Introduction

Introduction to the statistical physics of phase transitions and critical phenomena

• Emmanuel Trizac (Université Paris-Saclay)

The material covered deals with collective phenomena and the various approaches to treat phase transitions. We will start by discussing the notion of symmetry breakdown, the effect of dimensionality, and how order is inferred, down to the microscopic scale. We will then present how appropriate field theories can be constructed, where symmetry considerations play an important role. Perturbation approaches, exact calculations, and renormalization group will be employed to emphasize the emergence of scale invariance (self-similariry) and universality, which are important hallmarks of critical phenomena. Only basic familiarity with statistical physics will be assumed.

An introduction to hydrodynamic turbulence

• Basile Gallet (SPEC, CEA)
• Pierre-Philippe Cortet (CNRS, Université Paris-Saclay)
• Benjamin Favier (CNRS, Aix-Marseille University)

Lecture 1 by Benjamin Favier: Basics on hydrodynamic turbulence Lecture 2 by Pierre-Philippe Cortet: Turbulence in rotating fluids Lecture 3 by Basile Gallet: Turbulent convection Hydrodynamic turbulence ispart of our daily lives but remains a fundamental research challenge in fluid mechanics, with applications ranging from turbulent transfer and mixing in industrial flows to improved predictions of extreme weather events in a warming climate. In the first lecture, we will discuss the phenomenology of turbulence in three dimensions, characteristic of most fluid flows surrounding us, before addressing the two-dimensional case as a first model of large-scale geophysical flows. The second and the third lectureswill address turbulence subject to two important physical ingredients of natural flows: global rotation and thermal effects. Global rotation is one of the key ingredients of turbulent flows encountered in oceanic, atmospheric and astrophysical contexts. An important consequence of global rotation is the emergence of a specific class of waves, resulting from the action of the Coriolis force and propagating in the volume of the fluid. These waves and the classical vortex structures of fluid dynamics coexist and interact, which results in a strongly modified turbulence phenomenology. We will introduce this scenario and illustrate it with laboratory observations. Thermal convection refers to flows induced by unstable temperature gradients within a fluid: cool fluid is heavier than warm fluid and spontaneously "falls" under the latter. Turbulent convective flows arise in industrial, geophysical and astrophysical contexts, where the nature of the asymptotic turbulent convection regime remains a delicate and highlydebated topic. Motivated by geophysical and astrophysical flows, we will review the various theoretical predictions and their recent validation in laboratory experiments.

Statistical Physics of Active Matter

• Julien Tailleur (Université de Paris)

Active matter describes systems in which individual units dissipate energy to exert forces on their environment. Abundant in the biological world, active systems can also be engineered in the lab where they take the form of self-propelling droplets, particles and grains. The disconnection between dissipation and injection of energy at the microscopic scale drives these systems strongly out of thermal equilibrium. This leads to a phenomenology markedly different from that of equilibrium systems, such as the emergence of dense phases of matter in the absence of cohesive forces. In this lecture, I will review recent theoretical developments in the study of active-matter systems, from the discovery of their anomalous mechanical properties to the characterization of their rich many-body physics. In particular, I will show how disorder impacts scalar active matter much more strongly than in passive systems.

Introduction to the statistical physics of phase transitions and critical phenomena

• Emmanuel Trizac (Université Paris-Saclay)

The material covered deals with collective phenomena and the various approaches to treat phase transitions. We will start by discussing the notion of symmetry breakdown, the effect of dimensionality, and how order is inferred, down to the microscopic scale. We will then present how appropriate field theories can be constructed, where symmetry considerations play an important role. Perturbation approaches, exact calculations, and renormalization group will be employed to emphasize the emergence of scale invariance (self-similariry) and universality, which are important hallmarks of critical phenomena. Only basic familiarity with statistical physics will be assumed.

Statics and Dynamics of Disordered Elastic Systems

• Elisabeth Agoritsas (EPFL)
• Thierry Giamarchi (University of Geneva)

The theoretical framework of disordered elastic systems has been successfully applied, over the last decades, to a wide range of physical systems with very different microphysics and characteristic scales. These range for instance from ferroic domain walls, vortices in superconductors, biophysics interfaces to fracture cracks and earthquakes. Experimentally, this framework provides effective descriptions at a mesoscopic scale, theoretically tractable and experimentally testable. From a fundamental point of view, it encompasses prototypical models of classical statistical physics, where the role of disorder can be systematically investigated, while triggering the development of new theoretical tools to tackle out-of-equilibrium issues. 

 This lecture will be an introduction to the statics and dynamics of these systems, both from theoretical and experimental perspectives. We will in particular focus on the dynamical critical phenomena they exhibit in response to external forces –such as the depinning transition and the response to small forces (creep)– and on the analogy drawn with other driven complex systems, such as shear amorphous materials and their corresponding ‘yielding’ transition.

