Ian Turner

Is the unigram relevance model term independent? Classifying term dependencies in query expansion

Publisher: ACM

Date: 05-12-2012

DOI: 10.1145/2407085.2407102

Two new implicit numerical methods for the fractional cable equation

Publisher: ASME International

Date: 04-10-2011

DOI: 10.1115/1.4002269

Abstract: The cable equation is one of the most fundamental equations for modeling neuronal dynamics. Cable equations with fractional order temporal operators have been introduced to model electrotonic properties of spiny neuronal dendrites. In this paper, we consider the following fractional cable equation involving two fractional temporal derivatives: ∂u(x,t)/∂t=D0t1−γ1(κ(∂2u(x,t)/∂x2))−μ02Dt1−γ2u(x,t)+f(x,t), where 0 γ1, γ2 , κ , and μ02 are constants, and D0t1−γu(x,t) is the Rieman–Liouville fractional partial derivative of order 1−γ. Two new implicit numerical methods with convergence order O(τ+h2) and O(τ2+h2) for the fractional cable equation are proposed, respectively, where τ and h are the time and space step sizes. The stability and convergence of these methods are investigated using the energy method. Finally, numerical results are given to demonstrate the effectiveness of both implicit numerical methods. These techniques can also be applied to solve other types of anomalous subdiffusion problems.

Analytical and numerical solutions of the space and time fractional bloch-torrey equation

Publisher: ASMEDC

Date: 2011

DOI: 10.1115/DETC2011-47613

Abstract: Fractional order dynamics in physics, particularly when applied to diffusion, leads to an extension of the concept of Brownian motion through a generalization of the Gaussian probability function to what is termed anomalous diffusion. As MRI is applied with increasing temporal and spatial resolution, the spin dynamics are being examined more closely such examinations extend our knowledge of biological materials through a detailed analysis of relaxation time distribution and water diffusion heterogeneity. Here the dynamic models become more complex as they attempt to correlate new data with a multiplicity of tissue compartments where processes are often anisotropic. Anomalous diffusion in the human brain using fractional order calculus has been investigated. Recently, a new diffusion model was proposed by solving the Bloch-Torrey equation using fractional order calculus with respect to time and space (see R.L. Magin et at, J. Magnetic Resonance, 190 (2008) 255–270). However effective numerical methods and supporting error analyses for the fractional Bloch-Torrey equation are still limited. In this paper, the space and time fractional Bloch-Torrey equation (ST-FBTE) is considered. The time and space derivatives in the ST-FBTE are replaced by the Caputo and the sequential Riesz fractional derivatives, respectively. Firstly, we derive an analytical solution for the ST-FBTE with initial and boundary conditions on a finite domain. Secondly, we propose an implicit numerical method (INM) for the ST-FBTE, and the stability and convergence of the INM are investigated. We prove that the implicit numerical method for the ST-FBTE is unconditionally stable and convergent. Finally, we present some numerical results that support our theoretical analysis.

Analytical solutions for the multi-term time-space Caputo-Riesz fractional advection-diffusion equations on a finite domain

Publisher: Elsevier BV

Date: 05-2012

DOI: 10.1016/J.JMAA.2011.12.055

Computationally efficient numerical methods for time- and space-fractional Fokker-Planck equations

Publisher: IOP Publishing

Date: 10-2009

DOI: 10.1088/0031-8949/2009/T136/014026

Stability and convergence of the difference methods for the space-time fractional advection-diffusion equation

Publisher: Elsevier BV

Date: 08-2007

DOI: 10.1016/J.AMC.2006.08.162

The Use of Finite Difference/Element Approaches for Solving the Time-Fractional Subdiffusion Equation

Publisher: Society for Industrial & Applied Mathematics (SIAM)

Date: 2013

DOI: 10.1137/130910865

Effective cell-centred time-domain Maxwell’s equations numerical solvers

Publisher: Elsevier BV

Date: 05-2005

DOI: 10.1016/J.APM.2004.10.002

Numerical Investigation into Coarse-Scale Models of Diffusion in Complex Heterogeneous Media

