Overview

Phase transitions are common occurrences observed in nature and many engineering techniques exploit certain types of phase transition. A phase transition is the transformation of a thermodynamic system from one phase or state of matter to another. Phase transitions often (but not always) take place between phases with different symmetry. Generally, we may speak of one phase in a phase transition as being more symmetrical than the other. The transition from the more symmetrical phase to the less symmetrical one is a symmetry-breaking process. When symmetry is broken, one needs to introduce one or more extra variables (order parameter) to describe the state of the system. The order parameter may take the form of a complex number, a vector, or even a tensor, the magnitude of which goes to zero at the phase transition. The study in phase transitions involves a combination of modeling, simulation, mathematical analysis and physical predictions.

Phase transition has now become an important field in the interdisciplinary researches. This approach has been widely applied in the research of applied mathematics, physics, chemistry, biology, and material science. The purpose of the program is to bring together people from these different disciplines, to contribute their recent researches, exchange the ideas and discuss further topics.

We will invite leading experts in phase transitions from those fields to introduce their researches at one workshop and give tutorial courses to cover both theoretical materials as well as most recent research results. Interdisciplinary discussion will be run twice a week. Major topics to be covered include modeling and simulation of phase transitions, phase diagram of complex systems, nucleation and rare events, phase transition in non-equilibrium systems, characterization on stability and transition etc.

The program participants will:

  1.present recent development in mathematical theories, including modeling, analysis and computational techniques that is relevant to phase transition.

  2.discuss and compare different, recent-proposed phase transition models related to the latest emerging applications.

  3.identify critical scientific issues in the understanding of phase transition and difficulties of common interest within different disciplines as well as issues that are specific to individual areas.

  4.accelerate the interaction of mathematicians and applied scientists by stimulating lively debate on important research issues related to phase transition, and promote the highly interdisciplinary research with emerging applications and cross fertilization of ideas.

  5.develop and foster international and local collaborations of scientific researches in phase transition.

Visitors and Participants

• - Overseas visitors
• - Local visitors
• - Graduate students
• - Registered local participants

Activities

The program activities will consist of the international summer school, two workshops, tutorial lectures, working seminars and collaborative research.

1. Collaborative research: 1 Sep 2011 - 31 Dec 2011
During the period of the program, Beijing International Center for Mathematical Research will provide an excellent research environment for local and international visitors from applied and pure mathematics, physics, chemistry, materials science and computational science to discuss and to conduct collaborating research.

2. International Summer School: 12 - 23 Sep 2011 - [Schedule]
Title: Phase Transitions and Metastability
Mini courses:
Ralf Kornhuber: Nonlinear PDE models and associated simulation methods for phase transitions
Christof Schütte: Metastability and Dynamics of Phase Transitions
An-Chang Shi: Physics of Phase Transitions
Weinan E: Metastability, Rare Events and Spectral Geometry

3. Workshop I: 26 - 28 Sep 2011
Title: Nucleation and Rare Events
Rationale: This workshop will focus on recent developments in mathematical theory and computational methods in nucleation and rare events with applications in materials science, biophysics and chemistry as well as complex fluids. Participants are a combination of pure and applied mathematicians and theoretical and computational material scientists, biophysicists and/or chemists.

4. Workshop II: 7 - 11 Nov 2011 - [Schedule]
Title: Mathematical Theory and Simulation of Phase Transitions
Rationale: This workshop will focus on recent developments in mathematical theory and computational methods in phase transition with applications in quantum physics, materials science，biophysics and chemistry as well as complex fluids. Participants will explore rigorous analysis, efficient simulation algorithms, and emerging applications in some fields with modeling and simulation of phase transitions, phase diagram of complex systems, nucleation and rare events, phase transition in non-equilibrium systems, characterization on stability and transition etc. Participants are a combination of pure and applied mathematicians and theoretical and computational material scientists, physicists and/or chemists.

5. Tutorial lectures
Distinguished researchers will give tutorial lectures on topics in physical modeling, mathematical theory, computational methods and applications related to phase transition and applications.

Students and researchers who are interested in attending these activities (except invited participants) and who do not require financial aid are requested to send an e-mail to Ying Sun (sunying_bicmr@yahoo.cn), Xianghui Yu (xianghuiyu@gmail.com).