2. Population,
2016
Illinois Mathematics and Science Academy
2. Population, Ruth Dover
Differential Equations
Introduction to logistic population growth.
3: Drugs And De's,
2016
Illinois Mathematics and Science Academy
3: Drugs And De's, Ruth Dover
Differential Equations
Making a connection between discrete recursion and differential equations.
Existence Of Periodic Solutions For A Quantum Volterra Equation,
2016
University of Dayton
Existence Of Periodic Solutions For A Quantum Volterra Equation, Muhammad Islam, Jeffrey T. Neugebauer
Mathematics Faculty Publications
The objective of this paper is to study the periodicity properties of functions that arise in quantum calculus, which has been emerging as an important branch of mathematics due to its various applications in physics and other related fields. The paper has two components. First, a relation between two existing periodicity notions is established. Second, the existence of periodic solutions of a q-Volterra integral equation, which is a general integral form of a first order q-difference equation, is obtained. At the end, some examples are provided. These examples show the effectiveness of the relation between the two periodicity notions that …
Positive Solutions For A Singular Fourth Order Nonlocal Boundary Value Problem,
2016
Baylor University
Positive Solutions For A Singular Fourth Order Nonlocal Boundary Value Problem, John M. Davis, Paul W. Eloe, John R. Graef, Johnny Henderson
Mathematics Faculty Publications
Positive solutions are obtained for the fourth order nonlocal boundary value problem, u(4)=f(x,u), 0 < x < 1, u(0) = u''(0) = u'(1) = u''(1) - u''(2/3)=0, where f(x,u) is singular at x = 0, x=1, y=0, and may be singular at y=∞. The solutions are shown to exist at fixed points for an operator that is decreasing with respect to a cone.
Almost Automorphic Solutions Of Delayed Neutral Dynamic Systems On Hybrid Domains,
2016
Izmir University
Almost Automorphic Solutions Of Delayed Neutral Dynamic Systems On Hybrid Domains, Murat Adıvar, Halis Can Koyuncuoğlu, Youssef Raffoul
Mathematics Faculty Publications
We study the existence of almost automorphic solutions of the delayed neutral dynamic system on hybrid domains that are additively periodic. We use exponential dichotomy and prove uniqueness of projector of exponential dichotomy to obtain some limit results leading to sufficient conditions for existence of almost automorphic solutions to neutral system. Unlike the existing literature we prove our existence results without assuming boundedness of the coefficient matrices in the system. Hence, we significantly improve the results in the existing literature. Finally, we also provide an existence result for an almost periodic solutions of the system.
Stochastic Models Of Evidence Accumulation In Changing Environments,
2016
University of Dayton
Stochastic Models Of Evidence Accumulation In Changing Environments, Alan Veliz-Cuba, Zachary P. Kilpatrick, Krešimir Josić
Mathematics Faculty Publications
Organisms and ecological groups accumulate evidence to make decisions. Classic experiments and theoretical studies have explored this process when the correct choice is fixed during each trial. However, we live in a constantly changing world. What effect does such impermanence have on classical results about decision making? To address this question we use sequential analysis to derive a tractable model of evidence accumulation when the correct option changes in time. Our analysis shows that ideal observers discount prior evidence at a rate determined by the volatility of the environment, and the dynamics of evidence accumulation is governed by the information …
Necessary And Sufficient Conditions For Stability Of Volterra Integro-Dynamic Equation Systems On Time Scales,
2016
University of Dayton
Necessary And Sufficient Conditions For Stability Of Volterra Integro-Dynamic Equation Systems On Time Scales, Youssef Raffoul
Mathematics Faculty Publications
In this research we establish necessary and sufficient conditions for the stability of the zero solution of scalar Volterra integro-dynamic equation on general time scales. Our approach is based on the construction of suitable Lyapunov functionals. We will compare our findings with known results and provides application to quantum calculus.