Publisher: Springer Science and Business Media LLC

Date: 21-08-2021

DOI: 10.1007/S11242-021-01665-4

Numerical Algorithms for Time-Fractional Subdiffusion Equation with Second-Order Accuracy

Publisher: Society for Industrial & Applied Mathematics (SIAM)

Date: 2015

DOI: 10.1137/14096390X

Time-dependent fractional advection-diffusion equations by an implicit MLS meshless method

Publisher: Wiley

Date: 10-05-2011

DOI: 10.1002/NME.3223

Characterization of anomalous relaxation using the time-fractional Bloch equation and multiple echo T₂*-weighted magnetic resonance imaging at 7 T

Publisher: Wiley

Date: 26-03-2016

DOI: 10.1002/MRM.26222

Abstract: To study the utility of fractional calculus in modeling gradient-recalled echo MRI signal decay in the normal human brain. We solved analytically the extended time-fractional Bloch equations resulting in five model parameters, namely, the litude, relaxation rate, order of the time-fractional derivative, frequency shift, and constant offset. Voxel-level temporal fitting of the MRI signal was performed using the classical monoexponential model, a previously developed anomalous relaxation model, and using our extended time-fractional relaxation model. Nine brain regions segmented from multiple echo gradient-recalled echo 7 Tesla MRI data acquired from five participants were then used to investigate the characteristics of the extended time-fractional model parameters. We found that the extended time-fractional model is able to fit the experimental data with smaller mean squared error than the classical monoexponential relaxation model and the anomalous relaxation model, which do not account for frequency shift. We were able to fit multiple echo time MRI data with high accuracy using the developed model. Parameters of the model likely capture information on microstructural and susceptibility-induced changes in the human brain. Magn Reson Med 77:1485-1494, 2017. © 2016 International Society for Magnetic Resonance in Medicine.

Numerical methods for fractional partial differential equations with Riesz space fractional derivatives

Publisher: Elsevier BV

Date: 2010

DOI: 10.1016/J.APM.2009.04.006

Automatic query expansion: A structural linguistic perspective

Publisher: Wiley

Date: 26-02-2014

DOI: 10.1002/ASI.23065

A spatially second-order accurate implicit numerical method for the space and time fractional Bloch-Torrey equation

Publisher: Springer Science and Business Media LLC

Date: 17-09-2013

DOI: 10.1007/S11075-013-9768-X

Surface reconstruction of wheat leaf morphology from three-dimensional scanned data

Publisher: CSIRO Publishing

Date: 2015

DOI: 10.1071/FP14058

Abstract: Realistic virtual models of leaf surfaces are important for several applications in the plant sciences, such as modelling agrichemical spray droplet movement and spreading on the surface. In this context, the virtual surfaces are required to be smooth enough to facilitate the use of the mathematical equations that govern the motion of the droplet. Although an effective approach is to apply discrete smoothing D2-spline algorithms to reconstruct the leaf surfaces from three-dimensional scanned data, difficulties arise when dealing with wheat (Triticum aestivum L.) leaves, which tend to twist and bend. To overcome this topological difficulty, we develop a parameterisation technique that rotates and translates the original data, allowing the surface to be fitted using the discrete smoothing D2-spline methods in the new parameter space. Our algorithm uses finite element methods to represent the surface as a linear combination of compactly supported shape functions. Numerical results confirm that the parameterisation, along with the use of discrete smoothing D2-spline techniques, produces realistic virtual representations of wheat leaves.

