MASTER'S DEGREE IN FUNDAMENTAL PHYSICS AND APPLICATIONS

This module covers the fundamentals of physics and technology of semiconductor-based components. Most of the course focuses on component physics. Based on equations describing material properties, the main types of junctions are examined (p/n, metal/SC, MIS). Based on this knowledge, the operation of elementary components (diodes, transistors) is explained. In the second part, the first building blocks of component manufacturing process technology are presented.

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English tutorial course for students enrolled in the Master 1 Physics program who wish to become proficient in scientific English.

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This course is part of the foundation of modern physics. It provides a foundation of knowledge that is essential for all physics courses, as it lays the groundwork for the theoretical description of the interaction between the electromagnetic field and elementary quantum elements such as two-level systems, atoms, and molecules. It also provides the necessary knowledge for understanding LASERs, modern optical devices, and spectroscopic methods and analyses.

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The aim of this module is to enable students to compare experimental reality with their theoretical knowledge. Particular attention is paid to writing up results and presenting them in the form of oral presentations. The work is organized into eight-hour sessions for which a topic is chosen by the students. They record their results and analyses in a laboratory notebook based on the protocols used in laboratories. At the end of the semester, students choose a topic, which they develop in the form of a final report that they defend orally. This course prepares students for the internships they will undertake during their studies.

Examples of experiments available: optical spectroscopy (IR, visible), gamma, X-ray, acoustic; low-temperature photoluminescence; near-field spectroscopy (AFM, STM); electron microscopy...

The range of experiments on offer covers the areas of physics taught in the various physics courses. Students must choose from among the different experiments those that seem most relevant to their interests. A significant effort has been made to integrate new data acquisition technologies and the use of computer tools in order to compare experiment and theory.

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Through two specific examples (X-ray diffraction and vibrations), this module shows in detail how the physical properties of a solid are modeled. The formalism will also be applied to finite systems, such as nanoparticles, and will remain valid for amorphous materials, but particular attention will be paid to periodic systems (from linear chains to protein crystals, graphene, and silicon). Associated with this periodicity, the notion of reciprocal lattices will naturally arise.

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This course includes an upgrade and deepening of programming techniques as well as an introduction to computational physics. We will begin with a review of procedural programming using the Python 3 language. We will then take an in-depth look at numerical methods relevant to physics, studying a selection of classic algorithms from numerical analysis and applying them to physical problems.

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The EU "Condensed Matter Physics 2: Electronic Properties" is intended for students interested in solid-state physics.

Following on from the course unit "Condensed Matter Physics 1: Structural Properties," this course unit addresses the properties of electrons in crystalline solids, the band structure of electronic levels, and the basic concepts of semiconductor physics.

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Current experimental physics generally requires the implementation of a more or less complex acquisition chain involving different types of instruments: sources, sensors, actuators, etc., and a controller (such as a computer). The objective of this course unit is to familiarize students with this type of issue so that they can set up such a data acquisition system. At the controller level, the control part will be implemented in Python (in particular with the PyVisa library).  

- Presentation of the most common communication interfaces/ports: serial (RS-232, USB), parallel (GPIB), and network (Ethernet) (CM).

- Implementation of simple examples of communication, device configuration, and data acquisition (tutorial).

- Development of a more comprehensive acquisition chain through projects (practical work). 

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This module focuses on understanding the physical processes involved in light emission and absorption in semiconductor devices, as well as the technologies used to manufacture such devices. These issues are addressed in the clean room project, which involves the production and characterization of an optoelectronic component.

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Knowing how to acquire and process data are essential skills in a scientific and/or technical professional context. The objective of this course is to address three types of standard skills in the professional environment:

· Advanced use of spreadsheets/graphing software (MS EXCEL, LO-CALC) for scientific and technical purposes

· Network interconnections: infrastructure, TCP/IP protocol suite, security

· Introduction to relational databases (MS ACCESS, LO-BASE) – concepts & vocabulary, creating queries, graphical reports, forms.

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Introductory research internship in a university laboratory

Dates: May-June

Duration: 7 weeks minimum, extendable in July

Prior to the internship, students analyze an article suggested by their internship supervisors to prepare them for the internship topic and for in-depth reading of scientific publications.

After the internship, as part of a peer review process, students submit their written reports and oral presentations for critical review by other students, who are responsible for helping them improve their work before it is finally submitted to the internship jury.

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This course is designed to provide students with skills in the field of numerical solution of the Schrödinger equation in order to simulate complex quantum well structures. The course begins by studying situations where the solution is analytical, then situations where the solution is semi-analytical, before moving on to the finite difference (FD) method. Various FD schemes are proposed, each with an evaluation of convergence based on different key parameters (domain truncation, number of samples, etc.). Finally, examples of concrete physical applications are studied.    

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Third and final part of the course devoted to micro, nano, and optoelectronic device fabrication processes. The latest technological building blocks not yet covered in previous semesters are presented in detail. The modeling and simulation aspects of technological processes are emphasized, as an introduction to TCAD solutions. Finally, all of these lessons are synthesized in a practical manner, with a sequence of all of these technological steps in order to produce discrete and integrated components, from wafers to packaged devices.

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This EU presents the physical properties of different nanostructures such as quantum wells, 1D photonic crystals, carbon nanotubes, and graphene. Electronic (structure and transport), vibrational, and optical properties are discussed, as well as radiation-matter interaction.

This will involve describing the development of low-dimensional materials and the associated electronic, photonic, and phononic structures, studying transport phenomena, electron-photon and electron-phonon couplings, excitons, and the absorption, emission, and scattering of light.

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English tutorial course for students enrolled in the Master 2 Physics program who are seeking professional integration in English in a contemporary context.

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This module gives students the opportunity to discover the specifics of the world of work and prepare themselves to enter it in the best possible conditions, in particular through sharing experiences with professionals from the field. Students practice how to successfully apply for a job, using a methodical approach, optimizing their analysis of the job offer, writing a targeted resume and cover letter, and preparing for the job interview (role-playing, simulations).

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Design of experiments is part of the quality process. It is a method of conducting tests and analyzing data that saves time and money. That is why it is very useful in industry.

The emphasis is on understanding the basics.

It is an interactive course, with an example-based approach.

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This module aims to teach the operating principles of the main techniques used to characterize the structure (in volume and on the surface) and properties (optical, electronic, etc.) of condensed matter:

• X-ray and electron diffraction techniques
• optical spectroscopy techniques (absorption, reflection, luminescence)
• local probe microscopy

  This module aims to teach the operating principles of the main techniques used to characterize the structure (in volume and on the surface) and properties (optical, electronic, etc.) of condensed matter:

  • X-ray and electron diffraction techniques
  • optical spectroscopy techniques (absorption, reflection, luminescence)
  • local probe microscopy

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End-of-course internship, in a company or university laboratory

This significant professional experience (up to six months) aims to demonstrate the student's ability to perform executive-level duties (engineer or doctoral researcher) or to pursue a thesis in the areas of expertise covered by the program.

