This summer school provides a week-long introduction to the field of theoretical, computational, and experimental soft matter and biophysics. Soft matters, including biomaterials, colloids, and polymers, etc. are essential in our daily life. Understanding the structure, function, and dynamics of soft matters as well as their interplay is crucial in the fields of biology, chemistry, and material science, etc. Our program brings together internationally recognized experimentalists, modelers, and theoreticians to illustrate the diverse approaches in this exciting field. The 2018 summer school on soft matter and biophysics is sponsored by the Institute of Natural Sciences at Shanghai Jiao Tong University, and the National Natural Science Foundation of China.

July 1 - 5, 2018

Room 601, Pao Yue-Kong Library, Minhang Campus, Shanghai Jiao Tong University, No.800 Dongchuan Road

Please register online. Apply Online

No registration fee. Participants should cover their own lodging and meals.

- Heng Xu, Shanghai Jiao Tong University
- Liang Hong, Shanghai Jiao Tong University
- Zhenwei Yao, Shanghai Jiao Tong University
- Hepeng Zhang, Shanghai Jiao Tong University
- Jie Zhang, Shanghai Jiao Tong University

- Raphael Blumenfeld, Imperial College London
- Walter Kob, University Montpellier
- Ralf Metzler, University of Potsdam
- Keith Weninger, North Carolina State University

Date | Time | Speaker |

July 1 | 14:00 ~ 15:00 | Ralf Metzler |

July 1 | 15:30 ~ 16:30 | Ralf Metzler |

July 2 | 09:00 ~ 10:00 | Ralf Metzler |

July 2 | 10:30 ~ 11:30 | Ralf Metzler |

July 2 | 14:00 ~ 15:00 | Raphael Blumenfeld |

July 2 | 15:30 ~ 16:30 | Raphael Blumenfeld |

July 3 | 09:00 ~ 10:00 | Walter Kob |

July 3 | 10:30 ~ 11:30 | Walter Kob |

July 3 | 14:00 ~ 15:00 | Keith Weninger |

July 3 | 15:30 ~ 16:30 | Keith Weninger |

July 4 | 09:00 ~ 10:00 | Raphael Blumenfeld |

July 4 | 10:30 ~ 11:30 | Raphael Blumenfeld |

July 4 | 14:00 ~ 15:00 | Walter Kob |

July 4 | 15:30 ~ 16:30 | Walter Kob |

July 5 | 09:00 ~ 10:00 | Keith Weninger |

July 5 | 10:30 ~ 11:30 | Keith Weninger |

July 5 | 14:00 ~ 16:30 | Discussion |

*Raphael Blumenfeld, Imperial College London and Cambridge University*

In this short course I will present advances on two important problems in the physics of particulate systems. One is the formulation of statistical mechanics for such a-thermal systems and the other is the development of a stress field theory for idealised granular materials. The introduction of statistical mechanics to a-thermal particulate systems jump-started the field as a rigorous branch of soft matter physics. I will review briefly the Edwards formalism, which was extended to cellular and porous materials, and highlight some of the problems with the early formulations. I will discuss how those problems are overcome. I will then illustrate the usage of the improved formulation for deriving an equation of state and an equivalent of the equipartition principle. I will discuss the different types of entropy associated with the formalism and use this discussion to highlight, and point to the resolution of, a current debate in the field regarding the extensivity of the entropy in these systems. Time permitting I will discuss the extension of this formalism to slow dynamics of dense particulate systems, thus bridging for the first time between statics and dynamics of these non-ergodic systems. In the second part of the course, I will discuss the uniquely non-uniform manner by which jammed granular matter transmits stress. Jamming is caused by self-organization of the material under external loads, often resulting in what is known as force chains. The development of a continuum field theory to describe such stresses has been ongoing since the mid 90s. I will present the current state of the art in this field, show that the stress in idealised such materials cannot be described by any strain-based theory, which also invalidates elasticity theory. I will present the emergent new theory and show that it gives rise to rich and sometimes strange solutions, all of which observed experimentally. Time permitting, I will show that the nature of the jamming transition as a critical point means that the solutions for the idealised systems persist even for non-ideal systems and give us a handle on constructing a stress theory for more realistic systems, which should be regarded as two phase materials: one ideal and the other over-connected, thus paving the way to a new stato-elasticity theory.