Long exposure localization in darkness using consumer cameras

Publisher: IEEE

Date: 05-2013

DOI: 10.1109/ICRA.2013.6631105

A hybrid technique for computing the power distribution generated in a lossy medium during microwave heating

Publisher: Elsevier BV

Date: 12-2006

DOI: 10.1016/J.CAM.2005.10.031

Series expansion solutions for the multi-term time and space fractional partial differential equations in two- and three-dimensions

Publisher: Springer Science and Business Media LLC

Date: 09-2013

DOI: 10.1140/EPJST/E2013-01972-2

Efficient simulation of unsaturated flow using exponential time integration

Publisher: Elsevier BV

Date: 03-2011

DOI: 10.1016/J.AMC.2011.01.041

An advanced numerical modeling for Riesz space fractional advection–dispersion equations by a meshfree approach

Publisher: Elsevier BV

Date: 09-2016

DOI: 10.1016/J.APM.2016.03.036

Numerical simulation for the three-dimension fractional sub-diffusion equation

Publisher: Elsevier BV

Date: 08-2014

DOI: 10.1016/J.APM.2014.03.031

Numerical simulation for two-dimensional Riesz space fractional diffusion equations with a nonlinear reaction term

Publisher: Walter de Gruyter GmbH

Date: 2013

DOI: 10.2478/S11534-013-0296-Z

Abstract: Fractional differential equations have attracted considerable interest because of their ability to model anomalous transport phenomena. Space fractional diffusion equations with a nonlinear reaction term have been presented and used to model many problems of practical interest. In this paper, a two-dimensional Riesz space fractional diffusion equation with a nonlinear reaction term (2D-RSFDE-NRT) is considered. A novel alternating direction implicit method for the 2D-RSFDE-NRT with homogeneous Dirichlet boundary conditions is proposed. The stability and convergence of the alternating direction implicit method are discussed. These numerical techniques are used for simulating a two-dimensional Riesz space fractional Fitzhugh-Nagumo model. Finally, a numerical ex le of a two-dimensional Riesz space fractional diffusion equation with an exact solution is given. The numerical results demonstrate the effectiveness of the methods. These methods and techniques can be extended in a straightforward method to three spatial dimensions, which will be the topic of our future research.

Fast Bayesian analysis of spatial dynamic factor models for multitemporal remotely sensed imagery

Publisher: Oxford University Press (OUP)

Date: 26-10-2010

DOI: 10.1111/J.1467-9876.2010.00739.X

Abstract: Remote sensing is one ex le where data sets that vary across space and time have become so large that ‘standard’ approaches employed by statistical modellers for applied analysis are no longer feasible. We present a Bayesian methodology, which makes use of recently developed algorithms in applied mathematics, for the analysis of large space–time data sets. In particular, a Markov chain Monte Carlo algorithm is proposed for the efficient estimation of spatial dynamic factor models. The spatial dynamic factor model is specified whereby spatial dependence is modelled though the columns of the factor loadings matrix by using a Gaussian Markov random field. Krylov subspace methods are used to take advantage of the sparse matrix structures that are inherent in the model. The methodology is used to analyse remotely sensed data from the Moderate Imaging Spectroradiometer satellite. In particular, the methodology proposed is used in conjunction with high resolution imagery for the classification, in terms of land type, of two regions in central Queensland, Australia.

A new fractional finite volume method for solving the fractional diffusion equation

Publisher: Elsevier BV

Date: 08-2014

DOI: 10.1016/J.APM.2013.10.007

A dual-scale modeling approach for drying hygroscopic porous media

Publisher: Society for Industrial & Applied Mathematics (SIAM)

Date: 2013

DOI: 10.1137/120873005

Finite volume and finite element methods for solving a one-dimensional space-fractional Boussinesq equation

Publisher: Elsevier BV

Date: 08-2014

DOI: 10.1016/J.APM.2013.10.008

Modelling water droplet movement on a leaf surface

Publisher: Elsevier BV

Date: 04-2011

DOI: 10.1016/J.MATCOM.2010.09.003

A finite volume scheme with preconditioned Lanczos method for two-dimensional space-fractional reaction-diffusion equations

Publisher: Elsevier BV

Date: 08-2014

DOI: 10.1016/J.APM.2014.02.005

A Crank-Nicolson adi spectral method for a two-dimensional Riesz space fractional nonlinear reaction-diffusion equation