Start date: February

Duration: four to six months, ending no later than August 31.

End-of-course internship, in a company or university laboratory

This significant professional experience (up to six months) aims to demonstrate the student's ability to perform executive-level duties (engineer or doctoral researcher) or to pursue a thesis in the areas of expertise covered by the program.

Start date: February

Duration: four to six months, ending no later than August 31.

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This course is an experimental training program in the main techniques of nanocaracterization and nanotechnology:

• AFM
• SEM
• Photoluminescence
• X-ray diffraction
• Ellipsometry
• Optical Microscopy
• Source meter
• Capacitance meter
• Processes for manufacturing microdevices in clean rooms

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The course describes the different detectors and physical processes involved in particle detection in high-energy physics. Next, we will describe how the main particle accelerators work, which are used in high-energy physics but also in many other fields such as medicine, industry, materials science, archaeology, etc.

The course provides a detailed description of the physical processes and experimental techniques involved in detecting charged and neutral particles in detectors, as these detections form the basis of all physical measurements.

A detailed description of the different types of radiation and particle-matter interactions will be provided.

We will focus on describing the systematics associated with these processes and their statistical treatment.

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English tutorial course for students enrolled in the Master 2 Physics program who are seeking professional integration in English in a contemporary context.

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This course covers the essentials needed for a good understanding of the physics of atmospheres and stellar winds. The key elements of radiation transfer theory are covered, both in local thermodynamic equilibrium (LTE) and off-LTE, as well as the description of gas (equation of state) and its interaction with the radiation field (opacities). Modern models and simulations are presented with their application to the determination of stellar parameters, in particular chemical composition, via spectroscopy. The different types of stellar winds (pressure, radiative, hybrid) are described using theories compared with observations.

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During the Observational Astrophysics Workshop 2 course, students must complete all stages of an observational astrophysics study. From defining the spectroscopic or photometric observations to be carried out during a four-night stay at the Haute-Provence Observatory, to modeling and critically discussing their measurements and writing a scientific report, students are actively involved in this course.

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Interstellar medium: physicochemical processes – phases – radio astronomy.

This course provides students with an understanding of the physical and chemical processes that are important for the interstellar medium (dynamic, thermal, and chemical processes) as well as the associated observational diagnostics (molecular spectroscopy, radio astronomy). The main phases of the interstellar medium (ionized, atomic, and molecular phases) are also presented.

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This course provides a comprehensive description of the Standard Model of Particle Physics. We will begin by studying the Dirac equation, a quantum description of the dynamics of a spin ½ particle. We will then see how to describe electromagnetic interactions using quantum electrodynamics theory. Next, we will discuss weak interactions and their unified description with electromagnetic interactions through electroweak theory. Finally, we will study gauge theories and their spontaneous breaking in order to present the complete theory of the Standard Model of Particle Physics. To conclude, we will give a brief overview of theories beyond the Standard Model.

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This course is an introduction to relativistic quantum field theory and its applications in particle physics. Using the example of a scalar field, we will develop the formalisms of canonical quantization and path integral quantization before introducing perturbation theory and some notions of renormalization. We will discuss the quantization of spin 1/2 and spin 1 fields, concluding with a discussion of quantum electrodynamics.

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This course is an introduction to the standard model of cosmology in its theoretical and phenomenological aspects. It focuses on the hot inflationary Big Bang model. It builds on the M1 course in general relativity and cosmology.

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The practical work involves detecting and measuring cosmic rays (muons).

The aim is to familiarize students with an acquisition chain dedicated to measuring cosmic rays (mainly muons). Students will need to understand how the various components of the acquisition chain work individually (power supplies, photomultipliers, scintillators, discriminators, oscilloscopes, etc.) and then build their own acquisition device using these components. One of the objectives of the device could be to determine the mass of the muon, but other purposes are possible and left to the students' imagination.

Students will then have to collect data from their device and analyze it, taking into account systematic and statistical errors in the data set.

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This course describes the theoretical and observational foundations of the problem known as cosmological dark matter. Dark matter manifests itself through gravitational effects at different astrophysical scales, from the scale of galaxies to cosmological scales (the observable universe as a whole). It constitutes approximately 85% of the total matter in the universe, and it is impossible for it to be composed of the elementary particles that characterize ordinary known matter. The course will focus in particular on potential solutions to this problem, connecting the infinitely small (elementary particles) to the infinitely large (the universe on a large scale).

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3- to 6-month internship (21 ECTS) in a laboratory with the aim of immersing students in the world of research and preparing them for their thesis. This internship can be carried out in a research laboratory in France or abroad. It runs from March¹ to May 31, when the written report is due. An oral defense takes place at the beginning of June. The internship may be extended until August 31 in order to move directly on to the thesis. Topics cover a wide spectrum ranging from theoretical physics (cosmology, particle physics, and astroparticle physics) to experimental physics (LHC experiments, search for gravitational waves or dark matter, large-field cosmological surveys, etc.).

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This course is an introduction to the acceleration, propagation, and radiation mechanisms of energetic particles in astrophysical environments. It will cover the fundamental concepts.

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The Observational Astrophysics Workshop 1 is an introduction to conducting observational studies (photometry or spectroscopy) of astrophysical objects (stars, nebulae) at the M1 level. Students carry out all stages of the process, from planning and conducting observations at the Faculty of Science's astronomical observatory to calibrating and analyzing the data obtained. This module is designed as preparation for the M2 Observational Astrophysics Workshop 2 (HAP905P) module.

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In this course, we study the theory of general relativity, which is the modern description of universal gravitation. After reviewing some concepts from special relativity, we will familiarize ourselves with the basic concepts of general relativity using a few specific solutions to these equations in well-defined physical contexts: weak fields at the Earth's surface, geometry around an isolated spherical star, and the universe on large scales. This will allow us to generalize our understanding and construct the theory, then deduce the field equations, i.e., Einstein's equations. The course will conclude with a discussion of black holes and gravitational waves.

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This course aims to provide basic concepts in astronomy and astrophysics, which will be useful in other astrophysics courses in the master's program. It also illustrates the application of physics concepts to the description of astrophysical objects. Most of the concepts covered will be explored in greater depth in^second-year courses.

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Fluids are all around us at all times and on all scales. Understanding fluid mechanics means understanding the mechanics of our surroundings, particularly air and water. As such, hydrodynamics is part of a physicist's basic knowledge.

Hydrodynamics is an introduction to the mechanics of incompressible perfect fluids (Euler) and viscous Newtonian fluids (Navier-Stokes). Classical flows are presented, as well as the concepts of boundary layer, instability, and turbulence. The emphasis is placed more on physical ideas than on advanced mathematical or numerical solution methods.

