MASTER IN FUNDAMENTAL PHYSICS AND APPLICATIONS

This module is devoted to the basics of physics and technology of semiconductor based components. The major part of the UE is devoted to the physics of the component. Based on the equations that describe the properties of materials, the main cases 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 bricks of the process technology of components manufacturing are presented.

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English tutorials for students in the Master 1 Physics program who are aiming for professional autonomy in scientific English.

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This teaching is part of the foundation of modern physics. It provides a foundation of knowledge that is strictly necessary for all courses in physics since it lays the foundation 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 teaching for the understanding of LASER, modern optical devices, and spectroscopic methods and analyses.

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This module aims to allow students to confront the experimental reality with their theoretical knowledge. Particular attention is paid to the writing of results and their presentation in the form of oral communication. The work is organized in eight-hour sessions for which a theme is chosen by the students. They record their results and analyses in an experimental notebook based on the model of the protocols used in laboratories. At the end of the semester, the student chooses a theme, which he develops in the form of a final report that he presents orally. This teaching is a preparation for the internships carried out by the students 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 panel of experiments proposed covers the fields of physics taught in the different Physics courses. The student has to choose among the different experiments those which seem to him the closest to his interests. An important effort is made to integrate the new technologies of data acquisition and the use of computer tools in order to compare experiment and theory.

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

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This UE includes a refresher and deepening of programming techniques as well as an introduction to numerical physics. We will start with a review of procedural programming with the Python 3 language. Then we will take an in-depth look at numerical methods relevant to physics, studying a selection of classical algorithms from numerical analysis and applying them to physical problems.

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

In the continuity of the course "Condensed Matter Physics 1: structural properties" this course deals with 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 controller (computer type). The objective of this course is to familiarize students with this type of problem 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) or network (Ethernet) (CM).

- Implementation of simple examples of communication, device settings and data acquisition (TD).

- Development of a more complete acquisition chain, via projects (TP). 

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This module is devoted to the physical understanding of the processes of light emission and absorption in semiconductor devices, and to the technologies used to manufacture such devices. These issues are concretized in the clean room project, with the realization and characterization of an opto-electronic component.

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

- Advanced use of spreadsheets/plotters (MS EXCEL, LO-CALC) for scientific and technical use

- 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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Initiation to research in a university laboratory

Dates: May-June

Duration: 7 weeks minimum, extendable in July

Prior to the internship, the analysis of an article proposed by the internship tutors prepares the student for the theme of the internship and for the in-depth reading of scientific publications.

After the internship, as part of a peer evaluation process, the student submits his or her written report and oral presentation to the critical eye of other students, who are responsible for improving them accordingly before their final presentation to the internship jury.

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This course is designed to give students skills in the numerical solution of the Schrödinger equation in order to simulate complex quantum well structures. The course starts with the study of situations where the solution is analytical, then situations where the solution is semi-analytical before attacking on the finite difference method FD. Different FD schemes are proposed with, each time, an evaluation of the convergence according to different key parameters (truncation of the domain, number of samples...). Finally, examples of concrete physical applications are studied.    

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Third and last part of the courses dedicated to the elaboration processes of micro, nano- and opto-electronic devices. The last technological building blocks not yet covered in the previous semesters are presented in detail. The modeling and simulation of technological processes is predominant, as an introduction to TCAD solutions. Finally, the synthesis of all these teachings is carried out in a concrete way with the sequence of all these technological steps in order to realize discrete and integrated components, from wafer to packaged devices.

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

The aim is to describe the elaboration of low dimensional materials, the associated electronic, photonic and phononic structures, to study the transport phenomena, the electron-photon and electron-phonon couplings, the excitons as well as the absorption, emission and diffusion of light.

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TD courses in English, for students in the Master 2 Physics program, aiming at professional insertion in English in a contemporary context.

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This module is an opportunity for students to discover the specificities of the working world and to prepare themselves to enter it under the best possible conditions, notably through sharing experiences with professional speakers. Students practice applying for a job in a methodical way, optimizing the analysis of the offer, the targeted writing of the CV and the cover letter, the preparation of the job interview (role plays, simulations).

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

The emphasis is on understanding the basics.

It is an interactive course, with an approach by example.

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This module aims to teach the operating principles of the main techniques for characterizing the structure (volume and surface) and properties (optical, electronic, ...) of condensed matter:

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

  This module aims to teach the operating principles of the main techniques for characterizing the structure (volume and surface) and properties (optical, electronic, ...) of condensed matter:

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

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End of course internship in a company or university laboratory

This significant professional experience (up to six months) is intended to demonstrate the student's ability to occupy executive-level positions (engineer or researcher-doctorate), or to pursue a thesis, in the areas of competence of the training.

Start date: February

Duration: four to six months, ending before August 31.