Publisher: Society for Industrial & Applied Mathematics (SIAM)

Date: 2014

DOI: 10.1137/130934192

Spray retention on whole plants: modelling, simulations and experiments

Publisher: Elsevier BV

Date: 10-2016

DOI: 10.1016/J.CROPRO.2016.06.003

On the Order of the Fractional Laplacian in Determining the Spatio-Temporal Evolution of a Space-Fractional Model of Cardiac Electrophysiology

Publisher: Public Library of Science (PLoS)

Date: 02-12-2015

DOI: 10.1371/JOURNAL.PONE.0143938

A computationally effective alternating direction method for the space and time fractional Bloch–Torrey equation in 3-D

Publisher: Elsevier BV

Date: 12-2012

DOI: 10.1016/J.AMC.2012.10.056

A meshless method based on Point Interpolation Method (PIM) for the space fractional diffusion equation

Publisher: Elsevier BV

Date: 04-2015

DOI: 10.1016/J.AMC.2015.01.092

An Approximate Solution for the Rayleigh-Stokes Problem for a Heated Generalized Second Grade Fluid with Fractional Derivative Model Using the Adomian Decomposition Method

Publisher: SAGE Publications

Date: 12-2009

DOI: 10.1260/174830109789621310

Abstract: The Rayleigh-Stokes problem for a generalized second grade fluid subject to a flow on a heated flat plate and within a heated edge is investigated. Fractional calculus is used for description of such a viscoelastic fluid. We employ the Adomian decomposition method to construct an approximate solution. Some ex les are presented to show the efficiency and simplicity of the method.

A meshfree radial basis function method for simulation of multi‐dimensional conservation problems

Publisher: Wiley

Date: 30-12-2023

DOI: 10.1002/NUM.22980

Abstract: Many computational fluid dynamics problems utilize finite volume frameworks for simulation, due to the simplifications provided by conservative formulation of the driving partial differential equations (PDEs). However, fluid dynamics applications can often involve temporal shifts in the domain structure—such as moving boundaries, or pore structure changes—requiring mesh adaptation throughout computation. These mesh adaptations often render classical numerical methods such as the finite volume method infeasible, due to their reliance on a well‐defined static mesh structure. This limitation has led to the development of a wide variety of meshless methods—techniques that can simulate PDEs without requiring a rigid connective structure between nodes. However, most meshless methods are typically based on finite element or finite difference formulations, and the limited number of meshless finite volume methods (MFVMs) either introduce a weak background mesh, or use weak‐form approximations that do not take full advantage of the strong conservative form of the driving equations. Addressing this gap within this study we outline a meshfree numerical scheme for simulation of partial different equations, based on strong‐form finite volume style formulations. Building upon the previously developed MFVM, this technique uses radial basis functions to interpolate the problem domain, and approximate fluxes in a disjoint finite volume scheme, removing reliance on a mesh structure. We present method derivation, including promising new techniques for enforcing boundary conditions in a meshless environment. Following this we discuss method accuracy and computational performance across a variety of problems in two and three dimensions. We then illustrate how this method may prove beneficial for applications in porous media modeling, and computational fluid dynamics. For completeness, we provide a sensitivity analysis of the method hyper‐parameters and investigate the conservative properties of the method. We also illustrate similarities of this approach to the widely used meshless point collocation methods. We close with a discussion of the strengths, limitations, and broader applicability of the technique.

