Seminar: Geometry-originated universal relation for arbitrary convex hard particles

ABSTRACT

We have discovered that two significant quantities within hard particle systems: the probability of successfully inserting an additional particle at random and the scale distribution function, can be connected by a concise relation. We anticipate that this relation holds universal applicability for convex hard particles. Our investigations encompassed a range of particle shapes, including one-dimensional line segments, two-dimensional disks, equilateral and non-equilateral triangles, squares, rectangles, and three-dimensional spheres. Remarkably, we have observed a close alignment between the two sides of the relation in all cases we examined. Furthermore, we show that this relation can be derived from the fundamental thermodynamic relation that connects entropy, pressure, and chemical potential. Our study unveils a geometrically rooted relation that underpins essential thermodynamic relations, shedding light on the intricate interplay of geometry and thermodynamics in hard particle systems.

References:
[1] D. Wan and S. C. Glotzer, Soft Matter 14, 3012 (2018)
[2] D. Wan. Phys. Rev. E 106, 034609 (2022)
[3] Y. Yang and D. Wan, arXiv: 2310.10551（2024）

BIOGRAPHY

Prof. Duanduan Wan received her B.S. degree from Wuhan University in 2010 and her Ph.D. from Syracuse University in 2016, under the guidance of Prof. Mark J. Bowick. She conducted post-doctoral research at the University of Michigan from 2016 to 2018, working with Prof. Sharon C. Glotzer. In January 2019, she joined the faculty of the School of Physics and Technology at Wuhan University as an Assistant Professor. As of February 2024, she has been promoted to Associate Professor at the same institution. Prof. Wan's primary research areas are soft matter and statistical physics, with a focus on: （1）Self-assembly of nanoparticles and colloidal particles (shape entropy, phase transitions, optical and mechanical properties), （2）Statistical mechanics of elastic membranes (elasticity, renormalization of bending rigidity and elastic moduli at finite temperature), and（3）The interplay between defects and geometry in soft matter systems.