## Mathematical Analysis and Modelling Research Group

#### About Us

The Mathematical Analysis and Modelling Research Group has a broad range of interests that span pure and applied mathematics. We study a number of problems due to their intrinsic mathematical interest and their applications in various areas of science, technology and industry. Our research areas include differential equations, real and complex differential geometry, topology, CR-geometry, mathematical biology, combinatorics and operations research. Our research is applicable to, or is applied directly in, multiple branches of science including biology, chemistry, physics, rural sciences, sports science, economics and data science, as well as in business and industry.

#### Our Staff

No results were found

Kumbu Dorji

Masoud Ganjiarjenaki

Benniao Li

Reginald Page

Basim Alsaedi

Kamruzzaman Khan

Rajnesh Mudaliar

#### Our Research Projects

**Project title:** Propagation Described by Partial Differential Equations with Free Boundary

**Principal investigator:** Prof. Yihong Du (UNE)

**Other participants:**

Dr Maolin Zhou (UNE), Dr Weiwei Ding (UNE), Prof. Bendong Lou (Shanghai Normal Univ), Prof Xing Liang (Univ of Sci and Tech of China)

**Funding body: ** Australian Research Council (2015-2018)

**Project description:**

Front propagation appears in many branches of sciences; examples include the propagation of nerve impulses, the propagation of premixed flames, the spreading of advantageous genes, and the spreading of an invasive species. Although the sources of propagation are diverse, the basic phenomena have been observed to follow certain rules that can be captured by mathematical models of nonlinear partial differential equations (PDEs) or systems of such equations. Thus it is possible for a mathematical theory based on a set of such equations to provide vital insights and useful predictions for the spreading of a variety of subjects arising in different areas of sciences. This topic has been investigated by many leading mathematicians in the past several decades, and extensive research in this area is conducted by several first rate research groups around the world. With the advances of the relevant sciences, more and more demanding questions arise in this area, and many important and basic questions still remain open. The aim of this project is to develop new mathematics for better applications and deeper insights into the propagation phenomena. We modify existing models by introducing a free boundary to represent the spreading front, and so the partial differential equations are satisfied over a varying spatial domain whose boundary evolves with time, which need to be solved together with the partial differential equation. This makes the model more realistic but at the same time makes the mathematical treatment of the model much more difficult to handle. This research is mostly theoretical though numerical simulations are also needed from time to time.

**Related publications:**

- Y. Du, Mingxin Wang and Maolin Zhou,
, J. Math. Pure Appl., 107(2017), 253-287.*Semi-wave and spreading speed for the diffusive competition model with a free boundary* - Weiwei Ding, Y. Du and Xing Liang,
, J. Diff. Eqns., 262(2017), 4988-5021.*Spreading in space-time periodic media governed by a monostable equation with free boundaries, Part 1: Continuous initial functions* - Y. Du, Hiroshi Matsuzawa and Maolin Zhou,
, J. Math. Pures Appl., 103(2015), 741-787.*Spreading speed and profile for nonlinear Stefan problems in high space dimensions* - Y. Du and Xing Liang,
, Ann. Inst. Henri Poincare Anal. Non Lineaire, 32(2015), 279-305.*Pulsating semi-waves in periodic media and spreading speed determined by a free boundary model* - Y. Du and Bendong Lou,
, J. Eur. Math. Soc., 17(2015), 2673-2724.*Spreading and vanishing in nonlinear diffusion problems with free boundaries* - Y. Du, Hiroshi Matsuzawa and Maolin Zhou,
, SIAM J. Math. Anal., 46(2014), 375-396.*Sharp estimate of the spreading speed determined by nonlinear free boundary problems* - Y. Du, Hiroshi Matano and Kelei Wang,
, Arch. Rational Mech. Anal., 212(2014), 957-1010.*Regularity and asymptotic behavior of nonlinear Stefan problems* - Y. Du and Zhigui Lin,
, Discrete Cont. Dyn. Syst.-B, 19(2014), 3105-3132.*The diffusive competition model with a free boundary: Invasion of a superior or inferior competitor* - Y. Du, Zongming Guo and Rui Peng,
, J. Funct. Anal., 265 (2013), 2089-2142.*A diffusive logistic model with a free boundary in time-periodic environment* - Y. Du,
, in "The Balance of Nature and Human Impact", edited by Klaus Rohde, Cambradge Univ Press, 2013, pp231-238.*Establishment or vanishing: fate of an invasive species based on mathematical models*

**Project title:** Nonlinear free boundary problems: propagation and regularity

**Principal investigator:** Dr Maolin Zhou (UNE)

**Funding body: ** Australian Research Council (2017-2020)

**Project description:**

Nonlinear free boundary problems arise from many applied fields, and pose great challenges to the theory of nonlinear partial differential equations, as the underlying domain of the solution to such problems has to be solved together with the solution itself. This project aims to completely understand the propagation profile and regularity of two important classes of free boundary problems, which would greatly enhance the existing theory of partial differential equations, and extend its applications to situations not covered before.

**Related publications:**

- Y.Du, B.Lou and M.Zhou, Spreading and vanishing for nonlinear Stefan problems in high space dimensions, J. Elliptic and Parabolic Equations, 2 (2016), 297-321.
- Y.Du, M.Wang and M.Zhou, Semi-wave and spreading speed for the diffusive competition model with a free boundary, J. Math. Pures Appl. (9) 107(2017), 253-287.
- W.Lei, G.Zhang and M.Zhou, Long time behavior for solutions of the diffusive logistic equation with advection and free boundary, Calculus of Variations and PDEs 55 (2016), no. 4, 1-34.
- X.Chen, B.Lou, M.Zhou and T.Giletti, Long time behavior of solutions of a reaction diffusion equation on unbounded intervals with Robin boundary conditions, Ann. Inst. H. Poincare Anal. Non Lineaire 33 (2016), no. 1, 67-92.
- H.Gu, B.Lou and M.Zhou, Long time behavior of solutions of Fisher-KPP equation with advection and free boundaries, J. Funct. Anal. 269 (2015), no. 6, 1714-1768.
- T.Giletti, L.Monsaingeo and M.Zhou, A KPP road-field system with spatially periodic exchange terms, Nonlinear Anal. 128 (2015), 273-302.
- Y.Du, B.Lou and M.Zhou, Nonlinear diffusion problems with free boundaryes: convergence, transition speed and zero number arguments, SIAM J. Math. Anal. 47 (2015), no. 5, 3555-3584.
- Y.Du, H.Matsuzawa and M.Zhou, Spreading speed and profile for nonlinear Stefan problems in high space dimensions, J. Math. Pures Appl. (9) 103 (2015), no. 3, 741-787.
- J.Cai, B.Lou and M.Zhou, Asymptotic behavior of solutions of a reaction diffusion equation with free boundary conditions, J. Dynam. Differential Equations 26 (2014), no. 4, 1007-1028.
- Y.Du, H.Matsuzawa and M.Zhou, Sharp estimate of the spreading speed determined by nonlinear free boundary problems, SIAM J. Math. Anal. 46 (2014), no. 1, 375-396.

**Project title:** Nonlinear Partial Differential Equations: Bubbles, Layers and Stability

**Principal investigators:** Prof. Shusen Yan (UNE), Prof. Norm Dancer (Univ of Sydney), Prof. Yihong Du (UNE) and Prof. Chang-Shou Lin (National Taiwan Univ.)

**Funding body: ** Australian Research Council (2017-2019)

** Project description: **

In this project we investigate several nonlinear elliptic partial differential equations that are of great concern in the recent study of the elliptic problems. They arise from well-established models in various applied fields, and the treatment of them poses great challenges to the current mathematical theory. We want to answer a number of important questions on these equations through deep analysis of the properties of their solutions, therefore enriching and expanding the existing mathematical theory in this area. One of the properties of the solutions under our investigation is known as bubbling, which describes the situation that as a key parameter in the equation approaches a certain critical value, the solution \mass" concentrates more and more at some points in the underlying space, like a Dirac delta function (in the limit). Such solutions are called "bubbling solutions", or "blowup solutions", and they frequently arise in various applied sciences, such as condensed matter physics and fluid mechanics. Many important phenomena in the natural sciences are also described by solutions with sharp layers, representing sharp transitions of phases in physics, chemistry or biology. In the limit, a solution with a sharp layer converges to a discontinuous function. Since bubbling and sharp layered solutions do not converge to a continuous function in the limit, they pose great difficulties in partial differential equations, and have been a central topic of research of many groups of first rate mathematicians around the world. Another important property of the solutions that we will study in this project is characterized by the level of stability, measured by the Morse indices of the solutions. The bigger the Morse index, the less stable the solution, with Morse index 0 meaning the solution is stable under small perturbations (or is a stable equilibrium solution of the corresponding parabolic problem). We want to show that the behavior of solutions with finite Morse index is usually not beyond reach and can sometimes be completely classified.

** Related publications: **

- Musso, Monica; Wei, Juncheng; Yan, Shusen;
Proc. Lond. Math. Soc. (3) 112 (2016), no. 1, 1-26.*Infinitely many positive solutions for a nonlinear field equation with super-critical growth.* - Deng, Yinbin; Peng, Shuangjie; Yan, Shusen;
J. Differential Equations 260 (2016), no. 2, 1228-1262.*Critical exponents and solitary wave solutions for generalized quasilinear Schrödinger equations.* - Cao, Daomin; Peng, Shuangjie; Yan, Shusen;
Adv. Math. 270 (2015), 263-301.*Planar vortex patch problem in incompressible steady flow.* - Deng, Yinbin; Lin, Chang-Shou; Yan, Shusen;
J. Math. Pures Appl. (9) 104 (2015), no. 6, 1013-1044.*On the prescribed scalar curvature problem in R^N, local uniqueness and periodicity.* - Du, Yihong; Guo, Zongming;
Calc. Var. Partial Differential Equations 54 (2015), no. 3, 3161-3181.*Finite Morse index solutions of weighted elliptic equations and the critical exponents.* - Du, Yihong; Wei, Lei;
J. Lond. Math. Soc. (2) 91 (2015), no. 3, 731-749.*Boundary behavior of positive solutions to nonlinear elliptic equations with Hardy potential.* - Dancer, E. N.;
Differential Integral Equations 27 (2014), no. 5-6, 483-488.*A remark on stable solutions of nonlinear elliptic equations on R^3 or R^4.* - Du, Yihong; Guo, Zongming; Wang, Kelei;
Calc. Var. Partial Differential Equations 50 (2014), no. 3-4, 615-638.*Monotonicity formula and e-regularity of stable solutions to supercritical problems and applications to finite Morse index solutions.* - Lin, Chang-Shou; Yan, Shusen;
Comm. Pure Appl. Math. 66 (2013), no. 7, 991-1027.*Bubbling solutions for the SU(3) Chern-Simons model on a torus.* - Lin, Chang-Shou; Yan, Shusen;
Arch. Ration. Mech. Anal. 207 (2013), no. 2, 353-392.*Existence of bubbling solutions for Chern-Simons model on a torus.* - Du, Yihong; Guo, Zongming;
Adv. Differential Equations 18 (2013), no. 7-8, 737-768.*Finite Morse-index solutions and asymptotics of weighted nonlinear elliptic equations.* - Dancer, E. N.; Du, Yihong; Efendiev, Messoud;
Adv. Nonlinear Stud. 13 (2013), no. 1, 115-136.*Quasilinear elliptic equations on half- and quarter-spaces.*

**Project title:** Analysis and Modelling of Collective Animal Motion

** Project participants:** Dr Timothy Schaerf (University of New England), Professor Ashley Ward (University of Sydney)

** Project description: **

The spectacular patterns of collective movement have been, and remain, a long standing and major interest in many branches of science, including biology, mathematics, physics and computational science. From the early 1980s until the late 2000s computational self-propelled particle models were the dominant methods for examining how, and what type of, individual-level interactions could result in the amazing emergent patterns formed by groups such as flocking birds, shoaling fish and even crowds of humans. The influence of these models on the study of collective motion has been immense, with multiple model-based studies led by contemporary researchers cited thousands of times each. It is only in the last decade that advances in automated tracking methods have led to the exciting development of techniques for estimating the local rules of interaction used by real animals to coordinate collective motion directly from observational data (as opposed to inferring possible rules using models). In spite of these advances, many of the techniques for analysis are still in their infancy. This project will focus on refining existing techniques and developing new techniques for quantifying individual-interactions from automated tracking data. The more accurate analysis of experimental data will then be used to help refine and build on simulation models for collective animal movement.

