ICTS

2D liquid monolayer membranes of aligned rod like particles form in presence of depletion attraction in- duced by non-adsorbing polymer coils [1]. Surface ten- sion drives these monolayers to be circular in shape with edge fluctuations controlled by the chirality of the constituent rods [2]. Surprisingly, we find that fluid membranes assembled form mixtures of long and short rods are cyclic polygonal in shape with short rods forming the outer lobes and longer rods forming the inner faceted core of the polygon. We show that the origin of this anisotropic shape of membranes lies in the phenomenon of how one liquid spreads over an- other in presence of pinning sites. We outline the nec-essary and sufficient constraints on the nature of rods to obtain the stable out of equilibrium cyclic poly- gon membranes. Our results show the unique counter- intuitive scenario where disorder lead to self assembly of ordered structures.

We would like to acknowledge IISc, ISRO-STC and SERB-DST for funding this work.

Corresponding author:  prerna@iisc.ac.in

1. Edward Barry, and Zvonimir Dogic, Proceedings of the National Academy of Sciences 107, 10348 (2010).
2. T. Gibaud et al., Nature 481, 348 (2012).

To explain experimental results showing shape, size and dynamics of E.coli chromosomes in growing cells, we consider a polymer model consisting of a circular backbone to which side-loops are attached, confined to a cylindrical cell [1, 2]. Such a model chromosome spon- taneously adopts a helical shape, which is further com- pacted by molecular crowders to occupy a nucleoid-like sub-volume (Fig. 1). With increasing cell length, the longitudinal size of the chromosome increases in a non- linear fashion to finally saturate, its morphology gradu- ally opening up while displaying an increasing number of helical turns. For shorter cells and low crowder densi- ties, the chromosome extension varies non-monotonically with cell size, which we show is associated with a ra- dial to longitudinal spatial reorganization of the crow- ders. Confinement and crowders constrain chain dynam- ics leading to anomalous diffusion. While the scaling ex- ponent for the mean squared displacement of centre of mass grows and saturates with cell length, that of indi- vidual loci displays broad distribution with a well-defined maximum. Despite several experimental efforts, in E.coli bacteria, the mechanism for chromosome segregation re- mains elusive. We propose chromosomal segregation via inter-chromosome repulsion mediated by protein produc- tion. The simulation results show good agreement with experiments.

Corresponding author: debc@iopb.res.in

1. Fabai Wu, Pinaki Swain, Louis Kuijpers, Xuan Zheng, Kevin Felter, Margot Guurink, Debasish Chaudhuri, Bela Mulder, Cees Dekker, bioRxiv doi: https://doi.org/10.1101/348052.
2. D. Chaudhuri and B. M. Mulder, Physical Review Letters 108, 268305 (2012).

The second law of thermodynamics states that the entropy of a closed system increases with time. Life represents a remarkable example of the opposite trend in an open, non-equilibrium system. Indeed, both informational and thermodynamic entropies decrease in the course of biological evolution reflecting ever-increasing complexity of living organisms and their communities \cite{schroedinger}. Conceptually, the problem of the origin of life can be viewed as a search for the simplest physical system capable of such spontaneous reduction of entropy and growth of complexity \cite{anderson}.

Self-replicating systems based on information-coding polymers are of crucial importance in biology. We have carried out a general theoretical and numerical analysis of the problem of spontaneous emergence of autocatalysis for heteropolymers capable of template-assisted ligation driven by cyclic changes in the environment \cite{JCP}. One of our key results is the existence of the first order transition between the regime dominated by free monomers and that with a self-sustaining population of sufficiently long chains. We provide a simple, mathematically tractable model supported by numerical simulations, which predicts the distribution of chain lengths and the onset of autocatalysis in terms of the overall monomer concentration and two fundamental rate constants.

The template-assisted ligation allows for heritable transmission of the information encoded in chain sequences thus opening up the possibility of long-term memory and evolvability in such systems. In order to explore this scenario, we focus at a reduced version of our original model \cite{arxiv}, by assuming that a template of just two ‘letters’ long is sufficient to catalyze a ligation of two chain ends. Within this reduced model, we can study both numerically and analytically the evolution of the sequence pool of such autocatalytic heteropolymers made of Z types of monomers (‘letters’). Remarkably we find that the sequence entropy, initially at its maximum (consistent with the Random Sequence Approximation used in \cite{JCP}), gets slowly reduced to a much lower value. A closer analysis shows that out of...

Our model, while not detailing specific chemical realization, describes a generic mechanism of formation of long autocatalytic heteropolymers. Furthermore, we show that this system is inherently unstable with respect to symmetry breaking in the sequence space. This leads to reduction of sequence entropy, signaling a spontaneous increase in the information. This can be interpreted as an onset of Darwinian behavior, and may explain future emergence of the natural selection.

The sequence information entropy in a pool of autocatalitic heteropolymers (black lines), and the natural logarithm of the number of surviving two-letter words, 2-mers (red lines) plotted vs. time in 5 different realizations of our system. b)-c) The heatmap visualizing concentrations of 2-mers at the early (b) and late (c) stages of the system’s evolution.

Acknowledgements

This research used resources of the Center for Functional Nanomaterials, which is a U.S. DOE Office of Science Facility, at Brookhaven National Laboratory under Contract No. DE-SC0012704.

1. {schroedinger} Schr\"{o}dinger E. What is Life – the Physical Aspect of the Living Cell. Cambridge: Cambridge University Press.; 1944. NB: Strictly speaking, due to the exchange of energy and material with the environment, the appropriate measure of the reduction of thermodynamic entropy by living systems is the local accumulation of Gibbs free energy.
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Many molecular processes involve ranges of length and time scales that cannot be tackled with atomic-scale simulations. Instead, coarse-grained molecular models are necessary to interrogate such systems from a theoretical point of view. We discuss a fundamental approach to the identification of such models and more generally of emergent physical behavior from many-body systems. We proposed that a quantity called the relative entropy measures the information lost upon coarse graining and is the natural thermodynamic metric for such tasks [1,2]; its minimization provides a universal variational principle for coarse-graining [3,4]. In particular, this broad statistical-mechanical framework can improve simulation models of complex biomolecular and liquid-state systems, and uncover important driving forces and degrees of freedom [4–6]. We discuss conceptual and numerical aspects of this approach and illustrate its use in several case studies, including our recent efforts to improve models of hydrophobic interactions and complex mixtures using mean-field, multibody interaction potentials inspired by embedded atom models of metallic systems [7,8].

Corresponding author:  michael.gruenwald@utah.edu

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Macroscopic objects formed from particle assemblies are typically brittle, precluding their use in several ap- plications. We have demonstrated that ice-templating an aqueous dispersion of rigid colloidal particles and polymer, and crosslinking this polymer in the frozen state results in the formation of remarkably flexible colloidal assemblies[1]. Centimeter-scale monoliths prepared in this manner recover elastically after com- pression to 10% of their original size. This is remark- able when we consider that the monoliths are predom- inantly inorganic, with a particle weight fraction of 90%. Monoliths prepared in this manner are soft, with moduli in the range of tens of kPa. The Poisson ratio for monolith deformation can be calculated based on the change in sample dimensions during compression, and from the ratio of shear and Young’s moduli. The methods are consistent, and yield values close to zero. The scaling of moduli with density suggests the me- chanical response of the monolith in the linear regime is governed by thickening of the pore walls, rather than wall bending. For higher strains, there is a dra- matic increase in stress corresponding to buckling of pore walls.

The moduli of the monoliths increase linearly with temperature, indicating that the mechanical response is entropic in origin. We have demonstrated that flex- ible elastic hybrid monoliths can be prepared using different particles, different polymers and even dif- ferent crosslinking chemistries. Therefore, the me- chanical response appears to be a function largely of the microstructure developed by the preparation pro- cess viz. ice templating, followed by crosslinking in the frozen state. We demonstrate that this protocol results in the formation of a unique microstructure: polymers crosslinked in the frozen state form a mesh around particles in the pore walls[2, 3].

