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Articles 541 - 570 of 848
Full-Text Articles in Applied Mathematics
Modeling Mayfly Nymph Length Distribution And Population Dynamics Across A Gradient Of Stream Temperatures And Stream Types, Jeremy Anthony, Jennifer Baccam, Imanuel Bier, Emily Gregg, Leif Halverson, Ryan Mulcahy, Emmanuel Okanla, Samira A. Osman, Adam R. Pancoast, Kevin C. Schultz, Alex Sushko, Jennifer Vorarath, Yia Vue, Austin Wagner, Emily Gaenzle Schilling, John Zobitz
Modeling Mayfly Nymph Length Distribution And Population Dynamics Across A Gradient Of Stream Temperatures And Stream Types, Jeremy Anthony, Jennifer Baccam, Imanuel Bier, Emily Gregg, Leif Halverson, Ryan Mulcahy, Emmanuel Okanla, Samira A. Osman, Adam R. Pancoast, Kevin C. Schultz, Alex Sushko, Jennifer Vorarath, Yia Vue, Austin Wagner, Emily Gaenzle Schilling, John Zobitz
Faculty Authored Articles
We analyze a process-based temperature model for the length distribution and population over time of mayfly nymphs. Model parameters are estimated using a Markov Chain Monte Carlo parameter estimation method utilizing length distribution data at five different stream sites. Two different models (a standard exponential model and a modified Weibull model) of mayfly mortality are evaluated, where in both cases mayfly length growth is a function of stream temperature. Based on model-data comparisons to the modeled length distribution and the Bayesian Information Criterion, we found that approaches that length distribution data can reliably estimate 2–3 model parameters. Future model development …
Modeling The Disappearance Of The Neanderthals Using Concepts Of Population Dynamics And Ecology, Michael F. Roberts, Stephen E. Bricher
Modeling The Disappearance Of The Neanderthals Using Concepts Of Population Dynamics And Ecology, Michael F. Roberts, Stephen E. Bricher
Faculty Publications
Current hypotheses regarding the disappearance of Neanderthals (NEA) in Europe fall into two main categories: climate change, and competition. Here we review current research and existing mathematical models that deal with this question, and we propose an approach that incorporates and permits the investigation of the current hypotheses. We have developed a set of differential equations that model population dynamics of anatomically modern humans (AMH) and NEA, their ecological relations to prey species, and their mutual interactions. The model allows investigators to explore each of the two main categories or combinations of both, as well as various forms of competition …
Modeling Public Opinion, Arden Baxter
Modeling Public Opinion, Arden Baxter
Honors Program Theses
The population dynamics of public opinion have many similarities to those of epidemics. For example, models of epidemics and public opinion share characteristics like contact rates, incubation times, and recruitment rates. Generally, epidemic dynamics have been presented through epidemiological models. In this paper we adapt an epidemiological model to demonstrate the population dynamics of public opinion given two opposing viewpoints. We find equilibrium solutions for various cases of the system and examine the local stability. Overall, our system provides sociological insight on the spread and transition of a public opinion.