** Related publications: **

- M J Hansen, T M Schaerf and A J W Ward, The influence of nutritional state on individual and group movement behaviour in shoals of crimson-spotted rainbowfish (
*Melanotaenia duboulayi*), Behavioral Ecology and Sociobiology, 69(10):1713-1722, (2015). - M J Hansen, T M Schaerf and A J W Ward, The effect of hunger on the exploratory behaviour of shoals of mosquitofish
*Gambusia holbrooki*, Behavior, 152:12-13, (2015). - J E Herbert-Read, S Krause, L J Morrell, T M Schaerf, J Krause and A J W Ward, The role of individuality in collective group movement, Proceedings of the Royal Society B, 280:20122564, (2013).
- A Strandburg-Peshkin et al., Visual sensory networks and effective information transfer in animal groups, Current Biology, 23:R709-R711, (2013).
- Y Katz, K Tunstrøm, C C Ioannou, C Huepe and I D Couzin, Inferring the structure and dynamics of interactions in schooling fish, Proceedings of the National Academy of Sciences of the United States of America, 108:18720-18725, (2011).
- J E Herbert-Read, A Perna, R P Mann, T M Schaerf, D J T Sumpter and A J W Ward, Inferring the rules of interaction of shoaling fish, Proceedings of the National Academy of Sciences of the United States of America, 108:18726-18731, (2011).
- M Nagy, Z Àkos, D Biro and T Vicsek, Hierarchical group dynamics in pigeon flocks, Nature, 464:890-893, (2010).
- R Lukeman, Y X Li and L Edlestein-Keshet, Inferring individual rules from collective behaviour, Proceedings of the National Academy of Sciences of the United States of America, 107(28):12576-12580, (2010).
- M Ballerini et al., Interaction ruling animal collective behavior depends on topological rather than metric distance: evidence from a field study, Proceedings of the National Academy of Sciences of the United States of America, 105(4):1232-1237, (2008).
- I D Couzin, J Krause, N R Franks and S A Levin, Effective leadership and decision-making in animal groups on the move, Nature, 433:513-516, (2005).
- I D Couzin, J Krause, R James, G D Ruxton and N R Franks, Collective memory and spatial sorting in animal groups, Journal of Theoretical Biology, 218:1-11, (2002).
- D Helbing, I Farkas and T Vicsek, Simulating dynamical features of escape panic, Nature, 407:487-490, (2000).
- W L Romey, Individual differences make a difference in the trajectories of simulated fish schools, Ecological Modelling, 92:65-77, (1996).
- T Vicsek, A Czirók, E Ben-Jacob, I Cohen and O Shochet, Novel type of phase transition in a system of self-driven particles, Physical Review E, 75(6):1226-1229, (1995).
- D Helbing and P Molnar, Social force model for pedestrian dynamics, Physical Review E, 51(5):4282-4286, (1995).
- A Huth and C Wissel, The simulation of fish schools in comparison with experimental data, Ecological Modelling, 75:135-146, (1994).
- A Huth and C Wissel, The simulation of the movement of fish schools, Journal of Theoretical Biology, 156(3):365-385, (1992).
- D Helbing, A mathematical model for the behavior of pedestrians, Behavioral Science, 36(4):298-310, (1991).
- C W Reynolds, Flocks, herds, and schools: a distributed behavioral model, Computer Graphics, 21:25-34, (1987).
- I Aoki, A simulation study on the schooling mechanism in fish, Bulletin of the Japanese Society of Scientific Fisheries, 48(8):1081-1088, (1982).

**Project title:** Removable Singularities for Monopoles on a Sasakian 3-manifold (PhD project)

**Supervisor:** Dr Adam Harris (UNE)

**PhD student:** Mr Kumbu Dorji

**Funding:** UNE International Postgraduate Scholarship

**Project description:**

A classic problem of higher-dimensional complex analysis concerns the extension of complex-analytic structures, such as holomorphic functions or vector bundles, across a gap locus, which in the first instance may simply be a point. Theorems of this kind for functions are more than a century old, whereas "removable singularities" theorems for vector bundles have a more recent origin. A famous theorem of Uhlenbeck shows that point singularities of unitary vector bundles over a punctured ball in real four-dimensional space are removable if certain conditions are imposed on the curvature form associated with a choice of hermitian metric. Such conditions are typically representable as differential equations governing gauge-fields which arise in theoretical physics. One such is the so-called anti self-dual form of the Yang-Mills equation, in terms of which a unitary bundle can be endowed with a natural holomorphic structure. Techniques available for the study of removable singularities in this setting are applied to this project by means of a two-fold reduction from four dimensions to three. On one hand, a particular form of the magnetic monopole equation, first studied by Dirac, can be realised as a time-independent reduction of the anti self-dual equation. On the other, every Sasakian three-manifold is the canonical section of a certain complex Kahler surface.

**Related publications:**

- I. Biswas and J. Hurtubise, Monopoles on Sasakian three-folds, arXiv:1412.4050v1 (2014)
- C.P. Boyer and K. Galicki, Sasakian Geometry, Oxford Math. Monographs, OUP (2008)
- N.P. Buchdahl and A. Harris , Holomorphic connections and extension of complex vector bundles. Math. Nachr. 204 (1999) 29-39
- A. Harris and Y. Tonegawa, Analytic continuation of vector bundles with Lp-curvature. Int. J. Math. 11, No. 1 (2000) 29-40

**Project title:** Low dose X-ray phase-contrast imaging and tomography

** Principal investigator:**A/Prof. Konstantin Pavlov (UNE)

** PhD Student:**Mr Darren Thompson

** Other participants:** Dr T.E. Gureyev (UNE, Melbourne University, CSIRO, Monash University), Dr Y.I. Nesterets (UNE, CSIRO), Dr G. Tromba (ELETTRA), Dr S.C. Mayo (CSIRO), Dr A.W. Stevenson (CSIRO), Dr M.J. Kitchen (Monash University).

** Project description: **

Phase-contrast imaging is the future of X-ray imaging. This powerful type of X-ray imaging, which makes use of free-space propagation as well as optical elements made of perfect crystals, is specially tailored to image samples which are invisible to conventional X-ray techniques. Such "extended X-ray vision" is extremely important for imaging in medicine, biology and materials science. These techniques reveal the internal structure of low-absorption materials, where traditional X-ray radiography methods often struggle to provide sufficient contrast. In particular, this project is focused on development of low-dose high-sensitivity three-dimensional mammographic phase-contrast imaging, initially at synchrotrons and subsequently in hospitals and medical imaging clinics.