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English tutorial course for students enrolled in the Master 1 Physics program who wish to become proficient in scientific English.

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This course is part of the foundation of modern physics. It provides a foundation of knowledge that is essential for all physics courses, as it lays the groundwork for the theoretical description of the interaction between the electromagnetic field and elementary quantum elements such as two-level systems, atoms, and molecules. It also provides the necessary knowledge for understanding LASERs, modern optical devices, and spectroscopic methods and analyses.

See the full page

The aim of this module is to enable students to compare experimental reality with their theoretical knowledge. Particular attention is paid to writing up results and presenting them in the form of oral presentations. The work is organized into eight-hour sessions for which a topic is chosen by the students. They record their results and analyses in a laboratory notebook based on the protocols used in laboratories. At the end of the semester, students choose a topic, which they develop in the form of a final report that they defend orally. This course prepares students for the internships they will undertake during their studies.

Examples of experiments available: optical spectroscopy (IR, visible), gamma, X-ray, acoustic; low-temperature photoluminescence; near-field spectroscopy (AFM, STM); electron microscopy...

The range of experiments on offer covers the areas of physics taught in the various physics courses. Students must choose from among the different experiments those that seem most relevant to their interests. A significant effort has been made to integrate new data acquisition technologies and the use of computer tools in order to compare experiment and theory.

See the full page

This course includes an upgrade and deepening of programming techniques as well as an introduction to computational physics. We will begin with a review of procedural programming using the Python 3 language. We will then take an in-depth look at numerical methods relevant to physics, studying a selection of classic algorithms from numerical analysis and applying them to physical problems.

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This course is intended as an introduction to astroparticle physics (cosmic accelerators, gamma rays, multi-messengers, experimental techniques, etc.).

The course builds on the knowledge acquired in L3 to offer students a brief introduction to astroparticle physics. After a description of the general context, two examples of detectors in gamma-ray astronomy will be detailed, followed by an introduction to the physics of multi-messenger astrophysics (in particular via the detection of gravitational waves). The course will then address the physics of cosmic rays (CR), the issue of CR acceleration and propagation, and the hypothesis of supernova remnants as galactic CR accelerators (description of the first-order Fermi acceleration mechanism).

The course will conclude with a description of the cosmological challenges of future large-scale ground-based and space-based surveys (LSST and Euclid in particular).

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This course aims to introduce and develop several fundamental concepts and tools of non-relativistic quantum physics necessary for understanding the physical processes describing the interactions between the elementary constituents of matter and radiation. We will also address second quantization and the path integral formulation of quantum mechanics, which provide the ideal framework for the development of quantum field theory and its various applications (e.g., high-energy physics, condensed matter physics).

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Introduction to advanced statistical physics: grand canonical ensemble; quantum statistics; quantum fluids (Bose-Einstein condensation, thermal radiation; Sommerfeld theory); phase transitions; Ising model; mean field theory; dynamics of complex systems.

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This course is an introduction to the Standard Model of Particle Physics. We will begin by listing elementary particles and their interactions. Then we will see how to use Lie group theory to classify these elementary particles. Finally, we will discuss the concept of electromagnetic interactions for charged particles without spin (scalar electrodynamics theory).

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Fluid mechanics is a fundamental tool for the sciences of the Universe: from Earth and giant planets to stars, accretion disks, and the interstellar medium, it is an essential approach for studying astrophysical objects. The "Fluid Dynamics in Astrophysics and Cosmology" course builds on the "Hydrodynamics" course, focusing on three central themes in astrophysics: rotating fluids, thermal convection, and magnetohydrodynamics.

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This 7-week internship (usually from late April to late June) (10 ECTS) will give students their first taste of research in astrophysics, cosmology, or particle physics. Internships at the intersection of these disciplines, more commonly known as "astroparticles," are also available. Internships may be more theoretical or more experimental in nature, depending on the choices of students and supervisors.

This internship can be carried out in a research laboratory in France or abroad. However, it traditionally takes place in one of the two joint research units (UMR) at Montpellier 2 University: the Montpellier Laboratory of Universes and Particles (LUPM, IN2P3) or the Charles Coulomb Laboratory (L2C, INP).

The internship will enable students to interact with a research team (national and/or international) and begin to discover the research topics they would prefer to develop in their future studies.

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Fluids are all around us at all times and on all scales. Understanding fluid mechanics means understanding the mechanics of our surroundings, particularly air and water. As such, hydrodynamics is part of a physicist's basic knowledge.

Hydrodynamics is an introduction to the mechanics of incompressible perfect fluids (Euler) and viscous Newtonian fluids (Navier-Stokes). Classical flows are presented, as well as the concepts of boundary layer, instability, and turbulence. The emphasis is placed more on physical ideas than on advanced mathematical or numerical solution methods.

See the full page

English tutorial course for students enrolled in the Master 1 Physics program who wish to become proficient in scientific English.

See the full page

This course is part of the foundation of modern physics. It provides a foundation of knowledge that is essential for all physics courses, as it lays the groundwork for the theoretical description of the interaction between the electromagnetic field and elementary quantum elements such as two-level systems, atoms, and molecules. It also provides the necessary knowledge for understanding LASERs, modern optical devices, and spectroscopic methods and analyses.

See the full page

The aim of this module is to enable students to compare experimental reality with their theoretical knowledge. Particular attention is paid to writing up results and presenting them in the form of oral presentations. The work is organized into eight-hour sessions for which a topic is chosen by the students. They record their results and analyses in a laboratory notebook based on the protocols used in laboratories. At the end of the semester, students choose a topic, which they develop in the form of a final report that they defend orally. This course prepares students for the internships they will undertake during their studies.

Examples of experiments available: optical spectroscopy (IR, visible), gamma, X-ray, acoustic; low-temperature photoluminescence; near-field spectroscopy (AFM, STM); electron microscopy...

The range of experiments on offer covers the areas of physics taught in the various physics courses. Students must choose from among the different experiments those that seem most relevant to their interests. A significant effort has been made to integrate new data acquisition technologies and the use of computer tools in order to compare experiment and theory.

See the full page

Through two specific examples (X-ray diffraction and vibrations), this module shows in detail how the physical properties of a solid are modeled. The formalism will also be applied to finite systems, such as nanoparticles, and will remain valid for amorphous materials, but particular attention will be paid to periodic systems (from linear chains to protein crystals, graphene, and silicon). Associated with this periodicity, the notion of reciprocal lattices will naturally arise.

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The course aims to provide a general introduction to cellular and molecular biology and to contextualize the use of modern physics, through its quantitative methods and approaches, to describe biological systems and their complexity from the molecular to the cellular and tissue levels.

