About

Bo Li is a faculty member in the Department of Mathematics at UC San Diego. He holds a Ph.D. in Mathematics from the University of Minnesota, obtained in 1996. His research areas include Mathematical Modeling and Applied Analysis, Mathematical Biology, Biological Physics, Continuum Mechanics, Applied PDE and Dynamical Systems, Numerical Analysis, and Scientific Computing. His work focuses on applying mathematical techniques to biological and physical systems, developing models and computational methods to understand complex phenomena in these fields.

Research topics

• Computer Science
• Physics
• Quantum mechanics
• Mathematics
• Chemistry
• Classical mechanics
• Geometry
• Telecommunications
• Condensed matter physics
• Chemical physics
• Statistical physics
• Computational chemistry

Selected publications

• Fractional Bessel Operators of Order Near Zero

  Mediterranean Journal of Mathematics · 2025-09-08

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  PublisherDOI

• Spatiotemporal development of expanding bacterial colonies driven by emergent mechanical constraints and nutrient gradients

  Nature Communications · 2025-05-26 · 14 citations

  articleOpen access

  Bacterial colonies growing on solid surfaces can exhibit robust expansion kinetics, with constant radial growth and saturating vertical expansion, suggesting a common developmental program. Here, we study this process for Escherichia coli cells using a combination of modeling and experiments. We show that linear radial colony expansion is set by the verticalization of interior cells due to mechanical constraints rather than radial nutrient gradients as commonly assumed. In contrast, vertical expansion slows down from an initial linear regime even while radial expansion continues linearly. This vertical slowdown is due to limitation of cell growth caused by vertical nutrient gradients, exacerbated by concurrent oxygen depletion. Starvation in the colony interior results in a distinct death zone which sets in as vertical expansion slows down, with the death zone increasing in size along with the expanding colony. Thus, our study reveals complex heterogeneity within simple monoclonal bacterial colonies, especially along the vertical dimension. The intricate dynamics of such emergent behavior can be understood quantitatively from an interplay of mechanical constraints and nutrient gradients arising from obligatory metabolic processes.

  PublisherOA PDFDOI

• On the Dirichlet problem for the elliptic equations with boundary values in variable Morrey-Lorentz spaces

  Journal of Differential Equations · 2024-06-27 · 5 citations

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• Second harmonic of higher-order Poincaré sphere beam with two orthogonal 5%MgO:PPLN crystals

  APL Photonics · 2024-05-01 · 7 citations

  articleOpen access

  In this work, the second harmonic (SH) of higher-order Poincaré sphere (HOPS) beam was introduced and demonstrated with two orthogonal 5%MgO:PPLN crystals. Based on the quasi-phase-matching technique, the vectorial coupled wave equations were derived to simulate the SH of HOPS beams through the two crystals, including the cylindrical vector beams (CVBs), elliptically polarized CVBs (EPCVBs), and circularly polarized vortex beams. Then, the experimental setup was established to reveal that the SH of CVBs and EPCVBs present the four-lobed structure and still exhibit vector characteristics. Meanwhile, the circularly polarized vortex beams become the linearly polarized vortex beams with double phase topology, confirming the conservation of orbital angular momentum. Moreover, the maximum SH conversion efficiency of CVBs, EPCVBs, and circularly polarized vortex beams can reach 25.3%, 23.4%, and 29.4%, respectively, which may be instructive for promoting the SH generation of vector vortex beams with high efficiency.

  PublisherOA PDFDOI

• Variational implicit solvation with Legendre-transformed Poisson–Boltzmann electrostatics

  Proceedings of the Royal Society A Mathematical Physical and Engineering Sciences · 2024-03-01 · 1 citations

  articleSenior authorCorresponding

  The variational implicit-solvent model (VISM) is an efficient approach to biomolecular interactions, where electrostatic interactions are crucial. The total VISM free energy of a dielectric boundary (i.e. solute–solvent interface) consists of the interfacial energy, solute–solvent interaction energy and dielectric electrostatic energy. The last part is the maximum value of the classical and concave Poisson–Boltzmann (PB) energy functional of electrostatic potentials, with the maximizer being the equilibrium electrostatic potential governed by the PB equation. For the consistency of energy minimization and computational stability, here we propose alternatively to minimize the convex Legendre-transformed Poisson–Boltzmann (LTPB) electrostatic energy functional of all dielectric displacements constrained by Gauss’ Law in the solute region. Both integrable and discrete solute charge densities are treated, and the duality of the LTPB and PB functionals is established. A penalty method is designed for the constrained minimization of the LTPB functional. In application to biomolecular interactions, we minimize the total VISM free energy iteratively, while in each step of such iteration, minimize the LTPB energy. Convergence of such a min–min algorithm is shown. Our numerical results on the solvation of a single ion indicate that the LTPB performs better than the PB formulation, providing possibilities for efficient biomolecular simulations.