** Related publications: **

- G. Tromba, S. Pacilè , Y.I. Nesterets, F. Brun, C. Dullin, D. Dreossi, S.C. Mayo, A.W. Stevenson, K.M. Pavlov, M.J. Kitchen, D. Thompson, J.M.C. Brown, D. Lockie, M. Tonutti, F. Stacul, F. Zanconati, A. Accardo and T.E. Gureyev. Phase-contrast clinical breast CT: optimization of imaging setups and reconstruction workflows. Lecture Notes in Computer Science, v. 9699, p. 625-634 (2016)
- Y.I. Nesterets, T.E. Gureyev, S.C. Mayo, A.W. Stevenson, D. Thompson, J.M.C. Brown, M.J. Kitchen, K.M. Pavlov, D. Lockie and G. Tromba. A feasibility study of X-ray phase-contrast mammographic tomography at the Imaging and Medical beamline of the Australian Synchrotron. J. Synchr. Rad. 22, 1509-1523 (2015). (IF=2.794)
- P. Vagovic, L. Sveda, A. Cecilia, E. Hamann, D. Pelliccia, E. N. Gimenez, D. Korytar, K. M. Pavlov, Z. Zaprazny, M. Zuber, T. Koenig, M. Olbinado, W. Yashiro, A. Momose, M. Fiederle, and T. Baumbach. X-ray Bragg Magnifier Microscope as a linear shift invariant imaging system: image formation and phase retrieval. Optics Express 22(18), 21508-21520 (2014). (IF=3.488)
- T E Gureyev, S C Mayo, Ya I Nesterets, S. Mohammadi, D Lockie, R H Menk, F Arfelli, K M Pavlov, M J Kitchen, F Zanconati, C Dullin and G Tromba. Investigation of the imaging quality of synchrotron-based phase-contrast mammographic tomography. J. Phys. D: Appl. Phys. 47, 365401 (2014). (IF=2.721)
- T.W. Baillie, T.E. Gureyev, J.A. Schmalz, and K.M. Pavlov. Phase-contrast X-ray tomography using Teague's method. Optics Express 20(15), 16913-16925 (2012). (IF=3.488)
- J.A. Schmalz, T.E. Gureyev, D.M. Paganin, K.M. Pavlov. Phase retrieval using radiation and matter wave fields: Validity of Teague's method for solution of the transport of intensity equation. Physical Review A 84, 023808 (2011). (IF=2.808)
- M.J. Kitchen, D.M. Paganin, K. Uesugi, B.J. Allison, R.A. Lewis, S.B. Hooper, K.M. Pavlov. Phase contrast image segmentation using a Laue analyser. Phys. Med. Biol. 56, 515-534 (2011). (IF=2.761)
- M.J. Kitchen, D.M. Paganin, K. Uesugi, B.J. Allison, R.A. Lewis, S.B. Hooper and K.M. Pavlov. X-ray phase, absorption and scatter retrieval using two or more phase contrast images. Optics Express 18(19), 19994-20012 (2010). (IF=3.488)
- J.A. Schmalz, G. Schmalz, T.E. Gureyev and K.M. Pavlov. On the derivation of the Green function for the Helmholtz equation using generalized functions. American J. Phys 78(2), 181-186 (2010).
- D.J. Vine, D. M. Paganin, K. M. Pavlov, K. Uesugi, A. Takeuchi, Y. Suzuki, N. Yagi, T. Kämpfe, E.-B. Kley, E. Förster. Deterministic Green's function retrieval using hard X-rays. Phys. Rev. Lett. 102, 043901 (2009). (IF=7.512)
- M.J. Kitchen, K.M. Pavlov, S.B. Hooper, D.J. Vine, K.K.W. Siu, M.J. Wallace, M.L.L. Siew, N. Yagi, K. Uesugi, R.A. Lewis. Simultaneous acquisition of dual analyser-based phase contrast X-ray images for small animal imaging, Eur J. Radiol, 68S, S49-S53 (2008). (IF=2.369)
- D. J. Vine, D. M. Paganin, K. M. Pavlov, J. Kräußlich, O. Wehrhan, I. Uschmann, and E. Förster. Analyser-based phase contrast imaging and phase retrieval using a rotating anode X-ray source. Appl. Phys. Lett. 91, 254110 (2007). (IF=3.302)
- S.B. Hooper, M.J. Kitchen, M.J. Wallace, N. Yagi, K. Uesugi, M.J. Morgan, C. Hall, K.K.W. Siu, I.M. Williams, M. Siew, S.C. Irvine, K. Pavlov, R.A. Lewis. Imaging lung aeration and lung liquid clearance at birth. FASEB (The Journal of the Federation of American Societies for Experimental Biology) 21, 3329-3337 (2007). (IF=5.043)
- M.J. Kitchen, K.M. Pavlov, K.K.W. Siu, R.H. Menk, G. Tromba, R.A. Lewis. Analyser-based phase-contrast image reconstruction using geometrical optics. Phys.Med. Biol. 52, 4171 -4187 (2007). (IF=2.761)
- D.J. Vine, D.M. Paganin, K.M. Pavlov, and S.G. Podorov. Unambiguous reconstruction of the complex amplitude reflection coefficient of a laterally homogeneous crystal using analyser-based phase-contrast imaging. J. Appl. Cryst. 40, 650-657 (2007). (IF=3.984)
- T.E. Gureyev, Ya.I. Nesterets , K.M. Pavlov and S.W. Wilkins. Computed tomography with linear shift-invariant optical systems. J. Opt. Soc. Am. A. 24(8), 2230-2241 (2007). (IF=1.558)
- Ya.I. Nesterets, T.E. Gureyev, K.M. Pavlov, D.M. Paganin, S.W. Wilkins Combined analyser-based and propagation-based phase-contrast imaging of weak objects. Opt. Comm., 259(1), 19-31 (2006). (IF=1.449)
- K. M. Pavlov, T. E. Gureyev, D. Paganin, Y. I. Nesterets, M. Kitchen, K. K.W. Siu, J. Gillam, K. Uesugi, N. Yagi, M. J. Morgan, R. A. Lewis. Unification of analyser-based and propagation-based X-ray phase-contrast imaging. Nucl. Instr. And Meth. A 548, 163-168 (2005). (IF=1.216)
- R.A. Lewis, N. Yagi, M.J. Kitchen, M.J. Morgan, D. Paganin, K.K.W. Siu, K. Pavlov, I. Williams, K. Uesugi, M.J.Wallace, C.J. Hall, J. Whitley, S.B. Hooper. Dynamic imaging of the lungs using X-ray phase contrast. Phys. Med. Biol. 50, 5031-5040 (2005). (IF=2.761)
- D. Briedis, K.K.W. Siu, D.M. Paganin, K.M. Pavlov and R.A. Lewis. Analyser-based mammography using single-image reconstruction. Phys. Med. Biol., 50 3599-3611 (2005). (IF=2.761)
- M.J. Kitchen, R.A. Lewis, N. Yagi, K. Uesugi, D. Paganin, S.B. Hooper, G. Adams, S. Jureczek, J. Singh, C.R. Christensen, A.P. Hufton, C.J. Hall, K.C. Cheung, and K.M. Pavlov. Phase contrast X-ray imaging of mice and rabbit lungs: a comparative study. British J. Radiology. 78, 1018-1027 (2005). (IF=2.026)
- K. K.W. Siu, M. J. Kitchen, K.M. Pavlov, John. E. Gillam, R.A. Lewis, K. Uesugi, N. Yagi. An improvement to the diffraction enhanced imaging method that permits imaging of dynamic systems. Nucl. Instr. And Meth. A 548, 169-174 (2005). (IF=1.216)
- S. Rigley, L. Rigon, K. Ataelmannan, D. Chapman, R. Doucette, R. Griebel, B. Juurlink, F. Arfelli, R. Menk, G. Tromba, R.C. Barroso, T. Beveridge, R. Lewis, K. Pavlov, K. Siu, C. Hall, E. Schültke,. Absorption edge substraction imaging for volumetric measurement in an animal model of malignant brain tumor. Nucl. Instr. And Meth. A 548, 88-93 (2005). (IF=1.216)
- K.A. Mannan, E. Schültke, R.H. Menk, K. Siu, K. Pavlov, M. Kelly, G. McLoughlin, T. Beveridge, G. Tromba, B.H. Juurlink, D. Chapman, L. Rigon, R.W. Griebel. Synchrotron supported DEI/KES of a brain tumor in an animal model: The search for a microimaging modality. Nucl. Instr. And Meth. A 548, 106-110 (2005). (IF=1.216)
- K.M. Pavlov, T.E. Gureyev, D. Paganin, Ya.I. Nesterets, M.J. Morgan, and R.A. Lewis, Linear systems with slowly varying transfer functions and their application to X-ray phase-contrast imaging. J. Phys. D: Appl. Phys. 37, 2746-2750 (2004). (IF=2.721)
- Ya.I. Nesterets, T.E. Gureyev, D. Paganin, K.M. Pavlov, S.W. Wilkins, Quantitative diffraction-enhanced X-ray imaging of weak objects. J. Phys. D: Appl. Phys. 37, 1262-1274 (2004). (IF=2.721)
- D. Paganin, T.E. Gureyev, K.M. Pavlov, R.A. Lewis, M. Kitchen, Phase retrieval using coherent imaging systems with linear transfer functions. Opt. Commun., 234, 87-105 (2004). (IF=1.449)
- Pavlov, K.M., Kewish, C.M., Davis, J.R. and Morgan, M.J. A variant on the geometrical optics approximation in diffraction enhanced tomography. J. Phys. D: Appl. Phys. 34, A168-A172 (2001). (IF=2.721)
- Kewish, C.M., Davis, J.R., Nikulin, A.Y., Benci, N., Pavlov, K.M., Morgan, M.J., and Hester, J.R. Implementation of an analyser crystal method for X-ray diffraction tomography. J. Phys. D: Appl.Phys. 34, 1059-1064 (2001). (IF=2.721)
- Pavlov, K.M., Kewish, C.M., Davis, J.R. and Morgan, M.J. A simple method for estimating linear attenuation coefficients from X-ray diffraction tomography data. Rev. Sci. Instrum. 72, 1918-1920 (2001). (IF=1.614)
- Pavlov, K.M., Kewish, C.M., Davis, J.R. and Morgan, M.J. A new theoretical approach to X-ray diffraction tomography. J. Phys. D: Appl. Phys. 33, 1596-1605 (2000). (IF=2.721)

**Project title:** Inverse problems in deterministic coherent diffractive imaging

** Principal investigator:**A/Prof. Konstantin Pavlov (UNE)

** Other participants:** Adj. Prof David Paganin (Monash University), Prof Vasily Punegov (Russian Academy of Sciences), Dr Sergey Kolosov (Russian Academy of Sciences), Dr Kaye Morgan (Monash University), A/Prof Gerd Schmalz (UNE), A/Prof Nikolai Faleev (Arizona State University), Dr David Vine (ALS), Dr Lutz Kirste (IAF-FhG)

** Project description: **

This project includes development of novel imaging and diffraction approaches to extend the current capabilities of the characterisation techniques of condensed matter physics, e.g., development of deterministic approaches to Bragg/Laue coherent diffraction that are rapid, exact and give a unique analytical solution to the inverse problem with nano-resolution. In particular, this project deals with inverse problems in statistical dynamical X-ray diffraction theory to provide detailed knowledge of properties directly impacting on micro- and opto-electronic device functionality, such as structure, internal strain, growth modes and ordering. This technique helps elucidate the structure of self-assembled quantum dots (QDs) and wide band-gap semiconductors based on alloys of AlN, GaN and InN. This research is motivated by both the exciting fundamental physics to be uncovered in studying the link from structure to functionality, and by the sustained technological pressure to further develop micro- and opto-electronic materials.