Another fundamental topic covered is the quantification of phenomena, their physical interpretation, and their physical-mathematical modeling. The course introduces students to philosophy and the range of topics covered in this master's program, which focuses on the study of the physical principles of the organization and dynamics of living and complex matter.

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This course includes an upgrade and deepening of programming techniques as well as an introduction to computational physics. We will begin with a review of procedural programming using the Python 3 language. We will then take an in-depth look at numerical methods relevant to physics, studying a selection of classic algorithms from numerical analysis and applying them to physical problems.

See the full page

Introduction to advanced statistical physics: grand canonical ensemble; quantum statistics; quantum fluids (Bose-Einstein condensation, thermal radiation; Sommerfeld theory); phase transitions; Ising model; mean field theory; dynamics of complex systems.

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Seven-week laboratory internship aimed at immersing students in the world of fundamental and/or applied research.

This internship can be carried out in a research laboratory or technical platform in France or abroad.

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This course presents the concepts, fundamentals, and orders of magnitude of the physics and physical chemistry of interfaces that govern the mesoscopic scale of matter and ultimately determine the behavior and properties of everyday objects: soil, milk, cheese, paints, inks, cosmetics, adhesives, lubricants, etc., as well as numerous technological processes and biological cells and membranes.

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Knowing how to acquire and process data are essential skills in a scientific and/or technical professional context. The objective of this course is to address three types of standard skills in the professional environment:

· Advanced use of spreadsheets/graphing software (MS EXCEL, LO-CALC) for scientific and technical purposes

· Network interconnections: infrastructure, TCP/IP protocol suite, security

· Introduction to relational databases (MS ACCESS, LO-BASE) – concepts & vocabulary, creating queries, graphical reports, forms.

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The word "biomimicry" comes from ancient Greek: bios (bios), life, and mimesis, imitation.

This term refers to the study of extra- and intracellular biological phenomena using in vitro experimental techniques aimed at reproducing, i.e., "imitating," qualitatively and quantitatively the aspects that characterize these phenomena.

The biomimetic method approaches biological complexity "by subtraction": by assembling new minimal systems (with a small number of parameters) under highly controlled conditions using abottom-up approach; by identifying essential quantities; and by controlling the system's parameters.

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This course presents and develops different methods for modeling biological systems: from the physics of individual molecules to the physical study of systems and populations of objects (e.g., proteins) or organisms (bacteria).

These methods (both analytical and numerical) are derived mainly from statistical physics, stochastic process theory, and nonlinear physics.

Examples of studies are also provided based on the content of other modules in M1 and M2 to contextualize the various examples within the framework of physical theory and quantitative experimentation on living matter.

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Polymer physics, to which this course provides an introduction, focuses on the physical properties of covalent chain assemblies, ranging from a few dozen to several million elementary molecules: polymers or macromolecules.

These synthetic or natural molecules can be observed in the solid state, liquid state, in solution, in a colloidal state, or confined to an interface.

Their very specific physical properties have led to the development of specific theoretical tools and the emergence of this new branch of physics with numerous applications.

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English tutorial course for students enrolled in the Master 2 Physics program who are seeking professional integration in English in a contemporary context.

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This module gives students the opportunity to discover the specifics of the world of work and prepare themselves to enter it in the best possible conditions, in particular through sharing experiences with professionals from the field. Students practice how to successfully apply for a job, using a methodical approach, optimizing their analysis of the job offer, writing a targeted resume and cover letter, and preparing for the job interview (role-playing, simulations).

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This course provides an introduction to the field of complex fluids and active matter, with applications in both soft matter physics and chemistry and the physics of living organisms and biological objects.

It is common to both the PhyMV and SoftMat courses.

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Internship lasting a minimum of 5 months in a laboratory with the aim of immersing students in the world of fundamental and/or applied research and preparing them for a doctoral thesis. This internship can be carried out in research laboratories and technical platforms in France or abroad.

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Fluids are all around us at all times and on all scales. Understanding fluid mechanics means understanding the mechanics of our surroundings, particularly air and water. As such, hydrodynamics is part of a physicist's basic knowledge.

Hydrodynamics is an introduction to the mechanics of incompressible perfect fluids (Euler) and viscous Newtonian fluids (Navier-Stokes). Classical flows are presented, as well as the concepts of boundary layer, instability, and turbulence. The emphasis is placed more on physical ideas than on advanced mathematical or numerical solution methods.

See the full page

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English tutorial course for students enrolled in the Master 1 Physics program who wish to become proficient in scientific English.

See the full page

This course is part of the foundation of modern physics. It provides a foundation of knowledge that is essential for all physics courses, as it lays the groundwork for the theoretical description of the interaction between the electromagnetic field and elementary quantum elements such as two-level systems, atoms, and molecules. It also provides the necessary knowledge for understanding LASERs, modern optical devices, and spectroscopic methods and analyses.

See the full page

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Through two specific examples (X-ray diffraction and vibrations), this module shows in detail how the physical properties of a solid are modeled. The formalism will also be applied to finite systems, such as nanoparticles, and will remain valid for amorphous materials, but particular attention will be paid to periodic systems (from linear chains to protein crystals, graphene, and silicon). Associated with this periodicity, the notion of reciprocal lattices will naturally arise.

See the full page

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Introduction to advanced statistical physics: grand canonical ensemble; quantum statistics; quantum fluids (Bose-Einstein condensation, thermal radiation; Sommerfeld theory); phase transitions; Ising model; mean field theory; dynamics of complex systems.

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A 10-ECTS supervised project during which groups of students work on developing software for research or teaching purposes.

This project is designed to give students their first semi-professional experience by working in groups of (>2) on a fairly large project, usually proposed by fellow researchers who want to develop and/or expand software for research purposes or for the general public.

Supervision is provided by fellow physicists and, where appropriate, computer scientists. Students submit a code with accompanying documentation. A report is written and an oral defense is held.    

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The EU "Condensed Matter Physics 2: Electronic Properties" is intended for students interested in solid-state physics.

Following on from the course unit "Condensed Matter Physics 1: Structural Properties," this course unit addresses the properties of electrons in crystalline solids, the band structure of electronic levels, and the basic concepts of semiconductor physics.

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Current experimental physics generally requires the implementation of a more or less complex acquisition chain involving different types of instruments: sources, sensors, actuators, etc., and a controller (such as a computer). The objective of this course unit is to familiarize students with this type of issue so that they can set up such a data acquisition system. At the controller level, the control part will be implemented in Python (in particular with the PyVisa library).  

- Presentation of the most common communication interfaces/ports: serial (RS-232, USB), parallel (GPIB), and network (Ethernet) (CM).

- Implementation of simple examples of communication, device configuration, and data acquisition (tutorial).

- Development of a more comprehensive acquisition chain through projects (practical work). 