End of course internship in a company or university laboratory

This significant professional experience (up to six months) is intended to demonstrate the student's ability to occupy executive-level positions (engineer or researcher-doctorate), or to pursue a thesis, in the areas of competence of the training.

Start date: February

Duration: four to six months, ending before August 31.

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This UE is an experimental training in the main techniques of nanocharacterizations and nanotechnologies:

• AFM
• MEB
• Photoluminescence
• X-ray diffraction
• Ellipsometry
• Optical Microscopy
• Source meter
• Capacimeter
• Manufacturing processes of micro-devices in clean room

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The course describes the different detectors and the physical processes involved in the detection of particles in high energy physics. In a second step, we will describe the operation of the main particle gas pedals that we find in high energy physics but also in many other fields such as medical, industry, material sciences, archaeology etc...

The course gives a detailed description of the physical processes and experimental techniques involved in the detection of charged and neutral particles in detectors, which are the basis of all physical measurements.

A detailed description of the different radiations and particle-matter interactions will be given.

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

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TD courses in English, for students in the Master 2 Physics program, aiming at professional insertion in English in a contemporary context.

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This course covers the basics necessary for a good understanding of the physics of atmospheres and stellar winds. The essential elements of radiation transfer theory are covered, both at ETL (local thermodynamic equilibrium) and outside ETL, as well as the description of the 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 the chemical composition, via spectroscopy. The different types of stellar winds (pressure, radiative, hybrid) are described via theories compared to observations.

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During the UE Observational Astrophysics Workshop 2, the students must carry out all the steps of an observational astrophysical study. From the definition of the spectroscopic or photometric observations to be carried out during a 4-night stay at the Haute-Provence Observatory, to the modeling and critical discussion of their measurements and the writing of a scientific report, the students are actors of this teaching.

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Interstellar medium: physicochemical processes - phases - radio astronomy.

This UE allows to acquire notions on the physico-chemical processes important for the interstellar medium (dynamic, thermal and chemical processes) as well as on the associated observational diagnostics (molecular spectroscopy, radioastronomy). 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 start by studying the Dirac equation, a quantum description of the dynamics of a particle of spin ½. Then we will see how to describe the electromagnetic interactions with the theory of quantum electrodynamics. Then we will discuss the weak interactions and their unified description with the electromagnetic interaction by the electroweak theory. Finally we will study the gauge theories and their spontaneous breaking to expose 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 the quantum theory of relativistic fields and its applications in particle physics. Using the example of a scalar field, the formalisms of canonical quantization and path integral quantization will be developed before introducing perturbation theory and some notions of renormalization. We will discuss the quantization of spin 1/2 and spin 1 fields and end 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 is based on the course of general relativity and cosmology of M1.

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The practical work concerns the detection and measurement of cosmic rays (muons).

The aim is to become familiar with an acquisition chain dedicated to the measurement of cosmic rays (mainly muons). The students will have to understand the individual functioning of the different elements involved in the acquisition chain (power supplies, photomultipliers, scintillators, discriminators, oscilloscopes...) and then realize by themselves an acquisition device from these elements. One of the objectives of the device could be the determination of the mass of the muon but other purposes are possible and left to the imagination of the students.

The students will then have to take data from their device and analyze the data, taking into account the systematic and statistical errors of the data set.

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This course describes the theoretical and observational foundations of the so-called cosmological dark matter problem. The latter 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 about 85% of the total matter in the universe, and it is excluded that it is composed of the elementary particles characterizing the known ordinary matter. The course will focus on potential solutions to this problem connecting the infinitely small (elementary particles) to the infinitely large (large scale universe).

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A 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 the thesis. This internship can be carried out in a research laboratory in France or abroad. It takes place from March^1st to May 31st, the date of the written report. An oral defense takes place at the beginning of June. The internship can be extended until August 31 in order to go directly to the thesis. The topics cover a wide spectrum from theoretical physics (cosmology, particle and astroparticle physics) to experimental physics (LHC experiments, search for gravitational waves or dark matter, large field cosmological surveys...).

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

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Fluids are all around us all the time at all scales. To understand fluid mechanics is to understand the mechanics of what surrounds us: air and water in particular. As such, hydrodynamics is part of the physicist's basic knowledge.

The UE Hydrodynamics is an introduction to incompressible perfect (Euler) and viscous Newtonian (Navier-Stokes) fluid mechanics. The classical flows are presented, as well as the notion of boundary layer, instability and turbulence. Emphasis is placed more on physical ideas than on advanced mathematical or numerical resolution methods.

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English tutorials for students in the Master 1 Physics program who are aiming for professional autonomy in scientific English.

See full page

This teaching is part of the foundation of modern physics. It provides a foundation of knowledge that is strictly necessary for all courses in physics since it lays the foundation 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 teaching for the understanding of LASER, modern optical devices, and spectroscopic methods and analyses.

