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 course is an optional course that introduces the concepts of physics used in nanoscience and nanotechnology. It will give students a better understanding of the specific phenomena associated with the nanoscale. It also includes an introduction to the four types of microscopy used to observe and measure at this scale: AFM, STM, SEM, TEM.

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

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The course aims to provide a general introduction to physics in relation to the biological sciences and to contextualize the use of modern physics concepts, methods, and approaches to describe biological systems and their complexity from the molecular to the cellular level. It is therefore necessary to understand the central role that physics has played for a century now in order to learn the principles of the organization and dynamics of living and complex matter (from cells to populations of individuals). At the same time, it is important 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 an eye toward new biomimetic applications.

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This course unit is a natural continuation of the course units on classical Newtonian mechanics.

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

In the second part of the EU, starting from an examination of the experimental limits of classical mechanics, a new theory of mechanics is introduced: quantum mechanics. This theory is conceptually completely different from previous classical theories, based on a description of physical phenomena in terms of probabilities and therefore no longer deterministic. This is a radical paradigm shift that revolutionized physics in the last century and led to a deeper understanding of physical nature, with fundamental and practical implications that have radically changed the lives of humanity (atomic physics, chemistry, nuclear energy, transistors, LASERS, to name but a few). 

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In the first part: deepen the basic concepts of differential calculus covered in L2.

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

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This course builds on the electromagnetism and waves courses taken in the second year.

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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, induction-coupled circuits), acoustic waves, some concepts of wave optics (diffraction and interference), the practical application of electronic circuits for the study of electrical components or systems (diodes, LEDs and photodiodes, transmission lines), and the study of some properties of matter (magnetism, the photoelectric effect, the Faraday effect).

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This first module in fluid mechanics aims to provide basic information on the behavior of industrial fluids (air, water, hydraulic fluid) with a view to designing simple systems involving fluids in static or dynamic conditions (flow rates, pressure, speed, pressure drops, etc.). The focus is 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 systems in equilibrium, using a bottom-up approach: starting with examples and then presenting the general principles. It draws heavily on the course taught by Harvey Gould and Jan Tobochnik. A historical introduction to the development of Brownian motion theory forms the final chapter of the course.

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The course builds on the knowledge acquired in L1 and L2 to teach the basics of special relativity (1/3 of the course) and offer students a brief introduction to subatomic particle physics (2/3 of the course). It will thus provide an introduction to the description of the intimate structure of matter. After developing the special relativity tools needed for the rest of the course, we will detail both the study of atomic nuclei (nuclear physics) and that of "elementary" particles (subatomic physics proper). We will give an initial description of the standard model of particle physics and the basic concepts of nuclear physics.

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Practical work in wave optics studies interference phenomena using Michelson and Fabry-Pérot interferometers as an application of high-resolution spectroscopy. (Michelson interferometer and Fabry-Pérot interferometer practical work)

Interference phenomena are also recorded on holographic plates for the reproduction and study of holograms. (Holography lab)

The polarization of light is studied and used to examine birefringent materials (such as calcite), liquid crystals, isotropic materials under stress (induced birefringence), etc. (birefringence practical)

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

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

The propagation speed of an intensity-modulated electromagnetic wave is measured by measuring the phase shift of its modulation induced by its propagation. (TP speed of light)

Objects are analyzed using Fourier optics, which, after filtering, allows certain details to be highlighted or hidden. The study is also compared to digital Fourier filtering (TP strioscopy).

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

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This course aims to introduce the basics of physical hydrodynamics. Kinematic aspects are covered first: Euler and Lagrange formalism, analysis of the motion of a fluid volume element, introduction of velocity current and potential 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 ideal fluids, then Navier-Stokes' equation describing the flow of viscous Newtonian fluids. This section will lead us to define the stress tensor and the Reynolds number, which can be used to determine whether a flow is laminar or turbulent. The course ends with an introduction to the mechanics of deformable solids: displacement field, dilation tensor, and deformation tensor.

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The supervised project is an experimental or digital simulation project carried out in groups of three students. It takes place in a practical work room, on one of the many physics and chemistry topics offered. It introduces students to the project approach and draws on their creativity, initiative, independence, and rigor in conducting experiments. The project concludes with a report and a defense, which are submitted for peer review and then evaluated by a jury.

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This module will cover selected methods of numerical physics with applications relevant to the Fundamental Physics track. After reviewing programming with Python 3, we will study numerical algorithms for solving nonlinear equations, ordinary differential equations, and systems of linear equations. A major part of the module will focus on numerical linear algebra and its applications in physics and numerical analysis. Finally, an introduction to computer algebra systems is planned.

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This course will build on the basic concepts previously acquired in Quantum Mechanics in semester 5. The course is structured around the following main topics: extension of 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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