Colloquium - J. M. Kosterlitz

• J. Michael Kosterlitz

Statics and Dynamics of Disordered Elastic Systems

• Thierry Giamarchi (University of Geneva)
• Elisabeth Agoritsas (EPFL)

The theoretical framework of disordered elastic systems has been successfully applied, over the last decades, to a wide range of physical systems with very different microphysics and characteristic scales. These range for instance from ferroic domain walls, vortices in superconductors, biophysics interfaces to fracture cracks and earthquakes. Experimentally, this framework provides effective descriptions at a mesoscopic scale, theoretically tractable and experimentally testable. From a fundamental point of view, it encompasses prototypical models of classical statistical physics, where the role of disorder can be systematically investigated, while triggering the development of new theoretical tools to tackle out-of-equilibrium issues. 

 This lecture will be an introduction to the statics and dynamics of these systems, both from theoretical and experimental perspectives. We will in particular focus on the dynamical critical phenomena they exhibit in response to external forces –such as the depinning transition and the response to small forces (creep)– and on the analogy drawn with other driven complex systems, such as shear amorphous materials and their corresponding ‘yielding’ transition.

Introduction to the statistical physics of phase transitions and critical phenomena

• Emmanuel Trizac (Université Paris-Saclay)

The material covered deals with collective phenomena and the various approaches to treat phase transitions. We will start by discussing the notion of symmetry breakdown, the effect of dimensionality, and how order is inferred, down to the microscopic scale. We will then present how appropriate field theories can be constructed, where symmetry considerations play an important role. Perturbation approaches, exact calculations, and renormalization group will be employed to emphasize the emergence of scale invariance (self-similariry) and universality, which are important hallmarks of critical phenomena. Only basic familiarity with statistical physics will be assumed.

An introduction to hydrodynamic turbulence

• Basile Gallet (SPEC, CEA)
• Benjamin Favier (CNRS, Aix-Marseille University)
• Pierre-Philippe Cortet (CNRS, Université Paris-Saclay)

Lecture 1 by Benjamin Favier: Basics on hydrodynamic turbulence Lecture 2 by Pierre-Philippe Cortet: Turbulence in rotating fluids Lecture 3 by Basile Gallet: Turbulent convection Hydrodynamic turbulence ispart of our daily lives but remains a fundamental research challenge in fluid mechanics, with applications ranging from turbulent transfer and mixing in industrial flows to improved predictions of extreme weather events in a warming climate. In the first lecture, we will discuss the phenomenology of turbulence in three dimensions, characteristic of most fluid flows surrounding us, before addressing the two-dimensional case as a first model of large-scale geophysical flows. The second and the third lectureswill address turbulence subject to two important physical ingredients of natural flows: global rotation and thermal effects. Global rotation is one of the key ingredients of turbulent flows encountered in oceanic, atmospheric and astrophysical contexts. An important consequence of global rotation is the emergence of a specific class of waves, resulting from the action of the Coriolis force and propagating in the volume of the fluid. These waves and the classical vortex structures of fluid dynamics coexist and interact, which results in a strongly modified turbulence phenomenology. We will introduce this scenario and illustrate it with laboratory observations. Thermal convection refers to flows induced by unstable temperature gradients within a fluid: cool fluid is heavier than warm fluid and spontaneously "falls" under the latter. Turbulent convective flows arise in industrial, geophysical and astrophysical contexts, where the nature of the asymptotic turbulent convection regime remains a delicate and highlydebated topic. Motivated by geophysical and astrophysical flows, we will review the various theoretical predictions and their recent validation in laboratory experiments.

From Sandpiles to Disordered Elastic Systems

• Kay Wiese (LPENS)

Sandpile models are discrete stochastic systems. We show how to map the Manna sandpile onto disordered elastic manifolds. This is surprising as the latter has quenched disorder, while the former does not. In our derivation we also learn how do model discrete stochastic systems via a continuous Langevin equation.

Statics and Dynamics of Disordered Elastic Systems

• Thierry Giamarchi (University of Geneva)
• Elisabeth Agoritsas (EPFL)

The theoretical framework of disordered elastic systems has been successfully applied, over the last decades, to a wide range of physical systems with very different microphysics and characteristic scales. These range for instance from ferroic domain walls, vortices in superconductors, biophysics interfaces to fracture cracks and earthquakes. Experimentally, this framework provides effective descriptions at a mesoscopic scale, theoretically tractable and experimentally testable. From a fundamental point of view, it encompasses prototypical models of classical statistical physics, where the role of disorder can be systematically investigated, while triggering the development of new theoretical tools to tackle out-of-equilibrium issues. 

 This lecture will be an introduction to the statics and dynamics of these systems, both from theoretical and experimental perspectives. We will in particular focus on the dynamical critical phenomena they exhibit in response to external forces –such as the depinning transition and the response to small forces (creep)– and on the analogy drawn with other driven complex systems, such as shear amorphous materials and their corresponding ‘yielding’ transition.

