# Faculty Publications

**2019:**

Jun Shen, Kening Lu and Bixiang Wang, *Convergence and center manifolds for differential equations driven by colored noise*, Discrete and Continuous Dynamical Systems, Series A, Accepted.

Renhai Wang, Yangrong Li and Bixiang Wang, *Random dynamics of fractional nonclassical diffusion equations driven by colored **noise*, Discrete and Continuous Dynamical Systems, Series A, Accepted.

Dingshi Li, Kening Lu, Bixiang Wang and Xiaohu Wang, *Limiting dynamics for non-autonomous stochastic retarded **reaction-diffusion equations on thin domains*, Discrete and Continuous Dynamical Systems, Series A, Accepted.

Bixiang Wang, *Weak pullback attractors for stochastic Navier-Stokes equations **with nonlinear diffusion terms*, Proceedings of the American Mathematical Society, 147 (2019), 1627-1638.

Bixiang Wang, *Weak Pullback Attractors for mean random dynamical systems **in Bochner spaces*, Journal of Dynamics and Differential Equations, DOI: 10.1007/s10884-018-9696-5

Anhui Gu and Bixiang Wang, *Random attractors of FitzHugh-Nagumo systems driven **by colored noise on unbounded domains*, Stochastics and Dynamics, DOI: 10.1142/S0219493719500357.

Yadong Shang, Jianjun Paul Tian and Bixiang Wang, *Asymptotic behavior of the stochastic Keller-Segel equations, **Discrete and Continuous Dynamical Systems*, Series B, 24 (2019), 1367-1391.

**2018:**

Rakhim Aitbayev, Peter W. Bates, Hong Lu, Lijun Zhang and Mingji Zhang. *Mathematical studies of Poisson-Nernst-Planck model for membrane channels: Finite
ion size effects without electroneutrality boundary conditions*. Journal of Computational and Applied Mathematics (accepted).

M. Zhang. *Boundary layer effects on ionic flows via classical Poisson-Nernst-Planck systems*. Computational and Mathematical Biophysics (Accepted).

H. Lu, B. Wang, J. Qi and M. Zhang.* Pullback D-attractors for non-autonomous stochastic fractional power dissipative
equations on R^n.* Discrete and Continuous Dynamical Systems, Series A, 39 (2019), 683-706.

H. Lu and M. Zhang. *The spectral method for long-time behavior of a fractional power dissipative system*. Taiwan J. Mathematics, 22(2) (2018), 453-483.

H. Lu, J. Li, J. Shackelford, J. Vorenberg and M. Zhang. *Ion size effects on individual fluxes via Poisson-Nernst-Planck systems with Bikerman's
local hard-sphare potential: Analysis without electroneutrality conditions*. Discrete and Continuous Dynamical Systems-B 23(4) (2018), 1623-1643.

H. Lu, P. W. Bates, W. Chen and M. Zhang. *The spectral collocation method for efficiently solving PDEs with fractional Laplacian*. Advances in Computational Mathematics, 44(3) (2018), 861-878.

Anhui Gu, Dingshi Li, Bixiang Wang and Han Yang. *Regularity of random attractors for fractional stochastic reaction-diffusion equations
on R^n*. Journal of Differential Equations, 264 (2018), 7094-7137.

Anhui Gu and Bixiang Wang. *Asymptotic behavior of random FitzHugh-Nagumo systems driven by colored noise*. Discrete and Continuous Dynamical Systems Series B, 23 (2018), 1689-1720.

Kening Lu and Bixiang Wang. *Wong-Zakai approximations and long term behavior of stochastic partial differential
equations*. Journal of Dynamics and Differential Equations, Accepted.

Xiaohu Wang, Kening Lu and Bixiang Wang. *Wong-Zakai approximations and attractors for stochastic reaction-diffusion equations
on unbounded domains*. Journal of Differential Equations, 264 (2018), 378-424.

Dingshi Li, Kening Lu, Bixiang Wang and Xiaohu Wang. *Limiting behavior of dynamics for stochastic reaction-diffusion equations with additive
noise on thin domains*. Discrete and Continuous Dynamical Systems, Series A, 38 (2018), 187-208.

