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Articles 1 - 5 of 5
Full-Text Articles in Applied Mathematics
On The Spatial Modelling Of Biological Invasions, Tedi Ramaj
On The Spatial Modelling Of Biological Invasions, Tedi Ramaj
Electronic Thesis and Dissertation Repository
We investigate problems of biological spatial invasion through the use of spatial modelling. We begin by examining the spread of an invasive weed plant species through a forest by developing a system of partial differential equations (PDEs) involving an invasive weed and a competing native plant species. We find that extinction of the native plant species may be achieved by increasing the carrying capacity of the forest as well as the competition coefficient between the species. We also find that the boundary conditions exert long-term control on the biomass of the invasive weed and hence should be considered when implementing …
Analytic Solution Of 1d Diffusion-Convection Equation With Varying Boundary Conditions, Małgorzata B. Glinowiecka-Cox
Analytic Solution Of 1d Diffusion-Convection Equation With Varying Boundary Conditions, Małgorzata B. Glinowiecka-Cox
University Honors Theses
A diffusion-convection equation is a partial differential equation featuring two important physical processes. In this paper, we establish the theory of solving a 1D diffusion-convection equation, subject to homogeneous Dirichlet, Robin, or Neumann boundary conditions and a general initial condition. Firstly, we transform the diffusion-convection equation into a pure diffusion equation. Secondly, using a separation of variables technique, we obtain a general solution formula for each boundary type case, subject to transformed boundary and initial conditions. While eigenvalues in the cases of Dirichlet and Neumann boundary conditions can be constructed easily, the Robin boundary condition necessitates solving a transcendental algebraic …
Using Differential Equations To Model A Cockatoo On A Spinning Wheel As Part Of The Scudem V Modeling Challenge, Miles Pophal, Chenming Zhen, Henry Bae
Using Differential Equations To Model A Cockatoo On A Spinning Wheel As Part Of The Scudem V Modeling Challenge, Miles Pophal, Chenming Zhen, Henry Bae
Rose-Hulman Undergraduate Mathematics Journal
For the SCUDEM V 2020 virtual challenge, we received an outstanding distinction for modeling a bird perched on a bicycle wheel utilizing the appropriate physical equations of rotational motion. Our model includes both theoretical calculations and numerical results from applying the Heaviside function for the swing motion of the bird. We provide a discussion on: our model and its numerical results, the overall limitations and future work of the model we constructed, and the experience we had participating in SCUDEM V 2020.
Hepatitis B And D: A Forecast On Actions Needed To Reduce Incidence And Achieve Elimination, Scott Greenhalgh, Andrew Klug
Hepatitis B And D: A Forecast On Actions Needed To Reduce Incidence And Achieve Elimination, Scott Greenhalgh, Andrew Klug
Spora: A Journal of Biomathematics
Viral hepatitis negatively affects the health of millions, with the worst health outcomes associated with the hepatitis D virus (HDV). Fortunately, HDV is rare and requires prior infection with the hepatitis B virus (HBV) before it can establish infection and transmit. Here, we develop a mathematical model of HBV and HDV transmission in Sub-Saharan Africa to investigate the effects of hepatitis B vaccination on both HBV and HDV. Our findings illustrate a hepatitis B vaccination rate above 0.006 year-1 reduces hepatitis D by over 90%, and a vaccination rate above 0.0221 year-1 reduces hepatitis B by over 90%, …
Positive Solutions To Semilinear Elliptic Equations With Logistic-Type Nonlinearities And Harvesting In Exterior Domains, Eric Jameson
Positive Solutions To Semilinear Elliptic Equations With Logistic-Type Nonlinearities And Harvesting In Exterior Domains, Eric Jameson
UNLV Theses, Dissertations, Professional Papers, and Capstones
Existing results provide the existence of positive solutions to a class of semilinear elliptic PDEs with logistic-type nonlinearities and harvesting terms both in RN and in bounded domains U ⊂ RN with N ≥ 3, when the carrying capacity of the environment is not constant. We consider these same equations in the exterior domain Ω, defined as the complement of the closed unit ball in RN , N ≥ 3, now with a Dirichlet boundary condition. We first show that the existing techniques forsolving these equations in the whole space RN can be applied to the exterior domain with some …