See the full page

Knowing how to acquire and process data are essential skills in a scientific and/or technical professional context. The objective of this course is to address three types of standard skills in the professional environment:

· Advanced use of spreadsheets/graphing software (MS EXCEL, LO-CALC) for scientific and technical purposes

· Network interconnections: infrastructure, TCP/IP protocol suite, security

· Introduction to relational databases (MS ACCESS, LO-BASE) – concepts & vocabulary, creating queries, graphical reports, forms.

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Teaching mathematics for numerical physics. Introduction to tools for studying partial differential equations (distributions, variational formulation, Sobolev spaces).

Introduction to integral methods and their numerical implementation. Applications to diffraction problems in harmonic regime.

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This course is designed to provide students with skills in the field of numerical solution of the Schrödinger equation in order to simulate complex quantum well structures. The course begins by studying situations where the solution is analytical, then situations where the solution is semi-analytical, before moving on to the finite difference (FD) method. Various FD schemes are proposed, each with an evaluation of convergence based on different key parameters (domain truncation, number of samples, etc.). Finally, examples of concrete physical applications are studied.    

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This course lays the foundations for using "atomistic" simulation tools, i.e., those based on microscopic interactions between constituents. Primarily, it lays the foundations for simulations known as "Molecular Dynamics" and "Monte Carlo."

He addresses the underlying theoretical concepts in order to build a solid understanding of the methods, as well as the practical implementation of the corresponding codes.

The critical and reasoned use of data is also discussed.

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This course provides an introduction to scientific image processing, with no prerequisites, in the context of physics and medical sciences.

Starting with the basics of digital image coding, we will introduce the main techniques aimed first at improving image data quality, then at extracting quantitative data. Deconvolution, denoising, thresholding, segmentation, Fourier transforms, and wavelets will be covered.

We will conclude with the specific problems posed by image sequences (films) or 3D images such as MRI data in a medical context.

The tool used will be the Matlab/Octave programming environment.

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This teaching unit is an introduction to artificial intelligence for physicists. It aims to explore uses of deep learning using the TensorFlow and Keras libraries. It includes a presentation of examples of use in physics.

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English tutorial course for students enrolled in the Master 2 Physics program who are seeking professional integration in English in a contemporary context.

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This module gives students the opportunity to discover the specifics of the world of work and prepare themselves to enter it in the best possible conditions, in particular through sharing experiences with professionals from the field. Students practice how to successfully apply for a job, using a methodical approach, optimizing their analysis of the job offer, writing a targeted resume and cover letter, and preparing for the job interview (role-playing, simulations).

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This teaching unit deals with solving electromagnetic problems using computers. Based on Maxwell's equations, it shows how to simulate the behavior of electromagnetic waves in different media. In particular, it includes a detailed implementation of simulations based on the finite difference time domain (FDTD) method.

An introduction to diffraction problems in harmonic regime by a bounded obstacle will be given for the case of scalar waves in 2D and 3D.

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This module introduces advanced practices in atomistic simulation methods, particularly Molecular Dynamics.

It thus includes the expansion of methods already acquired, both in terms of physics (ab initio simulations, density functional theory) , as well as in terms of implementation (optimization, parallelization) and application (introduction to the practice of simulations in a high-performance computing environment).

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A 5 ECTS supervised project during which students work individually on developing software for research and development and/or teaching.

This project builds on the experience gained during the supervised project already completed in M1. This time, students work individually, which is a different experience from the M1 project, which was carried out in groups. Students receive an order to develop software that meets specific specifications and must deliver functional code.   

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Six-month M2 internship (25 ECTS) carried out within a company or public organization (research laboratory, national organization/agency, etc.).

The internship must focus on a physical problem involving a numerical calculation component.  

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This course will cover the main aspects of star and planetary system formation in two parts of equal length. Star formation will address the stability of clouds in equilibrium and stability, the collapse of dense cores, protostars and their evolution, and the impact of young stars on their environment. Planetary formation will draw on constraints from the solar system and detections of extrasolar planets to discuss the structure and evolution of protoplanetary disks, and the formation of terrestrial planets and giant planets.

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English tutorial course for students enrolled in the Master 2 Physics program who are seeking professional integration in English in a contemporary context.

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This course covers the essentials needed for a good understanding of the physics of atmospheres and stellar winds. The key elements of radiation transfer theory are covered, both in local thermodynamic equilibrium (LTE) and off-LTE, as well as the description of gas (equation of state) and its interaction with the radiation field (opacities). Modern models and simulations are presented with their application to the determination of stellar parameters, in particular chemical composition, via spectroscopy. The different types of stellar winds (pressure, radiative, hybrid) are described using theories compared with observations.

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During the Observational Astrophysics Workshop 2 course, students must complete all stages of an observational astrophysics study. From defining the spectroscopic or photometric observations to be carried out during a four-night stay at the Haute-Provence Observatory, to modeling and critically discussing their measurements and writing a scientific report, students are actively involved in this course.

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The aim is to present the various observations and associated theoretical concepts—known as cosmological probes—that have helped to validate the ΛCDM cosmological model, known as the "concordance" model. The course is divided into chapters of roughly equal length. It is supplemented by a series of seminars presented by students (flipped classroom) that explore more observational and technical aspects (based on a publication from a major collaboration).

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Interstellar medium: physicochemical processes – phases – radio astronomy.

This course provides students with an understanding of the physical and chemical processes that are important for the interstellar medium (dynamic, thermal, and chemical processes) as well as the associated observational diagnostics (molecular spectroscopy, radio astronomy). The main phases of the interstellar medium (ionized, atomic, and molecular phases) are also presented.

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This EU lays the foundations for our understanding of the formation and evolution of galaxies, from the astrophysical processes involved on small scales in star formation to the effects of the environment on very large scales. A dual approach will be used, with theoretical aspects on the one hand and observational aspects on the other.

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Much of our understanding of the Universe relies on understanding and accurately modeling stars. Stars constitute a very important part of the integrated light of galaxies, and are major contributors to the chemical and dynamic evolution of galaxies. In this course, we will discuss the physics describing stellar structure and study how this structure evolves over time in the case of isolated stars.

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Four-month internship in a laboratory with the aim of immersing students in the world of research and preparing them for their thesis.

This internship can be carried out in a research laboratory in France or abroad.

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This EU presents astrophysics instruments and the signal processing tools associated with their operation.

The focus is on instruments with high angular resolution and high contrast (interferometry, adaptive optics, coronography, etc.).

In addition, this EU introduces the basics of digital signal processing and presents a general methodology, based on modeling instrumental effects, for image reconstruction or optimal use of measurements.

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Research in astrophysics is based on various approaches (observations, theory, modeling, simulation), all of which have in common the use of advanced digital tools.

In order to best prepare M2 Astrophysics students for research work, this module offers them the opportunity, in a different setting from that of an internship, to carry out individual supervised digital work on a project proposed by a tutor, focusing on the use and/or development of professional-level code to answer a specific astrophysical question.