** Related publications: **

- K. M. Pavlov, V. I. Punegov, K. S. Morgan, G. Schmalz, D. M. Paganin. Deterministic Bragg Coherent Diffraction Imaging. Scientific Reports (accepted 24 March 2017) (IF=5.228)
- V.I. Punegov, S.I. Kolosov and K.M. Pavlov. Bragg-Laue X-ray dynamical diffraction on perfect and deformed lateral crystalline structures. J. Appl. Cryst. 49, 1190-1202 (2016). (IF=2.57)
- V.I. Punegov, S.I. Kolosov, K.M. Pavlov. Darwin's approach to X-ray diffraction on lateral crystalline structures. Acta Cryst. A, 70(1), 64-71 (2014). (IF=2.325)
- S.G. Podorov, K.M. Pavlov and D.M. Paganin. A non-iterative reconstruction method for direct and unambiguous coherent diffractive imaging. Optics Express 15(16), 9954-9962 (2007). (IF=3.488)
- K.M. Pavlov, D.M. Paganin, D.J. Vine, and L. Kirste. Wide angle X-ray dynamical diffraction by deformed crystals: recurrence relations. Phys. Status Solidi A, 204(8), 2613-2619 (2007). (IF=1.616)
- V. I. Punegov, A. I. Maksimov, S. I. Kolosov, and K. M. Pavlov. Calculating X-Ray diffraction from multilayer lateral crystal structures with arbitrary shapes and composition profiles. Technical Physics Letters 33(2), 125-127 (2007).
- S.G. Podorov, N.N. Faleev, K.M. Pavlov, D.M. Paganin, S.A. Stepanov and E. Förster. A New Approach to Wide-Angle Dynamical X-ray Diffraction by Deformed Crystals. J. Appl. Cryst 39, 652-655 (2006). (IF=3.984)
- V.I.Punegov, S.I. Kolosov, K.M. Pavlov. X-ray diffraction theory on a lateral crystal with elastically bent atomic planes. Technical Physics Letters 32(18), 65-72 (2006)
- V.I. Punegov, D.V. Kazakov, K.M. Pavlov, S. Mudie, Y. Takeda, M. Tabuchi. Synchrotron x-ray scattering from InGaN nanostructures: Experiment and numerical modeling. Poverkhnost (Surface Investigation: X-Ray, Synchrotron and Neutron Techniques) No8, 25-31 (2005).
- L. Kirste, K.M. Pavlov, S.T. Mudie, V.I. Punegov and N. Herres. Analysis of the mosaic structure of an ordered (Al,Ga)N layer. J. Appl. Cryst. 38, 183-192 (2005) (IF=3.984)
- S.T. Mudie, K.M. Pavlov, M.J. Morgan, J.R. Hester, Y. Takeda, M. Tabuchi, Collection of reciprocal space maps using imaging plates at the Australian National Beamline Facility at the Photon Factory. J. Synchrotron Radiation 11, 406-413 (2004). (IF=2.794)
- K.M. Pavlov, V.I. Punegov, L. Kirste, N. Herres, Y. Takeda, M. Tabuchi, M.J. Morgan, S.T. Mudie, J. Hester, Applications of statistical X-ray diffraction theory for study of multilayer systems. Bulletin of the Russian Academy of Sciences (Physics) 68 (4), 650-654 (2004).
- Mudie, S.T., Pavlov, K.M., Morgan, M.J., Tabuchi, M., Takeda, Y. and Hester, J. High-resolution X-ray diffractometry investigation of interface layers in GaN/AlN structures grown on sapphire substrates. Surf. Rev. Lett. 10, No.2&3, 513-517 (2003).
- Pavlov, K.M., Petrakov, A.P., Punegov, V.I. and Jakovidis, G. Sulphur passivated GaAs investigation using high resolution X-ray diffractometry. Surf. Rev. Lett 10, No.2&3, 533-536 (2003).
- Pavlov, K.M. and Punegov, V.I. Statistical dynamical theory of X-ray diffraction in the Bragg case: application to triple-crystal diffractometry. Acta Cryst., A56 , 227-234 (2000). (IF=2.325)
- Faleev, N.N., Egorov, A.Yu., Zhukov, A.E., Kovsh, A.R., Mikhrin, S.S., Ustinov, V.M., Pavlov, K.M., Punegov, V.I., Tabuchi, M. and Takeda, Y. X-ray diffraction analysis of multilayer InAs-GaAs heterostructures with InAs quantum dots. Semicond. 33, 1229-1237 (1999).
- Pavlov, K., Faleev, N., Tabuchi, M. and Takeda, Y. Specific aspects of X-ray diffraction on statistically distributed QDs in a perfect crystal matrix. Jp. J. Appl. Phys. 38, 269-272 (1999). (IF=1.127)
- Faleev, N., Pavlov, K., Tabuchi, M. and Takeda, Y. CTR and DCXRD studies of lateral ordering of quantum dots in multilayer periodic structures. Jp. J. Appl. Phys. 38, 277-280 (1999). (IF=1.127)
- Nesterets, Ya.I, Punegov, V.I., Pavlov, K.M. and Faleev, N.N. High resolution X-ray diffractometry of the structural characteristics of a semiconducting (InGa)As/GaAs superlattice. Techn. Phys. 44, 171-179 (1999).
- Faleev, N., Pavlov, K., Tabuchi, M. and Takeda, Y. Influence of long-range lateral ordering in structures with quantum dots on the spatial distribution of diffracted X-ray radiation. Jp. J. Appl. Phys. 38, 818-821 (1999). (IF=1.127)
- Pavlov, K.M., Punegov, V.I. The equations of the statistical dynamical theory of X-ray diffraction for deformed crystals. Acta Crystallographica A 54, 214-218 (1998). (IF=2.325)
- Pavlov, K.M., Punegov, V.I. Comment on 'Characterization of InxGa1-xAs/InP epilayers by X-ray double crystal rocking curve peak profile analysis by Haiyan An, Ming Li, Shuren Yang, Zhenhong Mai, Shiyong Liu' [J. Crystal Growth 148 (1995) 31], J. Cryst. Growth 179, 328-329 (1997). (IF=1.698)
- Pavlov, K.M., Punegov, V.I. Der Einflu? kugelsymmetrischer Kristalldefekte auf die Winkelverteilung gebeugter Röntgenstrahlung. Phys. Status Solidi (b) 199, 5-15 (1997). (IF=1.469)
- Herres, N., Fuchs, F., Schmitz, J., Pavlov, K.M., Wagner, J., Ralston, J.D., Koidl, P., Gadaleta, C. and Scamarcio, G. Effect of interfacial bonding on the structural and vibrational properties of InAs/GaSb superlattices. Phys. Rev. B 53, 15688 - 15705 (1996). (IF=3.736)
- Pavlov, K.M. and Punegov, V. I. Models of spherically symmetric microdefects in the statistical dynamical theory of diffraction: II. Correlation length. Crystallogr. Rep. 41, 585-591 (1996).
- Punegov, V.I. and Pavlov, K.M. Models of spherically symmetric microdefects in the statistical dynamical theory of diffraction: I. Correlation function. Crystallogr. Rep. 41, 575-584 (1996).
- Punegov, V. I., Pavlov, K. M., Podorov, S. G., Faleev, N. N. Determination of structural parameters of a gradient epitaxial layer by high-resolution X-ray diffractometry. II. Solution of the inverse problem in terms of a kinematic and statistical dynamic theory of a diffraction. Physics of the Solid State 38, 148-152 (1996).
- Pavlov, K.M., Punegov, V.I., Faleev, N.N. X-ray diffraction diagnostics of laser structures. Journal of Experimental and Theoretical Physics (JETP) 80, 1090-1097 (1995).
- Punegov, V.I., Pavlov, K.M. Influence of elastic bending and defects of the crystal structure on the X-ray-acoustic resonance. Tech. Phys. 39, 1190-1192 (1994).
- Pavlov, K. M., Punegov, V. I. Dynamic Laue diffraction by an harmonic superlattice with randomly distributed amorphous clusters. Phys. Solid State 36, 518-525 (1994).
- Punegov V.I., Pavlov K.M. Kinematic theory of X-ray diffraction from a harmonic superlattice with microdefects. Crystallogr. Rep. 38(5), 602-606 (1993).
- Punegov, V. I., Pavlov, K. M. Effect of structural defects on the angular distribution of X-ray Laue-diffraction in a thin crystal. Sov. Tech. Phys. Lett. 18, 390-391 (1992).

**Project title:** Symmetries and Mappings in Real and Complex Geometry

** Principal investigator:** A/Prof. Gerd Schmalz (UNE)

** Other participants:** A/Prof. Vladimir Ejov (Flinders), Prof. Dmitri Alekseevsky (Moscow), A/Prof. Martin Kolar (Brno), Dr Alessandro Ottazzi (UNSW)

** Funding body:** Australian Research Council (2013-2016)

** Project description: **

This project is focused on a wide range of interrelated areas of Differential and Cauchy-Riemann geometry and Geometric Analysis. Cauchy-Riemann-geometry has its roots in the study of the geometric properties of boundaries of domains in complex space. In recent time it has received much attention in Differential and Riemannian geometry. On the one hand, Cauchy-Riemann manifolds serve as test objects for the general machinery of parabolic geometry, on the other hand, there is a deep relation between CR geometry and Riemannian, pseudo-Riemannian and conformal geometry, which was established by Fields prize winner (and 2016 Wolf prize winner) Charles Fefferman. Particular aims of the project are: studying mappings and embeddings of CR-manifolds into other CR-manifolds and complex space, exploring the relation between CR-manifolds and its generalisations with shear-free Lorentzian geometry, finding new classes of homogeneous CR-manifolds and classifying flat Sasakian manifolds.

** Related publications: **

- OTTAZZI, A., SCHMALZ, G., Singular multicontact structures. J. Math. Anal. Appl. 443:2, 1220-1231, 2016.
- EJOV, V., SCHMALZ, G., The zero curvature equation for rigid CR-manifolds, Complex Variables and Elliptic equations, 61:4, 443-447, 2016.
- JOO, Ch.-J., KIM, K.-T., SCHMALZ, G., On the generalization of Forelli's theorem, Mathematische Annalen, 365:3-4, 1187-1200, 2016.
- EJOV, V., SCHMALZ, G., Explicit description of spherical rigid hypersurfaces in C^2, Complex Analysis and its Synergies, 1.1, Paper no. 2, 10 pp, 2015.
- DE HOOG, F., SCHMALZ, G., GUREYEV, T.E., An uncertainty inequality, Appl. Math. Lett., 38, 84-86, 2014.
- EJOV, V., SCHMALZ, G., Spherical rigid hypersurfaces C^2, Differential Geom. Appl., 33, suppl., 267-271, 2014.
- JOO, Ch.-J., KIM, K.-T., SCHMALZ, G., A generalization of Forelli's theorem, Mathematische Annalen, 355, no. 3, 1171-1176, 2013.
- EJOV, V., Kolar, M., SCHMALZ, G., Normal forms and symmetries of real hypersurfaces of finite type in C^2, Indiana Univ. Math. J., 62, no. 1, 1-32, 2013.
- SCHMALZ, G., SLOVAK, J., Free CR distributions, Cent. Eur. J. Math., 10, 1896-1913, 2012.

**Project title: **Models of the honeybee nest-site selection process

**Project participants: **Dr Timothy Schaerf (University of New England), Professor Mary Myerscough (University of Sydney), Professor Madeleine Beekman (University of Sydney)

**Project description:**

As part of their reproductive cycle, colonies of honeybees issue swarms. These swarms must then find a site to establish a new colony quickly, as a swarm is unable to store food without established combs, and is often vulnerable to the elements. Aspects of the complex process used by the cavity nesting honeybee *Apis mellifera* to select a new nest-site are relatively well understood due to a century of scientific research founded on the works of Karl von Frisch and Martin Lindauer (*A. mellifera* is the species of honeybee used by the honey industry). It is only in the last decade that detailed scientific investigations of the nest-site selection process of other species, of which there are at least six, have been undertaken. Common to each of the species studied with some detail (the cavity nesting *A. mellifera*, the red dwarf honeybee, *A. florea*, and the giant honeybee, *A. dorsata*) swarms release scouts to investigate the surrounding landscape for potential nest-sites. Upon their return to the swarm, scouts that have found a suitable target then perform a waggle dance, a stylised behaviour first recognised by Karl von Frisch as encoding the distance and direction to a resource of interest in the environment (in the context of nest-site selection, this resource is a potential new home). Other bees on the swarm follow such waggle dances, and then use the encoded information to help them find and assess the advertised site themselves. If these recruited bees also think that the advertised site is suitable, then they will return to the swarm, and advertise the location of the site to other bees with their own waggle dances. Over time, if enough bees are recruited to a particular specific site (in the case of *A. mellifera*) or a general direction (as seems to be the case for *A. florea *and perhaps *A. dorsata*), then the swarm chooses that site as a collective, and then flies to the new site to start building their new colony.

A number of mathematical models have been developed to better understand the honeybee nest-site selection process, including systems of ordinary and stochastic differential equations, matrix models and individual-based simulation models. Most of these models have been developed specifically to examine nest-site selection by *A. mellifera*, and take into account a number of known species specific behaviours. Participants in this project will build on existing models, and develop new models, to best reflect current knowledge of the overall nest-site selection processes of *A. mellifera*, *A. florea *and *A. dorsata*. These models will then be used to examine effects of swarm size (and hence the number of active participants in nest-site selection), noisy communication, and the number and relative positions of viable nesting sites on the decision-making ability of swarms of each species. Further work could then include developing a multi-generational nest-site selection model to examine how quickly species can adjust their nest-site selection process, if at all, when changing environmental conditions force a change in the type of nest-site sought.