Mathematical Models Of Mosquito Populations, Hanna Reed
Mathematical Models Of Mosquito Populations, Hanna Reed
Honors Undergraduate Theses
The intent of this thesis is to develop ordinary differential equation models to better understand the mosquito population. We first develop a framework model, where we determine the condition under which a natural mosquito population can persist in the environment. Wolbachia is a bacterium which limits the replication of viruses inside the mosquito which it infects. As a result, infecting a mosquito population with Wolbachia can decrease the transmission of viral mosquito-borne diseases, such as dengue. We develop another ODE model to investigate the invasion of Wolbachia in a mosquito population. In a biologically feasible situation, we determine three coexisting …
Strong Stability Of A Class Of Difference Equations Of Continuous Time And Structured Singular Value Problem, Qian Ma, Keqin Gu, Narges Choubedar
Strong Stability Of A Class Of Difference Equations Of Continuous Time And Structured Singular Value Problem, Qian Ma, Keqin Gu, Narges Choubedar
SIUE Faculty Research, Scholarship, and Creative Activity
This article studies the strong stability of scalar difference equations of continuous time in which the delays are sums of a number of independent parameters tau_i, i = 1, 2, . . . ,K. The characteristic quasipolynomial of such an equation is a multilinear function of exp(-tau_i s). It is known that the characteristic quasipolynomial of any difference equation set in the form of one-delayper- scalar-channel (ODPSC) model is also in such a multilinear form. However, it is shown in this article that some multilinear forms of quasipolynomials are not characteristic quasipolynomials of any ODPSC difference equation set. The equivalence …
Hopf Bifurcation Analysis Of Chaotic Chemical Reactor Model, Daniel Mandragona
Hopf Bifurcation Analysis Of Chaotic Chemical Reactor Model, Daniel Mandragona
Honors Undergraduate Theses
Bifurcations in Huang's chaotic chemical reactor system leading from simple dynamics into chaotic regimes are considered. Following the linear stability analysis, the periodic orbit resulting from a Hopf bifurcation of any of the six fixed points is constructed analytically by the method of multiple scales across successively slower time scales, and its stability is then determined by the resulting final secularity condition. Furthermore, we run numerical simulations of our chemical reactor at a particular fixed point of interest, alongside a set of parameter values that forces our system to undergo Hopf bifurcation. These numerical simulations then verify our analysis of …
A Model To Predict Concentrations And Uncertainty For Mercury Species In Lakes, Ashley Hendricks
A Model To Predict Concentrations And Uncertainty For Mercury Species In Lakes, Ashley Hendricks
Dissertations, Master's Theses and Master's Reports
To increase understanding of mercury cycling, a seasonal mass balance model was developed to predict mercury concentrations in lakes and fish. Results indicate that seasonality in mercury cycling is significant and is important for a northern latitude lake. Models, when validated, have the potential to be used as an alternative to measurements; models are relatively inexpensive and are not as time intensive. Previously published mercury models have neglected to perform a thorough validation. Model validation allows for regulators to be able to make more informed, confident decisions when using models in water quality management. It is critical to quantify uncertainty; …
Using A Coupled Bio-Economic Model To Find The Optimal Phosphorus Load In Lake Tainter, Wi, Mackenzie Jones
Using A Coupled Bio-Economic Model To Find The Optimal Phosphorus Load In Lake Tainter, Wi, Mackenzie Jones
Williams Honors College, Honors Research Projects
In Dunn County, Wisconsin the lakes suffer from algae blooms due to excess phosphorus runoff. A coupled bio-economic model is studied with the intent of finding the optimal level of phosphorus that should be allowed into the lake depending on certain biologic and economic parameters. We model the algae and phosphorus concentration in the lake over time based off the phosphorus input. Community welfare is modeled by comparing the costs and benefits of phosphorus fertilizer. This model is proposed to find the phosphorus level that maximizes community welfare and then determine how certain environmental and social change initiatives will affect …
Understanding The Nature Of Nanoscale Wetting Through All-Atom Simulations, Oliver Evans
Understanding The Nature Of Nanoscale Wetting Through All-Atom Simulations, Oliver Evans
Williams Honors College, Honors Research Projects
The spreading behavior of spherical and cylindrical water droplets between 30Å and 100Å in radius on a sapphire surface is investigated using all-atom molecular dynamics simulations for durations on the order of tens of nanoseconds. A monolayer film develops rapidly and wets the surface, while the bulk of the droplet spreads on top of the monolayer, maintaining the shape of a spherical cap. Unlike previous simulations in the literature, the bulk radius is found to increase to a maximum value and receed as the monolayer continues to expand. Simple time and droplet size dependence is observed for monolayer radius and …