Subtle differences in the protocol for assembling nanoparticles play a critical role in determining their properties. Macroporous monoliths that are chemi- cally identical but that are prepared using small vari- ations in the ice templating protocol exhibit quali- tatively different mechanical behaviour, ranging from flexible elastic monoliths to plastic monoliths that fail at low compressive strains. We employ a variety of experimental techniques to characterize the structure and dynamics in these monoliths. We demonstrate that the preparation protocol modulates the spatial variation in crosslink density. Elastic scaffolds have a uniform distribution of crosslinks while scaffolds that have the same average crosslink density but spatially heterogeneous crosslinks exhibit brittle failure[2, 3].

Finally, I show that we can use the same ice tem- plating protocol to form flexible linear chain-like as- semblies that represent a convenient model system to study polymer physics. I will present results on the dynamics of active colloidal chains prepared using this protocol[4].

We would like to acknowledge SERB-Chemical En- gineering PAC, BRNS and IUSSTF for funding. KS, SC and BB acknowledge funding from CSIR and DST- Inspire.

Corresponding author:  g.kumaraswamy@ncl.res.in

1. R. Rajamanickam, S. Kumari, D. Kumar, S. Ghosh, J. C. Kim, G. Tae, S. Sengupta, G. Kumaraswamy, Chem. Mater. 26, 5161 (2014).
2. S. Karthika, S. Patil, P. R. Rajamohanan, G. Ku-maraswamy, Langmuir 32, 11623 (2016).
3. K. Suresh, R. Chulliyil, D. K. Sharma, Ketan, V. R. Kumar, A. Chowdhury, G. Kumaraswamy, Langmuir 34, 4603 (2018).
4. B. Biswas, R. Manna, A. Laskar, P. B. S. Kumar, R. Adhikari, G. Kumaraswamy, ACS Nano 11, 10025 (2017).

Soft-core particles interacting via Spring-like repul- sion exhibit multiple reentrant crystallizations with various solid structures. In this talk, we will present our recent observations of the novel two-dimensional melting scenario due to the reentrance and surprising finding of quasicrystals.

According to the KTHNY theory [1–4], the melting of a two-dimensional solid is a two-stage process. There exists an intermediate phase called hexatic phase be- tween solid and liquid. Transitions from solid to hex- atic and from hexatic to liquid are both continuous. Recently, it has been reported that the hexatic-liquid transition of hard particles is discontinuous [5] and the transition can evolve from discontinuous to continuous when the softness of particles is tuned [6]. For soft- core particle systems which reach the first maximum melting temperature T m at a crossover density ρ m , we find that ρ m acts as a transition point. Hexatic-liquid transition at ρ < ρ m exhibits strong first order tran- sition features. There is a density interval in which liquid and hexatic phases coexist. The interval de- creases with increasing temperature and tends to van- ish at T m . When ρ > ρ m , however, the hexatic-liquid transition becomes continuous. Therefore, in soft-core systems with reentrant crystallization, density should affect the nature of the hexatic-liquid transition [7].

At much higher densities after several reentrance, we surprisingly observe the existence of two-dimensional quasicrystals [8]. Up to now, quasicrystals have been found in multi-component systems such as al- loys [9] and in mono-component systems with mul- tiple length scales in particle interactions [10–15] or with anisotropic particles such as tetrahedral and patchy particles [16, 17]. In all these systems, multiple length scales are present in particle size, interaction, or anisotropy, which seem to be the consensual condi- tion for quasicrystals to occur. The quasicrystals that we found are unexpectedly formed by monodisperse, isotropic particles interacting via the simple soft-core potential without multiple length scales. We find not only dodecagonal but also octagonal quasicrystals, which have not been found yet in soft quasicrystals. In our quasicrystals, particles tend to form pentagons. A pentagon surrounded by an n-fold polygon constructs the complex structural unit to develop the n-fold qua- sicrystalline order. In liquid states prior to the liquid- solid transition, we already observe some signs of the development of the quasicrystalline order, including the accumulation of pentagons and the emergence of two competing length scales. We have also verified that our quasicrystals are stable by showing that their formation is independent of history and they have the lowest inherent structure potential energy, compared with other crystalline states.

Corresponding author:  ningxu@ustc.edu.cn

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Over the past decade, active hard spheres have be- come a benchmarking model system for studying the non-equilibrium physics in active matter. Although active hard spheres are intrisically out of equilibrium, we still find some equilibrium entropy-like effects in the system to drive the phase transition and self- organization in the system. In particular, I will talk about our recent work on active depletion forces [1], entropy driven active-passive demixing [2], and the formation of strongly hyperuniform fluids in systems of active hard spheres [3].

Corresponding author:  r.ni@ntu.edu.sg

1. R. Ni, M.A. Cohen Stuart, and P.G. Bolhuis, Phys. Rev. Lett. 114, 018302 (2015).
2. Z. Ma, Q. Lei, and R. Ni, Soft Matter, 13, 8940 (2017)
3. Q. Lei, M.P. Ciamarra, and R. Ni, arXiv:1802.03682 (2018)

An algorithm converts inputs to corresponding unique outputs through a sequence of actions. Algorithms are used as metaphors for complex biological processes such as organismal development. Here we make this metaphor rigorous for glycan biosynthesis. Glycans are branched carbohydrate oligomers that are attached to cell-surface proteins and convey cellular identity. Eukaryotic glycans are synthesized by collections of enzymes in Golgi compartments. A compartment can stochastically convert a single input oligomer to a heterogeneous set of possible output oligomers; yet a given type of protein is invariably associated with a narrow and reproducible glycan oligomer profile. Here we resolve this paradox by borrowing from the theory of algorithmic self-assembly. We rigorously enumerate the sources of glycan microheterogeneity: incomplete oligomers via early exit from the reaction compartment; tandem repeat oligomers via runaway reactions; and competing oligomer fates via divergent reactions. We demonstrate how to diagnose and eliminate each of these, thereby obtaining ``algorithmic compartments" that convert inputs to corresponding unique outputs. Given an input and a target output we either prove that the output cannot be algorithmically synthesized from the input, or explicitly construct a succession of algorithmic compartments that achieves this synthesis. Our theoretical analysis allows us to infer the causes of non-algorithmic microheterogeneity and species-specific diversity in real glycan datasets.

Consider a single particle gas confined in one dimension between a heavy piston and a Maxwell thermal reservoir. When the piston is held fixed the particle is expected to reach an equilibrium state after a long time. In the first part I will talk about how does the particle relax to equilibrium. When the piston is released with a force applied on it, it will start moving. But the motion will soon become stochastic due to the collisions with the particle. Is it possible to have an effective Langevin equation description of the piston motion? In the second part, I will talk about our attempt to answer this question.

Self-assembly is a key phenomenon in living matter, and at the same time, a booming field of modern material science and engineering. In my talk I will review emerging trends and ideas in this field, and give theorist's perspective on its conceptual challenges. I will discuss the strategy of programmable self-assembly that uses molecular recognition properties of DNA to build nano- and micro-scale building blocks with designed pairwise interactions. This approach opens an entirely new class of theoretical problems in statistical physics. Instead of studying phenomenology of a large system of particles with given properties, we must solve the inverse problem: finding the interactions that would result in a self-assembly of a desired macroscopic or mesoscopic morphology. I will start with a discussion of self-assembly in a very simple binary system of spherical particles, and gradually move towards a greater complexity of both the building blocks and the resulting structures. One structure that is notoriously challenging for self-assembly, and often viewed as a Holy Grail of the field, is a diamond lattice. I will therefore use diamond as a model system to illustrate general principles and specific approaches to programmable self-assembly. Some of those approaches are already implemented in experiments, while others are just theoretical prescriptions.

The entropic lattice Boltzmann model (ELBM) aims to construct a simplified kinetic picture on a lattice designed to capture the physics of macroscopic flow through simple local micro-scale operations.  

The method is unique in the sense that it enforces the numerical stability of a hydrodynamic solved by insisting on adherence to the thermodynamics at the discrete time level.   This compliance with the H theorem is typically enforced by
searching for the maximal discrete path length corresponding to the zero dissipation state by iteratively solving a nonlinear equation. We demonstrate that an exact solution for the path length can be obtained by
assuming a natural criterion of negative entropy change, thereby reducing the problem of solving an inequality.     Such a discrete space-time map can also be thought as geometric discretization of the dissipative Boltzmann dynamics.  Finally, I will discuss the possibility that such an implicit modeling of unresolved scales of the flow, via the thermodynamic route, may provide a new insight into subgrid modeling of turbulence.