Numerical simulation of the fractional Bloch equations

Publisher: Elsevier BV

Date: 2014

DOI: 10.1016/J.CAM.2013.06.027

A Three Species Model to Simulate Application of Hyperbaric Oxygen Therapy to Chronic Wounds

Publisher: Public Library of Science (PLoS)

Date: 31-07-2009

DOI: 10.1371/JOURNAL.PCBI.1000451

A RBF meshless approach for modeling a fractal mobile/immobile transport model

Publisher: Elsevier BV

Date: 2014

DOI: 10.1016/J.AMC.2013.10.008

Efficient Bayesian Estimation of Multivariate State Space Models

Publisher: Elsevier BV

Date: 10-2008

DOI: 10.1016/J.CSDA.2009.04.019

Finite element method for space-time fractional diffusion equation

Publisher: Springer Science and Business Media LLC

Date: 21-10-2015

DOI: 10.1007/S11075-015-0065-8

ICCM2012 – Topical Issue on computational methods, numerical modelling & simulation in Applied Mathematical Modelling

Publisher: Elsevier BV

Date: 08-2014

DOI: 10.1016/J.APM.2014.04.006

A coarse-grained multiscale model to simulate morphological changes of food-plant tissues undergoing drying

Publisher: Royal Society of Chemistry (RSC)

Date: 2019

DOI: 10.1039/C8SM01593G

Abstract: The design and force interaction field of coarse-grained multiscale model to study the morphological behaviour of plant tissues during drying.

Simulating droplet motion on virtual leaf surfaces

Publisher: The Royal Society

Date: 05-2015

DOI: 10.1098/RSOS.140528

Abstract: A curvilinear thin film model is used to simulate the motion of droplets on a virtual leaf surface, with a view to better understand the retention of agricultural sprays on plants. The governing model, adapted from Roy et al. (2002 J. Fluid Mech. 454, 235–261 ( doi:10.1017/S0022112001007133 )) with the addition of a disjoining pressure term, describes the gravity- and curvature-driven flow of a small droplet on a complex substrate: a cotton leaf reconstructed from digitized scan data. Coalescence is the key mechanism behind spray coating of foliage, and our simulations demonstrate that various experimentally observed coalescence behaviours can be reproduced qualitatively. By varying the contact angle over the domain, we also demonstrate that the presence of a chemical defect can act as an obstacle to the droplet's path, causing break-up. In simulations on the virtual leaf, it is found that the movement of a typical spray size droplet is driven almost exclusively by substrate curvature gradients. It is not until droplet mass is sufficiently increased via coalescence that gravity becomes the dominating force.

Minimising wave drag for free surface flow past a two-dimensional stern

Publisher: AIP Publishing

Date: 07-2011

DOI: 10.1063/1.3609284

Abstract: Free surface flow past a two-dimensional semi-infinite curved plate is considered, with emphasis given to solving the shape of the resulting wave train that appears downstream on the surface of the fluid. This flow configuration can be interpreted as applying near the stern of a wide blunt ship. For steady flow in a fluid of finite depth, we apply the Wiener-Hopf technique to solve a linearised problem, valid for small perturbations of the uniform stream. Weakly nonlinear results obtained by a forced KdV equation are also presented, as are numerical solutions of the fully nonlinear problem, computed using a conformal mapping and a boundary integral technique. By considering different families of shapes for the semi-infinite plate, it is shown how the litude of the waves can be minimised. For plates that increase in height as a function of the direction of flow, reach a local maximum, and then point slightly downwards at the point at which the free surface detaches, it appears the downstream wavetrain can be eliminated entirely

Numerical investigation of three types of space and time fractional Bloch-Torrey equations in 2D

Publisher: Walter de Gruyter GmbH

Date: 2013

DOI: 10.2478/S11534-013-0220-6

Abstract: Recently, the fractional Bloch-Torrey model has been used to study anomalous diffusion in the human brain. In this paper, we consider three types of space and time fractional Bloch-Torrey equations in two dimensions: Model-1 with the Riesz fractional derivative Model-2 with the one-dimensional fractional Laplacian operator and Model-3 with the two-dimensional fractional Laplacian operator. Firstly, we propose a spatially second-order accurate implicit numerical method for Model-1 whereby we discretize the Riesz fractional derivative using a fractional centered difference. We consider a finite domain where the time and space derivatives are replaced by the Caputo and the sequential Riesz fractional derivatives, respectively. Secondly, we utilize the matrix transfer technique for solving Model-2 and Model-3. Finally, some numerical results are given to show the behaviours of these three models especially on varying domain sizes with zero Dirichlet boundary conditions.