**Related publications:**

1. T D Seeley and S C Buhrman, Group decision making in swarms of honey bees, Behavioral Ecology and Sociobiology, 45:19-31, (1999).

2. T D Seeley and S C Buhrman, Nest-site selection in honey bees: how well do swarms implement the “best-of-*N*” rule?, Behavioral Ecology and Sociobiology, 49:416-427, (2001).

3. N F Britton, N R Franks, S C Pratt and T D Seeley, Deciding on a new home: how do honeybees agree?, Proceedings of the Royal Society of London B, 269:1383-1388, (2002).

4. M R Myerscough, Dancing for a decision: a matrix model for nest-site choice by honeybees, Proceedings of the Royal Society of London B, 270:577-582, (2003).

5. K M Passino and T D Seeley, Modeling and analysis of nest-site selection by honeybee swarms: the speed and accuracy trade-off, 59:427-442, (2006).

6. B P Oldroyd, R S Gloag, N Even, W Wattanachaiyingcharoen and M Beekman, Nest site selection in the open-nesting honeybee *Apis florea*, Behavioral Ecology and Sociobiology, 62:1643-1653, (2008).

7. C List, C Elshotlz and T D Seeley, Independence and interdependence in collective decision making: an agent-based model of nest-site choice by honeybee swarms, Philosophical Transactions of the Royal Society Bm 364:755-762, (2009).

8. J C Makinson, B P Oldroyd, T M Schaerf, W Wattanachaiyingcharoen and M Beekman, Moving home: nest-site selection in the Red Dwarf honeybee (*Apis florea*), Behavioral Ecology and Sociobiology, 65:945-958, (2011).

9. K Diwold, T M Schaerf, M R Myerscough, M Middendorf and M Beekman, Deciding on the wing: in-flight decision making and search space sampling in the red dwarf honeybee *Apis florea*, Swarm Intelligence, 5:121-141, (2011).

10. T M Schaerf, M R Myerscough, J C Makinson and M Beekman, Inaccurate and unverified information in decision making: a model for the nest site selection process of *Apis florea*, Animal Behaviour, 82:995-1013, (2011).

12. T D Seeley, P K Visscher, T Schlegel, P M Hogan, N R Franks and J A R Marshall, Stop signals provide cross inhibition in collective decision-making by honeybee swarms, Science, 335:108-111, (2012).

13. T M Schaerf, J C Makinson, M R Myerscough and M Beekman, Do small swarms have an advantage when house hunting? The effect of swarm size on nest-site selection by *Apis mellifera*, Journal of the Royal Society Interface, 10:20130533, (2013).

14. J C Makinson, T M Schaerf, A Rattanawannee, B P Oldroyd and M Beekman, Consensus building in giant Asian honeybee, *Apis dorsata*, swarms on the move, Animal Behaviour, 93:191-199, (2014).

15. M Beekman, J C Makinson, M J Couvillon, K Preece and T M Schaerf, Honeybee linguistics – a comparative analysis of the waggle dance among species of *Apis*, Frontiers in Ecology and Evolution, 3:11, (2015).

16. J C Makinson, T M Schaerf, A Rattanawannee, B P Oldroyd and M Beekman, How does a swarm of the giant Asian honeybee *Apis dorsata* reach consensus? A study of the individual behaviour of scout bees, Insectes Sociaux, 63:395-406, (2016).

17. J C Makinson, T M Schaerf, N Wagner, B P Oldroyd and M Beekman, Collective decision making in the red dwarf honeybee *Apis florea*: do the bees simply follow the flowers?, Insectes Sociaux, 64:557-566, (2017).

**Project title: **Modelling the effects of climate change on dung beetle populations

**Project participants: **Associate Professor Nigel Andrew (University of New England), Dr Timothy Schaerf (University of New England)

**Project description: **As part of their life-cycle, dung beetles actively remove dung from the environment, either for use as food or breeding chambers for their offspring. The removal of dung by these beetles is also an important ecosystem service, with impact that extends to human agriculture. For example, in Australia dung beetles remove pasture dung, and as a consequence: enhance soil nutrient cycling, water penetration and soil aeration; destroy pest-fly breeding sites; and reduce the impacts of livestock gastro-intestinal parasites.

Available evidence suggests that climate change will have a substantial impact on dung beetles. At the individual level, warming advances egg laying and hatching rates, decreases egg and larval size, and decreases dung beetle survival. At population levels, warmer conditions have been linked to altitudinal shifts in the ranges of dung beetle species, and to changes in habitat selection by dung beetles. There is also evidence that warming substantially reduces dung breakdown by beetles, with an associated reduction in growth of plants surrounding dung patches. Logically, the impacts on beetles are likely to effect the services that they provide to their ecosystems.

This project will involve the development of individual based models that model dung beetle growth, development and reproductive output using dynamic energy budget theory (systems of ordinary differential equations that model how organisms allocate available energy resources in order to grow and reproduce). These models will be informed by experimental and observational work performed by Associate Professor Nigel Andrew and members of the Insect Ecology Laboratory at the University of New England. Observational data from multiple species present in Australia will include the effects of variable climate on beetle growth, maturation and reproductive output, competition within and between species for available dung resources, movements of beetles through their environment, and the general availability of dung. The models can be developed to examine possible climate effects on dung beetle populations at varying spatial scales, and to examine possible adaptation of beetles across multiple generations subject to changing climatic conditions.

**Related publications:**

1. X Wu and S Sun, Artificial warming advances egg-laying and decreases larval size in the dung beetle *Aphodius erraticus* (Coleoptera: Scarabaeidae) in a Tibetan alpine meadow, Annales Zoologci Fennici, 49:174-180, (2012).

2. T H Larsen, Upslope range shifts of Andean dung beetles in response to deforestation: compounding and confounding effects of microclimatic change, Biotropica, 44:82-89, (2012).

3. R Menéndez and D Gutiérrez, Shifts in habitat associations of dung beetles in northern Spain: climate change implications, Écoscience, 11:329-337, (2004).

4. X Wu, J E Duffy, P B Reich and S Sun, A brown-world cascade in the dung decomposer food web of an alpine meadow: effects of predator interactions and warming, Ecological Monographs, 81: 313-328, (2011).

5. S A L M Kooijman, Dynamic Energy Budget Theory for Metabolic Organisation, Cambridge University Press, (2010).

6. B T Martin, E I Zimmer, V Grimm and T Jager, Dynamic energy budget theory meets individual-based modelling: a generic and accessible implementation, Methods in Ecology and Evolution, 3:445-449, (2012).

7. B T Martin, T Jager, R M Nisbet, T G Preuss and V Grimm, Predicting population dynamics from the properties of individuals: a cross-level test of dynamic energy budget theory, American Naturalist, 181:506-519, (2013).

8. M Renton, Aristotle and adding an evolutionary perspective to models of plant architecture in changing environments, Frontiers in Plant Science, 4:284, (2013).

9. M C Welch, P W Kwan and A S M Sajeev, Applying GIS and high performance agent-based simulation for managing old world screwworm fly invasion of Australia, Acta Tropica, 138S:S82-S93, (2014).

#### Our Grants

- Maolin Zhou, Nonlinear free boundary problems: propagation and regularity, ARC DECRA award, 2017-2019, $330,324.
- S. Yan, E.N. Dancer, Y. Du and C.S. Lin, Nonlinear partial differential equations: bubbles, layers and stability, ARC discovery grant, 2017-2019, $345,000.
- Y. Du, Propagation described by partial differential equations with free boundary, ARC discovery grant, 2015-2018, $415,000.
- S. Yan, E.N. Dancer and Y. Du, Singularity, degeneracy and related problems in nonlinear partial differential equations, ARC discovery grant, 2013-2015, $300,000.
- G. Schmalz, Y. Nikolayevsky, G. Cairns, V. Ejov and D. Alekseevsky, Symmetries in real and complex geometry, ARC discovery grant, 2013-2015, $258,000.
- Y. Du, Propagation and free boundary problems in nonlinear partial differential equations, ARC discovery grant, 2012-2014, $255,000.
- Y. Du, E.N. Dancer and S. Yan, Transitions and Singular Behaviour in Nonlinear Partial Differential Equations, ARC discovery grant, 2010-2012, $306,000.
- Y. Du, Mathematical modelling of the spreading of invasive species, UNE PVCR grant, 2010, $30,000.
- Y. Du, S, Yan, G. Schmalz and A. Harris,
*Singularities in nonlinear and complex analysis*, UNE IRL grant, 2009, $13,000. - Y. Du, E.N. Dancer and S. Yan,
*Sharp Transitions in Partial Differential Equations and Related Problems*, ARC discovery grant, 2007-2009, $240,000. - Y. Du, A. Harris, G. Schmalz and S. Yan,
*Partial differential equations and complex geometry*, UNE grant, 2007-2008, $11,000 - Y. Du and E.N. Dancer,
*Free Boundary Problems in Partial Differential Equations and Related Topics*, ARC discovery grant, 2003-2006, $158,000. - V. Ejov, G. Schmalz and A Spiro,
*Normal forms and Chern-Moser Connection in the Study of Cauchy-Riemann Manifolds*, ARC discovery grant, 2003-2006, $165,000. - Y. Du,
*Sharp transitions in partial differential equations and related problems*, UNE RPG, 2006, $14,500. - Y. Du,
*Singular perturbation and transition layers in heterogeneous environment*, Australian Academy of Science and JSPS (Japan), 2005, $7,600. - Y. Du,
*Partial differential equations with unconventional boundary conditions and applications*, UNE RPG, 2005, $13,000. - Y. Du,
*Partial differential equations with unconventional boundary conditions and applications*, UNE RPG, 2004, $10,000.

#### Publications

- X. Zhang and
**Y. Du**, Sharp conditions for the existence of boundary blow-up solutions to the Monge–Ampère equation, Calculus of Variations and Partial Differential Equations, 57 (2018) 30. - W. Bao,
**Y. Du**, Z. Lin and H. Zhu, Free boundary models for mosquito range movement driven by climate warming, Journal of mathematical biology, 76 (2018) 841-875. - C. Lei, H. Nie, W. Dong and
**Y. Du**, Spreading of two competing species governed by a free boundary model in a shifting environment, Journal of Mathematical Analysis and Applications, doi:10.1016/j.jmaa.2018.02.042 (2018). - A. L. Burns,
**T. M. Schaerf**and A. J. W. Ward, Behavioural consistency and group conformity in humbug damselfish, Behaviour, 154 (2018) 1343-1359. - A. J. W. Ward, J. E. Herbert-Read,
**T. M. Schaerf**and F. Seebacher, The physiology of leadership in fish shoals: leaders have lower maximal metabolic rates and lower aerobic scope, Journal of Zoology, doi:10.1111/jzo.12534, (2018). - R. Peng and
**M. Zhou**, Effects of large degenerate advection and boundary conditions on the principal eigenvalue and its eigenfunction of a linear second order elliptic operator, Indiana Univ. Math. J. (2018).