The self-assembly of discrete objects can take place via many schemes, ranging from the elegant efficiency of certain virus capsids (which assemble from multiple copies of just one protein) to the latest developments in addressable assembly (where every building block is unique). Programmable assembly refers to the ambition of controlling every individual site in a target structure as well as the pathways by which it forms. In this talk I will test different strategies for controlling and optimising the self-assembly of discrete targets using an idealised model of particles with patterned interactions. In particular, I will examine the special challenges that come into play in the case of addressable assembly. In this limit, each building block must be encoded with enough information to find its unique location in the target structure. Furthermore, independently growing structures must avoid becoming mutually incompatible, which would lead to frustration in the assembly process. Along the way, I will describe some new tools for design, simulation and analysis in the context of colloidal self-assembly

In this talk I will present highlights from two independent projects. Apart from the fact that they both deal with soft matter systems, the only (tenuous) link is that they both involve the use of non-standard Monte Carlo techniques that are specialised to the respective tasks.

The first case concerns phase transitions in curved two-dimensional spaces, such as colloidosomes, where colloidal spheres are confined to the surface of a spherical droplet. The curvature, finite extent and thermodynamic ensemble all have pronounced effects on the nucleation process. More exotic toroidal surfaces give rise to some entirely new considerations.

The second case is the percolation transition in composite materials containing carbon nanotubes, where the emergence of a system-spanning network of nanotubes confers electrical conductivity on the material. We have investigated the interplay of length polydispersity and external aligning fields on the percolation threshold of these highly elongated particles, leading to some important general conclusions for optimising the formulation of such materials.

In this talk I will discuss the dynamics of droplets in the vicinity of vortices. The dynamics is described by simple parameter-free equation which have a boundary layer structure. Droplets within a critical distance from the vortex centre can participate in caustics events, and seed rapid droplet growth by collisions and coalescence. Our simulations provide evidence for this in three dimensions. I will then discuss how small droplets falling under gravity are affected by the Basset history force, a force which is normally extremely cumbersome to compute, but which we solve by an efficient method. Finally I will discuss how turbulence is affected by condensation on droplets. I will discuss some of these in the context of clouds.

Jamming transition of athermal particles is characterized by the divergence of the viscosity. This transition looks very similar to the glass transition, but there are several key differences. One of the differences is that the dynamical slowing down is apparently absent in the jamming transition. In this talk, I will report our recent study on the dynamics near the jamming transition. We especially focus on the dynamics in the simplest setting. i.e. relaxation from the random configuration of soft particles without shear. I show that the relaxation exhibits remarkable slowing down. I also show that this relaxation is dominated by a non trivial anomalous mode and is quantitatively related to the viscosity divergence.

Lecture 1: Mayer cluster expansion for non-ideal gas, correlation and response functions

“Self-assembly (SA) in the classic sense can be defined as the spontaneous and reversible organization of molecular units into ordered structures by non-covalent interactions. The first property of a self-assembled system that this definition suggests is the spontaneity of the self-assembly process: the interactions responsible for the formation of the self-assembled system act on a strictly local level—in other words, the nanostructurebuilds itself. “ - WIkipedia

This lecture will first focus on the basics of self-assembly and will show that this process only occurs for special systems. The ideas of Israelachvili on the critical micelle concentration and the packing parameter will be introduced. This lecture then naturally leads to delineating the conformational entropy of the surfactant tail, which is driven by ideas of entropic elasticity first espoused by Flory and deGennes. The application of these ideas to block copolymer self-assembly, to polymer crystallization and nanoparticle self-assembly will be explored in lecture 3.

Texts:

Israelachvili, Intermolecular and Surface Forces, Academic Press, 1992

Rubinstein, Colby Polymer Physics, Oxford, 2003

Lecture 1 (Israleachvili, Chapters 16,17)

1. What is self-assembly. Examples including Crystallization – colloids, polymers; Surfactants – Small molecules, Block copolymers; Nanoparticles – their growth, assembly; Self-assembled monolayers; Templated Synthesis from Surfactant Assemblies – ZSM 5; Lipid Bilayers….

2. Mass action law- finite clusters vs. phase separation

3. CMC

4. Packing parameter idea

In my lectures, I will begin with an idiosyncratic discussion of the idea of organization, ordering, and order. I will then introduce some relevant ideas from information theory, including Shannon entropy, Kolmogorov complexity, and elementary concepts from coding theory, followed by to a discussion of data compression and its relation to Shannon entropy. This will lead to a resume of results from ongoing research into the identification and quantification of order in systems far from equilibrium.

Lecture 2: Elements of liquid-state theory, introduction to classical density functional theory

Lecture 2 (Rubinstein & Colby, Chapters 2, 3, 5)

1. Importance of chain entropy

2. Flory entropy idea

3. Entropic springs

4. Scaling

5. Chain dimensions under stretching, good solvent etc.

In my lectures, I will begin with an idiosyncratic discussion of the idea of organization, ordering, and order. I will then introduce some relevant ideas from information theory, including Shannon entropy, Kolmogorov complexity, and elementary concepts from coding theory, followed by to a discussion of data compression and its relation to Shannon entropy. This will lead to a resume of results from ongoing research into the identification and quantification of order in systems far from equilibrium.

Lecture 3 (Various sources)

1. Application of these ideas to BCP self-assembly

2. Application to polymer crystallization

3. Nanoparticle self assembly

4. How do you measure this - SANS.

Lecture 1: Introduction to Edwards’ ideas, Microcanonical and Canonical Ensembles, Concept of Compactivity and Angoricity.

I will begin with a general Langevin framework for active matter dynamics [1] in which the “active terms” are directly linked to a driving force most naturally interpreted as a chemical potential imbalance between fuel and reaction products. I will consider the entropy- production properties of specific instances of such equations of motion for individual active particles as well as for active field theories [2, 3]. I will also discuss the defect-unbinding transition of active nematic systems [4], which has a natural energy-entropy aspect.

I acknowledge support from the Tata Education and Development Trust and from a J C Bose Fellowship of the Science & Engineering Research Board.

Corresponding author: sriram@iisc.ac.in

1. S Ramaswamy, J Stat Mech 2017:054002
2. L P Dadhichi, A Maitra and S Ramaswamy, in preparation
3. C Nardini et al., Phys Rev X 7, 021007 (2017).
4. S Shankar et al., arXiv:1804.06350 

Lecture 2:  The dual networks of jammed packings:  Contact network and Force Tilings

In my lectures, I will begin with an idiosyncratic discussion of the idea of organization, ordering, and order. I will then introduce some relevant ideas from information theory, including Shannon entropy, Kolmogorov complexity, and elementary concepts from coding theory, followed by to a discussion of data compression and its relation to Shannon entropy. This will lead to a resume of results from ongoing research into the identification and quantification of order in systems far from equilibrium.

I will begin with a general Langevin framework for active matter dynamics [1] in which the “active terms” are directly linked to a driving force most naturally interpreted as a chemical potential imbalance between fuel and reaction products. I will consider the entropy- production properties of specific instances of such equations of motion for individual active particles as well as for active field theories [2, 3]. I will also discuss the defect-unbinding transition of active nematic systems [4], which has a natural energy-entropy aspect.

I acknowledge support from the Tata Education and Development Trust and from a J C Bose Fellowship of the Science & Engineering Research Board.

Corresponding author: sriram@iisc.ac.in

1. S Ramaswamy, J Stat Mech 2017:054002
2. L P Dadhichi, A Maitra and S Ramaswamy, in preparation
3. C Nardini et al., Phys Rev X 7, 021007 (2017).
4. S Shankar et al., arXiv:1804.06350 

I will begin with a general Langevin framework for active matter dynamics [1] in which the “active terms” are directly linked to a driving force most naturally interpreted as a chemical potential imbalance between fuel and reaction products. I will consider the entropy- production properties of specific instances of such equations of motion for individual active particles as well as for active field theories [2, 3]. I will also discuss the defect-unbinding transition of active nematic systems [4], which has a natural energy-entropy aspect.