Mathematical modelling of gas production and compositional shift of a CSG (coal seam gas) field: Local model development

Publisher: Elsevier BV

Date: 08-2015

DOI: 10.1016/J.ENERGY.2015.05.107

Computational Approaches to Solving Equations Arising from Wound Healing

Publisher: Springer Science and Business Media LLC

Date: 11-12-2008

DOI: 10.1007/S11538-008-9360-Z

Abstract: In the wound healing process, the cell movement associated with chemotaxis generally outweighs the movement associated with random motion, leading to advection-dominated mathematical models of wound healing. The equations in these models must be solved with care, but often inappropriate approaches are adopted. Two one-dimensional test problems arising from advection-dominated models of wound healing are solved using four algorithms--MATLAB's inbuilt routine pdepe.m, the Numerical Algorithms Group routine d03pcf.f, and two finite volume methods. The first finite volume method is based on a first-order upwinding treatment of chemotaxis terms and the second on a flux limiting approach. The first test problem admits an analytic solution which can be used to validate the numerical results by analyzing two measures of the error for each method: the average absolute difference and a mass balance error. These criteria as well as the visual comparison between the numerical methods and the exact solution lead us to conclude that flux limiting is the best approach to solving advection-dominated wound healing problems numerically in one dimension. The second test problem is a coupled nonlinear three species model of wound healing angiogenesis. Measurement of the mass balance error for this test problem further confirms our hypothesis that flux limiting is the most appropriate method for solving advection-dominated governing equations in wound healing models. We also consider two two-dimensional test problems arising from wound healing, one that admits an analytic solution and a more complicated problem of blood vessels growth into a devascularized wound bed. The results from the two-dimensional test problems also demonstrate that the flux limiting treatment of advective terms is ideal for an advection-dominated problem.

Numerical Modelling and Optimisation of a Microwave Enhanced Rapid Prototyping

Publisher: Springer Science and Business Media LLC

Date: 06-2001

DOI: 10.1007/S001700170102

A Variable Order Fractional Differential-Based Texture Enhancement Algorithm with Application in Medical Imaging

Publisher: Public Library of Science (PLoS)

Date: 17-07-2015

DOI: 10.1371/JOURNAL.PONE.0132952

Novel numerical methods for solving the time-space fractional diffusion equation in two dimensions

Publisher: Society for Industrial & Applied Mathematics (SIAM)

Date: 2011

DOI: 10.1137/100800634

Stability and convergence of an implicit numerical method for the space and time fractional Bloch–Torrey equation

Publisher: The Royal Society

Date: 13-05-2013

DOI: 10.1098/RSTA.2012.0150

Abstract: Fractional-order dynamics in physics, particularly when applied to diffusion, leads to an extension of the concept of Brownian motion through a generalization of the Gaussian probability function to what is termed anomalous diffusion. As magnetic resonance imaging is applied with increasing temporal and spatial resolution, the spin dynamics is being examined more closely such examinations extend our knowledge of biological materials through a detailed analysis of relaxation time distribution and water diffusion heterogeneity. Here, the dynamic models become more complex as they attempt to correlate new data with a multiplicity of tissue compartments, where processes are often anisotropic. Anomalous diffusion in the human brain using fractional-order calculus has been investigated. Recently, a new diffusion model was proposed by solving the Bloch–Torrey equation using fractional-order calculus with respect to time and space. However, effective numerical methods and supporting error analyses for the fractional Bloch–Torrey equation are still limited. In this paper, the space and time fractional Bloch–Torrey equation (ST-FBTE) in both fractional Laplacian and Riesz derivative form is considered. The time and space derivatives in the ST-FBTE are replaced by the Caputo and the sequential Riesz fractional derivatives, respectively. Firstly, we derive an analytical solution for the ST-FBTE in fractional Laplacian form with initial and boundary conditions on a finite domain. Secondly, we propose an implicit numerical method (INM) for the ST-FBTE based on the Riesz form, and the stability and convergence of the INM are investigated. We prove that the INM for the ST-FBTE is unconditionally stable and convergent. Finally, we present some numerical results that support our theoretical analysis.

