Project title: Propagation Described by Partial Differential Equations with Free Boundary
Principal investigator: Prof. Yihong Du (UNE)
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)
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.
- Y. Du, Mingxin Wang and Maolin Zhou, Semi-wave and spreading speed for the diffusive competition model with a free boundary, J. Math. Pure Appl., 107(2017), 253-287.
- Weiwei Ding, Y. Du and Xing 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, Hiroshi Matsuzawa and Maolin Zhou, Spreading speed and profile for nonlinear Stefan problems in high space dimensions, J. Math. Pures Appl., 103(2015), 741-787.
- Y. Du and Xing 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 Bendong Lou, Spreading and vanishing in nonlinear diffusion problems with free boundaries, J. Eur. Math. Soc., 17(2015), 2673-2724.
- Y. Du, Hiroshi Matsuzawa and Maolin Zhou, Sharp estimate of the spreading speed determined by nonlinear free boundary problems, SIAM J. Math. Anal., 46(2014), 375-396.
- Y. Du, Hiroshi Matano and Kelei Wang, Regularity and asymptotic behavior of nonlinear Stefan problems, Arch. Rational Mech. Anal., 212(2014), 957-1010.
- 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.
- Y. Du, Zongming Guo and Rui Peng, A diffusive logistic model with a free boundary in time-periodic environment, J. Funct. Anal., 265 (2013), 2089-2142.
- Y. Du, Establishment or vanishing: fate of an invasive species based on mathematical models, in "The Balance of Nature and Human Impact", edited by Klaus Rohde, Cambradge Univ Press, 2013, pp231-238.
Project title: Nonlinear free boundary problems: propagation and regularity
Principal investigator: Dr Maolin Zhou (UNE)
Funding body: Australian Research Council (2017-2020)
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.
- 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)
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 behaviour of solutions with finite Morse index is usually not beyond reach and can sometimes be completely classified.
- Musso, Monica; Wei, Juncheng; Yan, Shusen; Infinitely many positive solutions for a nonlinear field equation with super-critical growth. Proc. Lond. Math. Soc. (3) 112 (2016), no. 1, 1-26.
- Deng, Yinbin; Peng, Shuangjie; Yan, Shusen; Critical exponents and solitary wave solutions for generalized quasilinear Schrödinger equations. J. Differential Equations 260 (2016), no. 2, 1228-1262.
- Cao, Daomin; Peng, Shuangjie; Yan, Shusen; Planar vortex patch problem in incompressible steady flow. Adv. Math. 270 (2015), 263-301.
- Deng, Yinbin; Lin, Chang-Shou; Yan, Shusen; On the prescribed scalar curvature problem in R^N, local uniqueness and periodicity. J. Math. Pures Appl. (9) 104 (2015), no. 6, 1013-1044.
- Du, Yihong; Guo, Zongming; Finite Morse index solutions of weighted elliptic equations and the critical exponents. Calc. Var. Partial Differential Equations 54 (2015), no. 3, 3161-3181.
- Du, Yihong; Wei, Lei; Boundary behavior of positive solutions to nonlinear elliptic equations with Hardy potential. J. Lond. Math. Soc. (2) 91 (2015), no. 3, 731-749.
- Dancer, E. N.; A remark on stable solutions of nonlinear elliptic equations on R^3 or R^4. Differential Integral Equations 27 (2014), no. 5-6, 483-488.
- Du, Yihong; Guo, Zongming; Wang, Kelei; Monotonicity formula and e-regularity of stable solutions to supercritical problems and applications to finite Morse index solutions. Calc. Var. Partial Differential Equations 50 (2014), no. 3-4, 615-638.
- Lin, Chang-Shou; Yan, Shusen; Bubbling solutions for the SU(3) Chern-Simons model on a torus. Comm. Pure Appl. Math. 66 (2013), no. 7, 991-1027.
- Lin, Chang-Shou; Yan, Shusen; Existence of bubbling solutions for Chern-Simons model on a torus. Arch. Ration. Mech. Anal. 207 (2013), no. 2, 353-392.
- Du, Yihong; Guo, Zongming; Finite Morse-index solutions and asymptotics of weighted nonlinear elliptic equations. Adv. Differential Equations 18 (2013), no. 7-8, 737-768.
- Dancer, E. N.; Du, Yihong; Efendiev, Messoud; Quasilinear elliptic equations on half- and quarter-spaces. Adv. Nonlinear Stud. 13 (2013), no. 1, 115-136.
Project title: Analysis and Modelling of Collective Animal Motion
Project participants: Dr Timothy Schaerf (University of New England), Professor Ashley Ward (University of Sydney)
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.
- 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
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.
- 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).
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.
- 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: optimisation 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)
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.
- 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)
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.
- 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)
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.
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.
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).