I acknowledge support from the Tata Education and Development Trust and from a J C Bose Fellowship of the Science & Engineering Research Board.

Corresponding author: sriram@iisc.ac.in

1. S Ramaswamy, J Stat Mech 2017:054002
2. L P Dadhichi, A Maitra and S Ramaswamy, in preparation
3. C Nardini et al., Phys Rev X 7, 021007 (2017).
4. S Shankar et al., arXiv:1804.06350 

In this talk I will briefly review the dynamic phase diagram of colloidal particle interacting with a short-ranged attractive interactions. This realistic model posses a number of exotic properties such as a reentrant melting, two different kid of glass, an arrested phase separation resulting in a gel structure. Most of this unusual phenomenology has been now confirmed in experiments and computer simulations.

The above scenario, is restricted to isotropic colloid, however in recent years a lot of interest has been devoted to the effect of directional attractive forces due to the progress in particles synthesis. I will present some recent results on the effect of directionality on the dynamics of these systems in connection, in particular, with the idea of locally favoured structure of a glass former.

An overview will be presented of the phenomenolog y of glass forming liquids, glasses, and the glass transition, as a prelude to more extended expositions of specific themes that will be explored in the subsequent lectures in the school. The topics covered will include the nature and characterization of the dynamics, and dynamical slow down in glass forming liquids, the role of configurational entropy in descriptions of such dynamical slow down, heterogeneous dynamics, growing length scales in glass formers, and a mention of related topics concerning yielding of glasses and jamming.

Almost integrable systems are ubiquitous: weakly nonlinear waves, planetary systems, globular clusters, the Fremi-Pasta-Ulam problem, many well studied Quantm chains... The approach to equilibrium is slow, because it is done precisely through the integrability breaking. On the other hand, they offer us an opportu- nity of understanding the precise role played by Entropy at each stage, because the evolution is, in a sense, reversible.

1. Integrable systems. Constants of motion. Approximate constants of motion.
2. Examples: solar system, Fermi-Pasta-Ulam chain, weak turbulence.
3. Generalized Gibbs Ensemble. Approach to equilibrium.
4. A Fluctuation Theorem

An overview will be presented of the phenomenology of glass forming liquids, glasses, and the glass transition, as a prelude to more extended expositions of specific themes that will be explored in the subsequent lectures in the school. The topics covered will include the nature and characterization of the dynamics, and dynamical slow down in glass forming liquids, the role of configurational entropy in descriptions of such dynamical slow down, heterogeneous dynamics, growing length scales in glass formers, and a mention of related topics concerning yielding of glasses and jamming.

I will discuss the role of entropy in some of the most relevant self-assembly processes. The outline of the lectures is the following:

Introduction

• Entropy and Translational Order: Hard Sphere Crystallisation [1]
• Entropy and Orientational Order: Transition [2]
• Entropy Attracts: Depletion Interactions [3]
• Entropy Attracts: tions [4]
• Competition between energy and entropy in self-assembly [5]
• Entropy and flexibility in networks [6]

Corresponding author: francesco.sciortino@uniroma1.it

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4. A. Zilman, J. Kieffer, F. Molino, G. Porte, and S. Safran, Physical review letters 91, 015901 (2003).
5. F. Sciortino, Soft Matter Self-Assembly, Varenna School, Italian Physical Society 193, 1 (2016).
6. F. Smallenburg and F. Sciortino, Nature Physics 9, 554 (2013).

The development of a mean field theory of glasses started in the 80s, through the work of Kirkpatrick, Thirumalai and Wolynes. They identified a class of mean field spin glass models, whose qualitative behav- ior is very similar to the one of supercooled liquid and glasses measured in the laboratory. They proposed that these spin glass models could serve as represen- tative of a broad universality class, called the Ran- dom First Order Transition (RFOT) class, in which the glass transition would fall, at least at the mean field level. To substantiate this claim, they proposed that a system of d-dimensional interacting particles would fall in this class in the d → ∞ limit [1].

During the subsequent two decades, a lot of work has been done on RFOT spin glass models, which provided many important predictions on the thermodynamics and dynamics of RFOT systems: glass transition, aging, effective temperatures, complexity, dynamical heterogeneities... However, proving that the original conjecture of [1] is correct took another decade, and the program was completed in the last few years.

In these lectures I will review the solution of parti- cle systems in d → ∞. I will show that the behavior is precisely the one of the RFOT universality class. I will start by the study of the equilibrium dynamics and show the existence of a dynamical glass transition similar to the one of Mode-Coupling Theory [2]. Next, I will show how the long time limit of the dynamics in the glass phase can be studied via the replica method using the “state following” or Franz-Parisi construc- tion [3]. Finally, I will briefly discuss the Gardner and jamming transitions [4].

During the lectures, physical concepts such as the dy- namical glass transition, the complexity, the Kauz- mann transition, the out-of-equilibrium glass state, and the criticality of jamming will be discussed. Methodologically, we will introduce dynamical and replica techniques. The lectures are based on a book which is currently being written [5].

Corresponding author: www.phys.ens.fr/∼zamponi

1. T.R.Kirkpatrick and P. G. Wolynes, “Connections be-tween some kinetic and equilibrium theories of the glass transition”, Physical Review A 35, 3072 (1987).
2. T.Maimbourg, J.Kurchan, and F.Zamponi, “Solution of the dynamics of liquids in the large-dimensional limit”, Physical Review Letters 116, 015902 (2016).
3. C.Rainone, P.Urbani, H.Yoshino, and F.Zamponi, “Following the evolution of hard sphere glasses in in-finite dimensions under external perturbations: com-pression and shear strain”, Physical Review Letters 114, 015701 (2015).
4. P.Charbonneau, J.Kurchan, G.Parisi, P.Urbani, F.Zamponi, “Fractal free energy landscapes in struc-tural glasses”, Nature Communications 5, 3725 (2014).
5. G.Parisi, P.Urbani, F.Zamponi, “Theory of simple glasses”, book in preparation (Cambrige University Press).

In these lectures, I will employ the material presented in the introductory lectures, in particular the basics of liquid state theory and statistical mechanics to explain how the configurational entropy of supercooled liquids can be measured in computer simulations of supercooled liquids [1].

I will first explain why we must care about the configurational entropy, how it is defined and what are the conceptual problems associated to this important quantity, from the ill-defined concept of thermodynamic metastability to issues related to polydisperse liquid models.

I will then talk about computer simulations of super- cooled liquids, how they are done, and what can be hoped to be achieved using this important tool. In particular, I will emphasize the new opportunities offered by the recent development of the SWAP algorithm [2] to explore more ambitiously than before the thermodynamic properties of deeply supercooled liquids [3].

Then I will show how in practice one defines and mea- sures using computer simulations various proxies for the configurational entropy, from the potential energy landscape approach, from the Frenkel-Ladd thermodynamic construction, from the Franz-Parisi free energy, and from the point-to-set correlation length measurement.

These lectures have strong connections with the mean- field results presented in the parallel lectures by F. Zamponi and J. Kurchan.

Corresponding author: ludovic.berthier@umontpellier.fr

1. L. Berthier and G. Biroli, Theoretical perspective on the glass transition and amorphous materials, Rev. Mod. Phys. 83, 587 (2011).
2. A. Ninarello, L. Berthier, and D. Coslovich, Models and algorithms for the next generation of glass transition studies, Phys. Rev. X 7, 021039 (2017).
3. L. Berthier, P. Charbonneau, D. Coslovich, A. Ninarello, M. Ozawa, and S. Yaida, Configurational entropy measurements in extremely supercooled liquids that break the glass ceiling, Proc. Natl. Acad. Sci U. S. A. 114, 11356 (2017).

The development of a mean field theory of glasses started in the 80s, through the work of Kirkpatrick, Thirumalai and Wolynes. They identified a class of mean field spin glass models, whose qualitative behav- ior is very similar to the one of supercooled liquid and glasses measured in the laboratory. They proposed that these spin glass models could serve as represen- tative of a broad universality class, called the Ran- dom First Order Transition (RFOT) class, in which the glass transition would fall, at least at the mean field level. To substantiate this claim, they proposed that a system of d-dimensional interacting particles would fall in this class in the d → ∞ limit [1].