GPU accelerated algorithms for computing matrix function vector products with applications to exponential integrators and fractional diffusion

Publisher: Society for Industrial & Applied Mathematics (SIAM)

Date: 2016

DOI: 10.1137/15M1021672

A tensor encoding model for semantic processing

Publisher: ACM

Date: 29-10-2012

DOI: 10.1145/2396761.2398617

A new control-volume finite-element scheme for heterogeneous porous media: Application to the drying of softwood

Publisher: Wiley

Date: 28-06-2011

DOI: 10.1002/CEAT.201100060

Solving linear and non-linear space-time fractional reaction-diffusion equations by the Adomian decomposition method

Publisher: Wiley

Date: 28-08-2007

DOI: 10.1002/NME.2165

Stability and convergence of an effective numerical method for the time-space fractional fokker-planck equation with a nonlinear source term

Publisher: Hindawi Limited

Date: 2010

DOI: 10.1155/2010/464321

Abstract: Fractional Fokker-Planck equations (FFPEs) have gained much interest recently for describing transport dynamics in complex systems that are governed by anomalous diffusion and nonexponential relaxation patterns. However, effective numerical methods and analytic techniques for the FFPE are still in their embryonic state. In this paper, we consider a class of time-space fractional Fokker-Planck equations with a nonlinear source term (TSFFPENST), which involve the Caputo time fractional derivative (CTFD) of order (0, 1) and the symmetric Riesz space fractional derivative (RSFD) of order (1, 2]. Approximating the CTFD and RSFD using the L1-algorithm and shifted Grünwald method, respectively, a computationally effective numerical method is presented to solve the TSFFPE-NST. The stability and convergence of the proposed numerical method are investigated. Finally, numerical experiments are carried out to support the theoretical claims.

A variable-stepsize Jacobian-free exponential integrator for simulating transport in heterogeneous porous media: Application to wood drying

Publisher: Elsevier BV

Date: 2013

DOI: 10.1016/J.JCP.2012.07.024

Numerical treatment of a two-dimensional variable-order fractional nonlinear reaction-diffusion model

Publisher: IEEE

Date: 06-2014

DOI: 10.1109/ICFDA.2014.6967430

Two-scale computational modelling of water flow in unsaturated soils containing irregular-shaped inclusions

Publisher: Wiley

Date: 30-01-2014

DOI: 10.1002/NME.4625

Stability and convergence of two new implicit numerical methods for the fractional cable equation

Publisher: ASMEDC

Date: 2010

DOI: 10.1115/DETC2009-86578

Abstract: The cable equation is one the most fundamental equations for modeling neuronal dynamics. Cable equations with fractional order temporal operators have been introduced to model electrotonic properties of spiny neuronal dendrites. In this paper we consider the following fractional cable equation involving two fractional temporal derivatives: ∂u(x,t)∂t=0Dt1−γ1κ∂2u(x,t)∂x2−μ02Dt1−γ2u(x,t)+f(x,t), where 0 & γ1,γ2 & 1, κ & 0, and μ02 are constants, and 0Dt1−γu(x,t) is the Rieman-Liouville fractional partial derivative of order 1 − γ. Two new implicit numerical methods with convergence order O(τ + h2) and O(τ2 + h2) for the fractional cable equation are proposed respectively, where τ and h are the time and space step sizes. The stability and convergence of these methods are investigated using the energy method. Finally, numerical results are given to demonstrate the effectiveness of both implicit numerical methods. These techniques can also be applied to solve other types of anomalous subdiffusion problems.

