Xueying Wang(王雪莹)

I am a PhD student in the Department of Physics
at the University of Illinois at Urbana-Champaign.
I work with Professor Nigel Goldenfeld.

I am interested in critical phenomenon, non-equilibrium phase transition and turbulence.

You can find my CV here.

About me


University of Illinois at Urbana Champaign (UIUC)
Doctor of Philosophy in Physics
Research advisor: Professor Nigel Goldenfeld
Aug 2017 - present
Tongji University
Bachelor of Science in Applied Physics
Graduated with "Outstanding Graduates" award
Sep 2013 - Jun 2017


Programming:C, C++, Python, MATLAB, Mathematica
Software & Tools:LaTeX, Linux/Unix, Origin, Inkscape
Language:Chinese (native) , English (fluent), French (beginner)


Outstanding Bachelor Thesis Research Award of Tongji University
Shanghai Outstanding Graduates Award
China National Scholarship

Employee experience

Research assistantJun 2019 - present
Teaching assistant of physics department at UIUCAug 2017 - May 2019
Summer research internship at University of British ColumbiaJul 2016 - Sep 2016
Teaching assistant of physics laboratory at Tongji UniversityOct 2013 - Jul 2014


Generally speaking, I am interested in solving foundamental problems in physics using the tool of statistical mechanics.
I am particularly interested in critical phenomenon, non-equilibrium phase transition and turbulence, because the idea of universality these problems imply reveals the subtly and beauty in physics laws of nature.

Transition to turbulence

I am currently working on transition to turbulence from the prospective of non-equilibrium phase transition. Viewing the dynamics near the critical point as a result of the interaction and competition for energy between different modes, I model and analyze various behaviors of turbulent structures.

Generally, fluid becomes turbulent when Reynolds number is very large. When Reynolds number tends to infinity, it approaches a state known as fully developed turbulence. In this regime, fluid system satisfies both Kolmogorov's first and second similarity hypothesis and as a result the -5/3 scaling law. I am, however, working in a regime where Reynolds number is not that large. In this regime, the system satisfies Kolmogorov's first similarity hypothesis, but not the second one, and so the energy spectrum collapse onto a single curve with no inertial subrange, but exhibit the same small scale energy dissipation as higher Reynolds number turbulence.

There are two routes to turbulence, one is through a supercritical bifurcation where the system experiences a smooth, continuous transition to turbulence when Reynolds number is increased, and the other is through a subcritical bifurcation where the transition to turbulence is abrupt and discontinuous. I am interested the latter case that shows up in shear flow systems like pipe flow, channel flow, plane Couette flow and Taylor-Couette flow under some boundary conditions.

The subcritical transition to turbulence is believed, following Pomeau's pioneering idea, to be a non-equilibrium phase transition that belongs to the universality class of Directed Percolation. While numerous experimental and DNS works have proved the statement correct near the critical point, we seek to build a phenomenological model that describes the long wave length behavior of the system near the critical point and understand the interaction of the competing modes that gives rise to the phase transition (just like what Landau did for the equilibrium phase transition of the ferromagnetism transition).

A pioneering work in this direction is done by my collaborators. From DNS of Navier-Stokes equation in pipe flow geometry, they found an activator-inhibitor oscillation between the energy of two low energy modes, the local turbulence and a large-scale flow mode known as zonal flow. Turbulence activates the system and causes zonal flow energy to grow, while zonal flow shears turbulence and inhibits the growth of it. This model gives the correct statistics of turbulent puff splitting and decaying as well as the Directed Percolation statistics near the critical point.

However, this model fails to show the dynamical behavior of the system like the effective interaction between local turbulence spots and the expansion of turbulence spots, which are of great importance in understanding the route to turbulence. The reason the model fails in these aspect is that it neglected the interaction between mean flow and turbulence, which is precisely what gives these dynamical behaviors.

I took the interaction between mean flow and turbulence into consideration. This idea is as follows. Turbulence consumes energy in mean flow. Mean flow advects turbulence. So, stronger turbulence gets advected slower then weaker turbulence. Thus, the effective interaction between local turbulence spots is explained.

This revised model gives the correct phenomenology of what is known as turbulent puff, turbulent weak slug, turbulent strong slug in pipe flow and the statistics of puff splitting, puff decaying and Directed Percolation scaling behaviors. Preliminary results are shown below.

Puff Worldline

Snapshot of Puff Aplitude Profile

Weak Slug Worldline

Snapshot of Weak Slug Profile

Strong Slug Worldline

Snapshot of Strong Slug Profile

Worldline of puff splitting events

This model can do even more than that. By making slight changes to the model, it should be able to predict the dynamical behavior of other systems like channel flow and plane Couette flow near the critical point. More results to be expected in the near future.

Dynamics of large-scale circulation in turbulent rotating Rayleigh-Bénard convection

In my undergraduate years, I worked on the dynamics of large-scale circulation in turbulent rotating Rayleigh-Bénard convection. My collaborator built the Rayleigh-Bénard convection cell on a slowly rotating plain and operated it in the parameter regime where the large-scale circulation shows up. They measured how the average azimuthal rotating speed of the large-scale circulation plain changes with the Rossby number. In large Rossby number region, they discovered an unexpected growth of the relative retrograde azimuthal rotating speed of circulation plain with increasing Rossby number. This phenomenon could not be explained by existing theories.

From the experimental data, we found out that the growth of relative retrograde rotation speed is caused by rare stochastic events like cessation and reversal of the circulation plain that are neglected by existing theories. During these rare events, the circulation plain rotates much faster than usual.

To quantitatively check how much the rare events contribute to the abnormal growth, we started from the idea of an early model and a revised theory based on it, where the system is described by two Langevin equations with additive white noise that captures the dynamics of the azimuthal angular motion and the strength of the circulation plain.

By decoupling the linear rotating component, we were able to reduce the model to an Ornstein-Uhlenbeck process-like form and further estimate theoretical values of frequencies of rare events and average azimuthal displacement per event at different Rossby number region. Based on these values, we calculated theoretically how much the rare events contribute to total relative rotation speed, which agrees very well with experimental values. Thus, our guess was confirmed and the abnormal increase of rotation speed was explained -- the behavior of the large-scale circulation during those stochastic rare events really are the major cause of the unexpected growth in retrograde relative plain rotation speed.

We also estimated correction to previous models from Reynolds stress by fitting the probability distribution functions of plain rotation speed and circulation strength.

I did part of the theory (the stochastic calculus part) and most of the data analysis for this project.

Other ongoing and future projects

Besides turbulence, I am also working on projects like dynamical pattern formation and phase transition in laser systems and using Renormalization Group to solve differential equations. I am also interested in Neuroscience and would like to understand how brains work.


Jin-Qiang Zhong, Hui-Min Li, Xue-Ying Wang. Enhanced azimuthal rotation of the large-scale flow through stochastic cessations in turbulent rotating convection with large Rossby numbers. Phys. Rev. Fluids 2, 044602(2017).