During the subsequent two decades, a lot of work has been done on RFOT spin glass models, which provided many important predictions on the thermodynamics and dynamics of RFOT systems: glass transition, aging, effective temperatures, complexity, dynamical heterogeneities... However, proving that the original conjecture of [1] is correct took another decade, and the program was completed in the last few years.

In these lectures I will review the solution of parti- cle systems in d → ∞. I will show that the behavior is precisely the one of the RFOT universality class. I will start by the study of the equilibrium dynamics and show the existence of a dynamical glass transition similar to the one of Mode-Coupling Theory [2]. Next, I will show how the long time limit of the dynamics in the glass phase can be studied via the replica method using the “state following” or Franz-Parisi construc- tion [3]. Finally, I will briefly discuss the Gardner and jamming transitions [4].

During the lectures, physical concepts such as the dy- namical glass transition, the complexity, the Kauz- mann transition, the out-of-equilibrium glass state, and the criticality of jamming will be discussed. Methodologically, we will introduce dynamical and replica techniques. The lectures are based on a book which is currently being written [5].

Corresponding author: www.phys.ens.fr/∼zamponi

1. T.R.Kirkpatrick and P. G. Wolynes, “Connections be-tween some kinetic and equilibrium theories of the glass transition”, Physical Review A 35, 3072 (1987).
2. T.Maimbourg, J.Kurchan, and F.Zamponi, “Solution of the dynamics of liquids in the large-dimensional limit”, Physical Review Letters 116, 015902 (2016).
3. C.Rainone, P.Urbani, H.Yoshino, and F.Zamponi, “Following the evolution of hard sphere glasses in in-finite dimensions under external perturbations: com-pression and shear strain”, Physical Review Letters 114, 015701 (2015).
4. P.Charbonneau, J.Kurchan, G.Parisi, P.Urbani, F.Zamponi, “Fractal free energy landscapes in struc-tural glasses”, Nature Communications 5, 3725 (2014).
5. G.Parisi, P.Urbani, F.Zamponi, “Theory of simple glasses”, book in preparation (Cambrige University Press).

I will discuss the role of entropy in some of the most relevant self-assembly processes. The outline of the lectures is the following:

Introduction

• Entropy and Translational Order: Hard Sphere Crystallisation [1]
• Entropy and Orientational Order: Transition [2]
• Entropy Attracts: Depletion Interactions [3]
• Entropy Attracts: tions [4]
• Competition between energy and entropy in self-assembly [5]
• Entropy and flexibility in networks [6]

Corresponding author: francesco.sciortino@uniroma1.it

1. B. Alder and T. Wainwright, The Journal of chemical physics 27, 1208 (1957).
2. L. Onsager, Annals of the New York Academy of Sci-ences 51, 627 (1949).
3. H. N. Lekkerkerker and R. Tuinier, Colloids and the depletion interaction, Vol. 833 (Springer, 2011).
4. A. Zilman, J. Kieffer, F. Molino, G. Porte, and S. Safran, Physical review letters 91, 015901 (2003).
5. F. Sciortino, Soft Matter Self-Assembly, Varenna School, Italian Physical Society 193, 1 (2016).
6. F. Smallenburg and F. Sciortino, Nature Physics 9, 554 (2013).

Recent years have seen remarkable advances in the mean-field theory of glasses. But do these theoretical predictions actually explain the behavior of real physi- cal systems? In these lectures, we will study this ques- tion using numerical and theoretical tools that allow to systematically interpolate between one limit [1] and the other. By tuning spatial dimension or the inter- action range between particles, we can indeed identify theoretically robust features and physical phenomena that fall beyond the mean-field scenario.

In these lectures, I will build on the material presented in previous and parallel lectures, especially the basics of liquid state theory and the mean-field theory of glasses. While L. Berthier’s lectures will mostly fo- cus on the properties of glassy states, mine will center on the dynamical slowdown of an (metastable) equi- librium liquid. More specifically, I will explore the following topics.

1. The mechanics, advantages and challenges of running numerical simulations in higher dimen-sions [2–5].
2. The theoretical expectations for finite-dimensional systems from RFOT [6].
3. The theoretical and numerical results for the Mari-Kurchan (MK) model [5, 7–9].
4. The lessons from the MK model for going be-yond → ∞ mean-field, especially from insights void percolation and random Lorentz gas [10–12].

I thank warmly all my collaborators in this extended scientific effort. The last couple of years of this re- search program were supported by a grant from the Simons Foundation (No. 454937).

Corresponding author: https://chem.duke.edu/labs/charbonneau

1. P. Charbonneau, J. Kurchan, G. Parisi, P. Urbani, and F. Zamponi, Ann. Rev. Condens. Matter Phys. 8, 265 (2017).
2. P. Charbonneau, A. Ikeda, G. Parisi, and F. Zam-poni, Phys. Rev. Lett. 107, 185702 (2011).
3. B. Charbonneau, P. Charbonneau, and G. Tarjus, Phys. Rev. Lett. 108, 035701 (2012).
4. B. Charbonneau, P. Charbonneau, Y. Jin, G. Parisi, and F. Zamponi, J. Chem. Phys. 139, 164502 (2013).
5. P. Charbonneau, Y. Jin, G. Parisi, and F. Zamponi, Proc. Nat. Acad. Sci. U.S.A. 111, 15025 (2014).
6. L. Berthier and G. Biroli, Rev. Mod. Phys. 83, 587 (2011).
7. R. Mari, F. Krzakala, and J. Kurchan, Phys. Rev. Lett. 103, 025701 (2009).
8. R. Mari and J. Kurchan, J. Chem. Phys. 135, 124504 (2011).
9. M. Mézard, G. Parisi, M. Tarzia, and F. Zamponi, J. Stat. Mech. 2011, P03002 (2011).
10. F. Hoefling, T. Franosch, and E. Frey, Phys. Rev. Lett. 96, 165901 (2006).
11. T. Bauer, F. Hfling, T. Munk, E. Frey, and T. Fra-nosch, Eur. Phys. J. 189, 103 (2010).
12. Y. Jin and P. Charbonneau, Phys. Rev. E 91, 042313 (2015).

The development of a mean field theory of glasses started in the 80s, through the work of Kirkpatrick, Thirumalai and Wolynes. They identified a class of mean field spin glass models, whose qualitative behav- ior is very similar to the one of supercooled liquid and glasses measured in the laboratory. They proposed that these spin glass models could serve as represen- tative of a broad universality class, called the Ran- dom First Order Transition (RFOT) class, in which the glass transition would fall, at least at the mean field level. To substantiate this claim, they proposed that a system of d-dimensional interacting particles would fall in this class in the d → ∞ limit [1].

During the subsequent two decades, a lot of work has been done on RFOT spin glass models, which provided many important predictions on the thermodynamics and dynamics of RFOT systems: glass transition, aging, effective temperatures, complexity, dynamical heterogeneities... However, proving that the original conjecture of [1] is correct took another decade, and the program was completed in the last few years.

In these lectures I will review the solution of parti- cle systems in d → ∞. I will show that the behavior is precisely the one of the RFOT universality class. I will start by the study of the equilibrium dynamics and show the existence of a dynamical glass transition similar to the one of Mode-Coupling Theory [2]. Next, I will show how the long time limit of the dynamics in the glass phase can be studied via the replica method using the “state following” or Franz-Parisi construc- tion [3]. Finally, I will briefly discuss the Gardner and jamming transitions [4].

During the lectures, physical concepts such as the dy- namical glass transition, the complexity, the Kauz- mann transition, the out-of-equilibrium glass state, and the criticality of jamming will be discussed. Methodologically, we will introduce dynamical and replica techniques. The lectures are based on a book which is currently being written [5].