Introduction to the statistical physics of phase transitions and critical phenomena

• Emmanuel Trizac (Université Paris-Saclay)

The material covered deals with collective phenomena and the various approaches to treat phase transitions. We will start by discussing the notion of symmetry breakdown, the effect of dimensionality, and how order is inferred, down to the microscopic scale. We will then present how appropriate field theories can be constructed, where symmetry considerations play an important role. Perturbation approaches, exact calculations, and renormalization group will be employed to emphasize the emergence of scale invariance (self-similariry) and universality, which are important hallmarks of critical phenomena. Only basic familiarity with statistical physics will be assumed.

An introduction to hydrodynamic turbulence

• Pierre-Philippe Cortet (CNRS, Université Paris-Saclay)
• Benjamin Favier (CNRS, Aix-Marseille University)
• Basile Gallet (SPEC, CEA)

Lecture 1 by Benjamin Favier: Basics on hydrodynamic turbulence Lecture 2 by Pierre-Philippe Cortet: Turbulence in rotating fluids Lecture 3 by Basile Gallet: Turbulent convection Hydrodynamic turbulence ispart of our daily lives but remains a fundamental research challenge in fluid mechanics, with applications ranging from turbulent transfer and mixing in industrial flows to improved predictions of extreme weather events in a warming climate. In the first lecture, we will discuss the phenomenology of turbulence in three dimensions, characteristic of most fluid flows surrounding us, before addressing the two-dimensional case as a first model of large-scale geophysical flows. The second and the third lectureswill address turbulence subject to two important physical ingredients of natural flows: global rotation and thermal effects. Global rotation is one of the key ingredients of turbulent flows encountered in oceanic, atmospheric and astrophysical contexts. An important consequence of global rotation is the emergence of a specific class of waves, resulting from the action of the Coriolis force and propagating in the volume of the fluid. These waves and the classical vortex structures of fluid dynamics coexist and interact, which results in a strongly modified turbulence phenomenology. We will introduce this scenario and illustrate it with laboratory observations. Thermal convection refers to flows induced by unstable temperature gradients within a fluid: cool fluid is heavier than warm fluid and spontaneously "falls" under the latter. Turbulent convective flows arise in industrial, geophysical and astrophysical contexts, where the nature of the asymptotic turbulent convection regime remains a delicate and highlydebated topic. Motivated by geophysical and astrophysical flows, we will review the various theoretical predictions and their recent validation in laboratory experiments.

Recipes for Metastable States in Glasses

• Silvio Franz (Université Paris-Saclay, LPTMS)

1. Basic Glassy Phenomenology. 2. Order Parameter and Landau Free-energy for glasses. 3. Results of Simulations.  Glasses freeze in configurations that are as disordered as the one of the liquid. In such conditions -even neglecting crystalline configurations- the study of the Gibbs measure fails to detect the difference between the liquid and the glass. Glassy metastability can be studied through the introduction of conditional Gibbs measures, where the role of conditioning order parameter is played by the overlap with a random configuration. Within mean-field theory, the free-energy as a function of the order parameter has a double well shape similar to the ordinary Landau free-energy for first order transitions. I will discuss the theory that ensues and its tests in simulations.

Structure and dynamics of highly disordered systems

• Takeshi Egami (University of Tennessee)