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This module covers the fundamentals of physics and technology of semiconductor-based components. Most of the course focuses on component physics. Based on equations describing material properties, the main types of junctions are examined (p/n, metal/SC, MIS). Based on this knowledge, the operation of elementary components (diodes, transistors) is explained. In the second part, the first building blocks of component manufacturing process technology are presented.

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English tutorial course for students enrolled in the Master 1 Physics program who wish to become proficient in scientific English.

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This course is part of the foundation of modern physics. It provides a foundation of knowledge that is essential for all physics courses, as it lays the groundwork for the theoretical description of the interaction between the electromagnetic field and elementary quantum elements such as two-level systems, atoms, and molecules. It also provides the necessary knowledge for understanding LASERs, modern optical devices, and spectroscopic methods and analyses.

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The aim of this module is to enable students to compare experimental reality with their theoretical knowledge. Particular attention is paid to writing up results and presenting them in the form of oral presentations. The work is organized into eight-hour sessions for which a topic is chosen by the students. They record their results and analyses in a laboratory notebook based on the protocols used in laboratories. At the end of the semester, students choose a topic, which they develop in the form of a final report that they defend orally. This course prepares students for the internships they will undertake during their studies.

Examples of experiments available: optical spectroscopy (IR, visible), gamma, X-ray, acoustic; low-temperature photoluminescence; near-field spectroscopy (AFM, STM); electron microscopy...

The range of experiments on offer covers the areas of physics taught in the various physics courses. Students must choose from among the different experiments those that seem most relevant to their interests. A significant effort has been made to integrate new data acquisition technologies and the use of computer tools in order to compare experiment and theory.

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Through two specific examples (X-ray diffraction and vibrations), this module shows in detail how the physical properties of a solid are modeled. The formalism will also be applied to finite systems, such as nanoparticles, and will remain valid for amorphous materials, but particular attention will be paid to periodic systems (from linear chains to protein crystals, graphene, and silicon). Associated with this periodicity, the notion of reciprocal lattices will naturally arise.

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This course includes an upgrade and deepening of programming techniques as well as an introduction to computational physics. We will begin with a review of procedural programming using the Python 3 language. We will then take an in-depth look at numerical methods relevant to physics, studying a selection of classic algorithms from numerical analysis and applying them to physical problems.

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This course aims to introduce and develop several fundamental concepts and tools of non-relativistic quantum physics necessary for understanding the physical processes describing the interactions between the elementary constituents of matter and radiation. We will also address second quantization and the path integral formulation of quantum mechanics, which provide the ideal framework for the development of quantum field theory and its various applications (e.g., high-energy physics, condensed matter physics).

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Introduction to advanced statistical physics: grand canonical ensemble; quantum statistics; quantum fluids (Bose-Einstein condensation, thermal radiation; Sommerfeld theory); phase transitions; Ising model; mean field theory; dynamics of complex systems.

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The EU "Condensed Matter Physics 2: Electronic Properties" is intended for students interested in solid-state physics.

Following on from the course unit "Condensed Matter Physics 1: Structural Properties," this course unit addresses the properties of electrons in crystalline solids, the band structure of electronic levels, and the basic concepts of semiconductor physics.

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Internship supervised by a professor/researcher in the field of nanophysics and quantum physics.

Dates: May-June

Duration: 7 weeks minimum, extendable in July

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Knowing how to acquire and process data are essential skills in a scientific and/or technical professional context. The objective of this course is to address three types of standard skills in the professional environment:

· Advanced use of spreadsheets/graphing software (MS EXCEL, LO-CALC) for scientific and technical purposes

· Network interconnections: infrastructure, TCP/IP protocol suite, security

· Introduction to relational databases (MS ACCESS, LO-BASE) – concepts & vocabulary, creating queries, graphical reports, forms.

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Teaching mathematics for numerical physics. Introduction to tools for studying partial differential equations (distributions, variational formulation, Sobolev spaces).

Introduction to integral methods and their numerical implementation. Applications to diffraction problems in harmonic regime.

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This course is designed to provide students with skills in the field of numerical solution of the Schrödinger equation in order to simulate complex quantum well structures. The course begins by studying situations where the solution is analytical, then situations where the solution is semi-analytical, before moving on to the finite difference (FD) method. Various FD schemes are proposed, each with an evaluation of convergence based on different key parameters (domain truncation, number of samples, etc.). Finally, examples of concrete physical applications are studied.    

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This EU presents the physical properties of different nanostructures such as quantum wells, 1D photonic crystals, carbon nanotubes, and graphene. Electronic (structure and transport), vibrational, and optical properties are discussed, as well as radiation-matter interaction.

This will involve describing the development of low-dimensional materials and the associated electronic, photonic, and phononic structures, studying transport phenomena, electron-photon and electron-phonon couplings, excitons, and the absorption, emission, and scattering of light.

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This teaching unit is an introduction to artificial intelligence for physicists. It aims to explore uses of deep learning using the TensorFlow and Keras libraries. It includes a presentation of examples of use in physics.

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English tutorial course for students enrolled in the Master 2 Physics program who are seeking professional integration in English in a contemporary context.

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This teaching unit deals with solving electromagnetic problems using computers. Based on Maxwell's equations, it shows how to simulate the behavior of electromagnetic waves in different media. In particular, it includes a detailed implementation of simulations based on the finite difference time domain (FDTD) method.

An introduction to diffraction problems in harmonic regime by a bounded obstacle will be given for the case of scalar waves in 2D and 3D.

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This module aims to teach the operating principles of the main techniques used to characterize the structure (in volume and on the surface) and properties (optical, electronic, etc.) of condensed matter:

• X-ray and electron diffraction techniques
• optical spectroscopy techniques (absorption, reflection, luminescence)
• local probe microscopy

  This module aims to teach the operating principles of the main techniques used to characterize the structure (in volume and on the surface) and properties (optical, electronic, etc.) of condensed matter:

  • X-ray and electron diffraction techniques
  • optical spectroscopy techniques (absorption, reflection, luminescence)
  • local probe microscopy

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This EU is specific to the NanoQuant program and offers high-level fundamental training in the field of Quantum Technologies, i.e., current and future developments in new technologies based on concepts such as quantum coherence and entanglement, which enable functionalities and sensitivities that exceed their classical counterparts.

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Internship of at least five months in a laboratory, supervised by a professor-researcher or researcher in the fields of nanophysics or quantum physics.

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This course is an experimental training program in the main techniques of nanocaracterization and nanotechnology:

• AFM
• SEM
• Photoluminescence
• X-ray diffraction
• Ellipsometry
• Optical Microscopy
• Source meter
• Capacitance meter
• Processes for manufacturing microdevices in clean rooms

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This course aims to provide basic concepts in astronomy and astrophysics, which will be useful in other astrophysics courses in the master's program. It also illustrates the application of physics concepts to the description of astrophysical objects. Most of the concepts covered will be explored in greater depth in^second-year courses.