- S. Ai,
**Y. Du**and R. Peng, Traveling waves for a generalized Holling–Tanner predator–prey model, Journal of Differential Equations, 263 (2017) 7782-7814. - C. Lei and
**Y. Du**, Asymptotic profile of the solution to a free boundary problem arising in a shifting climate model, Discrete & Continuous Dynamical Systems-Series B, 22 (2017) 895-911. - L. Wei and
**Y. Du**, Exact singular behavior of positive solutions to nonlinear elliptic equations with a Hardy potential, Journal of Differential Equations, 262 (2017) 3864-3886. - W. Ding,
**Y. Du**and X. Liang, Spreading in space-time periodic media governed by a monostable equation with free boundaries, Part 1: Continuous initial functions, J. Diff. Eqns., 262 (2017) 4988-5021. **Y. Du**, L. Wei and L. Zhou, Spreading in a shifting environment modeled by the diffusive logistic equation with a free boundary, Journal of Dynamics and Differential Equations, (2017).- S. Davis, R. Lukeman,
**T. M. Schaerf**and A. J. W. Ward, Familiarity affects collective motion in shoals of guppies (*Poecilia reticulata*), Royal Society Open Science, 4 (2017) 170312. - C. Raven, R. Shine, M. Greenlees,
**T. M. Schaerf**and A. J. W. Ward, The role of biotic and abiotic cues in stimulating aggregation by larval cane toads (*Rhinella marina*), Ethology, 123 (2017) 724-735. - J. C. Makinson,
**T. M. Schaerf**, N. Wagner, B. P. Oldroyd and M. Beekman, Collective decision making in the red dwarf honeybee*Apis florea*: do the bees simply follow the flowers? Insectes Sociaux, 64 (2017) 557-566. - A. J. W. Ward,
**T. M. Schaerf**, J. E. Herbert-Read, L. Morrell, D. J. T. Sumpter and M. M. Webster, Local interactions and global properties of wild, free-ranging stickleback shoals, Royal Society Open Science, 4 (2017) 170043. **T. M. Schaerf**, P. W. Dillingham and A. J. W. Ward, The effects of external cues on individual and collective behavior of shoaling fish, Science Advances, 3 (2017) e1603201.**P. N. Loxley**,*The two-dimensional Gabor function adapted to natural image statistics: A model of simple-cell receptive fields and sparse structure in images,*

Neural Computation 29 (2017) 2769.- B. Lou, N. Sun and
**M. Zhou**, A diffusive Fisher-KPP equation with free boundaries and time-periodic advections, Calculus of Variations and PDEs 56 (2017), no. 3. **Y. Du**, M. Wang and**M. Zhou**, Semi-wave and spreading speed for the diffusive competition model with a free boundary, J. Math. Pures Appl. (9) 107 (2017) 253-287.- A. Ottazzi and
**G. Schmalz**, Normal forms of para-CR hypersurfaces, Diff. Geom. Appl., 52 (2017) 78–93. - V. Ejov, M. Kolář and
**G. Schmalz**, Rigid embeddings of Sasakian hyperquadrics in , published online first in J. Geom. Anal. (2017). - N. Boland,
**T. Kalinowski**and F. Rigterink, A polynomially solvable case of the pooling problem, Journal of Global Optimization, 67 (2017) 621-630. - N. Boland, S. Dey,
**T. Kalinowski**, M. Molinaro and F. Rigterink, Bounding the gap between the McCormick relaxation and the convex hull for bilinear functions, Mathematical Programming, 162 (2017) 523-535. **A. Harris**, "An intrinsic approach to stable embedding of normal surface deformations"*Methods and Applications of Analysis***24**(2017) 277-292.**K. M. Pavlov,**V. I. Punegov, K. S. Morgan, G. Schmalz and D. M. Paganin, Deterministic Bragg Coherent Diffraction Imaging, Scientific Reports 7 (2017) 1132.- V. I. Punegov,
**K. M. Pavlov**, A. V. Karpov and N. N. Faleev. Applications of dynamical theory of X-ray diffraction by perfect crystals to reciprocal space mapping*.*J. Appl. Cryst. 50 (2017) 1256-1266. - C.-S. Lin and
**S. Yan**, On condensate of solutions for the Chern-Simons-Higgs equation, Annales de l'Institut Henri Poincare 34 (2017) 1329-1354.

- M. Musso, J. Wei and
**S. Yan**, Infinitely many positive solutions for a nonlinear field equation with super-critical growth. Proc. Lond. Math. Soc*.*112 (2016)1–26. - Y. Deng, S. Peng and
**S. Yan**, Critical exponents and solitary wave solutions for generalized quasilinear Schrödinger equations. J. Differential Equations 260 (2016) 1228–1262. - J. C. Makinson,
**T. M. Schaerf**, A. Rattanawannee, B. P. Oldroyd and M. Beekman, How does a swarm of the giant honeybee*Apis dorsata*reach consensus? A study of the individual behaviour of scout bees, Insectes Sociaux, 63 (2016) 395-406. - M. J. Hansen,
**T. M. Schaerf**, S. J. Simpson and A. J. W. Ward, Group foraging decisions in nutritionally differentiated environments, Functional Ecology, 30 (2016) 1638—1647. - M. J. Hansen,
**T. M. Schaerf**, J Krause and A. J. W. Ward, Crimson spotted rainbowfish (*Melanotaenia duboulayi*) change their spatial position according to nutritional requirement, PLoS One, 11 (2016) e0148334. - M. Beekman, K. Preece and
**T. M. Schaerf**, Dancing for their supper: Do honeybees adjust their recruitment dance in response to the protein content of pollen?, Insectes Sociaux, 63 (2016) 117-126. **Y. Du**, B. Lou and**M. Zhou**, Spreading and vanishing for nonlinear Stefan problems in high space dimensions, J. Elliptic and Parabolic Equations 2 (2016) 297-321.- W. Lei, G. Zhang and
**M. Zhou**, Long time behavior for solutions of the diffusive logistic equation with advection and free boundary, Calculus of Variations and PDEs 55 (2016) 1-34. - X. Chen, B. Lou,
**M. Zhou**and T. Giletti, Long time behavior of solutions of a reaction diffusion equation on unbounded intervals with Robin boundary conditions, Ann. Inst. H. Poincaré Anal. Non Linéaire 33 (2016) 67-92. - A. Ottazzi and
**G. Schmalz**, Singular multicontact structures, J. Math. Anal. Appl., 443 (2016) 1220–1231. - C.-J. Joo, K.-T. Kim and
**G. Schmalz**, On the generalization of Forelli's theorem, Math. Ann., 365 (2016) 1187–1200. - V. Ejov and
**G. Schmalz**, The zero curvature equation for rigid CR-manifolds, Complex Var. Elliptic Equ. 61 (2016) 443-447. - N. Boland,
**T. Kalinowski**and F. Rigterink, New multi-commodity flow formulations for the pooling problem, Journal of Global Optimization, 66 (2016) 669-710. **T. Kalinowski**, U. Leck, C. Reiher and I.T. Roberts, Minimizing the regularity of maximal regular antichains of 2- and 3-sets, Australasian Journal of Combinatorics, 64 (2016) 277-288.- N. Boland, I. Dumitrescu, G. Froyland and
**T. Kalinowski,**Minimum cardinality non-anticipativity constraint sets for multistage stochastic programming, Mathematical Programming, 157 (2016) 69-93. **A. Harris**and G. P. Paternain, Conformal great-circle flows on the 3-sphere,*Proceedings of the American Mathematical Society***1**44 (2016) 1725-1734.- V. I. Punegov, S. I. Kolosov and
**K. M. Pavlov,**Bragg-Laue X-ray dynamical diffraction on perfect and deformed lateral crystalline structures, J. Appl. Cryst. 49 (2016) 1190-1202.

**Y. Du**and P. Polácik, Locally uniform convergence to an equilibrium for nonlinear parabolic equations on RN, Indiana University Mathematics Journal, 64 (2015) 787-824.**Y. Du**, S.-B. Hsu and Y. Lou, Multiple steady-states in phytoplankton population induced by photoinhibition, Journal of Differential Equations, 258 (2015) 2408-2434.**Y. Du**and X. Liang, Pulsating semi-waves in periodic media and spreading speed determined by a free boundary model, Ann. Inst. Henri Poincare Anal. Non Lineaire, 32 (2015) 279-305.**Y. Du**and B. Lou, Spreading and vanishing in nonlinear diffusion problems with free boundaries, J. Eur. Math. Soc., 17 (2015) 2673-2724.- D. Cao, S. Peng and
**S. Yan**, Planar vortex patch problem in incompressible steady flow,*Adv. Math.,*270 (2015) 263–301. **Y. Du**and Z. Guo, Finite Morse index solutions of weighted elliptic equations and the critical exponents.,*Calc. Var. Partial Differential Equations*, 54 (2015) 3161–3181.**Y. Du**and L. Wei, Lei Boundary behavior of positive solutions to nonlinear elliptic equations with Hardy potential.*J. Lond. Math. Soc.*91 (2015) 731–749.- M. J. Hansen,
**T. M. Schaerf**and A. J. W. Ward, The influence of nutritional state on individual and group movement behaviour in shoals of crimson-spotted rainbowfish (*Melanotaenia duboulayi*), Behavioral Ecology and Sociobiology, 69 (2015) 1713-1722. - M. J. Hansen,
**T. M. Schaerf**and A. J. W. Ward, The effect of hunger on the exploratory behaviour of shoals of mosquitofish*Gambusia holbrooki*, Behaviour, 152 (2015) 1659-1677. - J. R. Christie,
**T. M. Schaerf**and M. Beekman, Selection against heteroplasmy explains the evolution of uniparental inheritance of mitochondria, PLoS Genetics, 11 (2015) e1005112. - M. Beekman, J. C. Makinson, M. J. Couvillon, K. Preece and
**T. M. Schaerf**, Honeybee linguistics – a comparative analysis of the waggle dance among species of*Apis*, Frontiers in Ecology and Evolution, 3 (2015) doi:10.3389/fevo.2015.00011. - H. Gu, B. Lou and
**M. Zhou**, Long time behavior of solutions of Fisher-KPP equation with advection and free boundaries, J. Funct. Anal., 269 (2015) 1714–1768. - T. Giletti, L. Monsaingeo and
**M. Zhou**, A KPP road-field system with spatially periodic exchange terms, Nonlinear Anal. 128 (2015) 273–302. **Y. Du**, B. Lou and**M. Zhou**, Nonlinear diffusion problems with free boundaries: convergence, transition speed and zero number arguments, SIAM J. Math. Anal., 47 (2015) 3555–3584.**Y. Du**, H. Matsuzawa and**M. Zhou**, Spreading speed and profile for nonlinear Stefan problems in high space dimensions, J. Math. Pures Appl., 103 (2015) 741–787.- V. Ejov and
**G. Schmalz**, Explicit description of spherical rigid hypersurfaces in , Complex Analysis and its Synergies, 1-2 (2015). **T. Kalinowski**, D. Matsypura and M.W.P. Savelsbergh, Incremental network design with maximum flows, European Journal of Operational Research, 242 (2015) 51-62.- Y. I. Nesterets, T. E. Gureyev, S. C. Mayo, A. W. Stevenson, D. Thompson, J. M. C. Brown, M. J. Kitchen,
**K. M. Pavlov**, D. Lockie and G. Tromba, A feasibility study of X-ray phase-contrast mammographic tomography at the Imaging and Medical beamline of the Australian Synchrotron., J. Synchr. Rad. 22 (2015) 1509-1523. - H. Baues and
**B.Bleile**, The third homotopy group as a π₁-module, Applicable Algebra in Engineering, Communication and Computing, 26 (2015) 165-189. - Y. Deng, C.-S. Lin and
**S. Yan**, On the prescribed scalar curvature problem in , local uniqueness and periodicity, J. Math. Pures Appl. 104 (2015) 1013-1044. - P. Álvarez-Caudevilla,
**Y. Du**and R. Peng, Qualitative analysis of a cooperative reaction-diffusion system in a spatiotemporally degenerate environment, SIAM Journal on Mathematical Analysis, 46 (2015) 499-531.