1. Dynamic Aperiodic Matter (DAM) 1.1 Glassy behavior of systems with strong disorder The properties of an isolated lattice defect depend strongly on the nature of the mother lattice. But as the defect density increases the interaction among them becomes more important than the interaction with lattice, and they start to assume their own identity and show different, emergent, properties. Often, they show behaviors similar to those of glasses. For instance, magnetic impurities show spin-glass behavior, and certain crystals with high twin density show strain-glass behavior. Ferroelectric solids with strong chemical disorder show relaxor ferroelectric behavior, very similar to that of spin-glass. Soft-matter, including biological matter, often shows viscous liquid/glass behavior. Such glassy behaviors are ubiquitous, but not fully understood because of complexity, in spite of long history of research. This represents a challenging broad field of research. 1.2 Dynamic aperiodic matter; liquid, glass, and human society Liquids, gels, colloids, and polymers are called “soft-matter”, but this naming is misleading. Softness is relative, and really does not catch the special nature of these materials which are outside the scope of the usual condensed-matter physics focused on crystals. A better name is “dynamic aperiodic matter (DAM)”. DAM includes not only the conventional soft-matter, but also large objects such as human society. They are not random assembly of particles as in gas, but are condensed matter, held together by a cohesive force. The structure and dynamics of the system are highly cooperative with strong inter-particle correlation. They key of understanding DAM is to determine and elucidate these dynamic correlations. 1.3 Fluctuation-dissipation theorem The correlation functions that characterize the cooperative dynamics are directly related to the properties of the system through the fluctuation-dissipation theorem for linear response. The derivation of this theorem, an important milestone in statistical physics, is presented, and examples on diffusivity and viscosity are discussed. 2. Real-space characterization of DAM by scattering 2.1 Pair-distribution function In characterizing the structure and dynamics of crystals through x-ray or neutron scattering, the reciprocal space is a natural arena because of the periodicity of the lattice. But it is not the most convenient place to describe the deviations, such as defects. Deviations from periodicity result in diffuse scattering, which requires extensive modeling to interpret. A more direct approach is to Fourier-transform the structure function, S(Q), including diffuse scattering (total scattering), to real space to obtain the pair-distribution function (PDF), g(r). The PDF tells you the distribution of atomic distances for both periodic and aperiodic structures. In crystals with chemical disorder the local structure is often quite different from the average structure. If a low-symmetry phase changes into a high-symmetry phase at high temperatures, the high-symmetry phase is usually a dynamic mosaic of low-symmetry local structure. Because the properties are usually determined by the local structure rather than the average structure the accurate knowledge of the local structure is important in elucidating the properties of the solid. Some technical details of the PDF method and examples of its application are discussed. 2.2 Van Hove function The atomic structure of liquid is customarily described by the PDF. However, the term, “structure of liquid” is an oxymoron, because liquid is inherently dynamic and there is no elastic scattering from liquid. The PDF is the same-time correlation function, a thermal average of snapshots. This can be expanded to the two-time correlation function, the Van Hove function (VHF), G(r, t). The VHF is obtained through the double-Fourier-transformation of the dynamic structure factor, S(Q, ω), where E = ω is the energy transfer in inelastic scattering. The VHF describes how the atomic correlation evolves with time. The decay of the VHF with time typically shows two steps. The first decay is due to vibrational motions (phonons), whereas the second decay describes the topological excitations due to the changes in the local topology of atomic connectivity. Technical details of the VHF measurement by inelastic x-ray/neutron scattering and examples of its application are discussed. 3. Understanding strong correlation 3.1 Potential energy landscape In the absence of periodicity, it is difficult to describe the structure and dynamics of DAM in a meaningful way. A powerful approach is the potential energy landscape (PEL) concept. The PEL is the energy surface of a N-particle system in 3N dimensions, made of numerous valleys and hills. The PEL is so vast that it is difficult even to visualize it; it is usually hand-written. However, the relevant and accessible portion of the PEL is not so large, because the information transfer is limited in space and time by dynamic disorder. We discuss the local PEL of high-temperature liquid, and the nature of the saddle-point of the PEL where local configurational melting disrupts memory transfer. 3.2 Nature of the glass transition The viscosity, η, of a typical liquid, such as water, is of the order of 10-2 poise (= 10-3 Pa.s). As temperature is reduced, if crystallization can be avoided by supercooling, viscosity increases rapidly by many orders of magnitude. The glass transition is defined by viscosity reaching 1013 poise, when the Maxwell relaxation time, τM = η/G∞, where G∞ is the high-frequency shear modulus, reaches of the order of a minute, so that the system behaves like a solid in the experimental time-scale. Why viscosity increases by as much as 15 orders of magnitude over a relatively small temperature range has been a major question in condensed-matter theory. We discuss various theories and speculations on the nature of the glass transition. A leading idea assumes there is a real phase transition, but the transition is frustrated and the system slows down into practical freezing before the critical temperature is reached. 3.3 Medium-range order in liquid and glass The PDF of liquid and glass shows many peaks extending to an nm-scale. The first peak describes the short-range order (SRO) in the nearest neighbor atoms, whereas the peaks beyond the first peak depicts the medium-range order (MRO). However, they are different in nature. The SRO describes the atom-atom, or point-to-point correlation, while the MRO describes the correlation between the central atom and a group of atoms, point-to-set correlation. The MRO is produced by density waves induced by the interatomic potential. Currently many theories attempt to link the SRO, the structure of the near neighbors, directly to properties. However, atomic dynamics that controls viscosity and diffusivity in supercooled liquid is characterized by dynamic cooperativity. Evidence suggests that the MRO, which describes the cooperative dynamics, is the key quantity in atomic transport and the glass transition.

Structure and dynamics of highly disordered systems

• Takeshi Egami (University of Tennessee)