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Fluids are all around us at all times and on all scales. Understanding fluid mechanics means understanding the mechanics of our surroundings, particularly air and water. As such, hydrodynamics is part of a physicist's basic knowledge.

Hydrodynamics is an introduction to the mechanics of incompressible perfect fluids (Euler) and viscous Newtonian fluids (Navier-Stokes). Classical flows are presented, as well as the concepts of boundary layer, instability, and turbulence. The emphasis is placed more on physical ideas than on advanced mathematical or numerical solution methods.

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English tutorial course for students enrolled in the Master 1 Physics program who wish to become proficient in scientific English.

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This course is part of the foundation of modern physics. It provides a foundation of knowledge that is essential for all physics courses, as it lays the groundwork for the theoretical description of the interaction between the electromagnetic field and elementary quantum elements such as two-level systems, atoms, and molecules. It also provides the necessary knowledge for understanding LASERs, modern optical devices, and spectroscopic methods and analyses.

See the full page

The aim of this module is to enable students to compare experimental reality with their theoretical knowledge. Particular attention is paid to writing up results and presenting them in the form of oral presentations. The work is organized into eight-hour sessions for which a topic is chosen by the students. They record their results and analyses in a laboratory notebook based on the protocols used in laboratories. At the end of the semester, students choose a topic, which they develop in the form of a final report that they defend orally. This course prepares students for the internships they will undertake during their studies.

Examples of experiments available: optical spectroscopy (IR, visible), gamma, X-ray, acoustic; low-temperature photoluminescence; near-field spectroscopy (AFM, STM); electron microscopy...

The range of experiments on offer covers the areas of physics taught in the various physics courses. Students must choose from among the different experiments those that seem most relevant to their interests. A significant effort has been made to integrate new data acquisition technologies and the use of computer tools in order to compare experiment and theory.

See the full page

Through two specific examples (X-ray diffraction and vibrations), this module shows in detail how the physical properties of a solid are modeled. The formalism will also be applied to finite systems, such as nanoparticles, and will remain valid for amorphous materials, but particular attention will be paid to periodic systems (from linear chains to protein crystals, graphene, and silicon). Associated with this periodicity, the notion of reciprocal lattices will naturally arise.

See the full page

This course aims to introduce and develop several fundamental concepts and tools of non-relativistic quantum physics necessary for understanding the physical processes describing the interactions between the elementary constituents of matter and radiation. We will also address second quantization and the path integral formulation of quantum mechanics, which provide the ideal framework for the development of quantum field theory and its various applications (e.g., high-energy physics, condensed matter physics).

See the full page

Introduction to advanced statistical physics: grand canonical ensemble; quantum statistics; quantum fluids (Bose-Einstein condensation, thermal radiation; Sommerfeld theory); phase transitions; Ising model; mean field theory; dynamics of complex systems.

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The EU "Condensed Matter Physics 2: Electronic Properties" is intended for students interested in solid-state physics.

Following on from the course unit "Condensed Matter Physics 1: Structural Properties," this course unit addresses the properties of electrons in crystalline solids, the band structure of electronic levels, and the basic concepts of semiconductor physics.

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• Educational approach

Students practice by conducting experiments under exam conditions in order to reinforce their knowledge and experimental skills and develop effective communication.

• Main training content

The topics covered are taken directly from the list of physics experiments included in the current CAPES physics and chemistry entrance exam program (list published each year in the Official Bulletin of National Education).

• Digital space

Acquisition (with computer interface) of physical data from an experiment (Orphy_Lab and Orphi_GTI cards, Caliens camera).

- Analysis of a physics problem (mechanics, electricity, thermodynamics, waves, electromagnetism, wave optics) using data processing software (Regressi).

- Basic coding and algorithmic practice using the Python language (option to use offline editors such as EduPython or online editors such as Jupyter). Display and use of experimental data.

Application to solving simple differential equations in physics.

• Link to other EUs

This module, which begins in semester 3, revisits the content covered in the first year in the "Teaching Physics" course units.

Students also use teaching situations encountered during their internships, as well as content covered in the course units "Didactic and Pedagogical Support for Internships" (S1, S2, S3, and S4) and "Didactics, Epistemology, and History of Science" (S2).

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Fluids are all around us at all times and on all scales. Understanding fluid mechanics means understanding the mechanics of our surroundings, particularly air and water. As such, hydrodynamics is part of a physicist's basic knowledge.

Hydrodynamics is an introduction to the mechanics of incompressible perfect fluids (Euler) and viscous Newtonian fluids (Navier-Stokes). Classical flows are presented, as well as the concepts of boundary layer, instability, and turbulence. The emphasis is placed more on physical ideas than on advanced mathematical or numerical solution methods.

See the full page

English tutorial course for students enrolled in the Master 1 Physics program who wish to become proficient in scientific English.

See the full page

This course is part of the foundation of modern physics. It provides a foundation of knowledge that is essential for all physics courses, as it lays the groundwork for the theoretical description of the interaction between the electromagnetic field and elementary quantum elements such as two-level systems, atoms, and molecules. It also provides the necessary knowledge for understanding LASERs, modern optical devices, and spectroscopic methods and analyses.

See the full page

The aim of this module is to enable students to compare experimental reality with their theoretical knowledge. Particular attention is paid to writing up results and presenting them in the form of oral presentations. The work is organized into eight-hour sessions for which a topic is chosen by the students. They record their results and analyses in a laboratory notebook based on the protocols used in laboratories. At the end of the semester, students choose a topic, which they develop in the form of a final report that they defend orally. This course prepares students for the internships they will undertake during their studies.

Examples of experiments available: optical spectroscopy (IR, visible), gamma, X-ray, acoustic; low-temperature photoluminescence; near-field spectroscopy (AFM, STM); electron microscopy...

The range of experiments on offer covers the areas of physics taught in the various physics courses. Students must choose from among the different experiments those that seem most relevant to their interests. A significant effort has been made to integrate new data acquisition technologies and the use of computer tools in order to compare experiment and theory.

See the full page

Through two specific examples (X-ray diffraction and vibrations), this module shows in detail how the physical properties of a solid are modeled. The formalism will also be applied to finite systems, such as nanoparticles, and will remain valid for amorphous materials, but particular attention will be paid to periodic systems (from linear chains to protein crystals, graphene, and silicon). Associated with this periodicity, the notion of reciprocal lattices will naturally arise.

See the full page

The course aims to provide a general introduction to cellular and molecular biology and to contextualize the use of modern physics, through its quantitative methods and approaches, to describe biological systems and their complexity from the molecular to the cellular and tissue levels.

