I am currently a graduate student in the Physics Department and James Franck Institute at the University of Chicago. I received my B.S. degree in Physics and Mathematics (Double Degree) from Peking University in 2006. After that, I came to the University of Chicago to continue my study in Physics. I received my M.S degree in Physics in 2007 and expect to defend my PhD thesis in early 2012. My research falls into the areas of theoretical and computational fluid dynamics, singularity formation in dynamical systems, and numerical solution of nonlinear PDEs (see below for more details). Besides that, I also have strong interests in mathematics and computer science, especially improving or inventing efficient and stable algorithms. Right now, I am actively looking for further research opportunities such as a postdoc in related fields in Physics, Engineering and Applied Mathematics. I would be very happy for a further discussion on any research/interests related topics. I can be reached via both email and phone as listed above.
Research Interests [back to top]
I have broad interests in physics and interdisciplinary areas. Among those attract me the most are mathematical physics, fluid dynamics, complex dynamical systems, instability and pattern formation. I would like to approach those problems both analytically by developing simple models to capture the essential physics, and numerically by improving existing algorithms or creating more efficient and stable methods. I am fascinated not only by how small changes in microscopic properties or control parameters lead to qualitatively different behaviors at larger spatial or temporal scales, but also in finding out simple description and understanding underlying superficially complex phenomena. I am also interested in how that knowledge could be used in engineering, especially in how the understanding of motions in fluids (swimming, flying etc.) could lead to innovations in mechanical designs. I am a fan of mathematics as well, especially in Geometry and Topology, and I am very willing to merge them into my future research projects. Besides that, I am interested in using computer simulation to increase our knowledge of Physics. Computers are changing how we can solve problems and I would like to push the limit on how those technologies could improve our understanding about the nature.
Current Project [back to top]
My current research is supervised by Professor Wendy Zhang at the University of Chicago. Our study focuses on how the formation of finite time singularity in free surface flows is affected by initial/boundary conditions. One typical system we investigated is the underwater air bubble breakup.
Physics:
When one bulk of fluid breaks up into smaller pieces, at the breakup point, the area of that fluid shrinks towards zero. Thus, the local stress described by the surface tension multiplied by the local curvature diverges (as well as the velocity field), which corresponds to a physical singularity in finite time. This breakup singularity was thought to be universal, one independent of initial/boundary conditions due to the separation in length/time scale between the singular breakup dynamics and any initial/boundary conditions (one good example of universal behavior is the breakup of water drop in air, a process driven by surface tension). However, previous studies indicated that how an air bubble breaks up (or an air cavity collapses) underwater, a process driven by inertia, doesn't fall into this category and various forms of air bubble breakup are observed in experiments depending on different choices of initial/boundary conditions. (In a hand-waving way, the dependence on initial condition stems from the fact that the dominant flow (water) takes "information" into the region of concern, as opposed to the case of water breakup where water is squeezed out of the neck region. This "memory" of initial conditions is also observed in other setups such as when a less viscous fluid breaks up in a more viscous fluid.) In the axisymetric breakup, imagining the bubble neck about to breakup as a vertical cylinder, then the breakup singularity corresponds to the radius of the minimum cross-section of this cylinder shrinking down to zero. Linear stability analysis has revealed that any azimuthal perturbation to that circular cross-section excites azimuthal vibrations in the form of standing waves. The amplitude of each vibrational mode stays constant while the phase "chirps". As the neck gets thinner, the "constant" amplitude always becomes "large" compared to the typical size of the cross-section. when those two length scales are comparable to each other, the air-water interface is severely distorted. Thus, the dynamics inevitably evolves into a nonlinear region no matter how small the azimuthal perturbation it has initially. Our work focusing on the dynamics in the nonlinear region is thus essential to provide a fundamental understanding to such a problem. Our simulation results show that the symmetric breakup singularity is preempted by those azimuthal vibrations. Different forms of breakup are also observed in simulation, qualitatively consistent with experiments. With the simulation I developed independently using the boundary integral method, we are now able to look through the seemingly complicated outcomes and dig into the fundamental difference among various forms of breakup. They are classified into two categories: one is the smooth contact solution where the interface evolves into self-contact smoothly and the dynamics could be approximated by linear wave model (this work was published in PRL 09, 124501, see also my talk on DFD (Nov, 2008)). The other is the "finger" solution. In the second case, some regions on the interface first develop high curvatures. Water jets resembling the form of fingers are then generated in those highly curved regions. Transition from smooth contact solution to "finger" solution coincides with the interference between lower wave modes going from being constructive to being destructive (paper in preparation and also my short talk on DFD (Nov, 2011)). Furthermore, my simulation using adaptive mesh and time-stepping provides us enough resolution to investigate one possible curvature singularity in the "finger" solution. We found that given the vibrational amplitude, there is a threshold value of initial phase of the azimuthal vibration where the interface appears to evolve towards a curvature singularity. However, when we start with the initial phase identical to that threshold value, the interface actually evolves into a smooth contact. Thus, in this case, the curvature singularity is preempted by smooth contact and can't be realized (thesis in preparation and also see my talk on DFD(Nov, 2010)).