Corresponding author: www.phys.ens.fr/∼zamponi

1. T.R.Kirkpatrick and P. G. Wolynes, “Connections be-tween some kinetic and equilibrium theories of the glass transition”, Physical Review A 35, 3072 (1987).
2. T.Maimbourg, J.Kurchan, and F.Zamponi, “Solution of the dynamics of liquids in the large-dimensional limit”, Physical Review Letters 116, 015902 (2016).
3. C.Rainone, P.Urbani, H.Yoshino, and F.Zamponi, “Following the evolution of hard sphere glasses in in-finite dimensions under external perturbations: com-pression and shear strain”, Physical Review Letters 114, 015701 (2015).
4. P.Charbonneau, J.Kurchan, G.Parisi, P.Urbani, F.Zamponi, “Fractal free energy landscapes in struc-tural glasses”, Nature Communications 5, 3725 (2014).
5. G.Parisi, P.Urbani, F.Zamponi, “Theory of simple glasses”, book in preparation (Cambrige University Press).

In these lectures, I will employ the material presented in the introductory lectures, in particular the basics of liquid state theory and statistical mechanics to explain how the configurational entropy of supercooled liquids can be measured in computer simulations of supercooled liquids [1].

I will first explain why we must care about the configurational entropy, how it is defined and what are the conceptual problems associated to this important quantity, from the ill-defined concept of thermodynamic metastability to issues related to polydisperse liquid models.

I will then talk about computer simulations of super- cooled liquids, how they are done, and what can be hoped to be achieved using this important tool. In particular, I will emphasize the new opportunities offered by the recent development of the SWAP algorithm [2] to explore more ambitiously than before the thermodynamic properties of deeply supercooled liquids [3].

Then I will show how in practice one defines and mea- sures using computer simulations various proxies for the configurational entropy, from the potential energy landscape approach, from the Frenkel-Ladd thermodynamic construction, from the Franz-Parisi free energy, and from the point-to-set correlation length measurement.

These lectures have strong connections with the mean- field results presented in the parallel lectures by F. Zamponi and J. Kurchan.

Corresponding author: ludovic.berthier@umontpellier.fr

L. Berthier and G. Biroli, Theoretical perspective on the glass transition and amorphous materials, Rev. Mod. Phys. 83, 587 (2011).
A. Ninarello, L. Berthier, and D. Coslovich, Models and algorithms for the next generation of glass transition studies, Phys. Rev. X 7, 021039 (2017).
L. Berthier, P. Charbonneau, D. Coslovich, A. Ninarello, M. Ozawa, and S. Yaida, Configurational entropy measurements in extremely supercooled liquids that break the glass ceiling, Proc. Natl. Acad. Sci U. S. A. 114, 11356 (2017).

Recent years have seen remarkable advances in the mean-field theory of glasses. But do these theoretical predictions actually explain the behavior of real physi- cal systems? In these lectures, we will study this ques- tion using numerical and theoretical tools that allow to systematically interpolate between one limit [1] and the other. By tuning spatial dimension or the inter- action range between particles, we can indeed identify theoretically robust features and physical phenomena that fall beyond the mean-field scenario.

In these lectures, I will build on the material presented in previous and parallel lectures, especially the basics of liquid state theory and the mean-field theory of glasses. While L. Berthier’s lectures will mostly fo- cus on the properties of glassy states, mine will center on the dynamical slowdown of an (metastable) equi- librium liquid. More specifically, I will explore the following topics.

1. The mechanics, advantages and challenges of running numerical simulations in higher dimen-sions [2–5].
2. The theoretical expectations for finite-dimensional systems from RFOT [6].
3. The theoretical and numerical results for the Mari-Kurchan (MK) model [5, 7–9].
4. The lessons from the MK model for going be-yond → ∞ mean-field, especially from insights void percolation and random Lorentz gas [10–12].

I thank warmly all my collaborators in this extended scientific effort. The last couple of years of this re- search program were supported by a grant from the Simons Foundation (No. 454937).

Corresponding author: https://chem.duke.edu/labs/charbonneau

1. P. Charbonneau, J. Kurchan, G. Parisi, P. Urbani, and F. Zamponi, Ann. Rev. Condens. Matter Phys. 8, 265 (2017).
2. P. Charbonneau, A. Ikeda, G. Parisi, and F. Zam-poni, Phys. Rev. Lett. 107, 185702 (2011).
3. B. Charbonneau, P. Charbonneau, and G. Tarjus, Phys. Rev. Lett. 108, 035701 (2012).
4. B. Charbonneau, P. Charbonneau, Y. Jin, G. Parisi, and F. Zamponi, J. Chem. Phys. 139, 164502 (2013).
5. P. Charbonneau, Y. Jin, G. Parisi, and F. Zamponi, Proc. Nat. Acad. Sci. U.S.A. 111, 15025 (2014).
6. L. Berthier and G. Biroli, Rev. Mod. Phys. 83, 587 (2011).
7. R. Mari, F. Krzakala, and J. Kurchan, Phys. Rev. Lett. 103, 025701 (2009).
8. R. Mari and J. Kurchan, J. Chem. Phys. 135, 124504 (2011).
9. M. Mézard, G. Parisi, M. Tarzia, and F. Zamponi, J. Stat. Mech. 2011, P03002 (2011).
10. F. Hoefling, T. Franosch, and E. Frey, Phys. Rev. Lett. 96, 165901 (2006).
11. T. Bauer, F. Hfling, T. Munk, E. Frey, and T. Fra-nosch, Eur. Phys. J. 189, 103 (2010).
12. Y. Jin and P. Charbonneau, Phys. Rev. E 91, 042313 (2015).

In these lectures, I will employ the material presented in the introductory lectures, in particular the basics of liquid state theory and statistical mechanics to explain how the configurational entropy of supercooled liquids can be measured in computer simulations of supercooled liquids [1].

I will first explain why we must care about the configurational entropy, how it is defined and what are the conceptual problems associated to this important quantity, from the ill-defined concept of thermodynamic metastability to issues related to polydisperse liquid models.

I will then talk about computer simulations of super- cooled liquids, how they are done, and what can be hoped to be achieved using this important tool. In particular, I will emphasize the new opportunities offered by the recent development of the SWAP algorithm [2] to explore more ambitiously than before the thermodynamic properties of deeply supercooled liquids [3].

Then I will show how in practice one defines and mea- sures using computer simulations various proxies for the configurational entropy, from the potential energy landscape approach, from the Frenkel-Ladd thermodynamic construction, from the Franz-Parisi free energy, and from the point-to-set correlation length measurement.

These lectures have strong connections with the mean- field results presented in the parallel lectures by F. Zamponi and J. Kurchan.

Corresponding author: ludovic.berthier@umontpellier.fr

L. Berthier and G. Biroli, Theoretical perspective on the glass transition and amorphous materials, Rev. Mod. Phys. 83, 587 (2011).
A. Ninarello, L. Berthier, and D. Coslovich, Models and algorithms for the next generation of glass transition studies, Phys. Rev. X 7, 021039 (2017).
L. Berthier, P. Charbonneau, D. Coslovich, A. Ninarello, M. Ozawa, and S. Yaida, Configurational entropy measurements in extremely supercooled liquids that break the glass ceiling, Proc. Natl. Acad. Sci U. S. A. 114, 11356 (2017).

Recent years have seen remarkable advances in the mean-field theory of glasses. But do these theoretical predictions actually explain the behavior of real physi- cal systems? In these lectures, we will study this ques- tion using numerical and theoretical tools that allow to systematically interpolate between one limit [1] and the other. By tuning spatial dimension or the inter- action range between particles, we can indeed identify theoretically robust features and physical phenomena that fall beyond the mean-field scenario.

In these lectures, I will build on the material presented in previous and parallel lectures, especially the basics of liquid state theory and the mean-field theory of glasses. While L. Berthier’s lectures will mostly fo- cus on the properties of glassy states, mine will center on the dynamical slowdown of an (metastable) equi- librium liquid. More specifically, I will explore the following topics.

1. The mechanics, advantages and challenges of running numerical simulations in higher dimen-sions [2–5].
2. The theoretical expectations for finite-dimensional systems from RFOT [6].
3. The theoretical and numerical results for the Mari-Kurchan (MK) model [5, 7–9].
4. The lessons from the MK model for going be-yond → ∞ mean-field, especially from insights void percolation and random Lorentz gas [10–12].

I thank warmly all my collaborators in this extended scientific effort. The last couple of years of this re- search program were supported by a grant from the Simons Foundation (No. 454937).

