Emeritus Professor Vo Anh

Research theme: Environment, Energy Research discipline: Mathematical Sciences Research projects

• New methods in theory and applications of spherical random fields

This project aims to investigate and model spherical random fields which are described as solutions of infinite-dimensional stochastic differential equations on a sphere. The project studies properties and develops spectral analysis of these solutions. The obtained theoretical results will be used to construct new methods for numerical approximation and statistical estimation of these random fields. In particular, novel asymptotic and statistical methodology will be developed for tensor-valued spherical random fields. The results will be applied to model and analyse cosmic microwave background data. The work will improve the accuracy in determining cosmological parameters and provide novel tools for better understanding of the Universe during its early stages.

• Stochastic modelling of spatiotemporal nonlinear diffusion processes with multifractal characteristics

This project aims at developing new mathematical and statistical tools for modelling and prediction of spatiotemporal nonlinear systems with multifractal scaling, including the Burgers equation and the KPZ equation. The renormalised solutions of these equations, leading to their scaling laws and non-Gaussian central limit theorems, are obtained. Their spectral properties and higher-order spectra are derived.

• Statistical estimation and approximation of anomalous diffusion

This project develops a comprehensive theory of diffusion and transport processes, such as heat conduction and fluid flow, in highly heterogeneous media based on recent advances in mathematical and statistical research. The theory produces analytical tools and faster algorithms for statistical estimation, numerical approximation and prediction of anomalous diffusion.

• Diffusion and transport of saltwater in coastal aquifers

Saltwater intrusion is a severe environmental problem in coastal regions of Australia, resulting in loss of agricultural land at an alarming rate. This project aims to develop a three-dimensional mathematical model for the simulation and prediction of saltwater intrusion into complex coastal aquifers based on recent advances in the theory of anomalous diffusion, stochastic modelling and numerical methods. Areas of expertise

• Stochastic Processes and Random Fields
• Stochastic modelling
• Time series analysis
• Environmental modelling
• Financial modelling

Grants from the Australian Research Council (ARC)

