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Articles 1 - 9 of 9
Full-Text Articles in Ordinary Differential Equations and Applied Dynamics
Time-Marching Quantum Algorithm For Simulation Of Nonlinear Lorenz Dynamics, Efstratios Koukoutsis, George Vahala, Min Soe, Kyriakos Hizanidis, Linda Vahala, Abhay K. Ram
Time-Marching Quantum Algorithm For Simulation Of Nonlinear Lorenz Dynamics, Efstratios Koukoutsis, George Vahala, Min Soe, Kyriakos Hizanidis, Linda Vahala, Abhay K. Ram
Electrical & Computer Engineering Faculty Publications
Simulating nonlinear classical dynamics on a quantum computer is an inherently challenging task due to the linear operator formulation of quantum mechanics. In this work, we provide a systematic approach to alleviate this difficulty by developing an explicit quantum algorithm that implements the time evolution of a second-order time-discretized version of the Lorenz model. The Lorenz model is a celebrated system of nonlinear ordinary differential equations that has been extensively studied in the contexts of climate science, fluid dynamics, and chaos theory. Our algorithm possesses a recursive structure and requires only a linear number of copies of the initial state …
A Dynamical Systems Approach For Modeling Malware Propagating Through A Network And Potential Solutions Towards Mitigating Spread, James Johnson
A Dynamical Systems Approach For Modeling Malware Propagating Through A Network And Potential Solutions Towards Mitigating Spread, James Johnson
Cybersecurity Undergraduate Research Showcase
Many people draw close parallels between malware propagating through a network and an epidemic spreading through a population. Epidemics are often modeled by a Susceptible-Infected-Recovered (SIR) model, in which a similar system of equations can model the spread of a virus through a computer network, and can be simplified when making assumptions about the network itself and its fixed number of nodes and edges. In this instance, malware propagating in a network also should reflect the network it is propagating through, in which the dynamical system will factor in the nodes of the network and their properties. The system itself …
Multipatch Stochastic Epidemic Model For The Dynamics Of A Tick-Borne Disease, Milliward Maliyoni, Holly D. Gaff, Keshlan S. Govinder, Faraimunashe Chirove
Multipatch Stochastic Epidemic Model For The Dynamics Of A Tick-Borne Disease, Milliward Maliyoni, Holly D. Gaff, Keshlan S. Govinder, Faraimunashe Chirove
Biological Sciences Faculty Publications
Spatial heterogeneity and migration of hosts and ticks have an impact on the spread, extinction and persistence of tick-borne diseases. In this paper, we investigate the impact of between-patch migration of white-tailed deer and lone star ticks on the dynamics of a tick-borne disease with regard to disease extinction and persistence using a system of Itô stochastic differential equations model. It is shown that the disease-free equilibrium exists and is unique. The general formula for computing the basic reproduction number for all patches is derived. We show that for patches in isolation, the basic reproduction number is equal to the …
Undetermined Coefficients: A Fully Generalized Approach, Taylor Powell
Undetermined Coefficients: A Fully Generalized Approach, Taylor Powell
Undergraduate Research Symposium
In this presentation, I outline the development of a fully-generalized solution of linear, non-homogeneous differential equations with constant coefficients and whose non-homogeneous function is any product of sinusoidal, exponential, and polynomial functions. This particular method does not require the reader to work with annihilator operators or additional related ODEs, and only requires an understanding of summation notation, matrix multiplication, and calculus. Additionally, this method provides a straightforward way to develop a program to implement the technique, and potentially reduces the time-complexity for solutions with comparisons to other methods.
An Adaptive Method For Calculating Blow-Up Solutions, Charles F. Touron
An Adaptive Method For Calculating Blow-Up Solutions, Charles F. Touron
Mathematics & Statistics Theses & Dissertations
Reactive-diffusive systems modeling physical phenomena in certain situations develop a singularity at a finite value of the independent variable referred to as "blow-up." The attempt to find the blow-up time analytically is most often impossible, thus requiring a numerical determination of the value. The numerical methods often use a priori knowledge of the blow-up solution such as monotonicity or self-similarity. For equations where such a priori knowledge is unavailable, ad hoc methods were constructed. The object of this research is to develop a simple and consistent approach to find numerically the blow-up solution without having a priori knowledge or resorting …
Three Methods For Solving The Low Energy Neutron Boltzmann Equation, Tony Charles Slaba
Three Methods For Solving The Low Energy Neutron Boltzmann Equation, Tony Charles Slaba
Mathematics & Statistics Theses & Dissertations
The solution to the neutron Boltzmann equation is separated into a straightahead component dominating at high energies and an isotropic component dominating at low energies. The high-energy solution is calculated using HZETRN-05, and the low-energy isotropic component is modeled by two non-coupled integro-differential equations describing both forward and backward neutron propagation. Three different solution methods are then used to solve the equations. The collocation method employs linear I3-splines to transform each equation into a system of ODES; the resulting system is then solved exactly and evaluated using numerical integration techniques. Wilson's method uses a perturbational approach in which a fundamental …
A Forward-Backward Fluence Model For The Low-Energy Neutron Boltzmann Equation, Gary Alan Feldman
A Forward-Backward Fluence Model For The Low-Energy Neutron Boltzmann Equation, Gary Alan Feldman
Mathematics & Statistics Theses & Dissertations
In this research work, the neutron Boltzmann equation was separated into two coupled integro-differential equations describing forward and backward neutron fluence in selected materials. Linear B-splines were used to change the integro-differential equations into a coupled system of ordinary differential equations (O.D.E.'s). Difference approximations were then used to recast the O.D.E.'s into a coupled system of linear equations that were solved for forward and backward neutron fluences. Adding forward and backward fluences gave the total fluence at selected energies and depths in the material. Neutron fluences were computed in single material shields and in a shield followed by a target …
Steady Incompressible Magnetohydrodynamic Flow Near A Point Of Reattachment, J. M. Dorrepaal, S. Moosavizadeh
Steady Incompressible Magnetohydrodynamic Flow Near A Point Of Reattachment, J. M. Dorrepaal, S. Moosavizadeh
Mathematics & Statistics Faculty Publications
The oblique stagnation-point flow of an electrically conducting fluid in the presence of a magnetic field is a highly nonlinear problem whose solution is of interest even in the simplest of geometries. The problem models the flow of a viscous conducting fluid near a point where a separation vortex reattaches itself to a rigid boundary. A similarity solution exists which reduces the problem to a coupled system of four ordinary differential equations which can be integrated numerically. The problem has two independent parameters, the conductivity of the fluid and the strength of the magnetic field. Solutions are tabulated for a …
A Generalization Of Linear Multistep Methods, Leon Arriola
A Generalization Of Linear Multistep Methods, Leon Arriola
Mathematics & Statistics Theses & Dissertations
A generalization of the methods that are currently available to solve systems of ordinary differential equations is made. This generalization is made by constructing linear multistep methods from an arbitrary set of monotone interpolating and approximating functions. Local truncation error estimates as well as stability analysis is given. Specifically, the class of linear multistep methods of the Adams and BDF type are discussed.