Topic Analysis Of Tweets On The European Refugee Crisis Using Non-Negative Matrix Factorization,
2016
Claremont McKenna College
Topic Analysis Of Tweets On The European Refugee Crisis Using Non-Negative Matrix Factorization, Chong Shen
CMC Senior Theses
The ongoing European Refugee Crisis has been one of the most popular trending topics on Twitter for the past 8 months. This paper applies topic modeling on bulks of tweets to discover the hidden patterns within these social media discussions. In particular, we perform topic analysis through solving Non-negative Matrix Factorization (NMF) as an Inexact Alternating Least Squares problem. We accelerate the computation using techniques including tweet sampling and augmented NMF, compare NMF results with different ranks and visualize the outputs through topic representation and frequency plots. We observe that supportive sentiments maintained a strong presence while negative sentiments such …
Signal Velocity In Oscillator Arrays,
2016
Portland State University
Signal Velocity In Oscillator Arrays, Carlos E. Cantos, David K. Hammond, J. J. P. Veerman
Mathematics and Statistics Faculty Publications and Presentations
We investigate a system of coupled oscillators on the circle, which arises from a simple model for behavior of large numbers of autonomous vehicles. The model considers asymmetric, linear, decentralized dynamics, where the acceleration of each vehicle depends on the relative positions and velocities between itself and a set of local neighbors. We first derive necessary and sufficient conditions for asymptotic stability, then derive expressions for the phase velocity of propagation of disturbances in velocity through this system. We show that the high frequencies exhibit damping, which implies existence of well-defined signal velocities c+>0 and c−f(x−c+t) in the direction …
Hamiltonian Formulation For Wave-Current Interactions In Stratified Rotational Flows,
2016
University of Vienna
Hamiltonian Formulation For Wave-Current Interactions In Stratified Rotational Flows, Adrian Constantin, Rossen Ivanov, Calin-Iulian Martin
Articles
We show that the Hamiltonian framework permits an elegant formulation of the nonlinear governing equations for the coupling between internal and surface waves in stratified water flows with piecewise constant vorticity.
On The N-Wave Equations With Pt-Symmetry,
2016
Institute for Nuclear Research and Nuclear Energy, Bulgarian Academy of Sciences, 72 Tsarigradsko chaussee, 1784 Sofia, BULGARIA
On The N-Wave Equations With Pt-Symmetry, Vladimir Gerdjikov, Georgi Grahovski, Rossen Ivanov
Articles
We study extensions of N-wave systems with PT-symmetry. The types of (nonlocal) reductions leading to integrable equations invariant with respect to P- (spatial reflection) and T- (time reversal) symmetries is described. The corresponding constraints on the fundamental analytic solutions and the scattering data are derived. Based on examples of 3-wave (related to the algebra sl(3,C)) and 4-wave (related to the algebra so(5,C)) systems, the properties of different types of 1- and 2-soliton solutions are discussed. It is shown that the PT symmetric 3-wave equations may have regular multi-soliton solutions for some specific choices of their parameters.
The Dynamics Of Flat Surface Internal Geophysical Waves With Currents,
2016
Technological University Dublin
The Dynamics Of Flat Surface Internal Geophysical Waves With Currents, Alan Compelli, Rossen Ivanov
Articles
A two-dimensional water wave system is examined consisting of two discrete incompressible fluid domains separated by a free common interface. In a geophysical context this is a model of an internal wave, formed at a pycnocline or thermocline in the ocean. The system is considered as being bounded at the bottom and top by a flatbed and wave-free surface respectively. A current profile with depth-dependent currents in each domain is considered. The Hamiltonian of the system is determined and expressed in terms of canonical wave-related variables. Limiting behavior is examined and compared to that of other known models. The linearised …
An Interactive Tool For The Computational Exploration Of Integrodifference Population Models,
2016
Harvey Mudd College
An Interactive Tool For The Computational Exploration Of Integrodifference Population Models, Kennedy Agwamba
HMC Senior Theses
Mathematical modeling of population dynamics can provide novel insight to the growth and dispersal patterns for a variety of species populations, and has become vital to the preservation of biodiversity on a global-scale. These growth and dispersal stages can be modeled using integrodifference equations that are discrete in time and continuous in space. Previous studies have identified metrics that can determine whether a given species will persist or go extinct under certain model parameters. However, a need for computational tools to compute these metrics has limited the scope and analysis within many of these studies. We aim to create computational …
Hopper Bands: Locust Aggregation,
2016
Harvey Mudd College
Hopper Bands: Locust Aggregation, Ryan C. Jones
HMC Senior Theses