Copula Theory And Regression Analysis, Mayooran Thevaraja
Copula Theory And Regression Analysis, Mayooran Thevaraja
All Graduate Theses, Dissertations, and Other Capstone Projects
Researchers are often interested to study in the relationships between one variable and several other variables. Regression analysis is the statistical method for investigating such relationship and it is one of the most commonly used statistical Methods in many scientific fields such as financial data analysis, medicine, biology, agriculture, economics, engineering, sociology, geology, etc. But basic form of the regression analysis, ordinary least squares is not suitable for actuarial applications because the relationships are often nonlinear and the probability distribution of the response variable may be non-Gaussian distribution. One of the method that has been successful in overcoming these challenges …
Delay Differential Equations And Their Application To Micro Electro Mechanical Systems, Asset Ospanov
Delay Differential Equations And Their Application To Micro Electro Mechanical Systems, Asset Ospanov
Theses and Dissertations
Delay differential equations have a wide range of applications in engineering. This work is devoted to the analysis of delay Duffing equation, which plays a crucial role in modeling performance on demand Micro Electro Mechanical Systems (MEMS). We start with the stability analysis of a linear delay model. We also show that in certain cases the delay model can be efficiently approximated with a much simpler model without delay. We proceed with the analysis of a non-linear Duffing equation. This model is a significantly more complex mathematical model. For instance, the existence of a periodic solution for this equation is …
Flow Anisotropy Due To Thread-Like Nanoparticle Agglomerations In Dilute Ferrofluids, Alexander Cali, Wah-Keat Lee, A. David Trubatch, Philip Yecko
Flow Anisotropy Due To Thread-Like Nanoparticle Agglomerations In Dilute Ferrofluids, Alexander Cali, Wah-Keat Lee, A. David Trubatch, Philip Yecko
Department of Applied Mathematics and Statistics Faculty Scholarship and Creative Works
Improved knowledge of the magnetic field dependent flow properties of nanoparticle-based magnetic fluids is critical to the design of biomedical applications, including drug delivery and cell sorting. To probe the rheology of ferrofluid on a sub-millimeter scale, we examine the paths of 550 μm diameter glass spheres falling due to gravity in dilute ferrofluid, imposing a uniform magnetic field at an angle with respect to the vertical. Visualization of the spheres’ trajectories is achieved using high resolution X-ray phase-contrast imaging, allowing measurement of a terminal velocity while simultaneously revealing the formation of an array of long thread-like accumulations of magnetic …
On The Qualitative Behaviors Of A Functional Differential Equation Of Second Order, Cemil Tunç
On The Qualitative Behaviors Of A Functional Differential Equation Of Second Order, Cemil Tunç
Applications and Applied Mathematics: An International Journal (AAM)
The aim of this paper is first to investigate the stability of the zero solution to a new Liénard type equation with multiple variable delays by two different methods. The methods to be used in the proofs involve the Lyapunov-Krasovskiĭ functional approach and the fixed point technique under an exponentially weighted metric, respectively. We make a comparison between the applications of these methods with the established conditions on the same stability problems. Then, we obtain three new results for uniformly stability and boundedness/ uniformly boundedness of the solutions to the considered equation by the Lyapunov-Krasovskiĭ functional approach. An example is …
A New Hybrid Method For Solving Nonlinear Fractional Differential Equations, R. Delpasand, M. M. Hosseini, F. M. Maalek Ghaini
A New Hybrid Method For Solving Nonlinear Fractional Differential Equations, R. Delpasand, M. M. Hosseini, F. M. Maalek Ghaini
Applications and Applied Mathematics: An International Journal (AAM)
In this paper, numerical solution of initial and boundary value problems for nonlinear fractional differential equations is considered by pseudospectral method. In order to avoid solving systems of nonlinear equations resulting from the method, the residual function of the problem is constructed, as well as a suggested unconstrained optimization model solved by PSOGSA algorithm. Furthermore, the research inspects and discusses the spectral accuracy of Chebyshev polynomials in the approximation theory. The following scheme is tested for a number of prominent examples, and the obtained results demonstrate the accuracy and efficiency of the proposed method.