Simulation techniques:
We have implemented two simulation codes in studying this problem:
- Spectral method: In studying wave breaking and Rayleigh-Taylor instability, previous research indicates the existence of one nonlinear transformation which efficiently reduces the degree of nonlinearity while solving potential flow problem with nonlinear boundary conditions. In our case, the Fourier modes in variables after transformation behave closer to normal modes for the azimuthal shape vibrations providing us an easier way to understand the dynamics. Time evolution of each mode is solved numerically and an understanding of the contact solution is obtained assuming the dynamics is linear based on the fact that those Fourier modes are closer to normal modes as mentioned above. Other related techniques are conformal mapping and Fast Fourier Transform (FFT).
- Boundary integral method: This method has been proven to be an efficient way to solve potential flow problems (Laplace's equation). When the surface is reentrant, the spectral method fails due to the fact that conformal mapping intrinsically has a poor resolution in reentrant regions. A simulation using boundary integral method specified for 2D dynamics with prescribed implosion volume flux is implemented to overcome this problem.
Past Projects [back to top]
My undergraduate thesis was supervised by Dr. Miao Li with the title "Review: from Black Hole's Entropy to Holographical Principle". Before that, Haipeng An and I worked together on modeling the asymmetric distribution between electrons and positrons in near earth orbit as observed by Alpha Magnetic Spectrometer (AMS). This work was supervised by Professor Boqiang Ma and supported by the President's Fund of Peking University. As an undergrad, I also participated in designing new experimental courses in the Center of General Physics Experiments. My work focused on designing experiment (including writing manuals) regarding the vibrations and standing waves on a single string.
Publications [back to top]
Asymmetric Disconnection of an Underwater Air Bubble: Persistent Neck Vibrations Evolve into a Smooth Contact, K. S. Turitsyn, L. Lai and W. W. Zhang, Phys. Rev. Lett. 103, 124501 (2009)
In preparation:
Curvature Singularity and Fingers in Air Bubble Breakup under Water, L. Lai (thesis in preparation) Wave Dynamics near Air Bubble Breakup, L. Lai, N. C. Keim, K. Fezzaa, W. W. Zhang, and S. R. Nagel (in preparation) Combining Vibrational Modes in Bubble Breakup, S. D. Oberdick, L. Lai, and W. W. Zhang (in preparation)
Posters, Talks and Videos [back to top]
Posters:
Wave Dynamics near Breakup of Underwater Bubble(Best Poster Award), Dynamics Days, IL (2010)[Download PDF] "Bubble Breakup: Persistence of Asymmetry near a Singularity", Nonlinear Science Gordon Research Conference, MA (2009) [Download PDF]
Talks:
Nonlinear Interference in Bubble Breakup Dynamics, 64th Annual Meeting, American Physical Society - Division of Fluid Dynamics, MD (2011)[Download PDF] [links to movies (cross-section rescaled by its average size)]: movie 1: linear wave (avi, wmv) | movie 2: smooth contact (avi, wmv) movie 3: finger solution (avi, wmv) | movie 4: finger solution - zoom in of the tip (avi, wmv)] Saddle Point Dynamics in Bubble Breakup, 63rd Annual Meeting, American Physical Society - Division of Fluid Dynamics, CA (2010)[Download PDF] Diffraction: Wave Dynamics near Breakup of Underwater Bubble, 62nd Annual Meeting, American Physical Society - Division of Fluid Dynamics, MN (2009)[Download PDF] Asymmetric Bubble Collapse, 61st Annual Meeting, American Physical Society - Division of Fluid Dynamics, TX (2008)[Download PDF]
Videos:
3D bubble breakup (collapse of the bubble neck) reconstructed from 2D simulation results (video produced for APS March Meeting 2009)
Two demos (use Mathematica CDF) I made for the institute's open house -- "Physics with a Bang" (2011) demo 1: random walk | demo 2: smoke diffusion and advection
Awards [back to top]
- Best Poster Award, Dynamics Days, Northwestern University (2010)
- Sachs Fellowship, Physics Department, The University of Chicago (2007)
- Benz Scholarship, Peking University (2002 ¨C 2006) - Four-year fellowship for top students in Peking University
- Third prize in "Jiang Zehan" Mathematical Contest in Modeling at Peking University (2005)
- First prize in Chinese Mathematical Olympiad in High School (provincial level) (2000 and 2001)
- First prize in Chinese Physics Olympiad in High School (provincial level) (2000 and 2001)
Contact [back to top]
I can be reached by email (the best way): lplai@uchicago.edu. Or you could call the phone in my office: (773)702-0946 (which is actually shared by two offices). My "physical" address is:
Gordon Center for Integrative Science The University of Chicago 929 E. 57th St., CIS E208 Chicago, IL 60637
More about Me [back to top]
I have a very broad interest in many things. Here you can find a collection of papers I wrote in college (it is in Chinese though...). I am also fascinated in all sorts of sports - from table tennis, swiming to basketball and skiing. I also like painting, calligraphy, photography and music.