**Y. Du**, H. Matano and K. Wang, Regularity and asymptotic behavior of nonlinear Stefan problems, Arch. Rational Mech. Anal., 212 (2014) 957-1010.**Y. Du**, Z. Guo and K. Wang, Monotonicity formula and*ε*-regularity of stable solutions to supercritical problems and applications to finite Morse index solutions.*Calc. Var. Partial Differential Equations*50 (2014) 615–638.**Y. Du**and Zhigui Lin, The diffusive competition model with a free boundary: Invasion of a superior or inferior competitor, Discrete Cont. Dyn. Syst.-B, 19 (2014) 3105-3132.- J. C. Makinson,
**T. M. Schaerf**, A. Rattanawanne, B. P. Oldroyd and M. Beekman, Consensus building in the giant Asian honeybee,*Apis dorsata*, swarms on the move, Animal Behaviour, 93 (2014) 191-199. - J. Cai, B. Lou and
**M. Zhou**, Asymptotic behavior of solutions of a reaction diffusion equation with free boundary conditions, J. Dynam. Differential Equations 26 (2014) 1007–1028. **Y. Du**, H. Matsuzawa and**M. Zhou**, Sharp estimate of the spreading speed determined by nonlinear free boundary problems, SIAM J. Math. Anal. 46 (2014) 375–396.- F. de Hoog,
**G. Schmalz**and T. E. Gureyev, An uncertainty inequality, Appl. Math. Lett. 38 (2014) 84-86. - T. Gureyev, Y. Nesterets, F. de Hoog,
**G. Schmalz**, S. C. Mayo, S. Mohammadi and G. Tromba, Duality between noise and spatial resolution in linear systems, Optics Express, 22 (2014) 9087-9094. - V. Ejov and
**G.Schmalz**, Spherical rigid hypersurfaces in , Differential Geom. Appl. 33 (2014) 267-271. - N. Boland,
**T. Kalinowski**, H. Waterer and L. Zheng, Scheduling arc maintenance jobs in a network to maximize total flow over time, Discrete Applied Mathematics, 163 (2014) 34-52. - M. Baxter, T. Elgindy, A.T. Ernst,
**T. Kalinowski**and M.W.P. Savelsbergh, Incremental network design with shortest paths, European Journal of Operational Research, 238 (2014) 675-684. **A. Harris**and M. Kolar, On hyperbolicity of domains with strictly pseudoconvex ends, Canadian Journal of Mathematics, 66 (2014) 197-204.- P. Vagovic, L. Sveda, A. Cecilia, E. Hamann, D. Pelliccia, E. N. Gimenez, D. Korytar,
**K. M. Pavlov**, Z. Zaprazny, M. Zuber, T. Koenig, M. Olbinado, W. Yashiro, A. Momose, M. Fiederle and T. Baumbach, X-ray Bragg Magnifier Microscope as a linear shift invariant imaging system: image formation and phase retrieval, Optics Express 22 (2014) 21508-21520. - T. E. Gureyev, S. C. Mayo, Ya I. Nesterets, S. Mohammadi, D. Lockie, R. H. Menk, F. Arfelli,
**K. M. Pavlov**, M. J. Kitchen, F. Zanconati, C. Dullin and G Tromba, Investigation of the imaging quality of synchrotron-based phase-contrast mammographic tomography, J. Phys. D: Appl. Phys., 47 (2014) 365401. - V. I. Punegov, S. I. Kolosov and
**K.M. Pavlov**, Darwin's approach to X-ray diffraction on lateral crystalline structures, Acta Cryst. A, 70 (2014) 64-71.

**T. M. Schaerf**, J. C. Makinson, M. R. Myerscough and M. Beekman, Do small swarms have an advantage when house hunting? – The effect of swarm size on nest-site selection by Apis mellifera, Journal of the Royal Society Interface, 10 (2013) 20130533.- J. E. Herbert-Read, S. Krause, L. Morrel,
**T. M. Schaerf,**J. Krause and A. J. W. Ward, The role of individuality in collective group movement, Proceedings of the Royal Society B, 280 (2013) 20122564. **P. N. Loxley**and B. T. Nadiga, Bistability and Hysteresis of Maximum-Entropy States in Decaying Two-Dimensional Turbulence, Physics of Fluids 25 (2013) 015113.**T. Kalinowski**, U. Leck and I.T. Roberts, Maximal antichains of minimum size, Electronic Journal of Combinatorics, 20 (2013) 1-14.- J.-C. Joo, K.-T. Kim and
**G. Schmalz**, A generalization of Forelli's theorem. Math. Ann. 355 (2013) 1171-1176. - C.-S. Lin and
**S. Yan**, Bubbling solutions for the SU(3) Chern-Simons model on a torus, Comm. Pure Appl. Math., 66 (2013) 991-1027. - C.-S. Lin and
**S. Yan**, Existence of bubbling solutions for Chern-Simons model on a torus, Arch. Ration. Mech. Anal. 207 (2013) 353-392. **S. Yan**and J. Yang, Infinitely many solutions for an elliptic problem involving critical Sobolev and Hardy-Sobolev exponents, Calc. Var. Partial Differential Equations 48 (2013) 587-610.- D. Cao, S. Peng and
**S. Yan**, On the Webster scalar curvature problem on the CR sphere with a cylindrical-type symmetry, J. Geom. Anal. 23 (2013), 1674-1702. - J. Wei and
**S. Yan**, Infinitely many nonradial solutions for the Henon equation with critical growth, Rev. Mat. Iberoam., 29 (2013) 997-1020. **Y. Du**, Z. Guo and R. Peng, A diffusive logistic model with a free boundary in time-periodic environment, J. Funct. Anal., 265 (2013), 2089-2142.- E. N. Dancer,
**Y. Du**and M. Efendiev, Quasilinear elliptic equations on half- and quarter-spaces, Adv. Nonlinear Studies (special issue dedicated to Klaus Schmitt), 13 (2013) 115-136. **Y. Du**and Z. M. Guo, Finite Morse index solutions and asymptotics of weighted nonlinear elliptic equations, Adv. Diff. Eqns., 18 (2013) 737-768.**Y. Du**and R. Peng, Sharp spatiotemporal patterns in the diffusive time-periodic logistic equation, J. Diff. Eqns., 254 (2013) 3794-3816.

- R. M. Brito,
**T. M. Schaerf**, M. R. Myerscough, T. A. Heard and B. P. Oldroyd, Brood comb construction by the stingless bees*Tetragonula hockingsi*and*Tetragonula carbonaria*, Swarm Intelligence, 6 (2012) 151-176. **T. M. Schaerf**and C. Macaskill, On contour crossings in contour-advective simulations – part 2 – analysis of crossing errors and methods for their prevention, Journal of Computational Physics, 231 (2012) 481-504.**T. M. Schaerf**and C. Macaskill, On contour crossings in contour-advective simulations – part 1 – alogirthm for detection and quantification, Journal of Computational Physics, 231 (2012) 465-480.- T. W. Baillie, T. E. Gureyev, J. A. Schmalz and
**K. M. Pavlov,**Phase-contrast X-ray tomography using Teague’s method, Optics Express 20 (2012) 16913-16925. - G. Bunting,
**Y. Du**and K. Krakowski, Spreading speed revisited: Analysis of a free boundary model, Networks and Heterogeneous Media (special issue dedicated to H. Matano), 7 (2012) 583-603. **Y. Du**and R. Peng, The periodic logistic equation with spatial and temporal degeneracies, Trans. Amer. Math. Soc., 364 (2012) 6039-6070.**Y. Du**and Z. M. Guo, The Stefan problem for the Fisher-KPP equation, J. Diff. Eqns., 253 (2012) 996-1035.**Y. Du**and L. Ma, A Liouville theorem for conformal Gaussian curvature type equations in , Calculus of Variations and PDEs, 43 (2012) 485-505.- D. Cao, S. Peng and
**S. Yan**, Infinitely many solutions for p-Laplacian equation involving critical Sobolev growth. J. Funct. Anal. 262 (2012) 2861-2902. - W. Chen, J. Wei and
**S. Yan**, Infinitely many solutions for the Schrödinger equations in with critical growth. J. Differential Equations 252 (2012) 2425-2447. **G. Schmalz**and J. Slovak, Free CR distributions. Cent. Eur. J. Math. 10 (2012) 1896-1913.

- J. E. Herbert-Read, A. Perna, R. Mann,
**T. M. Schaerf**, D. J. T. Sumpter and A. J. W. Ward, Inferring the rules of interaction of shoaling fish, Proceedings of the National Academy of Sciences, 108 (2011) 18726-18731. **T. M. Schaerf,**M. R. Myerscough, J. C. Makinson and M. Beekman, Inaccurate and unverified information in decision making – a model for the nest site selection process of Apis florea, Animal Behaviour, 82 (2011) 995-1013.- K. Diwold,
**T. M. Schaerf**, M. R. Myerscough, M. Middendorf and M. Beekman, Deciding on the wing: in-flight decision making and search space sampling in the red dwarf honeybee A. florea, Swarm Intelligence, 5 (2011) 121-141. - J. C. Makinson, B. P. Oldroyd,
**T. M. Schaerf,**W. Wattanachaiyingcharoen and M. Beekman, Moving home: nest-site selection in the red dwarf honeybee (Apis florea), Behavioral Ecology and Sociobiology, 65 (2011) 945—958. **P. N. Loxley**, L. M. A. Bettencourt, and G. T. Kenyon, Ultra-Fast detection of salient contours through horizontal connections in the primary visual cortex,