• ARC Discovery Grant DP190101889, 2019-2021, $339,000. F. Liu (QUT), V. Vegh (UQ), Q. Yang (QUT), V.V. Anh (QUT), R. Magin (U Illinois at Chicago), W. Tan (Peking U). Project: Fractional dynamic models for MRI to probe tissue microstructure.
• ARC Discovery Grant DP160101366, 2016-2018, $324,686. P. Broadbridge (La Trobe), A. Olenko (La Trobe), V.V. Anh (QUT), N.N. Leonenko (Cardiff). Project: New methods in theory and cosmic applications of spherical random fields.
• ARC Discovery Grant DP120103770, 2012-2014, $360,000. I. Turner (QUT), K. Burrage (QUT), V.V. Anh (QUT), T. Moroney (QUT). Project: From genes to organs: Understanding how heterogeneity in tissue modulates cellular behaviour in the heart.
• ARC Discovery Grant DP0986766, 2009-2011, $185,000. I. Turner (QUT), V.V. Anh (QUT). Project: A multi-scale approach for modeling coupled transport in heterogeneous and anisotropic porous media.
• ARC Discovery Grant DP0559807, 2005-2009, $353,000. V.V. Anh (QUT), K.S. Lau (Chinese University of Hong Kong), N.N. Leonenko (Cardiff University), J.M. Angulo and M.D. Ruiz-Medina (University of Granada). Project: Stochastic modeling of spatiotemporal nonlinear diffusion processes with multifractal characteristics.
• ARC Linkage-Infrastructure Equipment & Facilities LE0453501, 2004, $406,097 from ARC with $650,000 cash contributions from QUT and James Cook University. A.N. Pettitt (QUT), J.C. Patterson (JCU), D.L. McElwain (QUT), V.V. Anh (QUT), M. Mahendran (QUT), A.S. Hurn (QUT), S.R. Connolly (JCU), R.H. Crozier (JCU), T. Hardy (JCU), F.R. Keene (JCU). Project: A computational research grid serving regional and metropolitan Queensland.
• ARC Linkage-Projects Grant LP0348653, 2003-2006, $263,300 plus $60,000 cash contribution from Queensland Department of Natural Resources and Mines. V.V. Anh (QUT), I. Turner (QUT), K. Bajracharya (DNRM) and A. Durick (DNRM). Project: Diffusion and transport of saltwater in coastal aquifers.
• ARC Linkage International Grant LX0348297, 2003-2004, $24,200. V.V. Anh (QUT), J.M. Angulo and M.D. Ruiz-Medina (University of Granada). Project: Stochastic modeling and analysis of spatial-temporal processes with fractal characteristics.
• ARC Discovery Grant DP0345577, 2003-2005, $195,000. V.V. Anh (QUT), C.C. Heyde (Australian National University & Columbia University) and N.N. Leonenko (Cardiff University). Project: Statistical estimation and approximation of anomalous diffusion.
• ARC Large Grant A10024117, 2000-2002, $153,000. V.V. Anh (QUT) and C.C. Heyde (ANU & Columbia University). Project: Stochastic analysis of long-range dependent multifractals.
• ARC SPIRT Grant C10024101, 2000-2002, $225,000 plus $48,000 cash contribution from Queensland Department of Natural Resources. V.V. Anh (QUT), I. Turner (QUT), K. Bajracharya (DNR) and J. Arunakumaren (DNR) . Project: Monitoring and modelling of saltwater intrusion into heterogeneous aquifer systems.
• ARC Research Infrastructure Equipment & Facilities Grant R00002823, 2000, $692,000 from ARC, $596,000 from QUT and $100,000 from Griffith University. A.N. Pettitt (QUT), J. Diederich (QUT), D. Thiel (GU), V.V. Anh (QUT) and D.S. McElwain (QUT). Project: Queensland High Performance Computing (HPC) MetaCentre Enhancement.
• ARC Large Grant A69804041, 1998-2000, $186,000. V.V. Anh (QUT), C.C. Heyde (ANU) and M. Farge (CNRS, France). Project: Structural study of long-range dependence, infinite variance and coherent structures.
• ARC Large Grant A89601825, 1996-1998, $175,140. V.V. Anh (QUT), P.E. Kloeden (Deakin University & Goethe University) and W.H. Melbourne (Monash University). Project: Multifractal analysis and stochastic models of turbulence dispersion.
• ARC Collaborative Grant C19600199, 1996-1998, $180,000 plus $20,000 cash contribution from Environment Protection Authority of New South Wales. V.V. Anh (QUT), P.E. Kloeden (Deakin University & Goethe University) and G. Johnson (CSIRO, Sydney). Project: Stochastic models for air quality management.
• ARC Large Grant A69531724, 1995-1997, $91,330. V.V. Anh (QUT) and C.C. Heyde (ANU). Project: Statistical analysis of data with long-range dependence.
• ARC Small Grant, 2000, $16,000. V.V. Anh (QUT). Project: Characterisation and representation of multifractals.
• ARC Small Grant, 1997, $12,500. V.V. Anh (QUT), C.C. Heyde (ANU) and P.E. Kloeden (Goethe University). Project: Financial stochastics.
• ARC Small Grant, 1995, $10,300. V.V. Anh (QUT). Project: Real-time forecasting models for air quality management.
• ARC Small Grant, 1994, $19,900. V.V. Anh (QUT). Project: Real-time forecasting models for air quality management.

QUT grants

• QUT Strategic Collaborative Program Grant, 2003-2004, $300,000. J. Hogan, P. Timms, A. Pettitt, V. Anh, P. Roe, W. Kelly, S. Geva, A. van Daal, P. Chen. Project: High performance computing and algorithms for molecular biology.
•  QUT Strategic Collaborative Program Grant, 2003-2004, $236,400. M. Cox, A. Goonetilleke, V. Anh, I. Turner, R. Frost. Project: Environmental hydrology and groundwater resource sustainability.
• QUT Strategic Links Scheme Grant, in collaboration with Queensland Department of Primary Industries-Forestry and Pacific Harbour, 2002-2004, $30,000. M. Cox, V.V. Anh and I. Turner. Project: Modelling of Bribie Island groundwater.
• QUT Meritorious Grant, 1993, $14,500 plus matching funds from Voxson Pty Ltd. V.V. Anh and S. Sridharan (School of Electrical & Electronic Systems Engineering). Project: Full motion picture video compression to MPEG standard.
• QUT Research Encouragement Award, 1992, $19,000. V.V. Anh and S. Sridharan (School of Electrical & Electronic Systems Engineering). Project: Statistical image compression.
• QUT R&D Grant, 1991, $14,000. V.V. Anh and S. Sridharan (School of Electrical & Electronic Systems Engineering). Project: Image compression for videotelephone systems.
• DEET Mechanism B funding, 1992, $114,000. V.V. Anh, Director, School Centre in Statistical Science.
• DEET Mechanism B funding, 1991, $150,000. V.V. Anh, Director, School Centre in Statistical Science.
• QUT Special Research Grant, 1990, $25,000. V.V. Anh, D. Huang (School of Mathematics) and J. Wong (School of Physics). Project:  Development of a low-cost 2D digital filter.