  PublisherDOI

• Finite-Difference Approximations and Local Algorithm for the Poisson and Poisson-Boltzmann Electrostatics

  arXiv (Cornell University) · 2024-09-24

  preprintOpen access1st authorCorresponding

  We study finite-difference approximations of both Poisson and Poisson-Boltzmann (PB) electrostatic energy functionals for periodic structures constrained by Gauss' law and a class of local algorithms for minimizing the finite-difference discretization of such functionals. The variable of Poisson energy is the vector field of electric displacement and that for the PB energy consists of an electric displacement and ionic concentrations. The displacement is discretized at midpoints of edges of grid boxes while the concentrations are discretize at grid points. The local algorithm is an iteration over all the grid boxes that locally minimizes the energy on each grid box, keeping Gauss' law satisfied. We prove that the energy functionals admit unique minimizers that are solutions to the corresponding Poisson's and charge-conserved PB equation, respectively. Local equilibrium conditions are identified to characterize the finite-difference minimizers of the discretized energy functionals. These conditions are the curl free for the Poisson case and the discrete Boltzmann distributions for the PB case, respectively. Next, we obtain the uniform bound with respect to the grid size h and O(h2)-error estimates in maximum norm for the finite-difference minimizers. The local algorithms are detailed, and a new local algorithm with shift is proposed to treat the general case of a variable coefficient for the Poisson energy. We prove the convergence of all these local algorithms, using the characterization of the finite-difference minimizers. Finally, we present numerical tests to demonstrate the results of our analysis.

  PublisherOA PDFDOI

• Deterministic relation between thermal-phonon dressings and a non-Hermitian multi-Fano interferences router in ion-doped microcrystals

  Chip · 2023 · 27 citations

  • Computer Science
  • Physics
  • Condensed matter physics

  We report the multi-Fano interference obtained through the simultaneous acquisition of bright and dark states in different phase transitions of Eu3+: BiPO4 (7:1, 6:1, 1:1, and 0.5:1) and Eu3+: NaYF4 (1:1/4) crystals. We employ multi-dressed spontaneous four-wave mixing and multi-dressed fluorescence (multi-order) to optimize the strong photon-phonon nested dressing effect resulting in more obvious multi-Fano interference. Firstly, the multi-Fano is produced through interference in continuous and multi-bound states. Secondly, five multi-Fano dips originate from nested five dressings (one photon and four phonons) under symmetrical splitting of 7F1 energy level. We depict that the pure H-phase (0.5:1) sample exhibits the strongest photon-phonon dressed effect (five Fano dips). Further, we investigate high-order non-Hermitian exceptional points in multi-Fano interference by adjusting the ratio of Rabi-frequency to de-phase rate through nested photon and phonon dressing. Our experimental results are validated by theoretical simulations, which may be applied to designing optoelectronic devices such as non-Hermitian multi-Fano interferences (multi-channel) router.

  PublisherDOI

• Cell Polarity and Movement with Reaction-Diffusion and Moving Boundary: Rigorous Model Analysis and Robust Simulations

  SIAM Journal on Applied Mathematics · 2023-11-16

  articleSenior author

  .Cell polarity and movement are fundamental to many biological functions. Experimental and theoretical studies have indicated that interactions of certain proteins lead to the cell polarization which plays a key role in controlling the cell movement. We study the cell polarity and movement based on a class of biophysical models that consist of reaction-diffusion equations for different proteins and the dynamics of a moving cell boundary. Such a moving boundary is often simulated by a phase-field model. We first apply the matched asymptotic analysis to give a rigorous derivation of the sharp-interface model of the cell boundary from a phase-field model. We then develop a robust numerical approach that combines the level-set method to track the sharp boundary of a moving cell and accurate discretization techniques for solving the reaction-diffusion equations on the moving cell region. Our extensive numerical simulations predict the cell polarization under various kinds of stimuli and capture both the linear and the circular trajectories of a moving cell for a long period of time. In particular, we have identified some key parameters controlling different cell trajectories that are less accurately predicted by reduced models. Our work has linked different models and also developed tools that can be adapted for the challenging three-dimensional simulations.Keywordscell polaritycell movementreaction-diffusion equationsinterface dynamicsmatched asymptotic analysisthe level-set methodMSC codes65M0692C17