1. Dynamic Aperiodic Matter (DAM) 1.1 Glassy behavior of systems with strong disorder The properties of an isolated lattice defect depend strongly on the nature of the mother lattice. But as the defect density increases the interaction among them becomes more important than the interaction with lattice, and they start to assume their own identity and show different, emergent, properties. Often, they show behaviors similar to those of glasses. For instance, magnetic impurities show spin-glass behavior, and certain crystals with high twin density show strain-glass behavior. Ferroelectric solids with strong chemical disorder show relaxor ferroelectric behavior, very similar to that of spin-glass. Soft-matter, including biological matter, often shows viscous liquid/glass behavior. Such glassy behaviors are ubiquitous, but not fully understood because of complexity, in spite of long history of research. This represents a challenging broad field of research. 1.2 Dynamic aperiodic matter; liquid, glass, and human society Liquids, gels, colloids, and polymers are called “soft-matter”, but this naming is misleading. Softness is relative, and really does not catch the special nature of these materials which are outside the scope of the usual condensed-matter physics focused on crystals. A better name is “dynamic aperiodic matter (DAM)”. DAM includes not only the conventional soft-matter, but also large objects such as human society. They are not random assembly of particles as in gas, but are condensed matter, held together by a cohesive force. The structure and dynamics of the system are highly cooperative with strong inter-particle correlation. They key of understanding DAM is to determine and elucidate these dynamic correlations. 1.3 Fluctuation-dissipation theorem The correlation functions that characterize the cooperative dynamics are directly related to the properties of the system through the fluctuation-dissipation theorem for linear response. The derivation of this theorem, an important milestone in statistical physics, is presented, and examples on diffusivity and viscosity are discussed. 2. Real-space characterization of DAM by scattering 2.1 Pair-distribution function In characterizing the structure and dynamics of crystals through x-ray or neutron scattering, the reciprocal space is a natural arena because of the periodicity of the lattice. But it is not the most convenient place to describe the deviations, such as defects. Deviations from periodicity result in diffuse scattering, which requires extensive modeling to interpret. A more direct approach is to Fourier-transform the structure function, S(Q), including diffuse scattering (total scattering), to real space to obtain the pair-distribution function (PDF), g(r). The PDF tells you the distribution of atomic distances for both periodic and aperiodic structures. In crystals with chemical disorder the local structure is often quite different from the average structure. If a low-symmetry phase changes into a high-symmetry phase at high temperatures, the high-symmetry phase is usually a dynamic mosaic of low-symmetry local structure. Because the properties are usually determined by the local structure rather than the average structure the accurate knowledge of the local structure is important in elucidating the properties of the solid. Some technical details of the PDF method and examples of its application are discussed. 2.2 Van Hove function The atomic structure of liquid is customarily described by the PDF. However, the term, “structure of liquid” is an oxymoron, because liquid is inherently dynamic and there is no elastic scattering from liquid. The PDF is the same-time correlation function, a thermal average of snapshots. This can be expanded to the two-time correlation function, the Van Hove function (VHF), G(r, t). The VHF is obtained through the double-Fourier-transformation of the dynamic structure factor, S(Q, ω), where E = ω is the energy transfer in inelastic scattering. The VHF describes how the atomic correlation evolves with time. The decay of the VHF with time typically shows two steps. The first decay is due to vibrational motions (phonons), whereas the second decay describes the topological excitations due to the changes in the local topology of atomic connectivity. Technical details of the VHF measurement by inelastic x-ray/neutron scattering and examples of its application are discussed. 3. Understanding strong correlation 3.1 Potential energy landscape In the absence of periodicity, it is difficult to describe the structure and dynamics of DAM in a meaningful way. A powerful approach is the potential energy landscape (PEL) concept. The PEL is the energy surface of a N-particle system in 3N dimensions, made of numerous valleys and hills. The PEL is so vast that it is difficult even to visualize it; it is usually hand-written. However, the relevant and accessible portion of the PEL is not so large, because the information transfer is limited in space and time by dynamic disorder. We discuss the local PEL of high-temperature liquid, and the nature of the saddle-point of the PEL where local configurational melting disrupts memory transfer. 3.2 Nature of the glass transition The viscosity, η, of a typical liquid, such as water, is of the order of 10-2 poise (= 10-3 Pa.s). As temperature is reduced, if crystallization can be avoided by supercooling, viscosity increases rapidly by many orders of magnitude. The glass transition is defined by viscosity reaching 1013 poise, when the Maxwell relaxation time, τM = η/G∞, where G∞ is the high-frequency shear modulus, reaches of the order of a minute, so that the system behaves like a solid in the experimental time-scale. Why viscosity increases by as much as 15 orders of magnitude over a relatively small temperature range has been a major question in condensed-matter theory. We discuss various theories and speculations on the nature of the glass transition. A leading idea assumes there is a real phase transition, but the transition is frustrated and the system slows down into practical freezing before the critical temperature is reached. 3.3 Medium-range order in liquid and glass The PDF of liquid and glass shows many peaks extending to an nm-scale. The first peak describes the short-range order (SRO) in the nearest neighbor atoms, whereas the peaks beyond the first peak depicts the medium-range order (MRO). However, they are different in nature. The SRO describes the atom-atom, or point-to-point correlation, while the MRO describes the correlation between the central atom and a group of atoms, point-to-set correlation. The MRO is produced by density waves induced by the interatomic potential. Currently many theories attempt to link the SRO, the structure of the near neighbors, directly to properties. However, atomic dynamics that controls viscosity and diffusivity in supercooled liquid is characterized by dynamic cooperativity. Evidence suggests that the MRO, which describes the cooperative dynamics, is the key quantity in atomic transport and the glass transition.

