Dr. Manmohan Singh   Senior Lecturer

Qualifications

Msc(Roorkee) PhD(Roorkee)

Major Research Interest

• Mathematical Biology
• Numerical Methods
• Theoretical Astrophysics

Teaching Area

• Engineering Mathematics

Membership of Professional organisations

• Australian Mathematical Society
• Society for Mathematical Biology

Supervision of higher degree by research (HDR) (Current students)

Name	Degree	Research Centre	Start year	Role	Institution
Hung Do	PhD	Faculty	2009	Associate Supervisor	Swinburne
Gaganjyoti Sandhu	A numerical study on biological control of invasive predator population to protect endangered prey population
	PhD	Faculty	2010	Primary Supervisor	Swinburne
Saleh Hassanzadeh Gharaie	PhD	Faculty	2011	Co-Supervisor	Swinburne
Afia Naheed	A study on the numerical modelling of the spatio-temporal spread of infectious diseases
	PhD	Maths	2011	Primary Supervisor	Swinburne

Previously Supervised higher degree by research (HDR) students

Name	Degree	Research Centre	Status	Role	Institution
Md Samsuzzoha	A study on numerical simulations of epidemic models
	PhD	Faculty	Completed	Primary Supervisor	Swinburne
Nooshin Sadeghi Taheri	MEng	Faculty	Completed	Co-Supervisor	Swinburne
Aspriha Chakraborty	A numerical study of modelling in a predator-prey system
	PhD		Completed	Primary Supervisor	Swinburne

Topics for Prospective Ph.D Students - View ALL topics for Dr. Manmohan Singh

A study on numerical simulations of epidemic models
In order to simulate the outbreak of a disease it is proposed to consider numerical simulations of deterministic differential equations in conjunction with stochastic environments. A strong partnership between deterministic and stochastic simulations will be developed to draw meaningful conclusions in the prevailing complex situations.

A Theoretical Study on the Formation of Spatial Patterns on Twospotted Spider Mite
The aim of this project is to predict the formation of spatial patterns on twospotted spider mite.

First, Logistic Lotka – Volterra predator – prey equations will be used to obtain the conditions for the spatial pattern generated by diffusion – driven instability.

Numerical Modelling of Tides
This project will focus on using the nonlinear shallow water wave equations to numerically model tides in bays, including ones with tidal flats and hence moving shorelines.

Selected Publications

1. Samsuzzoha M., Singh M. and Lucy D., Numerical study of an influenza epidemic model with diffusion, Applied Mathematics and Computation, 217, 3461-3479, 2010.
2. Chakraborty A., Singh M. and Ridland P., “Effects of prey–taxis on biological control of two–spotted mites– A numerical approach”, Journal of Mathematical and Computer Modelling, 50, 598–610, 2009.
3. Chakraborty A., Singh M., Lucy D. and Ridland P., “A Numerical study of the formation of spatial patterns in two–spotted spider mites”, Journal of Mathematical and Computer Modelling, 49, 482–498, 2009. Ranking
4. Chakraborty A. and Singh M.., “Effects of prey–taxis on the periodicity of predator–prey dynamics”, Journal of Canadian Applied Mathematics Quarterly (CAMQ), 16, No3 Fall 2008.
5. Arundell J., Blicblau A. Richards D. and Singh M., “Dynamic hip fracture modelling”, ANZIAM Journal (E), 50, C220––236, 2008.
6. Lai T.C., Morsi Y. S. and Singh M., Numerical Characterization of the flow field in a four-generation airway, Journal of Mechanics in Medicine and Biology, 8, No 1, 1-20, 2008.
7. Chakraborty A., Singh M., Lucy D. and Ridland P., “Predator–Prey Models with prey–taxis and diffusion”, Mathematical and Computer Modelling, 46, 482–498, 2007.
8. Kozlova I., Singh M., Easton A. and Ridland P., T“wospotted Spider Mite Predator–Prey Model”, Mathematical and Computer Modelling, 42, 1287–1298, 2005.
9. Kozlova I., Singh M. and Easton A., “Predator prey models with diffusion based on Luckinbill's experiment with Didinium and Paramecium”, Mathematical and Computer Modelling, 36, 83–102, 2002.
10. Singh M., Easton A. and Kozlova I., “Numerical study of the two–dimensional spruce budworm reaction–diffusion equation with hostile boundaries”, Natural Resource Modeling, 13, No 4, 535–554, 2000.
11. Freedman H. I., Singh M., Easton A. K and Baggs I., “Mathematical models of population distribution within a culture group”, Mathematical and Computer Modelling, 29, 57–67, 1999.
12. Singh M., Easton A., Cui G. and Kozlova I., “Numerical study of the two–dimensional spruce budworm reaction–diffusion equation with density dependent diffusion”, Natural Resource Modeling, 11, No 2, 143–54, 1998.
13. Singh M. and Singh G., “Several Composite Models of Critically Rotating and Tidally distorted Polytropes”; Journal Astronomical Society of Japan, 36, 119–122, 1984;; Journal Astronomical Society of Japan, 36, 119–122, 1984.
14. Singh M, “Effect of Central Condensation on the Pulsation Characteristics”, Monthly Notices Royal Astronomical Society, London, 140, 235–240, 1968.