  PublisherDOI

• A revisit to “On BMO and Carleson measures on Riemannian manifolds”

  Proceedings of the Royal Society of Edinburgh Section A Mathematics · 2023-07-18 · 9 citations

  article1st author

  Let $\mathcal {M}$ be an Ahlfors $n$ -regular Riemannian manifold such that either the Ricci curvature is non-negative or the Ricci curvature is bounded from below together with a bound on the gradient of the heat kernel. In the paper [IMRN, 2022, no. 2, 1245-1269] of Brazke–Schikorra–Sire, the authors characterised the BMO function $u : \mathcal {M} \to \mathbb {R}$ by a Carleson measure condition of its $\sigma$ -harmonic extension $U:\mathcal {M}\times \mathbb {R}_+ \to \mathbb {R}$ . This paper is concerned with the similar problem under a more general Dirichlet metric measure space setting, and the limiting behaviours of BMO & Carleson measure, where the heat kernel admits only the so-called diagonal upper estimate. More significantly, without the Ricci curvature condition, we relax the Ahlfors regularity to a doubling property, and remove the pointwise bound on the gradient of the heat kernel. Some similar results for the Lipschitz function are also given, and two open problems related to our main result are considered.

  PublisherDOI

• Mechanistic insights into the role of calcium in the allosteric regulation of the calmodulin-regulated death-associated protein kinase

  Frontiers in Molecular Biosciences · 2022-12-19 · 6 citations

  articleOpen access

  Calcium (Ca 2+ ) signaling plays an important role in the regulation of many cellular functions. Ca 2+ -binding protein calmodulin (CaM) serves as a primary effector of calcium function. Ca 2+ /CaM binds to the death-associated protein kinase 1 (DAPK1) to regulate intracellular signaling pathways. However, the mechanism underlying the influence of Ca 2+ on the conformational dynamics of the DAPK1−CaM interactions is still unclear. Here, we performed large-scale molecular dynamics (MD) simulations of the DAPK1−CaM complex in the Ca 2+ -bound and-unbound states to reveal the importance of Ca 2+ . MD simulations revealed that removal of Ca 2+ increased the anti-correlated inter-domain motions between DAPK1 and CaM, which weakened the DAPK1−CaM interactions. Binding free energy calculations validated the decreased DAPK1−CaM interactions in the Ca 2+ -unbound state. Structural analysis further revealed that Ca 2+ removal caused the significant conformational changes at the DAPK1−CaM interface, especially the helices α1, α2, α4, α6, and α7 from the CaM and the basic loop and the phosphate-binding loop from the DAPK1. These results may be useful to understand the biological role of Ca 2+ in physiological processes.

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Recent grants

• Hybrid Computational Models and Robust Numerical Methods for Electrostatic Interactions in Biomolecules

  NSF · $280k · 2013–2017

• Level-Set Variational Implicit-Solvent Approach to Biomolecular Interactions

  NIH · $1.2M · 2010–2015

• Computational Modeling and Numerical Analysis of Solvation of Molecules

  NSF · $160k · 2008–2012

• Collaborative Research: Hybrid Finite-Element Level-Set Methods for Stress-Driven Interface Dynamics

  NSF · $119k · 2004–2008

• Numerical Methods for Fluctuating Motion of Interface

  NSF · $300k · 2016–2020

Frequent coauthors

• J. Andrew McCammon

  University of California, San Diego

  84 shared

• Joachim Dzubiella

  50 shared

• Shenggao Zhou

  Shanghai Jiao Tong University

  38 shared

• Li‐Tien Cheng

  University of California, San Diego

  38 shared

• Jianwei Che

  33 shared

• Yang Xie

  University of California, San Diego

  9 shared

• Kai Chen

  Guangzhou Women and Children Medical Center

  8 shared

• Zhong-Ming Wang

  Central South University

  6 shared