Short talks by participants

Structure and dynamics of highly disordered systems

• Takeshi Egami (University of Tennessee)

1. Dynamic Aperiodic Matter (DAM) 1.1 Glassy behavior of systems with strong disorder The properties of an isolated lattice defect depend strongly on the nature of the mother lattice. But as the defect density increases the interaction among them becomes more important than the interaction with lattice, and they start to assume their own identity and show different, emergent, properties. Often, they show behaviors similar to those of glasses. For instance, magnetic impurities show spin-glass behavior, and certain crystals with high twin density show strain-glass behavior. Ferroelectric solids with strong chemical disorder show relaxor ferroelectric behavior, very similar to that of spin-glass. Soft-matter, including biological matter, often shows viscous liquid/glass behavior. Such glassy behaviors are ubiquitous, but not fully understood because of complexity, in spite of long history of research. This represents a challenging broad field of research. 1.2 Dynamic aperiodic matter; liquid, glass, and human society Liquids, gels, colloids, and polymers are called “soft-matter”, but this naming is misleading. Softness is relative, and really does not catch the special nature of these materials which are outside the scope of the usual condensed-matter physics focused on crystals. A better name is “dynamic aperiodic matter (DAM)”. DAM includes not only the conventional soft-matter, but also large objects such as human society. They are not random assembly of particles as in gas, but are condensed matter, held together by a cohesive force. The structure and dynamics of the system are highly cooperative with strong inter-particle correlation. They key of understanding DAM is to determine and elucidate these dynamic correlations. 1.3 Fluctuation-dissipation theorem The correlation functions that characterize the cooperative dynamics are directly related to the properties of the system through the fluctuation-dissipation theorem for linear response. The derivation of this theorem, an important milestone in statistical physics, is presented, and examples on diffusivity and viscosity are discussed. 2. Real-space characterization of DAM by scattering 2.1 Pair-distribution function In characterizing the structure and dynamics of crystals through x-ray or neutron scattering, the reciprocal space is a natural arena because of the periodicity of the lattice. But it is not the most convenient place to describe the deviations, such as defects. Deviations from periodicity result in diffuse scattering, which requires extensive modeling to interpret. A more direct approach is to Fourier-transform the structure function, S(Q), including diffuse scattering (total scattering), to real space to obtain the pair-distribution function (PDF), g(r). The PDF tells you the distribution of atomic distances for both periodic and aperiodic structures. In crystals with chemical disorder the local structure is often quite different from the average structure. If a low-symmetry phase changes into a high-symmetry phase at high temperatures, the high-symmetry phase is usually a dynamic mosaic of low-symmetry local structure. Because the properties are usually determined by the local structure rather than the average structure the accurate knowledge of the local structure is important in elucidating the properties of the solid. Some technical details of the PDF method and examples of its application are discussed. 2.2 Van Hove function The atomic structure of liquid is customarily described by the PDF. However, the term, “structure of liquid” is an oxymoron, because liquid is inherently dynamic and there is no elastic scattering from liquid. The PDF is the same-time correlation function, a thermal average of snapshots. This can be expanded to the two-time correlation function, the Van Hove function (VHF), G(r, t). The VHF is obtained through the double-Fourier-transformation of the dynamic structure factor, S(Q, ω), where E = ω is the energy transfer in inelastic scattering. The VHF describes how the atomic correlation evolves with time. The decay of the VHF with time typically shows two steps. The first decay is due to vibrational motions (phonons), whereas the second decay describes the topological excitations due to the changes in the local topology of atomic connectivity. Technical details of the VHF measurement by inelastic x-ray/neutron scattering and examples of its application are discussed. 3. Understanding strong correlation 3.1 Potential energy landscape In the absence of periodicity, it is difficult to describe the structure and dynamics of DAM in a meaningful way. A powerful approach is the potential energy landscape (PEL) concept. The PEL is the energy surface of a N-particle system in 3N dimensions, made of numerous valleys and hills. The PEL is so vast that it is difficult even to visualize it; it is usually hand-written. However, the relevant and accessible portion of the PEL is not so large, because the information transfer is limited in space and time by dynamic disorder. We discuss the local PEL of high-temperature liquid, and the nature of the saddle-point of the PEL where local configurational melting disrupts memory transfer. 3.2 Nature of the glass transition The viscosity, η, of a typical liquid, such as water, is of the order of 10-2 poise (= 10-3 Pa.s). As temperature is reduced, if crystallization can be avoided by supercooling, viscosity increases rapidly by many orders of magnitude. The glass transition is defined by viscosity reaching 1013 poise, when the Maxwell relaxation time, τM = η/G∞, where G∞ is the high-frequency shear modulus, reaches of the order of a minute, so that the system behaves like a solid in the experimental time-scale. Why viscosity increases by as much as 15 orders of magnitude over a relatively small temperature range has been a major question in condensed-matter theory. We discuss various theories and speculations on the nature of the glass transition. A leading idea assumes there is a real phase transition, but the transition is frustrated and the system slows down into practical freezing before the critical temperature is reached. 3.3 Medium-range order in liquid and glass The PDF of liquid and glass shows many peaks extending to an nm-scale. The first peak describes the short-range order (SRO) in the nearest neighbor atoms, whereas the peaks beyond the first peak depicts the medium-range order (MRO). However, they are different in nature. The SRO describes the atom-atom, or point-to-point correlation, while the MRO describes the correlation between the central atom and a group of atoms, point-to-set correlation. The MRO is produced by density waves induced by the interatomic potential. Currently many theories attempt to link the SRO, the structure of the near neighbors, directly to properties. However, atomic dynamics that controls viscosity and diffusivity in supercooled liquid is characterized by dynamic cooperativity. Evidence suggests that the MRO, which describes the cooperative dynamics, is the key quantity in atomic transport and the glass transition.