See full page

This module aims to allow students to confront the experimental reality with their theoretical knowledge. Particular attention is paid to the writing of results and their presentation in the form of oral communication. The work is organized in eight-hour sessions for which a theme is chosen by the students. They record their results and analyses in an experimental notebook based on the model of the protocols used in laboratories. At the end of the semester, the student chooses a theme, which he develops in the form of a final report that he presents orally. This teaching is a preparation for the internships carried out by the students 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 panel of experiments proposed covers the fields of physics taught in the different Physics courses. The student has to choose among the different experiments those which seem to him the closest to his interests. An important effort is made to integrate the new technologies of data acquisition and the use of computer tools in order to compare experiment and theory.

See full page

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

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The course aims to provide a general introduction to cellular and molecular biology and to put into context 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 scales.

A fundamental point addressed is also the quantification of phenomena, their physical interpretation and their physico-mathematical modeling. The course opens to the philosophy and to the set of themes of this master's course centered on the study of the physical principles of the organization and the dynamics of the living and complex matter.

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This UE includes a refresher and deepening of programming techniques as well as an introduction to numerical physics. We will start with a review of procedural programming with the Python 3 language. Then we will take an in-depth look at numerical methods relevant to physics, studying a selection of classical algorithms from numerical analysis and applying them to physical problems.

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Introduction to advanced statistical physics: grand canonical set; 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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7-week internship in a laboratory with the aim of immersing students in the world of research, both fundamental and applied.

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

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This course presents the concepts, foundations 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 ..., many technological processes and biological cells and membranes.

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

- Advanced use of spreadsheets/plotters (MS EXCEL, LO-CALC) for scientific and technical use

- 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 the ancient Greek: bios (bios), life, and mimesis, imitation.

This term designates the study of extra- and intracellular biological phenomena by using in vitro experimental techniques aiming to reproduce, i.e. to "imitate", qualitatively and quantitatively the aspects characterizing these phenomena.

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

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

These methods (analytical, but also numerical) come mainly from statistical physics, stochastic process theory and non-linear physics.

Examples of studies are also proposed on the basis of the teachings of the other modules in M1 and M2 to contextualize the different examples to physical theory and quantitative experimentation on living matter.

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Polymer physics, of which this course is an introduction, is concerned with the physical properties of covalent assemblies in chains, from a few tens to a few millions of elementary molecules: polymers or macromolecules.

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

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

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TD courses in English, for students in the Master 2 Physics program, aiming at professional insertion in English in a contemporary context.

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This module is an opportunity for students to discover the specificities of the working world and to prepare themselves to enter it under the best possible conditions, notably through sharing experiences with professional speakers. Students practice applying for a job in a methodical way, optimizing the analysis of the offer, the targeted writing of the CV and the cover letter, the preparation of the job interview (role plays, simulations).

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

It is common to both PhyMV and SoftMat courses.

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Internship of a minimum of 5 months in a laboratory with the aim of immersion in the world of research, fundamental and/or applied, and the possible preparation of 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 all the time at all scales. To understand fluid mechanics is to understand the mechanics of what surrounds us: air and water in particular. As such, hydrodynamics is part of the physicist's basic knowledge.

The UE Hydrodynamics is an introduction to incompressible perfect (Euler) and viscous Newtonian (Navier-Stokes) fluid mechanics. The classical flows are presented, as well as the notion of boundary layer, instability and turbulence. Emphasis is placed more on physical ideas than on advanced mathematical or numerical resolution methods.

See full page

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English tutorials for students in the Master 1 Physics program who are aiming for professional autonomy in scientific English.

See full page

This teaching is part of the foundation of modern physics. It provides a foundation of knowledge that is strictly necessary for all courses in physics since it lays the foundation 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 teaching for the understanding of LASER, modern optical devices, and spectroscopic methods and analyses.

See full page

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

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Introduction to advanced statistical physics: grand canonical set; 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 tutored project during which groups of students work on the development of a software for research or teaching.

This project is intended to give students their first semi-professional experience by working in a group of (>2) on a fairly large project usually proposed by fellow researchers wishing to develop and/or extend software for research or public use.

The supervision is provided by physicists and possibly computer scientists. The students deliver a code with its instructions. A report is written and an oral defense takes place.    

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

In the continuity of the course "Condensed Matter Physics 1: structural properties" this course deals with 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 controller (computer type). The objective of this course is to familiarize students with this type of problem 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) or network (Ethernet) (CM).

- Implementation of simple examples of communication, device settings and data acquisition (TD).

- Development of a more complete acquisition chain, via projects (TP). 