• Anh, V., Grecksch, W. & Yong, J. (2011). Regularity of backward stochastic volterra integral equations in Hilbert spaces. Stochastic Analysis and Applications, 29(1), 146–168. https://eprints.qut.edu.au/43181
• Ruiz-Medina, M., Anh, V. & Angulo, J. (2011). Multifractional markov processes in heterogeneous domains. Stochastic Analysis and Applications, 29(1), 15–47. https://eprints.qut.edu.au/42728
• Zhuang, P., Liu, F., Anh, V. & Turner, I. (2009). Numerical methods for the variable-order fractional advection-diffusion equation with a nonlinear source term. SIAM Journal on Numerical Analysis, 47(3), 1760–1781. https://eprints.qut.edu.au/29755
• Anh, V., Leonenko, N. & Shieh, N. (2008). Multifractality of products of geometric Ornstein-Uhlenbeck -type processes. Advances in Applied Probability, 40(4), 1129–1156. https://eprints.qut.edu.au/30855
• Zhuang, P., Liu, F., Anh, V. & Turner, I. (2008). New solution and analytical techniques of the implicit numerical method for the anomalous subdiffusion equation. SIAM Journal on Numerical Analysis, 46(2), 1079–1095. https://eprints.qut.edu.au/30905
• Anh, V., Leonenko, N. & Sakhno, L. (2007). Statistical Inference Using Higher-Order Information. Journal of Multivariate Analysis, 98(4), 706–742. https://eprints.qut.edu.au/7397
• Liu, F., Anh, V. & Turner, I. (2004). Numerical Solution of the Space Fractional Fokker-Planck Equation. Journal of Computational and Applied Mathematics, 166, 209–219. https://eprints.qut.edu.au/10113
• Anh, V., Heyde, C. & Leonenko, N. (2002). Dynamic models of long-memory processes driven by levy noise. Journal of Applied Probability, 39, 730–747. https://eprints.qut.edu.au/21675
• Anh, V. & Leonenko, N. (2002). Renormalization and Homogenization of Fractional Diffusion Equations with Random Data. Probability Theory and Related Fields, 124, 381–408. https://eprints.qut.edu.au/406
• Anh, V. & Leonenko, N. (2001). Spectral Analysis of Fractional Kinetic Equations with Random Data. Journal of Statistical Physics, 1349–1387. https://eprints.qut.edu.au/407

Title

From Genes to Organ Function: Understanding how Heterogeneity in Tissue Modulates Cellular Behaviour in the Heart

Primary fund type

CAT 1 - Australian Competitive Grant

Project ID

DP120103770

Start year

2012

Keywords

Heterogeneous Computing; Cardiovascular System; Mathematical Modelling; Simulation Algorithm

Title

A Multi-Scale Approach For Modelling Coupled Transport In Heterogeneous And Anisotropic Porous Media

Primary fund type

CAT 1 - Australian Competitive Grant

Project ID

DP0986766

Start year

2009

Keywords

Anomalous Diffusion; Fractional Partial Differential Equations; Finite Volume Method; Krylov Subspace Methods; Matrix Function Approximation; Computational Mathematics

• Fuzzy Methods for Analysis of Microarrays and Networks (2011)
• Multifractal Characterisation and Analysis of Complex Networks (2011)
• Stochastic modelling of financial time series with memory and multifractal scaling (2009)
• Stochastic Modelling of Financial Processes with Memory and Semi-Heavy Tails (2005)
• Estimation of a Class of Nonlinear Time Series Models (2004)

• Forecasting Time-Varying Value-at-Risk (2010)