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 physical concepts used in Nanoscience and Nanotechnology. It will enable students to better understand the specific phenomena associated with the nanometric scale. It also includes an introduction to the 4 microscopes used to observe and measure at this scale: AFM, STM, MEB, MET...

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

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The course aims to provide an initial general introduction to physics as it relates to the biological sciences, and to put into context the use of modern physics concepts, methods and approaches to describe biological systems and their complexity, from the molecular to the cellular scale. This means understanding the central role that physics has played over the past century in learning about the organization and dynamics of complex living matter (from cells to populations of individuals). At the same time, we need 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 also to new biomimetic applications.

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

In the first part of the course, we take Classical Mechanics from the principle of least action to 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 introduce Poisson brackets, which allow us to write the classical laws of temporal evolution of physical quantities in a form that already prefigures those of quantum mechanics.

In the second part of the course, starting from an examination of the experimental limits of classical mechanics, a new theory of mechanics is introduced: Quantum Mechanics. This is a theory that is conceptually completely different from previous classical theories, based on a description of physical phenomena in terms of probabilities and therefore no longer deterministic. It's a radical paradigm shift that has turned physics on its head over the last century, enabling a deeper understanding of physical nature, with fundamental and practical spin-offs that have radically changed the lives of mankind (atomic physics, chemistry, nuclear energy, transistors, LASERS, to name but a few). 

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

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

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This UE is a continuation of the electromagnetism and waves courses taken in L2.

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Practical work in various areas of physics.

Topics covered include the study of mechanical and electrical oscillating systems (simple and torsion pendulums, coupled pendulums, RLC circuits, inductively coupled circuits), acoustic waves, a few notions of wave optics (diffraction and interference), the use of electronic circuits to study components or electrical systems (diodes, LEDs and photodiodes, transmission lines) and the study of a few properties of matter (magnetism, photoelectric effect, Faraday effect).

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The aim of this first Fluid Mechanics module is to provide a basic understanding of the behavior of industrial fluids (air, water, hydraulic fluids), with a view to dimensioning simple systems involving static or dynamic fluids (flow rates, pressure, velocity, pressure drops, etc.). 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 the statistical physics of equilibrium systems, with a bottom-up approach: start with examples and then give the general principles. It draws heavily on Harvey Gould and Jan Tobochnik's course. A historical introduction to the construction 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 acquire the basics of special relativity (1/3 of the EU) and offer students a brief introduction to subatomic particle physics (2/3 of the EU). It will also provide an introduction to the description of the intimate structure of matter. After developing the tools of special relativity necessary for the rest of the course, we'll go into detail on 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 the basic concepts of nuclear physics will be given.

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

Interference phenomena are also recorded on holographic plates for the restitution and study of holograms (TP holography).

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

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

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

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

Objects are analyzed using Fourier optics, which, after filtering, brings out or removes certain details. The study is also compared with digital Fourier filtering (TP strioscopie).

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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The aim of this course is to introduce the basics of physical hydrodynamics. The kinematic aspects are dealt with first: Euler and Lagrange formalism, analysis of the motion of an element of fluid volume, introduction of current and potential velocity functions, and applications to different types of flow. In the following section on fluid dynamics, we establish Euler's equation and Bernoulli's relation for the flow of perfect fluids, followed by the Navier-Stokes equation describing the flow of viscous Newtonian fluids. This will lead to the definition of the stress tensor and the Reynolds number, enabling us to deduce whether a flow is laminar or turbulent. The course concludes with an introduction to the mechanics of deformable solids : displacement field, expansion and deformation tensors.

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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 workroom, on one of the many physics and chemistry topics on offer. It confronts students with the project approach, and mobilizes their creativity, initiative, autonomy and experimental rigor. The project culminates in a report and oral presentation, subject to peer and jury assessment.

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This module covers selected methods of numerical physics with applications relevant to the Fundamental Physics pathway. 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, there will be an introduction to formal calculus systems.

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This course builds on the basic concepts acquired in Quantum Mechanics in Semester 5. The course is structured around the following main themes: 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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