**2017:**

Bixiang Wang. *Asymptotic behavior of non-autonomous fractional stochastic reaction-diffusion equations*. Nonlinear Analysis TMA, 158 (2017), 60-82.

X. Gao, A. Huang, B. Kerr. *Efficient Band-to-Trap Tunneling Model Including Heterojunction Band Offset*. ECS Transactions 80 (10), 1005-1015. http://ecst.ecsdl.org/content/80/10/1005.short

Sameh A. Eisa, William Stone and Kevin Wedeward. *Mathematical analysis of wind turbines dynamics under control limits: boundedness,
existence, uniqueness, and multi time scale simulations*. International Journal of Dynamics and Control (2017).

H. Lu, P. W. Bates, W. Chen, and M. Zhang. *The Spectral Collocation Method for Efficiently Solving PDEs with Fractional Laplacian*. Advances in Computational Mathematics (2017).

P. W. Bates, W. Liu, H. Lu and M. Zhang. *Ion size and valence effects on ionic flows via Poisson-Nernst-Planck systems*. Communications in Mathematical Sciences, 15(4) (2017), 881-901.

Jianbao Zhang, D. Acheampong and M. Zhang. *Geometric singular approach to Poisson-Nernst-Planck models with excess chemical potentials:
Ion size effects on individual fluxes*. Molecular Based Mathematical Biology, 5(1) (2017), 58-77.

I. G. Avramidi. *Quantum heat traces*. Journal of Geometry and Physics, 112 (2017) 271-288.

Sameh A. Eisa, William Stone and Kevin Wedeward. *Mathematical Modeling, Stability, Bifurcation Analysis, and Simulations of a Type-3
DFIG Wind Turbine's Dynamics with Pitch Control*. 2017 Ninth Annual IEEE Green Technologies Conference (GreenTech), 2017, pp. 334-341.
doi:10.1109/GreenTech.2017.55.

Sameh A. Eisa, Kevin Wedeward, and William Stone. *Time Domain Study of a Type-3 DFIG Wind Turbine's Dynamics: Q Drop Function Effect
and Attraction VS Control Limits Analysis*. 2017 Ninth Annual IEEE Green Technologies Conference (GreenTech), 2017, pp. 350-357.
doi:10.1109/GreenTech.2017.57.

D. Li, B. Wang and X. Wang. *Limiting Behavior of non-autonomous stochastic reaction-diffusion equations on thin
domains*. Journal of Differential Equations, 262 (2017), 1575-1602.

B. Wang. *Multivalued non-autonomous random dynamical systems for wave equations without uniqueness*. Discrete and Continuous Dynamical Systems, Series B, 22 (2017), 2011-2051.

P. W. Bates, Y. Jia, W. Liu, H. Lu and M. Zhang. *Individual flux study via steady-state Poisson-Nernst-Planck systems: Effects from
boundary conditions*. SIAM J. on Applied Dynamical Systems, 16(1) (2017), 410-430.

H. Lu, S. Lv and M. Zhang. *Fourier spectral approximation to the dynamical behavior of 3D fractional Ginzburg-Landau
equation*. Discrete and Continuous Dynamical Systems-A, 37(5) (2017), 2539-2564.

**2016:**

H. Lu, P. W. Bate, S. Lv and M. Zhang. *Stochastic dynamics of 3D fractional complex Ginzburg-Landau equation with multiplicative
noise on **an unbounded domain*. Communications in Mathematical Sciences, 14(1) (2016), 273-295.

Sameh A. Eisa, Kevin Wedeward, and William Stone. *Sensitivity Analysis of a type-3 DFAG Wind Turbine's Dynamics with Pitch Control*. 2016 IEEE Green Energy and Systems Conference (IGESC), Pages1-6.

I. G. Avramidi and B. J. Buckman. *Heat Determinant on Manifolds*. Journal of Geometry and Physics, 104 (2016) 64-88, DOI:10.1016/j.geomphys.2016.02.004

Anwar M. Hossain and Gabriel Huerta. *Bayesian Estimation and Prediction for the Maxwell Failure Distribution Based on Type
II Censored Data*. Open Journal of Statistics, Vol 6, No.1, pp.49-60, February 2016.

