Mapundi Kondwani Banda - Academia.edu (original) (raw)

Papers by Mapundi Kondwani Banda

21th 4 / 35 Steel Rolling Model Particle Dynamics 1 • Let τ be a random processing time. We choos... more 21th 4 / 35 Steel Rolling Model Particle Dynamics 1 • Let τ be a random processing time. We choose P(τ = s) = Φ(s). • In case of an rolling event the thickness undergoes the deformation g(t + τ) = g(t) − F (T(t), g(t), τ). • Independent of the event (transport of rolling) we assume a temperature flux T(t + τ) = T(t) − τ c(T(t)).

arXiv (Cornell University), May 17, 2016

In this paper, the simultaneous identification of damping or anti-damping coefficient and initial... more In this paper, the simultaneous identification of damping or anti-damping coefficient and initial value for some PDEs is considered. An identification algorithm is proposed based on the fact that the output of system happens to be decomposed into a product of an exponential function and a periodic function. The former contains information of the damping coefficient, while the latter does not. The convergence and error analysis are also developed. Three examples, namely an anti-stable wave equation with boundary anti-damping, the Schrödinger equation with internal anti-damping, and two connected strings with middle joint anti-damping, are investigated and demonstrated by numerical simulations to show the effectiveness of the proposed algorithm.

The capability and practical use of mobile robots in real-world applications has resulted in them... more The capability and practical use of mobile robots in real-world applications has resulted in them being a topic of recent research interest. In this paper, motion planning for a mobile robot is considered. The Leapfrog algorithm, a method for solving nonlinear optimal control problems, is applied to generate optimal paths. The Leapfrog method is shown to produce optimal paths in simulations and for examples on a real robot and can find solutions where other solvers may fail.

This paper deals with finding optimal paths for a mobile manipulator in the presence of obstacles... more This paper deals with finding optimal paths for a mobile manipulator in the presence of obstacles. The motion planning of the robot kinematic system is formulated as an optimal control problem. Applying Pontryagin’s minimum principle, indirect conditions of optimality are derived for the optimal motion planning problem and solved numerically using the Leapfrog method. Simulation results for the mobile manipulator are presented to demonstrate the effectiveness of the proposed method.

CO-PUBLISHED WITH HIGHER EDUCATION PRESS eBooks, Dec 1, 2012

In this work, the Leapfrog algorithm from optimal control is presented as a method for optimal pa... more In this work, the Leapfrog algorithm from optimal control is presented as a method for optimal path planning for a mobile robot in the presence of obstacles. The proposed algorithm allows the robot to plan a collision-free path through static obstacles by minimizing a cost functional that includes energy terms and the Gaussian potential function. The Leapfrog path is initialized using the RRT planning algorithm and refines the RRT result to produce an optimal path. Comparison is made with the BVP4C optimization algorithm showing that similar path cost can be obtained with the Leapfrog approach. The Leapfrog algorithm shows value for continued development as an optimal path planning method since it initializes easily, creates a feasible path on each iteration, and can find solutions where other solvers may fail.

Mathematical Methods in The Applied Sciences, Nov 18, 2016

Communicated by F. Colombo This paper deals with an inverse problem of determining the diffusion ... more Communicated by F. Colombo This paper deals with an inverse problem of determining the diffusion coefficient, spacewise dependent source term, and the initial value simultaneously for a one-dimensional heat equation based on the boundary control, boundary measurement, and temperature distribution at a given single instant in time. By a Dirichlet series representation for the boundary observation, the identification of the diffusion coefficient and initial value can be transformed into a spectral estimation problem of an exponential series with measurement error, which is solved by the matrix pencil method. For the identification of the source term, a finite difference approximation method in conjunction with the truncated singular value decomposition is adopted, where the regularization parameter is determined by the generalized cross-validation criterion. Numerical simulations are performed to verify the result of the proposed algorithm.