Analytical solutions for the multi-term time-fractional diffusion-wave/diffusion equations in a finite domain

Publisher: Elsevier BV

Date: 11-2012

DOI: 10.1016/J.CAMWA.2012.02.042

Towards a model of spray–canopy interactions: Interception, shatter, bounce and retention of droplets on horizontal leaves

Publisher: Elsevier BV

Date: 10-2014

DOI: 10.1016/J.ECOLMODEL.2013.11.002

Project LE140100061

Start Date: 2014

End Date: 2014

Funder: Australian Research Council

(From Genes To Organ Function: Understanding How Heterogeneity In Tissue Modulates Cellular Behaviour In The Heart)

Start Date: 2012

End Date: 2014

Funder: Australian Research Council

(Modelling Interactions Of Spray Droplets With Plants)

Start Date: 2010

End Date: 2013

Funder: Australian Research Council

(Making The Most Of Remotely Sensed Data: Bayesian Spatio-temporal Models For Enhanced Natural Resource Management And Design)

Start Date: 2010

End Date: 2012

Funder: Australian Research Council

Discovery Projects - Grant ID: DP150103675

Start Date: 06-2015

End Date: 12-2019

Amount: $347,100.00

Funder: Australian Research Council

Linkage Projects - Grant ID: LP0775269

Start Date: 11-2007

End Date: 12-2010

Amount: $180,000.00

Funder: Australian Research Council

Linkage Projects - Grant ID: LP0348653

Start Date: 02-2004

End Date: 12-2007

Amount: $263,300.00

Funder: Australian Research Council

Discovery Projects - Grant ID: DP230102414

Start Date: 2023

End Date: 12-2025

Amount: $373,000.00

Funder: Australian Research Council

Discovery Projects - Grant ID: DP120103770

Start Date: 2012

End Date: 08-2016

Amount: $360,000.00

Funder: Australian Research Council

Linkage Projects - Grant ID: LP160100707

Start Date: 06-2017

End Date: 12-2022

Amount: $412,000.00

Funder: Australian Research Council

Discovery Projects - Grant ID: DP180103858

Start Date: 05-2018

End Date: 12-2021

Amount: $364,029.00

Funder: Australian Research Council

Linkage Projects - Grant ID: LP100200476

Start Date: 09-2011

End Date: 12-2013

Amount: $440,000.00

Funder: Australian Research Council

Discovery Projects - Grant ID: DP230102299

Start Date: 2023

End Date: 12-2025

Amount: $478,000.00

Funder: Australian Research Council

Discovery Projects - Grant ID: DP0986766

Start Date: 2009

End Date: 12-2011

Amount: $185,000.00

Funder: Australian Research Council

Linkage Infrastructure, Equipment And Facilities - Grant ID: LE0668502

Start Date: 2006

End Date: 12-2007

Amount: $500,000.00

Funder: Australian Research Council

Discovery Projects - Grant ID: DP0342985

Start Date: 12-2003

End Date: 01-2007

Amount: $135,000.00

Funder: Australian Research Council

Linkage Projects - Grant ID: LP130100703

Start Date: 07-2014

End Date: 06-2017

Amount: $300,000.00

Funder: Australian Research Council

Linkage Projects - Grant ID: LP100100565

Start Date: 10-2010

End Date: 12-2012

Amount: $360,000.00

Funder: Australian Research Council

ARC Centres Of Excellence - Grant ID: CE140100049

Start Date: 06-2014

End Date: 12-2021

Amount: $20,000,000.00

Funder: Australian Research Council

ARC Centres Of Excellence - Grant ID: CE0348165

Start Date: 2003

End Date: 12-2011

Amount: $13,749,290.00

Funder: Australian Research Council

Linkage Infrastructure, Equipment And Facilities - Grant ID: LE140100061

Start Date: 2014

End Date: 07-2015

Amount: $1,000,000.00

Funder: Australian Research Council

Special Research Initiatives - Grant ID: SR0354817

Start Date: 2004

End Date: 12-2004

Amount: $10,000.00

Funder: Australian Research Council