X. Wang, K. Lu and B. Wang. *Exponential stability of non-autonomous stochastic delay lattice systems with multiplicative
noise*. Journal of Dynamics and Differential Equations, 28 (2016), 1309-1335.

P. W. Bates, J. Li and M. Zhang. *Singular fold with real noise*. Discrete and Continuous Dynamical Systems-B, 21(7) (2016), 2091-2107.

Y. Jia, W. Liu and M. Zhang. *Qualitative properties of ionic flows via Poisson-Nernst-Planck systems with Bikerman's
local hard-sphere potential: Ion size effects*. Discrete and Continuous Dynamical Systems-B, 21(6) (2016), 1775-1802.

**2015:**

S. M. Marrero, F. M. Phillips, B. Borchers, N. Lifton, R. Aumer, and G. Balco. *Cosmogenic Nuclide Systematics and the CRONUScalc Program*. To appear in Quaternary Geochronology, 2015.

I. G. Avramidi and S. Collopy. *One-loop quantum gravity in Einstein Universe*, Journal of High Energy Physics, vol 11 (2015) p. 193, 49pp.

I. G. Avramidi. *Heat Kernel Method and Its Applications*, (Basel: Birkhauser, 2016).

M. Zhang. *Asymptotic expansions and numerical simulations on I-V relations via a Poisson-Nernst-Planck
system with zero permanent charge*. Rocky Mountain J. Mathematics, 45 (5) (2015), 1681-1708.

H. Lu, P. W. Bates, J. Xin and M. Zhang. *Asymptotic behavior of stochastic fractional power dissipative equations on R^n*. Nonlinear Analysis: TMA, 128 (2015), 176-198.

B. Wang. *Periodic and almost periodic random inertial manifolds for non-autonomous stochastic
equations*. 189-208, Continuous and Distributed Systems II: Theory and Applications, Edited
by V.A. Sadovnichiy and M.Z. Zgurovsky, Springer, 2015.

X. Wang, K. Lu and B. Wang. *Long term behavior of delay parabolic equations with additive noise and deterministic
time dependent forcing*. SIAM Journal on Applied Dynamical Systems, 14 (2015), 1018-1047.

B. Wang. *Stochastic bifurcation of pathwise random almost periodic and almost automorphic solutions
for random dynamical systems*. Discrete and Continuous Dynamical Systems, 35 (2015), 3745-3769.

B. Borchers, Shasta Marrero, Greg Balco, Marc Caffee, Brent Goehring, Nathaniel Lifton, Kunihiko
Nishiizumi, Fred Phillips, Joerg Schaefer, and John Ston. *Geological calibration of spallation production rates in the CRONUS-Earth project*. Quaternary Geochronology. In Press.

B. Borchers, J. Paul Brooks, and Laura McLay, editors. *Operations Research and Computing: Algorithms and Software for Analytics*. Proceedings of the 14th INFORMS Computing Society Conference, INFORMS, 2015. ISBN:
978-0-9843378-6-6.

**2014:**

E. E. Frisbee, J. B. J. Harrison, J. M. H. Hendrickx, and B. Borchers. *Remote sensing for soil map unit boundary detection*. Reviews in Engineering Geology 22 (2014): 119-129.

Margaret Snell, Anwar M. Hossain, Oleg Makhnin, and Snezna Rogelj. *Inverse associations between parabens and obesity/diabetes in adults*. Global Journal of Quantitative Science Vol. 1. No.4. December 2014 Issue, pp.1-7.

I. G. Avramidi. *Heat trace and functional determinant in one dimension*. Journal of Mathematical Physics 55, (2014)/123501; DOI: 10.1063/1.4902379; 25 pages.

R. Aitbayev and N. Yergaliyeva. *A Fourth-Order Collocation Scheme for Two-Point Interface Boundary Value Problems*. Advances in Numerical Analysis, vol. 2014, Article ID 875013, 8 pages, 2014. doi:10.1155/2014/875013.