PAMM, 2003

The Lattice Boltzmann equations are usually constructed to satisfy physical requirements like Gal... more The Lattice Boltzmann equations are usually constructed to satisfy physical requirements like Galilean invariance and isotropy as well as to possess a velocity‐independent pressure, no compressible effects, just to mention a few. In this paper, a stability criterion for such constructions is introduced and is used to derive a new relation of the parameters in a parametrized 2‐dimensional 9‐velocity model.

arXiv: Numerical Analysis, 2015

The stability of Lattice Boltzmann Equations modelling Shallow Water Equations in the special cas... more The stability of Lattice Boltzmann Equations modelling Shallow Water Equations in the special case of reduced gravity is investigated theoretically. A stability notion is defined as applied in incompressible Navier-Stokes equations in Banda, M. K., Yong, W.- A. and Klar, A: A stability notion for lattice Boltzmann equations. SIAM J. Sci. Comput. {\bf 27(6)}, 2098-2111 (2006). It is found that to maintain stability a careful choice of the value of the reduced gravity must be made. The stability notion is employed to investigate different shallow water lattice Boltzmann Equations. The effect of the reduced gravity on the mechanism of instability is investigated. Results are tested using the Lattice Boltzmann Method for various values of the governing parameters of the flow. It is observed that even for the discrete model the reduced gravity has a significant effect on the stability.

Atoms diffuse in a molten metal alloy under the influence of a temperature gradient at high press... more Atoms diffuse in a molten metal alloy under the influence of a temperature gradient at high pressure and temperature. They change phase and form synthetic crystals. An equation modelling the diffusion phenomenon is presented, relating the concentration of diffusing atoms to the temperature gradient and the crystal formation rate. Models for the crystal growth are also presented. The governing equation is first interpreted at microscopic level. Analytical and numerical solutions are then investigated. As observed experimentally, the sign and magnitude of the temperature gradient in the alloy affects the potential crystal formation and the rate of crystal growth. The value of the key physical parameters involved is discussed and model improvements are suggested. ∗Mathematics Applications Consortium for Science and Industry, Department of Mathematics and Statistics, University of Limerick, Limerick, Ireland. jean.charpin@ul.ie †School of Mathematical Sciences, University of KwaZulu-Nat...

Proceedings of the 2nd International Conference on Intelligent and Innovative Computing Applications, 2020

The motion planning for a mobile, autonomous system is solved using the Leapfrog algorithm from o... more The motion planning for a mobile, autonomous system is solved using the Leapfrog algorithm from optimal control. Numerical optimal control has some advantages for motion planning. Differential constraints can be included in the problem formulation, and it is relatively simple to change the performance index and the nonlinear system model. The proposed algorithm finds a collision-free path for a cost functional under nonlinear differential constraints. Numerical case studies are done to show the effectiveness and efficiency of the Leapfrog algorithm and are compared with the kinodynamic-RRT* algorithm, in which optimal control is also used, but employed in a piecewise manner, between randomly-selected nodes. Path cost and execution time are used for performance comparison. The simulation results show that the Leapfrog method produces less jagged and shorter paths with smaller path cost and lower execution time compared to kinodynamic-RRT*, indicating suitability of the Leapfrog algor...

Applied Mathematics & Optimization, 2020

In this paper, a linear hyperbolic system of balance laws with boundary disturbances in one dimen... more In this paper, a linear hyperbolic system of balance laws with boundary disturbances in one dimension is considered. An explicit candidate Input-to-State Stability (ISS)-Lyapunov function in L 2 −norm is considered and discretised to investigate conditions for ISS of the discrete system as well. Finally, experimental results on test examples including the Saint-Venant equations with boundary disturbances are presented. The numerical results demonstrate the expected theoretical decay of the Lyapunov function.

Computers & Chemical Engineering, 2018

Mathematical models for chemically reacting systems have high degrees of freedom (very large) and... more Mathematical models for chemically reacting systems have high degrees of freedom (very large) and are computationally expensive to analyse. In this discussion, we present and analyse a model reduction method that is based on stoichiometry and mass balances. This method can significantly reduce the high degrees of freedom of such systems. Numerical simulations are undertaken to validate and establish efficiency of the method. A practical example of acid mine drainage is used as a test case to demonstrate the efficacy of the procedure. Analytical results show that the stoichiometrically-reduced model is consistent with the original large model, and numerical simulations demonstrate that the method can accelerate convergence of the numerical schemes in some cases.