Locust swarms cause famine and hunger in parts of Sub-Saharan Africa as they travel across croplands and eat vegetation. Current models start with biological properties of locusts and analyze the macroscopic behavior of the system. These models exhibit the desired migratory behavior, but do so with too many parameters. To account for this, a new model, the Alignment and Intermittent Motion (AIM) model, is derived with minimal assumptions. AIM is constructed with regards to locust biology, allowing it to elicit biologically correct locust behavior: the most noteworthy being the fingering of hopper bands. A Particle-in-Cell method is used to optimize …
1. Coffee,
2016
Illinois Mathematics and Science Academy
An Investigation Of Inital Shock Cell Formation In Turbulent Coanda Wall Jets,
2016
James Madison University
An Investigation Of Inital Shock Cell Formation In Turbulent Coanda Wall Jets, Caroline P. Lubert, Christian R. Schwantes, Richard J. Shafer
Department of Mathematics and Statistics - Faculty Scholarship
Turbulent Coanda wall jets are present in a multitude of natural and man-made applications. Their obvious advantages in terms of flow deflection are often outweighed by disadvantages related to the increased noise levels associated with these jets. Primary high-frequency noise sources are turbulent mixing noise (TMN) and shock-associated noise (SAN). Clearly, accurate modeling of these noise sources will facilitate better predictions of the behavior of such jet noise with physical characteristics. This paper, which focuses on SAN, shows how the Method of Characteristics can be applied to a steady two-dimensional axisymmetric supersonic flow to rewrite the three governing partial differential …
Synthesis Of Satellite Microwave Observations For Monitoring Global Land-Atmosphere Co2 Exchange,
2016
The University of Montana
Synthesis Of Satellite Microwave Observations For Monitoring Global Land-Atmosphere Co2 Exchange, Lucas Alan Jones
Graduate Student Theses, Dissertations, & Professional Papers
This dissertation describes the estimation, error quantification, and incorporation of land surface information from microwave satellite remote sensing for modeling global ecosystem land-atmosphere net CO2 exchange. Retrieval algorithms were developed for estimating soil moisture, surface water, surface temperature, and vegetation phenology from microwave imagery timeseries. Soil moisture retrievals were merged with model-based soil moisture estimates and incorporated into a light-use efficiency model for vegetation productivity coupled to a soil decomposition model. Results, including state and uncertainty estimates, were evaluated with a global eddy covariance flux tower network and other independent global model- and remote-sensing based products.
Methodology For Analyzing Epoxy-Cnt Phononic Crystals For Wave Attenuation And Guiding,
2016
Michigan Technological University
Methodology For Analyzing Epoxy-Cnt Phononic Crystals For Wave Attenuation And Guiding, Madhu Kolati
Dissertations, Master's Theses and Master's Reports
Phononic crystals (PhnCs) control, direct and manipulate sound waves to achieve wave guiding and attenuation. This dissertation presents methodology for analyzing nanotube materials based phononic crystals to achieve control over sound, vibration and stress mitigation. Much of the analytical work presented is in identifying frequency band gaps in which sound or vibration cannot propagate through these PhnCs. Wave attenuation and mitigation analysis is demonstrated using finite element simulation. Engineering principles from current research areas of solid mechanics, solid-state physics, elasto-dynamics, mechanical vibrations and acoustics are employed for the methodology. A considerable effort is put to show that these PhnCs can …
Subgroups Of Finite Wreath Product Groups For P=3,
2016
University of Akron
Subgroups Of Finite Wreath Product Groups For P=3, Jessica L. Gonda
Williams Honors College, Honors Research Projects
Let M be the additive abelian group of 3-by-3 matrices whose entries are from the ring of integers modulo 9. The problem of determining all the normal subgroups of the regular wreath product group P=Z9≀(Z3 × Z3) that are contained in its base subgroup is equivalent to the problem of determining the subgroups of M that are invariant under two particular endomorphisms of M. In this thesis we give a partial solution to the latter problem by implementing a systematic approach using concepts from group theory and linear algebra.
Diffusive Behavior Of Physically Cross-Linked Hydrogels,
2016
The University of Akron
Diffusive Behavior Of Physically Cross-Linked Hydrogels, Morgan A. Stilke
Williams Honors College, Honors Research Projects
A hydrogel is a water swollen polymeric network that has the potential to transform a variety of biomedical applications because of its biocompatibility and water content. Unfortunately, hydrogels typically have poor mechanical robustness. The majority of the content is water, while the remaining structure consists of a physical network, a covalent network, or a combination of both, yielding strength and toughness. There are several strategies attempted to improve mechanical properties including double network hydrogels comprised of two interpenetrating networks: one being a highly crosslinked sacrificial network and the other being a weakly crosslinked network that maintains reversibility after deformation. However, …
