Research interests

Deterministic and stochastic differential equations and applications, fluid dynamics, geophysical fluid dynamics and the dynamics of the ionosphere, analytical electromagnetics, hydrodynamic stability, numerical methods for deterministic and stochastic differential equations and asymptotic and perturbation methods, and mathematical modelling. Use of special functions to evaluate non-elementary integrals and to study some problems in Probability, Statistics, science and applied sciences.

Statement of research

List of publications

Papers (peer-reviewed) and preprints

• V. Nijimbere, L. J. Campbell, Nonlinear critical-layer evolution of a forced monochromatic ionospheric gravity wave in the ionospheric F region heights . preprint
• V. Nijimbere, L. J. Campbell, M. Nadon, Ion drag effects on ionospheric gravity waves in the presence of a strong magnetic field, submitted for publication. preprint
• V. Nijimbere, L. J. Campbell, Temporal evolution of ionospheric gravity waves in the presence of a strong magnetic field, submitted for publication. preprint
• V. Nijimbere, L. J. Campbell, Upper atmosphere-lower atmosphere coupling: Large-scale travelling ionospheric disturbances (LSTIDs) and medium-scale atmospheric gravity waves (MSAGWs) interactions and their effects on the weather development in the lower atmosphere. preprint
• V. Nijimbere, Numerical modelling of travelling ionospheric disturbances (TIDs)/atmospheric gravity waves (AGWs) generated by the Joule heating, submitted for publication. Under review. preprint
• V. Nijimbere, L. J. Campbell, Numerical modelling of electro-magnetohydrodynamic (E-MHD) disturbances in the vertical plane in the ionosphere: small scale and medium scale ionospheric disturbances. Progress In Electromagnetics Research B 86 (2020), 39 - 57. paper
• V. Nijimbere, Implementation of a Wiener chaos expansion method for the numerical solution of the stochastic generalized Kuramoto-Sivashinsky equation driven by Brownian motion forcing. Journal of Advances in Applied Mathematics 4:4 (2019), 119 - 142. paper
• V. Nijimbere, On the classical electrodynamics in dispersive time-dependent linear isotropic media. Progress In Electromagnetics Research C 93 (2019), 185 - 198. paper
• V. Nijimbere, L. J. Campbell, Electromagnetic field solutions in an isotropic medium with weakly-random fluctuations in time and some applications in the electrodynamics of the ionosphere. Progress In Electromagnetics Research B 83 (2019), 77 - 92. paper
• V. Nijimbere, Asymptotic approximation of the eigenvalues and the eigenfunctions for the Orr-Sommerfeld equation on infinite intervals. Advances in Pure Mathematics 9:12 (2019), 967 - 989. paper
• V. Nijimbere, Hypothesis test and confidence interval for the negative binomial distribution via coincidence: A case for rare events. International Journal of Contemporary Mathematical Sciences, 12:5 (2017), 243 - 253. paper
• V. Nijimbere, Analytical and asymptotic evaluations of Dawson's integral and related functions in mathematical physics. Journal of Applied Analysis 25:2 (2019), 179 - 188. paper
• V. Nijimbere, Evaluation of some non-elementary integrals involving sine, cosine, exponential and logarithmic integrals: Part II. Ural Mathematical Journal 4:1 (2018), 43 - 55. paper
• V. Nijimbere, Evaluation of some non-elementary integrals involving sine, cosine, exponential and logarithmic integrals: Part I. Ural Mathematical Journal 4:1 (2018), 24 - 42. paper
• V. Nijimbere, Evaluation of the non-elementary integral $\int$e^λxα d x , α ≥2, and other related integrals. Ural Mathematical Journal 3:2 (2017), 130 - 142. paper
• V. Nijimbere, Goodness of Fit Test for the Proportion of Succcesses in Binomial Trials and Confidence Interval via Coincidence: A Case of Rare Events. International Journal of Research and Reviews in Applied Sciences, 30:2 (2017), 33 - 40. paper
• V. Nijimbere, Coincidences, Goodness of Fit Test and Confidence Interval for Poisson Distribution Parameter via Coincidence. American Journal of Applied Mathematics and Statistics, 4:6 (2016), 185 - 193. paper
• V. Nijimbere, L. J. Campbell, A nonlinear time-dependent radiation condition for simulations of internal gravity waves in geophysical fluids. Applied Numerical Mathematics 110 (2016) 75 - 92. paper
• V. Nijimbere, L. J. Campbell, Some exact expressions for the temporal evolution of long Rossby waves on a beta-plane. Wave Motion 58 (2015) 129 - 144. paper
• V. Nijimbere, L. J. Campbell, Exact expressions for transient forced internal gravity waves and spatially-localized wave packets in a boussinesq fluid. Wave Motion 58 (2015) 117 - 128. paper

If you need a copy of one of my preprints, please contact me at "victornijimbere@gmail.com".

Thesis

• V. Nijimbere, Ionospheric gravity wave interactions and their representation in terms of stochastic partial differential equations, Ph.D. thesis, Carleton University 2014. thesis
• V. Nijimbere, Time-dependent non-reflecting boundary conditions for simulations of wave propagation in geophysical shear flows, M.Sc. thesis, Carleton University 2010. thesis

Preprints in preparation

• On reflections of nonlinear ionospheric gravity waves in the ionospheric F region heights in the absence of a critical level.
• Implementation and accuracy assessment of a Wiener Chaos expansion method for the numerical solution of stochastic evolution equations driven by Brownian motion forcing (with L.J. Campbell).
• Numerical modelling of travelling atmospheric disturbances (TADs) (with L.J. Campbell).

Other projects

• Analytical and numerical studies of nonlinear interactions of atmospheric and ionospheric disturbances..
• Analytical Electromagnetics in conducting dispersive media.
• Numerical solutions of stochastic PDEs.

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