Another fundamental topic covered is the quantification of phenomena, their physical interpretation, and their physical-mathematical modeling. The course introduces students to philosophy and the range of topics covered in this master's program, which focuses on the study of the physical principles of the organization and dynamics of living and complex matter.

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This course includes an upgrade and deepening of programming techniques as well as an introduction to computational physics. We will begin with a review of procedural programming using the Python 3 language. We will then take an in-depth look at numerical methods relevant to physics, studying a selection of classic algorithms from numerical analysis and applying them to physical problems.

See the full page

Introduction to advanced statistical physics: grand canonical ensemble; quantum statistics; quantum fluids (Bose-Einstein condensation, thermal radiation; Sommerfeld theory); phase transitions; Ising model; mean field theory; dynamics of complex systems.

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Conducting a research project in an academic or industrial laboratory.

Dates: May-June

Duration: 7 weeks minimum, extendable in July

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The mechanical and thermal properties of materials are central to many applications in the field of energy materials. After an introduction to these different fields of application, this course unit aims to define the various concepts necessary for understanding both the mechanical and thermal properties of materials, limiting itself to bulk materials.

Hourly volumes:

            CM: 11 a.m.

            TD: 9 a.m.

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This course presents the concepts, fundamentals, and orders of magnitude of the physics and physical chemistry of interfaces that govern the mesoscopic scale of matter and ultimately determine the behavior and properties of everyday objects: soil, milk, cheese, paints, inks, cosmetics, adhesives, lubricants, etc., as well as numerous technological processes and biological cells and membranes.

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Knowing how to acquire and process data are essential skills in a scientific and/or technical professional context. The objective of this course is to address three types of standard skills in the professional environment:

· Advanced use of spreadsheets/graphing software (MS EXCEL, LO-CALC) for scientific and technical purposes

· Network interconnections: infrastructure, TCP/IP protocol suite, security

· Introduction to relational databases (MS ACCESS, LO-BASE) – concepts & vocabulary, creating queries, graphical reports, forms.

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One of the major issues related to the use of different materials in our daily lives is their durability and therefore their degradation. In this course, we will address issues related to the sustainability of materials (resources, reserves, criticality of materials, etc.) as well as methodologies for studying sustainability (types of surface/volume aging, temporal extrapolation, multi-scale, combination of effects, experimental representation, and industrial validation). This will then allow us to model the kinetics of aging using different models.

The different types of degradation affecting polymers will then be analyzed.

Finally, the aging of different types of materials will be illustrated by various concrete case studies (concrete, ceramics, metals, and elastomers).

Hours per week*: 11 hours CM:

                                    9 a.m. tutorial

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Polymer physics, to which this course provides an introduction, focuses on the physical properties of covalent chain assemblies, ranging from a few dozen to several million elementary molecules: polymers or macromolecules.

These synthetic or natural molecules can be observed in the solid state, liquid state, in solution, in a colloidal state, or confined to an interface.

Their very specific physical properties have led to the development of specific theoretical tools and the emergence of this new branch of physics with numerous applications.

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Bibliographic study on a research topic related to the course and potentially relevant to the M2 internship subject.

80 hours of independent work spread over the first semester of M2. Several project progress meetings will be scheduled with expert supervisors and scientific coordinators for the program.

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English tutorial course for students enrolled in the Master 2 Physics program who are seeking professional integration in English in a contemporary context.

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This module gives students the opportunity to discover the specifics of the world of work and prepare themselves to enter it in the best possible conditions, in particular through sharing experiences with professionals from the field. Students practice how to successfully apply for a job, using a methodical approach, optimizing their analysis of the job offer, writing a targeted resume and cover letter, and preparing for the job interview (role-playing, simulations).

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This course provides a general introduction to 1) the physics and mechanics of granular media and 2) their modeling using discrete methods (DEM). The multiscale nature of granular materials is discussed from the microscopic scale (contact interactions) to the macroscopic scale (structure scale). A phenomenological description of macroscopic behavior and microscopic properties is discussed for the static, quasi-static, and flow states of granular media. Micro-mechanical models and scale-changing approaches based on dimensionless analyses, averaged quantities, force transmissions, and the existence of anisotropies are introduced. The influence of particle properties and contact interactions on microstructure is also discussed. Discrete approaches (Discrete Element Methods (DEM)), regular approaches (Molecular Dynamics) and non-regular approaches (Contact Dynamics) are presented. In particular, the Contact Dynamics method will be implemented on simple examples using the LMGC90 calculation code.

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This module aims to teach the operating principles of the main techniques used to characterize the structure (in volume and on the surface) and properties (optical, electronic, etc.) of condensed matter:

• X-ray and electron diffraction techniques
• optical spectroscopy techniques (absorption, reflection, luminescence)
• local probe microscopy

  This module aims to teach the operating principles of the main techniques used to characterize the structure (in volume and on the surface) and properties (optical, electronic, etc.) of condensed matter:

  • X-ray and electron diffraction techniques
  • optical spectroscopy techniques (absorption, reflection, luminescence)
  • local probe microscopy

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This course provides an introduction to the field of complex fluids and active matter, with applications in both soft matter physics and chemistry and the physics of living organisms and biological objects.

It is common to both the PhyMV and SoftMat courses.

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Completion of a long-term research project (6 months) in an academic or industrial research laboratory.

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The first part of this course covers additional probability theory topics: conditional expectation, Gaussian vectors. The second part introduces one of the main families of discrete-time stochastic processes: Markov chains. These are sequences of dependent random variables, whose dependency relationship is relatively simple since each variable depends only on the previous one. They are also a very powerful modeling tool. We will study the main properties of these processes, as well as their long-term behavior and the estimation of their parameters.

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Fluids are all around us at all times and on all scales. Understanding fluid mechanics means understanding the mechanics of our surroundings, particularly air and water. As such, hydrodynamics is part of a physicist's basic knowledge.

Hydrodynamics is an introduction to the mechanics of incompressible perfect fluids (Euler) and viscous Newtonian fluids (Navier-Stokes). Classical flows are presented, as well as the concepts of boundary layer, instability, and turbulence. The emphasis is placed more on physical ideas than on advanced mathematical or numerical solution methods.

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The course aims to provide a general introduction to cellular and molecular biology and to contextualize the use of modern physics, through its quantitative methods and approaches, to describe biological systems and their complexity from the molecular to the cellular and tissue levels.

Another fundamental topic covered is the quantification of phenomena, their physical interpretation, and their physical-mathematical modeling. The course introduces students to philosophy and the range of topics covered in this master's program, which focuses on the study of the physical principles of the organization and dynamics of living and complex matter.

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Introduction to advanced statistical physics: grand canonical ensemble; quantum statistics; quantum fluids (Bose-Einstein condensation, thermal radiation; Sommerfeld theory); phase transitions; Ising model; mean field theory; dynamics of complex systems.

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