See full page

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

- Advanced use of spreadsheets/plotters (MS EXCEL, LO-CALC) for scientific and technical use

- 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 of mathematics for numerical physics. Introduction of tools for the study of partial differential equations (distributions, variational formulation, Sobolev spaces).

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

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This course is designed to give students skills in the numerical solution of the Schrödinger equation in order to simulate complex quantum well structures. The course starts with the study of situations where the solution is analytical, then situations where the solution is semi-analytical before attacking on the finite difference method FD. Different FD schemes are proposed with, each time, an evaluation of the convergence according to different key parameters (truncation of the domain, number of samples...). Finally, examples of concrete physical applications are studied.    

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This course lays the foundations for using 'atomistic' simulation tools, i.e. based on microscopic interactions between constituents. Mainly, it lays the foundations for the so-called 'Molecular Dynamics' and 'Monte Carlo' simulations.

It addresses the underlying theoretical notions, in order to build a good 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 is an introduction without pre-requisites to scientific image processing, in the context of physics but also of medical sciences.

Starting from the basic elements of digital image coding, we will introduce the main techniques aiming first at improving the quality of image data, and then at extracting quantitative data. Deconvolutions, denoising, thresholding, segmentations, Fourier transforms, wavelets will be presented.

We will conclude with the specific problems posed by image sequences (movies) 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 at discovering uses of deep learning using the TensorFlow and Keras libraries. It includes a presentation of examples of use for physics.

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TD courses in English, for students in the Master 2 Physics program, aiming at professional insertion in English in a contemporary context.

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This module is an opportunity for students to discover the specificities of the working world and to prepare themselves to enter it under the best possible conditions, notably through sharing experiences with professional speakers. Students practice applying for a job in a methodical way, optimizing the analysis of the offer, the targeted writing of the CV and the cover letter, the preparation of the job interview (role plays, simulations).

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This unit deals with the solution of electromagnetic problems on a computer. From Maxwell's equations, it shows how to simulate the behavior of electromagnetic waves in different media. It includes a detailed implementation of simulations based on the Finite Difference Time Domain (FDTD) method.

An introduction to the problems of diffraction in the 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 the advanced practice of atomistic simulation methods, and of Molecular Dynamics in particular.

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

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A 5 ECTS tutored project during which students work individually on the development of a software for research and development and/or teaching.

This project completes the experience acquired during the tutored project already done in M1. This time the students work individually which is a different experience from the M1 project done in group. The student receives an order to create a software that meets a set of specifications and must deliver a functional code.   

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

The internship must focus on a physical problem in which a numerical calculation component is involved.  

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The Observational Astrophysics Workshop 1 is an initiation to the realization of an observational study (photometry or spectroscopy) of astrophysical objects (stars, nebulae) at the M1 level. The students carry out all the steps from the planning and the realization of the observations at the astronomical observatory of the Faculty of Sciences, to the calibration and the analysis of the obtained data. This module is designed as a preparation for the M2 module Observational Astrophysics Workshop 2 (HAP905P).

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

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This course aims at providing basic notions in astronomy and astrophysics, which will be useful in the other astrophysics courses of the master. It is also an illustration of the application of the concepts of physics for the description of astrophysical objects. Most of the concepts discussed will be further developed in the^2nd year courses.

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Fluids are all around us all the time at all scales. To understand fluid mechanics is to understand the mechanics of what surrounds us: air and water in particular. As such, hydrodynamics is part of the physicist's basic knowledge.

The UE Hydrodynamics is an introduction to incompressible perfect (Euler) and viscous Newtonian (Navier-Stokes) fluid mechanics. The classical flows are presented, as well as the notion of boundary layer, instability and turbulence. Emphasis is placed more on physical ideas than on advanced mathematical or numerical resolution methods.

See full page

English tutorials for students in the Master 1 Physics program who are aiming for professional autonomy in scientific English.

See full page

This teaching is part of the foundation of modern physics. It provides a foundation of knowledge that is strictly necessary for all courses in physics since it lays the foundation 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 teaching for the understanding of LASER, modern optical devices, and spectroscopic methods and analyses.

See full page

This module aims to allow students to confront the experimental reality with their theoretical knowledge. Particular attention is paid to the writing of results and their presentation in the form of oral communication. The work is organized in eight-hour sessions for which a theme is chosen by the students. They record their results and analyses in an experimental notebook based on the model of the protocols used in laboratories. At the end of the semester, the student chooses a theme, which he develops in the form of a final report that he presents orally. This teaching is a preparation for the internships carried out by the students 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 panel of experiments proposed covers the fields of physics taught in the different Physics courses. The student has to choose among the different experiments those which seem to him the closest to his interests. An important effort is made to integrate the new technologies of data acquisition and the use of computer tools in order to compare experiment and theory.