On The Lp-Spaces Techniques In The Existence And Uniqueness Of The Fuzzy Fractional Korteweg-De Vries Equation’S Solution, F. Farahrooz, A. Ebadian, S. Najafzadeh
On The Lp-Spaces Techniques In The Existence And Uniqueness Of The Fuzzy Fractional Korteweg-De Vries Equation’S Solution, F. Farahrooz, A. Ebadian, S. Najafzadeh
Applications and Applied Mathematics: An International Journal (AAM)
In this paper, is proposed the existence and uniqueness of the solution of all fuzzy fractional differential equations, which are equivalent to the fuzzy integral equation. The techniques on LP-spaces are used, defining the LpF F ([0; 1]) for 1≤P≤∞, its properties, and using the functional analysis methods. Also the convergence of the method of successive approximations used to approximate the solution of fuzzy integral equation be proved and an iterative procedure to solve such equations is presented.
Thermoelastic Analysis Of A Nonhomogeneous Hollow Cylinder With Internal Heat Generation, V. R. Manthena, N. K. Lamba, G. D. Kedar
Thermoelastic Analysis Of A Nonhomogeneous Hollow Cylinder With Internal Heat Generation, V. R. Manthena, N. K. Lamba, G. D. Kedar
Applications and Applied Mathematics: An International Journal (AAM)
In the present paper, we have determined the heat conduction and thermal stresses of a hollow cylinder with inhomogeneous material properties and internal heat generation. All the material properties except Poisson’s ratio and density are assumed to be given by a simple power law in axial direction. We have obtained the solution of the two dimensional heat conduction equation in the transient state in terms of Bessel’s and trigonometric functions. The influence of inhomogeneity on the thermal and mechanical behavior is examined. Numerical computations are carried out for both homogeneous and nonhomogeneous cylinders and are represented graphically.
On The Existence Of Bogdanov-Takens Bifurcations, Zachary Deskin
On The Existence Of Bogdanov-Takens Bifurcations, Zachary Deskin
Graduate Theses/Dissertations
In bifurcation theory, there is a theorem (called Sotomayor's Theorem) which proves the existence of one of three possible bifurcations of a given system, provided that certain conditions of the system are satisfied. It turns out that there is a "similar" theorem for proving the existence of what is referred to as a Bogdanov-Takens bifurcation. The author is only aware of one reference that has the proof of this theorem. However, most of the details were left out of the proof. The contribution of this thesis is to provide the details of the proof on the existence of Bogdanov-Takens bifurcations.
Stochastic Analysis Of A Mammalian Circadian Clock Model: Small Protein Number Effects, David W. Morgens, Blerta Shtylla
Stochastic Analysis Of A Mammalian Circadian Clock Model: Small Protein Number Effects, David W. Morgens, Blerta Shtylla
Spora: A Journal of Biomathematics
The circadian clock, responsible for coordinating organism function with daily and seasonal changes in the day-night cycle, is controlled by a complex protein network that constitutes a robust biochemical oscillator. Deterministic ordinary differential equation models have been used extensively to model the behavior of these central clocks. However, due to the small number of proteins involved in the circadian oscillations, mathematical models that track stochastic variations in the numbers of clock proteins may reveal more complex and biologically relevant behaviors. In this paper, we compare the response of a robust yet detailed deterministic model for the mammalian circadian clock with …
Age-Structured And Vaccination Models Of Devil Facial Tumor Disease, Christopher D. Bruno, Timothy Comar, Megan O. Powell, Adjo Tameklo
Age-Structured And Vaccination Models Of Devil Facial Tumor Disease, Christopher D. Bruno, Timothy Comar, Megan O. Powell, Adjo Tameklo
Spora: A Journal of Biomathematics
Tasmanian devil populations have been devastated by devil facial tumor disease (DFTD) since its first appearance in 1996. The average lifespan of a devil has decreased from six years to three years. We present an age-structured model to represent how the disease has affected the age and breeding structures of the population. We show that with the recent increase in the breeding of juvenile devils, the overall devil population will increase but not nearly to pre-DFTD levels. The basic reproductive number may be increased with the influx of young breeding devils. In addition, our model shows that the release of …
Differential Equations Of Dynamical Order, Andrei Ludu, Harihar Khanal
Differential Equations Of Dynamical Order, Andrei Ludu, Harihar Khanal
Publications
No abstract provided.