Fracture and friction

• Elsa Bayart (ENS de Lyon)

The first part of this lecture will be an introduction to the linear elastic fracture mechanics of brittle solids. In particular, we will focus on the emergence of a mechanical singularity and the dynamics of propagative ruptures. In the second part, we will see that frictional motion is a fracture process. Sliding between two solids occurs once the solid contacts are broken via the propagation of a brittle shear crack. We will show that fracture mechanics is a powerful tool to characterize the frictional properties of a solid interface, but not only. We willshow that friction provides a versatile platform for studying fracture dynamics and mechanical singularities: propagation and arrest criteria, equation of motion.

Fracture and friction

• Elsa Bayart (ENS de Lyon)

The first part of this lecture will be an introduction to the linear elastic fracture mechanics of brittle solids. In particular, we will focus on the emergence of a mechanical singularity and the dynamics of propagative ruptures. In the second part, we will see that frictional motion is a fracture process. Sliding between two solids occurs once the solid contacts are broken via the propagation of a brittle shear crack. We will show that fracture mechanics is a powerful tool to characterize the frictional properties of a solid interface, but not only. We willshow that friction provides a versatile platform for studying fracture dynamics and mechanical singularities: propagation and arrest criteria, equation of motion.

Flash-talks by participants

The statistical physics of cities

• Marc Barthelemy (IPhT, Université Paris-Saclay)

Abstract:
Modelling the structure and evolution of cities is critical because policy makers need robust theories and new paradigms for mitigating various important problems such as air pollution, congestion,  socio-spatial inequalities, etc. Fortunately, the increased data available about urban systems opens the possibility of constructing a quantitative ‘science of cities’ with the aim of identifying and modelling essential phenomena. Statistical physics plays a major role in this effort by bringing tools and concepts able to bridge theory and empirical results. In these lectures, I will illustrate this point by discussing different topics: the distribution of urban population, segregation phenomena and spin like models, the polycentric transition of the activity organization, energy considerations about mobility and models inspired by gravity and radiation concepts, CO2 emitted by transport, and finally scaling that describes how various socio-economical and infrastructures evolve when cities grow.

Fracture and friction

• Elsa Bayart (ENS de Lyon)

The first part of this lecture will be an introduction to the linear elastic fracture mechanics of brittle solids. In particular, we will focus on the emergence of a mechanical singularity and the dynamics of propagative ruptures. In the second part, we will see that frictional motion is a fracture process. Sliding between two solids occurs once the solid contacts are broken via the propagation of a brittle shear crack. We will show that fracture mechanics is a powerful tool to characterize the frictional properties of a solid interface, but not only. We willshow that friction provides a versatile platform for studying fracture dynamics and mechanical singularities: propagation and arrest criteria, equation of motion.

Dense disordered active matter

• Lisa Manning (Syracuse University)

In active materials energy is injected at the scale of individual units, instead of at the boundaries as in sheared materials, and the motion is not governed by a thermal bath. At low and intermediate densities, broken time-reversal invariance can lead to interesting and well-studied phenomena like giant number fluctuations and motility-induced phase separation. In contrast, at high densities such macroscopic density fluctuations are suppressed, and the structure of the material is very similar to a disordered solid, while the dynamics exhibit interesting flows with non-trivial features such as long-range spatial correlations in the velocity field, intermittency, and avalanche dynamics.Inthe first lecture, I will discuss several frameworks that have been developed to understand the origin of long-range spatial correlations in the particle velocities/displacements [1,2]. In the second lecture, I will discuss intermittency, avalanches, and yielding in dense active matter, including recent work highlighting a direct link between active matter and sheared systems in the limit of infinite persistence [3,4]. References:[1] Szamel, G., & Flenner, E. (2021). Long-ranged velocity correlations indense systems of self-propelled particles. EPL (Europhysics Letters), 133(6), 60002. [2] Henkes, S., Kostanjevec, K., Collinson, J. M., Sknepnek, R., & Bertin, E. (2020). Dense active matter model of motion patterns in confluent cell monolayers. Nature communications, 11(1), 1-9. [3] Mandal, R., Bhuyan, P. J., Chaudhuri, P., Dasgupta, C., & Rao, M. (2020). Extreme active matter at high densities. Nature communications, 11(1), 1-8. [4] Morse, P. K., Roy, S., Agoritsas, E., Stanifer, E., Corwin, E. I., & Manning, M. L. (2021). A direct link between active matter and sheared granular systems. Proceedings of the National Academy of Sciences, 118(18)

The statistical physics of cities

• Marc Barthelemy (IPhT, Université Paris-Saclay)

Abstract:
Modelling the structure and evolution of cities is critical because policy makers need robust theories and new paradigms for mitigating various important problems such as air pollution, congestion,  socio-spatial inequalities, etc. Fortunately, the increased data available about urban systems opens the possibility of constructing a quantitative ‘science of cities’ with the aim of identifying and modelling essential phenomena. Statistical physics plays a major role in this effort by bringing tools and concepts able to bridge theory and empirical results. In these lectures, I will illustrate this point by discussing different topics: the distribution of urban population, segregation phenomena and spin like models, the polycentric transition of the activity organization, energy considerations about mobility and models inspired by gravity and radiation concepts, CO2 emitted by transport, and finally scaling that describes how various socio-economical and infrastructures evolve when cities grow.

