Publications:

A. Works on applied analysis:
  • Dynamics and steady state of squirmer motion in liquid crystal,
    (with L. Berlyand, H. Chi, M. Potomkin), European Journal of Applied Mathematics, 2023, 1-42

  • Stability of Self-similar Solutions to Geometric Flows,
    (with H. Du) Interfaces and Free Boundaries, 25(2023), 155-191

  • Minimal energy configurations of bilayer plates as a polynomial optimization problem,
    (with P. Mohan, T. Yu) Nonlinear Analysis, 2022

  • Energy Scaling and Asymptotic Properties of One-Dimensional Discrete System with Generalized Lennard-Jones (m, n) Interaction,
    (with T. Luo and Y. Xiang), Journal of Nonlinear Science, 31(2021)

  • Invariant measures for stochastic reaction-diffusion equations with weakly disspative nonlinearities,
    (with O. Misiats and O. Stanzhytsky), Stochastics, 2019.

  • Analysis of Diffusion Generated Motion for Mean Curvature Flow in Codimension Two: A Gradient-Flow Approach,
    (with T. Laux), Archive for Rational Mechanics and Analysis, 2018.

  • Asymptotic analysis and homogenization of invariant measures,
    (with O. Misiats and O. Stanzhytski), Stochastics and Dynamics 18(2018), no. 6, 1950015

  • Convergence of diffusion generated motion to motion by mean curvature,
    (with D. Swartz), Communications in Partial Differential Equations, 42(2017), no. 10, pp. 1598-1643

  • Crystalline Motion of Interfaces Between Patterns,
    (with A. Braides, M. Cicalese), Journal of Statistical Physics, 165(2016), no. 2, pp. 274-319

  • Convergence of Space-Time Discrete Thresholding Dynamics to Anisotropic Motion by Mean Curvature,
    (with O. Misiats), Discrete and Continuous Dynamical Systems-Series A, 36(2016), no. 11, pp. 6379-6411

  • Energy Scaling and Asymptotic Properties of Step Bunching in Epitaxial Growth with Elasticity Effects,
    (with T. Luo and Y. Xiang), SIAM Multiscale Modeling and Simulations, 14(2016), 737-771

  • Singular Perturbation and Bifurcation of Diffuse Transition Layers in Inhomogeneous Media, Part II,
    (with C. Huang), Networks and Heterogeneous Media, 10(2015), 897-948

  • Existence and Uniqueness of Invariant Measures for Stochastic Reaction Diffusion Equations in Unbounded Domains,
    (with O. Misiats, O. Stanzhytskyi), Journal of Theoretical Probability, Mar. 2015.

  • Long Time Behavior of Brownian Motion in Tilted Periodic Potential,
    (with L. Cheng), Physica D, 297(2015), 1-32

  • Finite Time Blow-Up of Parabolic Systems with Nonlocal Terms,
    (with F. Li), Indiana University Mathematics Journal, 63(2014), 783-829

  • Singular Perturbation and Bifurcation of Diffuse Transition Layers in Inhomogeneous Media, Part I,
    (with C. Huang), Networks and Heterogeneous Media, 8(2013), 1009-1034

  • A quantitative description of mesh dependence for the discretization of singularly perturbed non-convex problems,
    (with A. Braides), SIAM Journal of Numerical Analysis, 50 (2012), 1883-1898.

  • Renormalized Ginzburg-Landau Energy and the Location of Near Boundary Vortices,
    (with L. Berlyand, V. Rybalko), Networks and Heterogeneous Media, 7 (2012), 179-196

  • On the parabolic Stefan problem for Ostwald Ripening with kinetic undercooling and inhomogeneous driving force,
    (with D. Antonopoulou, G. Karali), Journal of Differential Equations, 252 (2012), 4679-4718

  • Long Time Behavior of Some Epidemic Models,
    (with F. Li), Discrete and Continuous Dynamical Systems (Series B), 16 (2011), 867-881

  • Pulsating Wave for Mean Curvature Flow in Inhomogeneous Medium
    (with N. Dirr, G. Karali) European Journal of Applied Mathematics, 19 (2008) 661-699

  • Nonuniqueness in a Free Boundary Problem from Combustion
    (with A. Petrosyan) Journal of Geometric Analysis, 18 (2008), 1098-1126

  • Structures of Stable Solutions for a One-Dimensional Variational Problem
    ESAIM: Control, Optimisation and Calculus of Variations, 12 (2006) 721-751

  • Pinning and De-Pinning Phenomena in Front Propagation in Heterogeneous Medium
    (with N. Dirr) Interfaces and Free Boundaries, 8 (2006) 79-109

  • Noise and Uniqueness of Motion by Mean Curvature
    (with P. E. Souganidis) Annales de L'Institut Henri Poincare-analyse non lineaire, 21 (2004) 1-23

  • Continuum Limit of a Step Flow Model
    (with R. V. Kohn, T. S. Lo) Materials Research Society Symposium Proceedings, 696 (2002) T1.7.1-T1.7.7.