Electromagnetic Resonant Scattering In Layered Media With Fabrication Errors, Emily Anne Mchenry
Electromagnetic Resonant Scattering In Layered Media With Fabrication Errors, Emily Anne Mchenry
LSU Doctoral Dissertations
In certain layered electromagnetic media, one can construct a waveguide that supports a harmonic electromagnetic field at a frequency that is embedded in the continuous spectrum. When the structure is perturbed, this embedded eigenvalue moves into the complex plane and becomes a “complex resonance” frequency. The real and imaginary parts of this complex frequency have physical meaning. They lie behind anomalous scattering behaviors known collectively as “Fano resonance”, and people are interested in tuning them to specific values in optical devices. The mathematics involves spectral theory and analytic perturbation theory and is well understood [16], at least on a theoretical …
Mathematical Modeling Of Tumor Immune Interactions: A Closer Look At The Role Of A Pd-L1 Inhibitor In Cancer Immunotherapy, Timothy Woods Ii
Mathematical Modeling Of Tumor Immune Interactions: A Closer Look At The Role Of A Pd-L1 Inhibitor In Cancer Immunotherapy, Timothy Woods Ii
Annual Symposium on Biomathematics and Ecology Education and Research
No abstract provided.
The Dynamics Of An Epidemiological Model For Human Papillomavirus With Partial Vaccination In A Heterogeneous Population, Stefano Chiaradonna
The Dynamics Of An Epidemiological Model For Human Papillomavirus With Partial Vaccination In A Heterogeneous Population, Stefano Chiaradonna
Annual Symposium on Biomathematics and Ecology Education and Research
No abstract provided.
Dftd Age Structure And Vaccination Modeling, Christopher D. Bruno
Dftd Age Structure And Vaccination Modeling, Christopher D. Bruno
Annual Symposium on Biomathematics and Ecology Education and Research
No abstract provided.
Modeling The Growth Of Psedomonas Putida By Gompertz Dynamic Equations, Elvan Akin
Modeling The Growth Of Psedomonas Putida By Gompertz Dynamic Equations, Elvan Akin
Annual Symposium on Biomathematics and Ecology Education and Research
No abstract provided.
When Is Closing A School Effective For Stopping Disease Spread?, Anthony Delegge
When Is Closing A School Effective For Stopping Disease Spread?, Anthony Delegge
Annual Symposium on Biomathematics and Ecology Education and Research
No abstract provided.
Optimal Control And Models For Alternative Pest Management To Alfalfa Agroecosystems, Mohammed Yahdi
Optimal Control And Models For Alternative Pest Management To Alfalfa Agroecosystems, Mohammed Yahdi
Annual Symposium on Biomathematics and Ecology Education and Research
No abstract provided.
The Kinetics Of Type I Interferons During Influenza A Virus Infection, Margaret A. Myers
The Kinetics Of Type I Interferons During Influenza A Virus Infection, Margaret A. Myers
Annual Symposium on Biomathematics and Ecology Education and Research
No abstract provided.
Modeling Cdc42 Oscillation In Fission Yeast, Bin Xu
Modeling Cdc42 Oscillation In Fission Yeast, Bin Xu
Annual Symposium on Biomathematics and Ecology Education and Research
No abstract provided.
One Tick, Two Tick, Two Pathogens, Oh No! Am I Sick?, Caleb L. Adams
One Tick, Two Tick, Two Pathogens, Oh No! Am I Sick?, Caleb L. Adams
Annual Symposium on Biomathematics and Ecology Education and Research
No abstract provided.