See full page

This UE includes a refresher and deepening of programming techniques as well as an introduction to numerical physics. We will start with a review of procedural programming with the Python 3 language. Then we will take an in-depth look at numerical methods relevant to physics, studying a selection of classical algorithms from numerical analysis and applying them to physical problems.

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This course is an introduction to astroparticle physics (cosmic gas pedals, gamma rays, multi-messengers, experimental techniques, ...).

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 problem of acceleration and propagation of CRs and the hypothesis of Supernova remnants as galactic gas pedals of CRs (description of the first order Fermi acceleration mechanism).

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

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This course aims at introducing and developing several fundamental concepts and tools of non-relativistic quantum physics necessary to understand the physical processes describing the interactions between the elementary constituents of matter and radiation. The second quantization and the path integral formulation of quantum mechanics will also be discussed as they represent 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 set; 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 first make an inventory of the elementary particles and their interactions. Then we will see how to use the theory of Lie groups to classify these elementary particles. Finally we will discuss the notion 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 the 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 is a deepening of the "Hydrodynamics" course organized around 3 central themes in astrophysics: rotating fluids, thermal convection, and magnetohydrodynamics.

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This 7-week internship (usually from ~ end of April to end of June) (10 ECTS) will give the student a first contact with the world of research in astrophysics, cosmology or particle physics. Internships at the intersection of these disciplines, more commonly called "astroparticles" are also proposed. The internships can have a more theoretical or more experimental orientation depending on the choice of the students and the supervisors.

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

The internship will allow the student to interact with a research team (national and/or international) and to begin to discover the research topics that he or she will prefer to develop in the future.

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This course will cover the broad outlines of star and planetary system formation in two parts of equal length. Star formation will deal with the stability of equilibrium and stable clouds, the collapse of dense cores, protostars and their evolution, and the impact of young stars on their environment. Planetary formation will use solar system constraints and extrasolar planet detections to address the structure and evolution of protoplanetary disks, and the formation of telluric and giant planets.

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TD courses in English, for students in the Master 2 Physics program, aiming at professional insertion in English in a contemporary context.

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This course covers the basics necessary for a good understanding of the physics of atmospheres and stellar winds. The essential elements of radiation transfer theory are covered, both at ETL (local thermodynamic equilibrium) and outside ETL, as well as the description of the 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 the chemical composition, via spectroscopy. The different types of stellar winds (pressure, radiative, hybrid) are described via theories compared to observations.

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During the UE Observational Astrophysics Workshop 2, the students must carry out all the steps of an observational astrophysical study. From the definition of the spectroscopic or photometric observations to be carried out during a 4-night stay at the Haute-Provence Observatory, to the modeling and critical discussion of their measurements and the writing of a scientific report, the students are actors of this teaching.

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The objective is to present the various observations and associated theoretical concepts - called cosmological probes - that have allowed the accreditation of the so-called "concordance" ΛCDM cosmological model. The EU is divided into chapters of roughly equal size. It is complemented by a series of seminars presented by the students (flipped classroom) and deepening more observational and technical aspects (based on a publication of a large collaboration).

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Interstellar medium: physicochemical processes - phases - radio astronomy.

This UE allows to acquire notions on the physico-chemical processes important for the interstellar medium (dynamic, thermal and chemical processes) as well as on the associated observational diagnostics (molecular spectroscopy, radioastronomy). The main phases of the interstellar medium (ionized, atomic and molecular phases) are also presented.

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This course lays the foundations of our knowledge of the formation and evolution of galaxies, from the astrophysical processes at play at small scales concerning star formation to the environmental effects at very large scales. A double approach will be used, with on the one hand theoretical aspects and on the other hand observational aspects.

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

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4-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 done in a research laboratory in France or abroad.

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This course introduces the instruments of astrophysics and the signal processing tools associated with their operation.

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

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

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Astrophysics research is based on various approaches (observations, theory, modeling, simulation) which all have in common the use of advanced numerical tools.

In order to prepare M2 Astrophysics students for a research activity, this module proposes to them, in a different framework from the internship, to carry out an individual digital work on a project proposed by a tutor concerning the use and/or the development of a professional level code to answer a precise astrophysical question.

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This module is devoted to the basics of physics and technology of semiconductor based components. The major part of the UE is devoted to the physics of the component. Based on the equations that describe the properties of materials, the main cases 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 bricks of the process technology of components manufacturing are presented.

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English tutorials for students in the Master 1 Physics program who are aiming for professional autonomy in scientific English.

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This teaching is part of the foundation of modern physics. It provides a foundation of knowledge that is strictly necessary for all courses in physics since it lays the foundation 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 teaching for the understanding of LASER, modern optical devices, and spectroscopic methods and analyses.

