Publications:

A. Works on applied analysis:

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 OneDimensional Discrete System with Generalized LennardJones (m, n)
Interaction,
(with T. Luo and Y. Xiang),
Journal of Nonlinear Science, 31 (2021)

Invariant measures for stochastic
reactiondiffusion 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 GradientFlow 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. 15981643

Crystalline Motion of Interfaces
Between Patterns,
(with A. Braides, M. Cicalese),
Journal of Statistical Physics,
165(2016), no. 2, pp. 274319

Convergence of SpaceTime Discrete
Thresholding Dynamics to Anisotropic Motion by Mean Curvature,
(with O. Misiats),
Discrete and Continuous Dynamical SystemsSeries A,
36(2016), no. 11, pp. 63796411

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), 737771

Singular Perturbation and
Bifurcation of Diffuse Transition Layers in Inhomogeneous Media,
Part II,
(with C. Huang),
Networks and Heterogeneous Media,
10(2015), 897948

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), 132

Finite Time BlowUp of
Parabolic Systems with Nonlocal Terms,
(with F. Li),
Indiana University Mathematics Journal,
63(2014), 783829

Singular Perturbation and
Bifurcation of Diffuse Transition Layers in Inhomogeneous Media,
Part I,
(with C. Huang),
Networks and Heterogeneous Media,
8(2013), 10091034

A quantitative description of
mesh dependence for the discretization of singularly perturbed nonconvex
problems,
(with A. Braides),
SIAM Journal of Numerical Analysis,
50 (2012), 18831898.

Renormalized
GinzburgLandau Energy and the Location of Near Boundary Vortices,
(with L. Berlyand, V. Rybalko),
Networks and Heterogeneous Media, 7 (2012), 179196

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), 46794718

Long Time Behavior of Some
Epidemic Models,
(with F. Li),
Discrete and Continuous Dynamical Systems (Series B),
16 (2011), 867881

Pulsating Wave for
Mean Curvature Flow in Inhomogeneous Medium
(with N. Dirr, G. Karali)
European Journal of Applied Mathematics,
19 (2008) 661699

Nonuniqueness in a Free Boundary
Problem from Combustion
(with A. Petrosyan)
Journal of Geometric Analysis,
18 (2008), 10981126

Structures of Stable Solutions for a
OneDimensional Variational Problem
ESAIM: Control, Optimisation and Calculus of Variations,
12 (2006) 721751

Pinning and DePinning Phenomena in
Front Propagation in Heterogeneous Medium
(with N. Dirr) Interfaces and Free Boundaries,
8 (2006) 79109
 Noise and Uniqueness of Motion
by Mean Curvature
(with P. E. Souganidis)
Annales de L'Institut Henri Poincareanalyse non lineaire,
21 (2004) 123
 Continuum Limit of a Step
Flow Model
(with R. V. Kohn, T. S. Lo)
Materials Research Society Symposium Proceedings,
696 (2002) T1.7.1T1.7.7.
 Continuum Theory of
Epitaxial Crystal Growth. I
(with W. E) Journal of Statistical Physics
104 (2001), 221253.
 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, 448453.
 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), 443460.
 Stochastic Motion by Mean
Curvature
Archive for Rational Mechanics and Analysis,
144 (1998), 313355.
 Existence of dendritic
crystal growth with stochastic
perturbations
Journal of Nonlinear Science,
8 (1998), 491579.
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), 692760, 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), 52625272

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(18)

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 MultipleObjective 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, 18101822.
(See also:
Stochastic Steepest Descent
Optimization of MultipleObjective 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 ProportionalShare 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 ProportionalShare Scheduling of Sensor
Coverage,
Proc. ACM International Conference on Emerging Networking
Experiments and Technologies (CoNEXT),
Madrid, Spain, Dec. 2008)
 On Optimal Information Capture by
EnergyConstrained Mobile Sensors
(S He, J. Chen, Y. Sun, D. K. Y. Yau, N. K. Yip),
IEEE Transactions on Vehicular Technology,
59(5) May, 2010, 24722484.
(See also:
On Optimal Information Capture by
EnergyConstrained 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 Adhoc and Sensor
Systems (MASS), Macau, China, Oct. 2009