P.W. Bates, K. Lu and B. Wang. *Attractors of non-autonomous stochastic lattice systems in weighted spaces*. Physica D, 289 (2014), 32-50.

A. Krause, M. Lewis and B. Wang. *Dynamics of the non-autonomous stochastic p-Laplace equation driven by multiplicative
noise*. Applied Mathematics and Computation, 246 (2014), 365-376.

I. G. Avramidi and B. J. Buckman. *Heat Determinant on Manifolds*. arXiv:1408.2265, 41 pages, Communications in Mathematical Physics (2014), submitted.

I. G. Avramidi. *Heat Kernel: with Applications to Finance*, (Springer, 2014), 360 pp. Accepted for publication.

J. Starrett. *Hyperreal Fractals and Integration*. American Mathematical Monthly. Accepted for publication.

A. Krause and B. Wang. *Pullback Attractors of Non-autonomous Stochastic Degenerate Parabolic Equations on
Unbounded Domains*. J. Mathematical Analysis and Applications, 417 (2014), 1018-1038.

B. Wang. *Existence and upper semicontinuity of attractors for stochastic equations with deterministic
non-autonomous terms*. Stochastics and Dynamics, 14 (2014), No. 4, 1450009, 1-31.

B. Wang. *Existence, stability and bifurcation of random complete and periodic solutions of
stochastic parabolic equations*. Nonlinear Analysis TMA, 103 (2014), 9-25.

B. Wang. *Random attractors for non-autonomous stochastic wave equations with multiplicative
noise*, Continuous and Discrete Dynamical Systems. 34 (2014), No.1, 269-300.

**2013:**

R. Aitbayev, *Existence and uniqueness for a two-point interface boundary value problem*, Electronic Journal of Differential Equations, Vol. 2013 (2013), No. 242, pp. 1-12.

R. L. Van Dam, J. M. H. Hendrickx, N. J. Cassidy, R. E. North, M. Dogan, and B. Borchers, *Effects of magnetite on high-frequency ground-penetrating radar*, Geophysics 78 (5), H1-H11, 2013.

R. C. Aster, B. Borchers, and C. H. Thurber. *Parameter Estimation and Inverse Problems*, 2nd ed., Academic Press, 2013.

S. H. Chung, T. L. Friesz, and R. D. Weaver, *Dynamic Sustainability Games for Renewable Resources - A Computational Approach*, 2013, IEEE Transactions on Computers, in press.

S. H. Chung, R. D. Weaver, and T. L. Friesz, *Strategic Response to Pollution Taxes in Supply Chain Networks: Dynamic, Spatial,
and Organizational Dimensions*, European Journal of Operational Research, 231(2), 314-327, 2013.

E. J. Bedrick and A. Hossain, *Conditional tests for homogeneity of zero-inflated Poisson and Poisson-hurdle distributions*. Journal of Computational Statistics and Data Analysis, Vol. 61, pp. 99-106, 2013.

J. Verley, E. Keiter, C. Hembree, C. Axness and B. Kerr, *A new time-dependent analytic compact model for radiation-induced photocurrent in
epitaxial structures*, Proc. of SISPAD, (2013), 228 - 231.

W.D. Stone, *Bifurcation Theory in Finite Dimensions*, The New Mexico Tech Press, 2013.

P. W. Bates, K. Lu and B. Wang, *Tempered random attractors for parabolic equations in weighted spaces*, Journal of Mathematical Physics, 54, 081505 (2013), 1-26.

A. Adili and B. Wang, *Random attractors for non-autonomous stochastic FitzHugh-Nagumo systems with multiplicative
noise*, Continuous and Discrete Dynamical Systems, Supplement (2013), 1-10.

B. Wang and B. Guo, *Asymptotic behavior of non-autonomous stochastic parabolic equations with nonlinear
Laplacian principal part*, Electronic Journal of Differential Equations, 2013 (2013), No. 191, 1-25.