Corresponding author: https://chem.duke.edu/labs/charbonneau

1. P. Charbonneau, J. Kurchan, G. Parisi, P. Urbani, and F. Zamponi, Ann. Rev. Condens. Matter Phys. 8, 265 (2017).
2. P. Charbonneau, A. Ikeda, G. Parisi, and F. Zam-poni, Phys. Rev. Lett. 107, 185702 (2011).
3. B. Charbonneau, P. Charbonneau, and G. Tarjus, Phys. Rev. Lett. 108, 035701 (2012).
4. B. Charbonneau, P. Charbonneau, Y. Jin, G. Parisi, and F. Zamponi, J. Chem. Phys. 139, 164502 (2013).
5. P. Charbonneau, Y. Jin, G. Parisi, and F. Zamponi, Proc. Nat. Acad. Sci. U.S.A. 111, 15025 (2014).
6. L. Berthier and G. Biroli, Rev. Mod. Phys. 83, 587 (2011).
7. R. Mari, F. Krzakala, and J. Kurchan, Phys. Rev. Lett. 103, 025701 (2009).
8. R. Mari and J. Kurchan, J. Chem. Phys. 135, 124504 (2011).
9. M. Mézard, G. Parisi, M. Tarzia, and F. Zamponi, J. Stat. Mech. 2011, P03002 (2011).
10. F. Hoefling, T. Franosch, and E. Frey, Phys. Rev. Lett. 96, 165901 (2006).
11. T. Bauer, F. Hfling, T. Munk, E. Frey, and T. Fra-nosch, Eur. Phys. J. 189, 103 (2010).
12. Y. Jin and P. Charbonneau, Phys. Rev. E 91, 042313 (2015).

I will discuss the role of entropy in some of the most relevant self-assembly processes. The outline of the lectures is the following:

Introduction

• Entropy and Translational Order: Hard Sphere Crystallisation [1]
• Entropy and Orientational Order: Transition [2]
• Entropy Attracts: Depletion Interactions [3]
• Entropy Attracts: tions [4]
• Competition between energy and entropy in self-assembly [5]
• Entropy and flexibility in networks [6]

Corresponding author: francesco.sciortino@uniroma1.it

1. B. Alder and T. Wainwright, The Journal of chemical physics 27, 1208 (1957).
2. L. Onsager, Annals of the New York Academy of Sci-ences 51, 627 (1949).
3. H. N. Lekkerkerker and R. Tuinier, Colloids and the depletion interaction, Vol. 833 (Springer, 2011).
4. A. Zilman, J. Kieffer, F. Molino, G. Porte, and S. Safran, Physical review letters 91, 015901 (2003).
5. F. Sciortino, Soft Matter Self-Assembly, Varenna School, Italian Physical Society 193, 1 (2016).
6. F. Smallenburg and F. Sciortino, Nature Physics 9, 554 (2013).

J. M. Olais-Govea, L. Lopez-Flores, and M. Medina-Noyola

A major stumbling block for statistical physics and materials science has been the lack of a universal principle that allows us to understand and predict elementary structural, morphological, and dynamical properties of non-equilibrium amorphous states of matter. The recently-developed non-equilibrium self-consistent generalized Langevin equation (NE-SCGLE) theory, however, has been shown to provide a fundamental tool for the understanding of the most essential features of the transformation of liquids into amorphous solids, such as their aging kinetics or their dependence on the protocol of fabrication. In this work we focus on the predicted kinetics of one of the main fingerprints of the formation of gels by arrested spinodal decomposition of suddenly and deeply quenched simple liquids, namely, the arrest of structural parameters associated with the morphological evolution from the initially uniform fluid, to the dynamically arrested sponge-like amorphous material. The comparison o f the theoretical predictions with simulation and experimental data measured on similar but more complex materials, suggests the universality of the predicted scenario.

Lecture 1: High-Dimensional Inference: Basic techniques

1. Bayesian inference
2. Principal Component Analysis (PCA)
3. Spiked covariance model and retarded learning phase transition
4. Role of prior information

References:

1. Information theory, inference, learning algorithms
   David MacKay, Cambridge University Press
2. http://www.inference.org.uk/itila/book.html
3. Introduction to the theory of neural computation
   John Hertz, Andreas Hertz, Richard Palmer, Santa Fe Institute series
4. Statistical physics and representations in real and artificial neural networks
   Simona Cocco, Remi Monasson, Lorenzo Posani, Sophie Rosay, Jerome Tubiana, Physica A (2018)
   https://arxiv.org/abs/1709.02470
5. Inverse statistical physics of protein sequences: a key issues review
   Simona Cocco, Christoph Feinauer, Matteo Figliuzzi, Remi Monasson, Martin Weigt, Rep. Phys. Prog. (2018)
   http://www.phys.ens.fr/~monasson/Articles/a107.pdf

We present responses of a small number of Coulomb-interacting particles in two-dimensional confinements, across the crossover from their solid- to liquid-like behaviors. Here, irregular confinements emulate the role of disorder.

Focusing first on the thermal melting, where zero-point motion of the particles are frozen, we explore the signatures of a 'hexatic-glass' like behavior. While static correlations, which investigate the translational and bond orientational order [1,2], indicate a hexatic-like phase at low temperatures, dynamical correlations show considerably slow relaxations. Using density correlations we probe intriguing inhomogeneities arising from the interplay of the irregularity in the confinement and long-range interactions. The relaxation at multiple time scales show stretched-exponential decay of spatial correlations for Coulomb-particles in irregular traps [1,3]. Temperature dependence of characteristic time scales, depicting the structural relaxation of the system, show strong similarities with those observed for the glassy systems. Our results indicate that some of the key features of supercooled liquids emerge in confined systems. more so with irregular confinements. The analysis of normal modes [4] elucidates how long time behavior of the system is encoded in the quasi-localized modes.

Time permitting, we extend our discussions to include the effects of quantum fluctuations. Our results, using quantum Monte Carlo techniques for Boltzmann particles, seem to indicate complementary mechanism for the quantum and thermal crossovers in Wigner molecules [5]. We will also discuss our recent analyses upon including the effects of quantum statistics.

1. B. Ash, J. Chakrabarti and A. Ghosal, Phys. Rev. E 96, 042105 (2017).
2. D. Bhattacharya and A. Ghosal, Eur. Phys. J. B 86, 499 (2013).
3. B. Ash, J. Chakrabarti and A. Ghosal, Euro. Phys. Lett., 114, 4, (2016).
4. B. Ash, C. Dasgupta and A. Ghosal, To appear in Phys. Rev. E (2018) (arXiv:1805.11180).
5. D. Bhattacharya, A. V. Filinov, A. Ghosal and M.Bonitz, Eur. Phys. J. B 89, 60, (2016).

High-Dimensional Inference: Unsupervised Learning with Neural Networks

1. What is Unsupervised learning?
2. Autoencoders and connection with PCA
3. Boltzmann machines and Restricted Boltzmann machines

Kolmogorov’s 1941 theory elucidating the spectrum of turbulent velocity fluctuations forms the cornerstone of contemporary turbulence research. This result requires one to measure the velocity everywhere within the turbulent flow at the same time instant. However, many situations exist where measurements are needed over time at one or few fixed spatial (Eulerian) locations, sometimes involving not velocity but its higher powers. The physical interpretation of such measurements strongly diverges from the Kolmogorov framework. In this talk, I will review the revised theoretical framework and support it with evidence from our experiments in two and three dimensional flows. I will then explain how this revised framework provides a toolkit to address a diverse range of questions in Energy, UAV mechanics, Environmental Sciences, and perhaps even Life Sciences.

High-Dimension Inference: Application to protein modeling

1. Biological motivations
2. Methods
3. Results

References:

1. Information theory, inference, learning algorithms
   David MacKay, Cambridge University Press
2. Link
3. Introduction to the theory of neural computation
   John Hertz, Andreas Hertz, Richard Palmer, Santa Fe Institute series
4. Statistical physics and representations in real and artificial neural networks
   Simona Cocco, Remi Monasson, Lorenzo Posani, Sophie Rosay, Jerome Tubiana, Physica A (2018)
   Link
5. Inverse statistical physics of protein sequences: a key issues review
   Simona Cocco, Christoph Feinauer, Matteo Figliuzzi, Remi Monasson, Martin Weigt, Rep. Phys. Prog. (2018)
   Link

We present recent results on non-spherical particles and elastic fibers in a turbulent flow. In particular, we discuss the issue of preferential sampling of flows by such "particles" with internal degrees of freedom and compare them with the more standard spherical particle approach. If time permits, we will present recent results on the emergence of collective motion for active rods and disks in fully developed turbulence.