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This module aims to allow students to confront the experimental reality with their theoretical knowledge. Particular attention is paid to the writing of results and their presentation in the form of oral communication. The work is organized in eight-hour sessions for which a theme is chosen by the students. They record their results and analyses in an experimental notebook based on the model of the protocols used in laboratories. At the end of the semester, the student chooses a theme, which he develops in the form of a final report that he presents orally. This teaching is a preparation for the internships carried out by the students 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 panel of experiments proposed covers the fields of physics taught in the different Physics courses. The student has to choose among the different experiments those which seem to him the closest to his interests. An important effort is made to integrate the new technologies of data acquisition and the use of computer tools in order to compare experiment and theory.

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

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This UE includes a refresher and deepening of programming techniques as well as an introduction to numerical physics. We will start with a review of procedural programming with the Python 3 language. Then we will take an in-depth look at numerical methods relevant to physics, studying a selection of classical algorithms from numerical analysis and applying them to physical problems.

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This course aims at introducing and developing several fundamental concepts and tools of non-relativistic quantum physics necessary to understand the physical processes describing the interactions between the elementary constituents of matter and radiation. The second quantization and the path integral formulation of quantum mechanics will also be discussed as they represent 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 set; 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 course "Condensed Matter Physics 2: Electronic Properties" is intended for students interested in solid state physics.

In the continuity of the course "Condensed Matter Physics 1: structural properties" this course deals with 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 teacher/researcher in the field of nano-physics and quantum physics.

Dates: May-June

Duration: 7 weeks minimum, extendable in July

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

- Advanced use of spreadsheets/plotters (MS EXCEL, LO-CALC) for scientific and technical use

- 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 of mathematics for numerical physics. Introduction of tools for the study of partial differential equations (distributions, variational formulation, Sobolev spaces).

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

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This course is designed to give students skills in the numerical solution of the Schrödinger equation in order to simulate complex quantum well structures. The course starts with the study of situations where the solution is analytical, then situations where the solution is semi-analytical before attacking on the finite difference method FD. Different FD schemes are proposed with, each time, an evaluation of the convergence according to different key parameters (truncation of the domain, number of samples...). Finally, examples of concrete physical applications are studied.    

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

The aim is to describe the elaboration of low dimensional materials, the associated electronic, photonic and phononic structures, to study the transport phenomena, the electron-photon and electron-phonon couplings, the excitons as well as the absorption, emission and diffusion of light.

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

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TD courses in English, for students in the Master 2 Physics program, aiming at professional insertion in English in a contemporary context.

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This unit deals with the solution of electromagnetic problems on a computer. From Maxwell's equations, it shows how to simulate the behavior of electromagnetic waves in different media. It includes a detailed implementation of simulations based on the Finite Difference Time Domain (FDTD) method.

An introduction to the problems of diffraction in the 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 for characterizing the structure (volume and surface) and properties (optical, electronic, ...) of condensed matter:

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

  This module aims to teach the operating principles of the main techniques for characterizing the structure (volume and surface) and properties (optical, electronic, ...) of condensed matter:

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

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This course is specific to the NanoQuant program and offers a high-level fundamental training in the field of Quantum Technologies, i.e. current and future realizations of new technologies based on concepts such as quantum coherence and entanglement that allow to reach functionalities and sensitivities that exceed their classical analogues.

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

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This UE is an experimental training in the main techniques of nanocharacterizations and nanotechnologies:

• AFM
• MEB
• Photoluminescence
• X-ray diffraction
• Ellipsometry
• Optical Microscopy
• Source meter
• Capacimeter
• Manufacturing processes of micro-devices in clean room

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This course aims at providing basic notions in astronomy and astrophysics, which will be useful in the other astrophysics courses of the master. It is also an illustration of the application of the concepts of physics for the description of astrophysical objects. Most of the concepts discussed will be further developed in the^2nd year courses.

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Fluids are all around us all the time at all scales. To understand fluid mechanics is to understand the mechanics of what surrounds us: air and water in particular. As such, hydrodynamics is part of the physicist's basic knowledge.

The UE Hydrodynamics is an introduction to incompressible perfect (Euler) and viscous Newtonian (Navier-Stokes) fluid mechanics. The classical flows are presented, as well as the notion of boundary layer, instability and turbulence. Emphasis is placed more on physical ideas than on advanced mathematical or numerical resolution methods.

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English tutorials for students in the Master 1 Physics program who are aiming for professional autonomy in scientific English.

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This teaching is part of the foundation of modern physics. It provides a foundation of knowledge that is strictly necessary for all courses in physics since it lays the foundation 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 teaching for the understanding of LASER, modern optical devices, and spectroscopic methods and analyses.