R. Jones and B. Wang, *Asymptotic behavior of a class of stochastic nonlinear wave equations with dispersive
and dissipative terms*, Nonlinear Analysis, Real World Applications, 14 (2013), 1308-1322.

A. Adili and B. Wang, *Random attractors for stochastic FitzHugh-Nagumo systems driven by deterministic non-autonomous
forcing*, Continuous and Discrete Dynamical Systems Series B, 18 (2013), 643-666.

**2012:**

I. G. Avramidi and S. Collopy, *Thermal Yang-Mills theory in Einstein Universe*, Journal of Physics A: Mathematical and Theoretical, 45 (2012) 374009.

I. G. Avramidi and S. Collopy, *Effective action and phase transitions in thermal Yang-Mills theory on spheres*, Communications in Mathematical Physics 311 (2012) 713-753.

S. H. Chung, R. D. Weaver, and T. L. Friesz, *Oligopolies in Pollution Permit Markets: A Dynamic Game Approach*, International Journal of Production Economics, 140(1), 48-56, 2012.

B. Kerr, C.L. Axness, J.C. Verley, C.E. Hembree, and E.R. Keiter, *A New Time-Dependent Analytic Model for Radiation-Induced Photocurrent in Finite 1D
Epitaxial Diodes*, SAND2012-2161, Sandia National Laboratories, Albuquerque, NM, 2012.

B. Wang, *Sufficient and necessary criteria for existence of pullback attractors for non-compact
random dynamical systems*, J. Differential Equations, 253 (2012), 1544-1583.

B. Wang, *Periodic random attractors for stochastic Navier-Stokes equations on unbounded domains*, Electron. J. Differential Equations, 2012 (2012), No. 59, 1-18.

I. Knowles and M. A. LaRussa, *Lavrentiev's theorem and error estimation in elliptic inverse problems*. In B. M. Brown, J. Lang, I. G. Wood (Eds.) Spectral Theory, Function Spaces and
Inequalities: New Techniques and Recent Trends, 91-104, Operator Theory: Advances
and Applications, volume 219, Springer Birkhauser, 2012, ISBN 978-3-0348-0262-8.

J. Starrett and C. Nicholas, *A suspension of the Henon map by periodic orbits*. Chaos, Solitons and Fractals, 45, 1486-1493, 2012.

J. Starrett, *Non-strange Chaotic Attractors Equivalent to their Templates*, Dynamical Systems: An International Journal, Volume 27, Number 2, 1 June 2012 ,
pp. 187-196(10).

W. Stone, M. Person, A. Hofstra, D. Sweetkind, D. Cohen, C.W. Gable and A. Banerjee, *Analytical and numerical models of hydrothermal fluid flow at fault intersections*, Geofluids, 2012.

**2011:**

B. Wang, *Asymptotic behavior of stochastic wave equations with critical exponents on R^3*, Transactions of AMS, 363 (2011), 3639-3663.

B. Wang, *Almost periodic dynamics of perturbed infinite-dimensional dynamical systems*, Nonlinear Analysis TMA, 74 (2011), 7252-7260.

S.-H. Hong, J. M. H. Hendrickx, and B. Borchers, *Down-Scaling of SEBAL Derived Evapotranspiration Maps From MODIS (250m) to LANDSAT
(30m) Scale*, International Journal of Remote Sensing, 32:6457-6477, 2011. Preprint.

J. K. MacCarthy, B. Borchers, and R. C. Aster, *Efficient stochastic estimation of the model resolution matrix diagonal and generalized
cross validation for large geophysical inverse problems*, Journal of Geophysical Research, 116, B10304, 2011. Preprint. The code from this
paper is also available.

J. M. H. Hendrickx, J. B. Harrison, B. Borchers, J. R. Kelley, S. Howington, and J. Ballard, *High-resolution soil moisture mapping in Afghanistan*. In SPIE Proceedings Volume 8017 Detection and Sensing of Mines, Explosive Objects,
and Obscured Targets XVI. Edited by R. S. Harmon, J. H. Holloway, and J. T. Broach,
801710, 2011.