The role of disorder for yielding and flow in the deformation process of amorphous materials

• Kirsten Martens (Université Grenoble Alpes)

In this course I shall introduce modelling approaches for the yielding and flow of dense disordered materials like foams, granular materials or glasses. These materials fall in the catagory of yield stress materials and in the case of soft glassy materials they typically represent complex fluids with interesting non-trivial flow regimes. Disorder plays a major role in the description of these materials and instead of dislocations like in crystallin materials the deformation process is governed by the formation of shear transformations that lead to long range elastic changes in their surroundings. The complex interplay between plastically deforming shear transformation zones, elastic interactions and disorder can lead to a variety of interesting phenomena that I shall address in this course. I will talk about the static and dynamic yielding transition, out-of-equilibrium flow transitions with the occurence of critical dynamics as well as the possible appearance of flow instabilities in the stationary state.

From Metamaterials to Machine Materials

• Martin Van Hecke (Leiden University)

TBAThe architecture of a material is crucial for its properties and functionality. This connection between form and function is leveraged by mechanical metamaterials, whose patterned microstructures are designed to obtain unusual behaviours.In the first lecture I will focus on metamaterials with unusual bulk properties such as negative response parameters, multistability or programmability. I will explain the basic mechanisms that underlie these properties, touching upon concepts such as mechanisms, non-affinity, and elastic instabilities. In the second lecture I will focus on machine materials, metamaterials that are spatially or sequentially heterogeneous. I will discuss shapemorphing and self folding, and introduce recent ideas on pathways, hysterons and mechanical information processing. Literature: Bertoldi K, Vitelli V, Christensen J, van Hecke M., Flexible mechanical metamaterials. Nature Reviews 2, 17066 (2017).

From Metamaterials to Machine Materials

• Martin Van Hecke (Leiden University)

The architecture of a material is crucial for its properties and functionality. This connection between form and function is leveraged by mechanical metamaterials, whose patterned microstructures are designed to obtain unusual behaviours.In the first lecture I will focus on metamaterials with unusual bulk properties such as negative response parameters, multistability or programmability. I will explain the basic mechanisms that underlie these properties, touching upon concepts such as mechanisms, non-affinity, and elastic instabilities. In the second lecture I will focus on machine materials, metamaterials that are spatially or sequentially heterogeneous. I will discuss shapemorphing and self folding, and introduce recent ideas on pathways, hysterons and mechanical information processing. Literature: Bertoldi K, Vitelli V, Christensen J, van Hecke M., Flexible mechanical metamaterials. Nature Reviews 2, 17066 (2017).

Dense disordered active matter

• Lisa Manning (Syracuse University)

In active materials energy is injected at the scale of individual units, instead of at the boundaries as in sheared materials, and the motion is not governed by a thermal bath. At low and intermediate densities, broken time-reversal invariance can lead to interesting and well-studied phenomena like giant number fluctuations and motility-induced phase separation. In contrast, at high densities such macroscopic density fluctuations are suppressed, and the structure of the material is very similar to a disordered solid, while the dynamics exhibit interesting flows with non-trivial features such as long-range spatial correlations in the velocity field, intermittency, and avalanche dynamics.Inthe first lecture, I will discuss several frameworks that have been developed to understand the origin of long-range spatial correlations in the particle velocities/displacements [1,2]. In the second lecture, I will discuss intermittency, avalanches, and yielding in dense active matter, including recent work highlighting a direct link between active matter and sheared systems in the limit of infinite persistence [3,4]. References:[1] Szamel, G., & Flenner, E. (2021). Long-ranged velocity correlations indense systems of self-propelled particles. EPL (Europhysics Letters), 133(6), 60002. [2] Henkes, S., Kostanjevec, K., Collinson, J. M., Sknepnek, R., & Bertin, E. (2020). Dense active matter model of motion patterns in confluent cell monolayers. Nature communications, 11(1), 1-9. [3] Mandal, R., Bhuyan, P. J., Chaudhuri, P., Dasgupta, C., & Rao, M. (2020). Extreme active matter at high densities. Nature communications, 11(1), 1-8. [4] Morse, P. K., Roy, S., Agoritsas, E., Stanifer, E., Corwin, E. I., & Manning, M. L. (2021). A direct link between active matter and sheared granular systems. Proceedings of the National Academy of Sciences, 118(18