Europhysics Letters 93 (2011) 64001.**T. Kalinowski**, A Minimum Cost Flow Formulation for Approximated MLC Segmentation, Networks, 57 (2011) 135-140.**J. A. Schmalz,**T. E. Gureyev, D. M. Paganin and**K.M. Pavlov**. Phase retrieval using radiation and matter wave fields: Validity of Teague's method for solution of the transport of intensity equation, Physical Review A 84(2011) 023808.**K. M. Pavlov,**D. M. Paganin, D. J. Vine,**J. A. Schmalz,**Y. Suzuki, K. Uesugi, A. Takeuchi, N. Yagi, A. Kharchenko, G. Blaj, J. Jakubek, M. Altissimo and J. N. Clark. Quantized hard-x-ray phase vortices nucleated by aberrated nanolenses. Physical Review A 83 (2011) 013813.- S. G. Podorov, A. I. Bishop, D .M. Paganin and
**K. M. Pavlov**, Mask-assisted deterministic phase–amplitude retrieval from a single far-field intensity diffraction pattern: two experimental proofs of principle using visible light, Ultramicroscopy, 111 (2011)782–787. - M. J. Kitchen, D. M. Paganin, K. Uesugi, B. J. Allison, R. A. Lewis, S. B. Hooper and
**K.M. Pavlov**, Phase contrast image segmentation using a Laue analyser, Phys. Med. Biol., 56 (2011) 515-534. **Y. Du**and L. Mei, On a nonlocal reaction-diffusion-advection equation modeling phytoplankton, Nonlinearity, 24 (2011) 319-349.**Y. Du**and Z. Guo, Spreading-vanishing dichotomy in the diffusive logistic model with a free boundary II, J. Diff. Eqns., 250 (2011) 4336-4366.- J. Wei and
**S. Yan**, Infinitely many positive solutions for an elliptic problem with critical or supercritical growth. J. Math. Pures Appl. 96 (2011) 307-333. - D. Cao and
**S. Yan**, Infinitely many solutions for an elliptic Neumann problem involving critical Sobolev growth. J. Differential Equations 251 (2011) 1389-1414. - L. Wang, J. Wei and
**S. Yan**, On Lin-Ni's conjecture in convex domains. Proc. Lond. Math. Soc. 102 (2011) 1099-1126. - V. Ezhov, B. McLaughlin and
**G. Schmalz**, From Cartan to Tanaka: getting real in the complex world, Notices Amer. Math. Soc., 58 (2011) 20-27. - H.-J. Baues and
**B. Bleile**, Self-maps of the product of two spheres fixing the diagonal, Topology Appl. 158 (2011) 2198-2204. **A. Harris**and M. Kolar, On infinitesimal deformations of the regular part of a complex cone singularity, Kyushu J. Math., 65 (2011) 25-38.

- M. J. Kitchen, D. M. Paganin, K. Uesugi, B. J. Allison, R. A. Lewis, S. B. Hooper and
**K.M. Pavlov**. X-ray phase, absorption and scatter retrieval using two or more phase contrast images*,*Optics Express 18 (2010) 19994-20012. - D. Cao, S. Peng and
**S. Yan**, Multiplicity of solutions for the plasma problem in two dimensions. Adv. Math. 225 (2010) 2741-2785. - F. Cirstea and
**Y. Du**,*Isolated singularities for weighted quasilinear elliptic equations,*J. Functional Anal., 259 (2010) 174-202. **Y. Du**and Z. Lin,*Spreading-vanishing dichotomy in the diffusive logistic model with a free boundary,*SIAM J. Math. Anal., 42 (2010) 377-405.**Y. Du**and Hiroshi Matano,*Convergence and sharp thresholds for propagation in nonlinear diffusion problems,*J. European Math. Soc., 12 (2010) 279-312.- J. Wei and
**S. Yan**, On a stronger Lazer-McKenna conjecture for Ambrosetti-Prodi type problems, Ann. Sc. Norm. Super. Pisa Cl. Sci. 9 (2010) 423-457. - C.-S. Lin and
**S. Yan**, Bubbling solutions for relativistic abelian Chern-Simons model on a torus, Comm. Math. Phys., 297 (2010) 733-758. - D. Cao and
**S. Yan**, Infinitely many solutions for an elliptic problem involving critical Sobolev growth and Hardy potential, Calc. Var. Partial Differential Equations, 38 (2010) 471-501. - L. Wang, J. Wei and
**S. Yan**, A Neumann problem with critical exponent in nonconvex domains and Lin-Ni's conjecture, Trans. Amer. Math. Soc., 362 (2010), 4581-4615. - J. Wei and
**S. Yan**, Infinitely many solutions for the prescribed scalar curvature problem on , J. Funct. Anal, 258 (2010) 3048-3081. - J. Wei and
**S. Yan**, Infinitely many positive solutions for the nonlinear Schrödinger equations in , Calc. Var. Partial Differential Equations 37 (2010) 423-439. **J. Schmalz**,**G. Schmalz**, T. Gureyev, and**K. Pavlov**, On the derivation of the Greens function for the Helmholtz equation using generalized functions, Am. J. Phys., 78 (2010) 181-186.**B. Bleile**, Poincare duality pairs of dimension three, Forum Math., 22 (2010) 277-301.- C. Albert,
**B. Bleile**and J. Frohlich, Batalin-Vilkovisky integrals in finite dimensions, J. Math. Phys., 51 (2010) 015213.

**P. N. Loxley**and P. A. Robinson, Soliton Model of Competitive Neural Dynamics during Binocular Rivalry, Physical Review Letters 102 (2009) 258701.- H. Henke, P. A. Robinson, P. M. Drysdale and
**P. N. Loxley**, Spatiotemporal dynamics of pattern formation in the primary visual cortex and hallucinations,

Biological Cybernetics, 101 (2009) 3. - M. Grüttmüller, S. Hartmann,
**T. Kalinowski,**U. Leck and I.T. Roberts, Maximal Flat Antichains of Minimum Weight, Electronic Journal of Combinatorics, 16 (2009) #R69. **T. Kalinowski,**A Dual of the Rectangle-Segmentation Problem for Binary Matrices, Electronic Journal of Combinatorics, 16 (2009) #R89.- W. X. Tang, D. E. Jesson,
**K. M. Pavlov**, M. J. Morgan and B. F. Usher, Ga droplet morphology on GaAs (001) studied by Lloyd’s Mirror photo-emission electron microscopy, J. Phys.: Condens. Matter, 21 (2009) 314022. - D. J. Vine, D. M. Paganin,
**K. M. Pavlov,**K. Uesugi, A. Takeuchi, Y. Suzuki, N. Yagi, T. Kämpfe, E.-B. Kley, E. Förster. Deterministic Green’s function retrieval using hard X-rays, Phys. Rev. Lett., 102 (2009) 043901. **Y. Du**and Y. Yamada, On the long-time limit of positive solutions to the degenerate logistic equation, Discrete and Continuous Dynamical Systems A, 25 (2009) 123-132.**Y. Du,**R. Peng and M. Wang, Effect of a protection zone in the diffusive Leslie predator-prey model, J. Diff. Eqns., 246 (2009) 3932-3956.**Y. Du**and Z. M. Guo, Positive solutions of an elliptic equation with negative exponent: stability and critical power, J. Diff. Eqns., 246 (2009) 2387-2414.- D. Cao, S. Peng and
**S. Yan**, Asymptotic behaviour of ground state solutions for the Henon equation, IMA J. Appl. Math., 74 (2009) 468-480. - E. N. Dancer, D. Hilhorst and
**S. Yan**, Peak solutions for the Dirichlet problem of an elliptic system, Discrete Contin. Dyn. Syst. 3 (2009) 731-761. - K. T. Kim, E. Poletsky and
**G. Schmalz,**Functions holomorphic along holomorphic vector fields, Journal of Geometric Analysis, 19 (2009) 655-666. - V. Ejov, M. Kolar and
**G. Schmalz**, Degenerate hypersurfaces with a two-parametric family of automorphisms, Complex Variables and Elliptic Equations, 54 (2009) 283-291.

**P. N. Loxley**, Rate of magnetization reversal due to nucleation of soliton-antisoliton pairs at point-like defects, Physical Review B, 77 (2008) 144424.- M. J. Kitchen,
**K. M. Pavlov,**S. B. Hooper, D. J. Vine, K. K. W. Siu, M. J. Wallace, M. L. L. Siew, N. Yagi, K. Uesugi and R.A. Lewis, Simultaneous acquisition of dual analyser-based phase contrast X-ray images for small animal imaging, Eur J. Radiol, 68S (2008) S49-S53. **Y. Du**and S.-B. Hsu, Concentration phenomena in a nonlocal quasiliear problem modelling phytoplankton I: Existence, SIAM J. Math. Anal., 40 (2008) 1419-1440.**Y. Du**and S.-B. Hsu, Concentration phenomena in a nonlocal quasiliear problem modelling phytoplankton II: Limiting profile, SIAM J. Math. Anal., 40 (2008) 1441-1470.**Y. Du,**P. Y. H. Pang and M. Wang, Qualitative analysis of a predator-prey model with stage structure for the predator, SIAM J. Appl. Math., 69 (2008) 596-620.**Y. Du**and X. Liang, A diffusive competition model with a protection zone, J. Diff. Eqns., 244 (2008) 61-86.**Y. Du**, The heterogeneous Allen-Cahn equation in a ball: solutions with layers and spikes, J. Diff. Eqns., 244 (2008) 117-169.**Y. Du**, Z. Liu, A. Pistoia and**S. Yan**, Sign changing solutions with clustered layers near the origin for singularly perturbed semilinear elliptic problems on a ball, Methods and Applications of Analysis (special issue dedicated to N.S. Trudinger), 15 (2008) 137-148.**A. Harris**and M. Kolar, A Remark on cohomology with supports in the complement of a cone singularity, RIMS Kokyuroku, 1610 (2008) 32-37.**A. Harris**and G. Paternain, Dynamically convex Finsler metrics and J-holomorphic embedding of asymptotic cylinders, Ann. Global Anal and Geom., 34 (2008) 115-134.**A. Harris**and K. Wysocki, Branch-structure of J-holomorphic curves near periodic orbits of a contact manifold, Trans. Amer. Math. Soc., 360 (2008) 2131-2152.- V. Beloshapka, V. Ejov and
**G. Schmalz**, Holomorphic classification of 4-dimensional surfaces in C3, Izv. Ross. Akad. Nauk Ser. Mat., 72 (2008) 3-18. - V. Ejov,
**G. Schmalz**and A. Spiro, CR-manifolds of codimension two of parabolic type, Indiana University Mathematics Journal, 57 (2008) 309-342. - C.-K. Han, J.-W. Oh and
**G. Schmalz**, Symmetry algebra for multi-contact structures given by 2n vector fields on , Mathematische Annalen, 341 (2008) 529-542. - D. Cao, E. S. Noussair and
**S. Yan**, Multiscale-bump standing waves with a critical frequency for nonlinear Schrödinger equations, Trans. Amer. Math. Soc., 360 (2008) 3813-3837. - E. N. Dancer and
**S. Yan,**The Lazer-McKenna conjecture and a free boundary problem in two dimensions, Journal of the London Mathematical Society, 78 (2008) 639-662. - E. N. Dancer and
**S. Yan**, On the Lazer-McKenna conjecture involving critical and supercritical exponents, Methods and Applications of Analysis, 15 (2008) 97-120. - H. J. Baues and
**B. Bleile,**Poincare duality complexes in dimension four, Algebr. Geom. Topol., 8 (2008) 2355-2389.