Journal of Computational Science, 2018

Mathematical modelling and numerical simulation of chemical transport phenomena are very challeng... more Mathematical modelling and numerical simulation of chemical transport phenomena are very challenging due to large numbers of species and reactions involved. Reactive transport models for such systems have high degrees of freedom, and therefore, are computationally expensive to solve. In this discussion, we present and numerically analyse stoichiometric decoupling method for reducing the high degrees of freedom and hence, cost of simulation. This method is a model reduction procedure that is based on some key properties of chemical systems. A multi-scale model of a passive treatment method for acidic mine effluents is used to test the efficacy of the reduction procedure. Moreover, reduced models are characteristically non-linear and stiff, thus, we used numerical techniques to study the reduction error in order to establish compatibility/efficiency of the reduction procedure.

2016 Pattern Recognition Association of South Africa and Robotics and Mechatronics International Conference (PRASA-RobMech), 2016

This work deals with formulating an optimal motion planning problem for a mobile robot in the pre... more This work deals with formulating an optimal motion planning problem for a mobile robot in the presence of obstacles using optimal control. For obstacle avoidance, a repulsive potential function defined as a Gaussian function is applied in the cost functional which minimizes the energy control effort. The Leapfrog method numerically solves the formulated optimal control problem. With Leapfrog one has only to choose the initial and final states. An initial feasible path is prescribed and subdivided into path segments. In this work, the trajectories produced by A− and RRT algorithms are used as initial feasible paths for Leapfrog. Simulations are performed to evaluate the effectiveness of the Leapfrog method. It is observed that the optimal path that Leapfrog produces does not depend on the initial path, nor on the method by which the initial path is formed.

Mathematical and Computational Applications, 2010

The well-posedness of a Riemann problem at a junction in a pipeline network is discussed. In addi... more The well-posedness of a Riemann problem at a junction in a pipeline network is discussed. In addition computational results on the dynamics of the flow of a multi-component gas at such network junctions are presented. The work presented here is a generalisation of [M. K. Banda, M. Herty, and J. M. T. Ngnotchouye, Towards a mathematical analysis of multiphase drift-flux model in networks, SIAM J. Sci. Comput., 31(6): 4633-4653, 2010] to models in which the equation of state has different compressibility factors or sonic speeds.

This special issue is focused on the application of differential equations to industrial mathemat... more This special issue is focused on the application of differential equations to industrial mathematics. Of particular interest is the role played by industrial mathematics in the development of new ideas and applications. We are particularly interested in industrial mathematics problems that come from industrial mathematics study group meetings, which take place regularly at universities across the world. These study group meetings are motivated by solving real-world problems that are posed by industry representatives at the start of the meeting. Graduate students and academics then spend one week developing mathematical models that simulate the problems presented. These mathematical models are then solved usually after some simplification , and conclusions relevant to the real-world problem are made. This special issue contains a paper that is based on a problem presented by the coal mining industry in South Africa at an industrial mathematics study group meeting. In the paper, the author considers the possible collapse of the roof between the pillar to be mined next in secondary coal mining and the first line of pillar remnants called snooks. Here, the Euler-Bernoulli beam equation is used to model the roof rock between the pillars, which is the working face between two pillars. The model predicts that the beam will break at the clamped end at the pillar. The failure of the beam for different values of the physical parameters is investigated computationally. Many industrial mathematics problems contain an aspect of heat conduction. This special issue contains a paper in which a new error measure is proposed for the heat balance

Hydrodynamics - Theory and Model, 2012

PAMM, 2007

In this talk some recent numerical results based on discrete‐velocity relaxation systems will be ... more In this talk some recent numerical results based on discrete‐velocity relaxation systems will be presented. Discrete‐velocity equations are derived from continuous Boltzmann‐type equations with appropriate approximations suitable for incompressible flows. A relaxation system is derived by taking moments of the discrete‐velocity equations. This approach is also extended to turbulence flows using Large‐Eddy Simulation as well as thermal flows. The schemes are tested by solving a collection of examples. In particular the developed methods demonstrate potential as tools for Large‐Eddy Simulation and flow with Radiative Heat transfer. (© 2008 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)