  • Continuum Theory of Epitaxial Crystal Growth. I
    (with W. E) Journal of Statistical Physics 104 (2001), 221-253.

  • Continuum Limits of Step Flow Models
    (with W. E) International Conference on Differential Equations, Berlin 1999, ed. B. Fiedler, K. Groger, J. Sprekels, Volume 1, 448-453.

  • Stochastic Curvature Driven Flows
    Stochastic Partial Differential Equations and Applications, ed. G. Da Prato, L. Tubaro, Lecture Notes in Pure and Applied Mathematics, 227 (2002), 443-460.

  • Stochastic Motion by Mean Curvature
    Archive for Rational Mechanics and Analysis, 144 (1998), 313--355.

  • Existence of dendritic crystal growth with stochastic perturbations
    Journal of Nonlinear Science, 8 (1998), 491--579.

    B. Works on interdisciplinary sciences:
  • Towards an Understanding of Residual Networks Using Neural Tangent Hierarchy (NTH)
    (Y. Li, T. Luo, N. Yip) CSIAM Trans. Appl. Math., 3(4), 692-760, 2022

  • Infinite server queues in a random fast oscillatory environment
    (Y. Liu, H. Honnappa, S. Tindel, N. Yip) Queueing Systems, 2021

  • Retrospective Approximation for Smooth Stochastic Optimization
    (D. Newton, R. Bollapragada, R. Pasupathy and N. K. Yip) OPT2020: 12th Annual Workhop on Optimization for Machine Learning

  • Optically Modulated Electrokinetic Manipulation and Concentration of Colloidal particles near an Electrode Surface
    (A. Kumar, J.-S. Kwon, S. J. Williams, N. G. Green, N. K. Yip, S. T. Wereley), Langmuir, 26(7) (2010), 5262-5272

  • Optically Diffusometry Techniques and Applications in Biological Agent Detection
    (A. Kumar, V. M. Gorti, H. Shang, G. U. Lee, N. K. Yip, S. T. Wereley), Journal of Fluids Engineering, 130(7) (2008), 111401(1-8)

  • Privacy Vulnerabilities of Published Anonymous Mobility Traces
    (C. Y. T. Ma, D. K. Y. Yau, N. K. Yip, N. S. V. Rao), IEEE Transactions on Networking, 2012.
    (See also: Privacy Vulnerabilities of Published Anonymous Mobility Traces, Proc. The 16th Annual International Conference on Mobile Computing and Networking (MobiCom), Chicago IL, Sept. 2010)

  • Stochastic Steepest Descent Optimization of Multiple-Objective Mobile Sensor Coverage
    (C. Y. T. Ma, D. K. Y. Yau, N. K. Yip, N. S. V. Rao, J. Chen), IEEE Transactions on Vehicular Technology, 61 May 2012, 1810-1822.
    (See also: Stochastic Steepest Descent Optimization of Multiple-Objective Mobile Sensor Coverage, Proc. The 30th International Conference on Distributed Computing Systems (ICDCS), Genoa, Italy, Jun. 2010)

  • Quality of Monitoring of Stochastic Events by Periodic and Proportional-Share Scheduling of Sensor Coverage
    (D. K. Y. Yau, N. K. Yip, C. Y. T. Ma, N. S. V. Rao, M. Shankar), ACM Transactions on Sensor Networks (TOSN), 7(2) Article 18, Aug. 2010.
    (See also: Quality of Monitoring of Stochastic Events by Periodic and Proportional-Share Scheduling of Sensor Coverage, Proc. ACM International Conference on Emerging Networking Experiments and Technologies (CoNEXT), Madrid, Spain, Dec. 2008)

  • On Optimal Information Capture by Energy-Constrained Mobile Sensors
    (S He, J. Chen, Y. Sun, D. K. Y. Yau, N. K. Yip), IEEE Transactions on Vehicular Technology, 59(5) May, 2010, 2472-2484.
    (See also: On Optimal Information Capture by Energy-Constrained Mobile Sensors, 17th International Workshop on Qaulity of Service, 2009. IWQoS, 2009)

  • Performance Analysis of Stochastic Network Coverage with Limited Mobility
    (C. Y. T. Ma, D. K. Y. Yau, N. K. Yip, N. S. V. Rao, J. Chen), Proc. IEEE International Conference on Mobile Ad-hoc and Sensor Systems (MASS), Macau, China, Oct. 2009