the next part of fluid dynamics, we establish Euler's equation and Bernoulli's relation for the flow of perfect fluids, then the Navier-Stokes equation describing the flow of viscous Newtonian fluids. This part will lead us to define the stress tensor and the Reynolds number to deduce the laminar or turbulent character of a flow. The course ends with an introduction to the mechanics of deformable solids : displacement field, expansion and deformation tensor.

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The tutored project is an experimental or digital simulation project carried out in groups of 3 students. It takes place in the practical work room, on one of the many physics and chemistry themes offered. It confronts the students with the project approach, and mobilizes their creativity, their spirit of initiative, their autonomy and their rigor in the experiments. The project concludes with a report and a defense, which is evaluated by peers and then by the jury.

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This module will cover selected methods of numerical physics with applications relevant to the Fundamental Physics track. After a review of programming with Python 3, numerical algorithms for solving nonlinear equations, ordinary differential equations and systems of linear equations will be studied. A major part of the module will concern numerical linear algebra and its applications in physics and numerical analysis. Finally, an introduction to systems of formal calculus is included.

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The basic notions acquired in Quantum Mechanics in semester 5 will be developed in this course. The course is articulated around the following main axes: extension of the wave mechanics formalism, angular momentum theory, hydrogen atom, perturbations, introduction to relativistic quantum mechanics.

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Introduce the basic tools of complex analysis.

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