*Relevant references*

(I) Statistical mechanics:

1. R. Blumenfeld and S. F. Edwards, Phys. Rev. Lett. 90, 114303 (2003);

2. R. Blumenfeld and S. F. Edwards, Eur. Phys. J. E 19 , 23 (2006);

3. R. Blumenfeld et al., Phys. Rev. Lett. 116, 148001 (2016);

4. S. Amitai and R. Blumenfeld, Phys. Rev. E 95, 052905 (2017);

5. D. Asenjo et al., Phys. Rev. Lett. 112, 098002 (2014);

6. R. Blumenfeld et al., Phys. Rev. Lett., 119, 039802 (2017);

7. S. Martiniani et al., Phys. Rev. E 93, 012906 (2016).

(II) Stress theory:

1. R. C. Ball and R. Blumenfeld, Phys. Rev. Lett., 88, 115505 (2002);

2. R. Blumenfeld, Phys. Rev. Lett. 93, 108301 (2004);

3. M. Gerritsen et al., Phys. Rev. Lett. 101, 098001 (2008);

4. R. Blumenfeld and J. Ma, J. Gran. Matt.19:29 (2017).

*Walter Kob, University of Montpellier*

Many properties of gases and crystals are well understood and thus can be found in most textbooks of condensed matter physics. The third state of matter, liquids, is understood much less since the absence of long range order makes it much harder to describe systems like liquids, glasses, foams, granular materials, polymers, etc. and therefore new concepts and tools are needed to describe such materials.

In these lectures I will give a brief introduction to the liquid state by discussing the quantities that one uses to characterize the static properties of these systems (static structure factor, radial distribution functions, direct correlation functions, many body correlation functions). Subsequently I will discuss the virial equation, as well as the energy and pressure equations. To conclude the static part I will present the so-called Percus-Yevick theory (including the Ornstein-Zernike equation) and the hypernetted chain approximations, two powerful theoretical approximations that are often used to obtain the static properties of liquids.
The second part of the lectures will be devoted to the dynamics of disordered systems. For this I will introduce quantities like the van Hove function, the intermediate scattering functions, dynamic susceptibilities,..). After having derived the BBGKY hierarchy I will present the so-called Vlasov equation and the resulting Boltzmann equation. Then I will discuss concepts like the de Gennes narrowing, the velocity-autocorrelation functions, the projection operator formalism as well as the mode-coupling approximations.

The goal of these lecture is to give a solid theoretical background that will allow participants to analyze in a rational manner the data from experiments and computer simulations of disordered materials.

*Ralf Metzler, University of Potsdam, Germany*

In this lecture course, I will first introduce the basic concepts of stochastic processes: random walks, Brownian motion, and the diffusion equation. In particular, the role of the central limit theorem, enforcing a Gaussian shape of the probability density function, will be addressed. The seminal experiments behind these theoretical approaches will be introduced. Motivated from these the concept of a random force will be defined and the Langevin equation discussed.

The concepts of diffusive motion will then be applied to the generic biological question of the search of regulatory proteins for their specific binding sites on a DNA molecule, in the process of gene regulation. As we see, dimensional reduction in the search process is an essential ingredient for the speed-up of this random search. Moreover, even in the confines of bacteria cells of less than a micron cubed in volume, the distance between release of the protein and its designated binding site matter.

In a next step widely observed deviations from the laws of regular, normal Brownian diffusion will be discussed: anomalous diffusion is seen in a massive range of systems, from semiclassical systems over microscopic biological cells up to the ranges of geophysical processes. Consequences are that statistical concepts such as ergodicity are violated and the shapes of the probability density may become non-Gaussian or the Markovian nature of the stochastic process violated. Specific processes discussed will be the continuous time random walk and fractional Brownian motion.

Some specific anomalous diffusive systems will be discussed in more detail: the motion of micron-sized tracer particles in complex liquids or inside a biological cell as well as individual molecules diffusing inside the sheet of a membrane. The role of crowding will be addressed from various aspects such as simulations and experiments.

*Further reading*

[1] R Zwanzig, Nonequilibrium statistical mechanics

[2] N van Kampen, Stochastic processes in physics & chemistry

[3] K Norregaard, R Metzler, C Ritter, K Berg-Sorensen, and L Oddershede, Manipulation and motion of organelles and single molecules in living cells, Chem Rev 117, 4342 (2017); open access review article

[4] R Metzler, J-H Jeon, A G Cherstvy, and E Barkai, Anomalous diffusion models and their properties: non-stationarity, non-ergodicity, and ageing at the centenary of single particle tracking, Phys Chem Chem Phys 16, 24128 (2014); open access review article

*Keith Weninger, North Carolina State University*

These lectures will focus on the field of single molecule biophysics. Most biochemical experimental methods measuring interactions between biological molecules provide average behaviors of millions or more molecular events in a liquid sample. Many processes in biology involve molecular interactions that are not synchronized in time or for which there are multiple pathways. Averaging over such ensembles often obscures the underlying molecular individuality important for key biological functions. The emergence of the field of single molecule biophysics measures behavior of molecules one at a time and does not suffer from the limitations of averaging over ensembles. In 4 lectures, a general overview of single molecule methods and applications will be provided. I will give particular focus to fluorescence resonance energy transfer (FRET) methodology and applications in the areas of DNA repair and intrinsically disordered proteins.