See full page

This module aims to allow students to confront the experimental reality with their theoretical knowledge. Particular attention is paid to the writing of results and their presentation in the form of oral communication. The work is organized in eight-hour sessions for which a theme is chosen by the students. They record their results and analyses in an experimental notebook based on the model of the protocols used in laboratories. At the end of the semester, the student chooses a theme, which he develops in the form of a final report that he presents orally. This teaching is a preparation for the internships carried out by the students 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 panel of experiments proposed covers the fields of physics taught in the different Physics courses. The student has to choose among the different experiments those which seem to him the closest to his interests. An important effort is made to integrate the new technologies of data acquisition and the use of computer tools in order to compare experiment and theory.

See full page

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

See full page

This course aims at introducing and developing several fundamental concepts and tools of non-relativistic quantum physics necessary to understand the physical processes describing the interactions between the elementary constituents of matter and radiation. The second quantization and the path integral formulation of quantum mechanics will also be discussed as they represent the ideal framework for the development of quantum field theory and its various applications (e.g. high energy physics, condensed matter physics).

See full page

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

See full page

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

In the continuity of the course "Condensed Matter Physics 1: structural properties" this course deals with the properties of electrons in crystalline solids, the band structure of electronic levels and the basic concepts of semiconductor physics.

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• Pedagogical approach

Students train by performing experimental tests under competition conditions to reinvest experimental knowledge and skills and develop effective communication.

• Main contents of the training

The topics covered are directly extracted from the list of physics assemblies in the current CAPES physics and chemistry admission exams (list published each year in the Bulletin Officiel de l'Education Nationale).

• The place of digital technology

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 a data processing software (Regressi).

- Elementary practice of coding and algorithmic using the Python language (possibility of using offline editors e.g. EduPython or online e.g. Jupyter). Display and exploitation of experimental data.

Application to the solution of simple differential equations in physics.

• Link with other EUs

This module and its beginning in semester 3 reinvest the contents approached in the first year in the UE "Teaching physics".

The students also use teaching situations encountered during the internship as well as the content covered in the UE "Didactic and pedagogical support of the internship" (S1, S2, S3 and S4) and "Didactics, Epistemology and History of Science" (S2).

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Fluids are all around us all the time at all scales. To understand fluid mechanics is to understand the mechanics of what surrounds us: air and water in particular. As such, hydrodynamics is part of the physicist's basic knowledge.

The UE Hydrodynamics is an introduction to incompressible perfect (Euler) and viscous Newtonian (Navier-Stokes) fluid mechanics. The classical flows are presented, as well as the notion of boundary layer, instability and turbulence. Emphasis is placed more on physical ideas than on advanced mathematical or numerical resolution methods.

See full page

English tutorials for students in the Master 1 Physics program who are aiming for professional autonomy in scientific English.

See full page

This teaching is part of the foundation of modern physics. It provides a foundation of knowledge that is strictly necessary for all courses in physics since it lays the foundation 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 teaching for the understanding of LASER, modern optical devices, and spectroscopic methods and analyses.

See full page

This module aims to allow students to confront the experimental reality with their theoretical knowledge. Particular attention is paid to the writing of results and their presentation in the form of oral communication. The work is organized in eight-hour sessions for which a theme is chosen by the students. They record their results and analyses in an experimental notebook based on the model of the protocols used in laboratories. At the end of the semester, the student chooses a theme, which he develops in the form of a final report that he presents orally. This teaching is a preparation for the internships carried out by the students 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 panel of experiments proposed covers the fields of physics taught in the different Physics courses. The student has to choose among the different experiments those which seem to him the closest to his interests. An important effort is made to integrate the new technologies of data acquisition and the use of computer tools in order to compare experiment and theory.

See full page

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

See full page

The course aims to provide a general introduction to cellular and molecular biology and to put into context 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 scales.

A fundamental point addressed is also the quantification of phenomena, their physical interpretation and their physico-mathematical modeling. The course opens to the philosophy and to the set of themes of this master's course centered on the study of the physical principles of the organization and the dynamics of the living and complex matter.

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This UE includes a refresher and deepening of programming techniques as well as an introduction to numerical physics. We will start with a review of procedural programming with the Python 3 language. Then we will take an in-depth look at numerical methods relevant to physics, studying a selection of classical algorithms from numerical analysis and applying them to physical problems.

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Introduction to advanced statistical physics: grand canonical set; 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 at the heart of many applications in the field of materials for energy. After an introduction to these different fields of application, this course aims to define the different concepts necessary to master both the mechanical and thermal properties of materials, limiting itself to bulk materials.

Hourly volumes* :

            CM : 11H

            TD : 9H

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This course presents the concepts, foundations 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 ..., many technological processes and biological cells and membranes.

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

- Advanced use of spreadsheets/plotters (MS EXCEL, LO-CALC) for scientific and technical use

- 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 life is their durability and therefore their degradation. In this course, we will address the issues related to the durability of materials (resources, reserves, criticality of materials, ...) as well as the methodologies for studying durability (types of aging surface / volume, temporal extrapolation, multi-scale, combination of effects, experimental representation and industrial validation). This will then allow to model the aging kinetics from 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 different concrete case studies (concrete, ceramic, metals and elastomers).