I. Knowles and M. A. LaRussa, *Conditional well-posedness for an elliptic inverse problem*. SIAM Journal on Applied Mathematics, 71(2011), 952-971. (Second most downloaded
article in July, 2011 and August, 2011.)

**2010:**

I. G. Avramidi, *Non-perturbative effective action in gauge theories and quantum gravity*, Advances in Theoretical and Mathematical Physics 14 (2010) 309-333.

I. G. Avramidi, *Mathemathical tools for calculation of the effective action in quantum gravity*, in: New Paths Towards Quantum Gravity, Ed. B. Booss-Bavnbek, G. Esposito and M.
Lesch, (Berlin, Springer, 2010), pp. 193-259.

T.L Friesz, S. H. Chung and R. D. Weaver, *Regional Infrastructure Investment Allocation for Sustainability*, in Sustainable and Resilient Critical Infrastructure Systems: Simulation, Modeling,
and Intelligent Engineering (Eds.: Kasthurirangan Gopalakrishnan and Srinivas Peeta),
Springer-Verlag, ISBN: 978-3-642-11404-5, 2010.

G. Fucci and I. G. Avramidi, *On the gravitationally induced Schwinger mechanism*, In: Proceedings of the International Conference "Quantum Field Theory under the
Influence of External Conditions" (QFEXT09). Eds. K. A. Milton and M. Bordag (Singapore:
World Scientific, 2010), pp. 485-491.

J. M. H. Hendrickx, B. J. Harrison, B. Borchers, G. Rodriguez-Marin, S. Howington, and J. Ballard, *High-resolution soil moisture mapping using operational optical satellite imagery*, In SPIE Proceedings Volume 7664 Detection and Sensing of Mines, Explosive Objects,
and Obscured Targets XV. Edited by Harmon, Russell S.; Holloway, John H., Jr.; Broach,
J. Thomas. pp. 76641O-76641O-14, 2010.

J. Brown, J. McCoy, and B. Borchers, *Theory and simulation of the dynamic heat capacity of the East Ising model*. Journal of Chemical Physics, 133, 064508 (2010). Reprint.

E. M. Engle, J. B. J. Harrison, J. M. H. Hendrickx, and B. Borchers, *Digital Soil Boundary Detection Using Quantitative Hydrologic Remote Sensing*. Progress in Soil Science, Volume 2, Part II, Section B, 123-136, 2010.

C.L. Axness, B. Kerr, and E.R. Keiter, *Analytic 1-D Junction Diode Photocurrent Solutions Following Ionized Radiation and
Including Time-Dependent Changes in the Carrier Lifetime From a Nonconcurrent Neutron
Pulse*, IEEE Transactions on Nuclear Science, Vol. 57, No. 6, December 2010, 3314-3321.

C.L. Axness, B. Kerr, and E.R. Keiter, *New Analytic 1D pn Junction Diode Photocurrent Solutions Following Ionizing Radiation
and Including Time-Dependent Changes in the Carrier Lifetime from a Non-Concurrent
Neutron Pulse*, Poster, 2010 IEEE NUCLEAR & SPACE RADIATION EFFECTS CONFERENCE, Denver, Colorado,
2010.

C.L. Axness, B. Kerr, and E.R. Keiter, *Analytic 1D pn Junction Diode Photocurrent Solutions Following Ionizing Radiation
and Including Time-Dependent Changes in the Carrier Lifetime from a Non-Concurrent
Neutron Pulse*, SAND2010-3284, Sandia National Laboratories, Albuquerque, NM, 2010.

W. Liu and B. Wang, *Poisson-Nernst-Planck systems for narrow tubular-like membrane channels*, J. Dynamics and Differential Equations, 22 (2010), 413-437.

K. Gabert and B. Wang, *Non-autonomous attractors for singularly perturbed parabolic equations on R^n*, Nonlinear Analysis TMA, 73 (2010), 3336-3347.

B. Wang and R. Jones, *Asymptotic behavior of a class of non-autonomous degenerate parabolic equations*, Nonlinear Analysis TMA, 72 (2010) 3887-3902.

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