AQS-automata arise naturally in the description of the athermal dynamics of a disordered system -- such as spin glasses -- when a slowly changing uniform driving force is applied. The response of such systems is characterized by abrupt transitions between quasi-static configurations which are generally irreversible, giving thus rise to hysteresis. The dynamical response of such systems can be described in terms of a pair of random, directed and acyclic graphs, capturing the transitions triggered by force increases and decreases, respectively. Properties such as return-point memory emerge then as features of these graphs. In this talk I will develop the graph-theoretic description of AQS-automata and then present recent work with T. Witten on modelling the AQS dynamics by random maps.

The perception of beauty is strongly linked to order and symmetry. These perceptions engraved into our evolutionary psychology as we survive by being the fittest. However, quantifying these perceptions, and the technical truth underlying them has many challenges, some of which will be shared in the context of hair. Two specific problems are (1) the dynamics of the tangling/detangling of hair, and (2) the movement of hair. Getting stronger analytical insights on the impact of microscale material parameters against macroscopic variations in the amount of structural disorder or momentum distributions would help design products for consumers.

Extreme active matter, comprising self-propelled particles characterised by large persistence time \tau_p and high Péclet number, exhibits remarkable behaviour at high densities. As \tau_p → 0, the material undergoes a conventional fluid-to-glass transition via density relaxation, as one reduces the active propulsion force f . In the other limit, \tau_p → ∞, the fluid jams at a critical point on lowering f to f^∗ (∞), with stresses concentrated along force-chains. In between these limits, the approach to dynamical arrest at low f , goes through a phase characterised by intermittency in the kinetic and potential energy. This intermittency is a consequence of long periods of jamming followed by bursts of plastic yielding associated with Eshelby deformations, akin to the response of dense amorphous solids to an externally imposed shear. In the vicinity of the intermittency-fluid phase boundary, correlated plastic events result in large scale vorticity and turbulence. Dense extreme active matter brings together the physics of glass, jamming, plasticity and turbulence, in a new state of driven classical matter.

School textbooks tell us that the main difference between a solid and a liquid is the ability of the former to retain its shape. Any attempt at changing the shape of a solid is resisted by an internal elastic stress unless the deformation crosses a limiting value; at which point the solid fails. This naive viewpoint, although of great practical value, is, however, fundamentally incorrect. For example, one can argue that given enough time, atoms in the solid can always rearrange to eliminate stress no matter how much, or how little, the solid is deformed. Resolution of this paradoxical result lies at the core of our understanding of the behavior of solids under deformation. Adapting ideas which were introduced recently to study glasses, we find that rigidity arises a result of a hidden first-order phase transition between phases which differ in the way they respond to changes of shape [1]. When deformed by any amount, howsoever small, the rigid solid goes into a meta-stable state analogous to superheated water. Eventually, this meta-stable state always decays by nucleating bubbles of the stable, stress-free, solid by a process very similar to how bubbles of steam appear in a kettle of boiling water. This fresh conceptual viewpoint curiously allows us to study failure of perfect crystalline solids in quantitative detail without invoking specifics of many-body, defect–defect interactions, raising hope of a more unified description of materials in the future.

[1] Nath et al. PNAS 115 E4322-E4329 (2018)

The mechanical response of two-dimensional frictional granular materials under an oscillatory shear in a constant volume are numerically investigated. It is confirmed that the shear storage modulus G′ depends on the initial amplitude of the oscillation to prepare the system before the measurement. For sufficiently large initial strain amplitude, the shear jammed state satisfying G′ > 0 is observed even if the packing fraction is below the jamming point. The fragile state is also identified as a long lived metastable state where G′ depends on the phase of the oscillatory shear. The dynamic viscosity evaluated from the shear loss modulus G′′ exhibits a sudden jump similar to the discontinuous shear thickening in the fragile state. In this talk we also show some preliminary results of hydrodynamic simulation for colloidal suspensions to discuss shear jamming and DST as well as the behavior of dry granular particles under the pressure control protocol.

The loss of rigidity in amorphous solids when subjected to external stress has been investigated actively in recent years. I will describe recent results regarding the nature of the yielding transition, including strain localisation in the yielded solid, annealing effects below and above the yielding threshold, obtained by computational investigations of amorphous solids subjected to oscillatory deformation.

Following a general discussion on universalities related to various structural and dynamical aspects of phase transitions, I will concentrate on nonequilibrium phenomena. In this domain a set of problems will be described with the objective of highlighting how various aspects of coarsening phenomena depend upon space dimension, morphology, etc. Finally, I will present results from two problems of my current interest. One is related to kinetics of vapor-solid transitions and the other deals with the ordering in popular Ising ferromagnet. The aim will be to project the breadth of diversity even in simple situations.

Connections between many-body chaos and ergodicity form the basis of statistical mechanics. Starting with an overview of recent interests in this area, I shall discuss our numerical results characterising spatio-temporal signatures of chaos in spin systems and point out their possible quantitative connection to measures of transport such as diffusion coefficients. I shall discuss how the physics of frustration in classical spin systems help retain the signatures of chaos even at low temperatures.

Existence and growth of amorphous and other structural order in supercooled liquids approaching glass transition is a subject of intense research. Even after decades of work, there is still no clear consensus on the molecular mechanisms that lead to a rapid slowing down of liquid dynamics approaching this putative transition. The existence of a correlation length associated with amorphous order has recently been postulated and also been estimated using multi-point correlation functions which cannot be calculated easily in experiments. Thus the study of growing amorphous order remains mostly restricted to systems like colloidal glasses and simulations of model glass-forming liquids. We proposed an experimentally realizable yet simple correlation function to study the growth of amorphous order. We then demonstrate the validity of this approach for a few well-studied model supercooled liquids and obtain results, which are consistent with other conventional methods. Finally I will discuss role of the static length-scale associated with this amorphous order in dynamics of glassy systems with medium range crystalline order. We tried to understand the molecular mechanisms for glass transition in liquids with and without medium range crystalline order. The issue is important to answer because if the liquid eventually starts to form crystalline domains while approaching the glass transition then the complexity of the problem may simplify and may just be governed by the physics of the growing crystalline order. If not then there exists a new class of glass forming materials whose molecular mechanism for slowing down of dynamics will probably be easier to understand in terms of the dynamics of the growing medium range crystalline order. We found evidence that dynamics of glasses with medium range crystalline order are generically different from other glass forming liquids with no predominant local order. 

Reference:

1. R Das, S Chakrabarty and S Karmakar, Soft Matter 13, 6929 (2017).

2. S Chakrabarty, I Tah, S Karmakar and C Dasgupta, PRL 119, 205502 (2017).

3. I Tah, S Sengupta, S Sastry, C Dasgupta and S Karmakar, PRL 121, 085703 (2018).

4. BP Bhowmik, I Tah and S Karmakar, PRE, 98, 022122 (2018)."

Understanding how quenched disorder affects the glassy behaviour of materials has been of interest, for quite some time, for example, in the context of type-II superconductors, metallic alloys etc. More recently, specific constructions in the form of pinned particles, have been used to investigate the onset of slow dynamics and exploring the ideal glass transition scenario. In this context, using numerical studies, we will discuss two different situations : (a) the interplay of a simple glass forming liquid with a spatially-varying external potential, motivated by recent optical realisations & (b) yielding dynamics of a glass embedded with impurities.

Though the physical laws at the atomic level interactions of amino acids in proteins are well defined and simple, understanding how proteins work is non-trivial. Protein sequence -> structure -> dynamics is believed to be the key to the hierarchy of their functional organization. There are several gaps in this perspective which are being filled with informatic methods these days. For example, using large scale evolutionary data of sequences to predict the structure or to derive relationship with dynamics. One of the commonly used tools for this purpose is mutual information. The lecture will cover the basics of this informatic method as well as its implications to the understanding of proteins.