Hourly volume* : 11h CM :

                                    9h TD

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Polymer physics, of which this course is an introduction, is concerned with the physical properties of covalent assemblies in chains, from a few tens to a few millions of elementary molecules: polymers or macromolecules.

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

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

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Bibliographical study on a research theme associated with the course and which may be related to the M2 internship subject.

80 hours of personal work spread over the first semester of M2. Several meetings to review the progress of the project will be scheduled with the expert supervisors and the scientific coordinators of the course.

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TD courses in English, for students in the Master 2 Physics program, aiming at professional insertion in English in a contemporary context.

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This module is an opportunity for students to discover the specificities of the working world and to prepare themselves to enter it under the best possible conditions, notably through sharing experiences with professional speakers. Students practice applying for a job in a methodical way, optimizing the analysis of the offer, the targeted writing of the CV and the cover letter, the preparation of the job interview (role plays, simulations).

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This course gives a general introduction to 1) the physics and mechanics of divided media and 2) their modeling through discrete methods (DEM). The multiscale character of a divided material is discussed from the microscopic scale (contact interactions), to the macroscopic scale (structure scale). A phenomenological description of the macroscopic behavior as well as the microscopic properties are discussed for static, quasi-static and flowing states of granular media. Micro-mechanical models and scaling approaches based on dimensionless analysis, averaged quantities, stress transmissions and anisotropies are introduced. The influence of particle properties and contact interactions on the microstructure is also discussed. Discrete Element Methods (DEM), regular (Molecular Dynamics) and non-regular (Contact Dynamics) numerical approaches are presented. In particular, the Contact Dynamics method will be implemented on simple examples through the LMGC90 computational code.

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This module aims to teach the operating principles of the main techniques for characterizing the structure (volume and surface) and properties (optical, electronic, ...) of condensed matter:

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

  This module aims to teach the operating principles of the main techniques for characterizing the structure (volume and surface) and properties (optical, electronic, ...) of condensed matter:

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

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

It is common to both PhyMV and SoftMat courses.

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

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The first part of this course concerns complements of probability theory: conditional expectation, Gaussian vectors. The second part presents one of the main families of stochastic processes in discrete time : Markov chains. These are sequences of dependent random variables, whose dependence relation is relatively simple since each variable depends only on the previous one. It is also a very powerful modeling tool. We will study the main properties of these processes, as well as their behavior in long time and the estimation of their parameters.

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Fluids are all around us all the time at all scales. To understand fluid mechanics is to understand the mechanics of what surrounds us: air and water in particular. As such, hydrodynamics is part of the physicist's basic knowledge.

The UE Hydrodynamics is an introduction to incompressible perfect (Euler) and viscous Newtonian (Navier-Stokes) fluid mechanics. The classical flows are presented, as well as the notion of boundary layer, instability and turbulence. Emphasis is placed more on physical ideas than on advanced mathematical or numerical resolution methods.

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This EU aims to provide a broad overview of emerging quantitative interdisciplinary fields in bioscience, ranging from advanced experimental techniques in microscopy and synthetic biology, to systems approaches.

In an innovative way, these methodological aspects will be presented in the context of biological and biophysical concepts such as robustness and optimality of biological systems, gene regulation and the fundamental principles underlying membrane and genome organization.

The main topics will be introduced first with traditional lectures and will be developed through individual or team projects where students will learn to apply specific techniques through examples, and see how these can be used to explore specific biological questions. These projects will involve literature reviews, use of existing code, or development of new code (depending on the student's experience) and will constitute half of the final assessment.

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The importance of statistical science in the process of scientific discovery and industrial advancement is that it allows the formulation of inferences about phenomena of interest to which one can associate risks of error or degrees of confidence. The calculation of these risks of error is based on probability theory, but the principles and methods for associating these risks with inferences constitute a theoretical corpus that serves as a basis for all statistical methodologies.

This module is intended to be a fairly complete presentation of these basic principles and of the tools, results and mathematical theorems used in inferential statistics. It develops the notions of point and interval estimation, hypothesis testing and fundamental concepts such as exponential families and the principle of maximum likelihood and the use of p-value.
For the implementation of certain applications, the adapted tools of the R software will be presented.

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The course aims to provide a general introduction to cellular and molecular biology and to put into context 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 scales.

A fundamental point addressed is also the quantification of phenomena, their physical interpretation and their physico-mathematical modeling. The course opens to the philosophy and to the set of themes of this master's course centered on the study of the physical principles of the organization and the dynamics of the living and complex matter.

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Introduction to advanced statistical physics: grand canonical set; 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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