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INFECTION AGE STRUCTURED VECTOR BORNE DISEASE MODEL WITH DIRECT TRANSMISSION.
Title
INFECTION AGE STRUCTURED VECTOR BORNE DISEASE MODEL WITH DIRECT TRANSMISSION.
Creator
Giri, Sunil, Tuncer, Necibe, Florida Atlantic University, Department of Mathematical Sciences, Charles E. Schmidt College of Science
Abstract/Description
Mathematical modeling is a powerful tool to study and analyze the disease dynamics prevalent in the community. This thesis studies the dynamics of two time since infection structured vector borne models with direct transmission. We have included disease induced death rate in the first model to form the second model. The aim of this thesis is to analyze whether these two models have same or different disease dynamics. An explicit expression for the reproduction number denoted by R0 is derived....
Show moreMathematical modeling is a powerful tool to study and analyze the disease dynamics prevalent in the community. This thesis studies the dynamics of two time since infection structured vector borne models with direct transmission. We have included disease induced death rate in the first model to form the second model. The aim of this thesis is to analyze whether these two models have same or different disease dynamics. An explicit expression for the reproduction number denoted by R0 is derived. Dynamical analysis reveals the forward bifurcation in the first model. That is when the threshold value R0 < 1, disease free-equilibrium is stable locally implying that if there is small perturbation of the system, then after some time, the system will return to the disease free equilibrium. When R0 > 1 the unique endemic equilibrium is locally asymptotically stable. For the second model, analysis of the existence and stability of equilibria reveals the existence of backward bifurcation i.e. where the disease free equilibrium coexists with the endemic equilibrium when the reproduction number R02 is less than unity. This aspect shows that in order to control vector borne disease, it is not sufficient to have reproduction number less than unity although necessary. Thus, the infection can persist in the population even if the reproduction number is less than unity. Numerical simulation is presented to see the bifurcation behaviour in the model. By taking the reproduction number as the bifurcation parameter, we find the system undergoes backward bifurcation at R02 = 1. Thus, the model has backward bifurcation and have two positive endemic equilibrium when R02 < 1 and unique positive endemic equilibrium whenever R02 > 1. Stability analysis shows that disease free equilibrium is locally asymptotically stable when R02 < 1 and unstable when R02 > 1. When R02 < 1, lower endemic equilibrium in backward bifurcation is locally unstable.
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Date Issued
2020
PURL
http://purl.flvc.org/fau/fd/FA00013552
Subject Headings
Vector Borne Diseases, Mathematical models, Simulations, Dynamics--Mathematical models
Format
Document (PDF)
Stability of an elliptical vortex in a time-dependent strain field
Title
Stability of an elliptical vortex in a time-dependent strain field.
Creator
Marshall, Marilyn P., Florida Atlantic University, Dhanak, Manhar R., College of Engineering and Computer Science, Department of Ocean and Mechanical Engineering
Abstract/Description
A theoretical study of the stability of two-dimensional elliptical vortices in a time-dependent, periodically varying external straining flow was conducted. The mean value of the oscillating straining flow was chosen so that the vortex would be stationary in the absence of fluctuations of the external field about the mean. If the frequency of straining is near to the natural frequency of the vortex for small-amplitude oscillations of the vortex core, so that the vortex is forced near its...
Show moreA theoretical study of the stability of two-dimensional elliptical vortices in a time-dependent, periodically varying external straining flow was conducted. The mean value of the oscillating straining flow was chosen so that the vortex would be stationary in the absence of fluctuations of the external field about the mean. If the frequency of straining is near to the natural frequency of the vortex for small-amplitude oscillations of the vortex core, so that the vortex is forced near its natural frequency, a resonance occurs such that the aspect ratio of the elliptical core boundary initially oscillates with an amplitude that increases linearly with time. After an initial period of growth, the aspect ratio will either follow a bounded limit cycle at large time or it will elongate exponentially with time. The nonlinear evolution of the vortex at large time is studied numerically, and distinct regions of behavior in the parameter space for the vortex are obtained.
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Date Issued
1992
PURL
http://purl.flvc.org/fcla/dt/14817
Subject Headings
Vortex--Motion, Fluid dynamics--Mathematical models
Format
Document (PDF)
Convex identification and nonlinear random vibration analysis of elastic and viscoelastic structures
Title
Convex identification and nonlinear random vibration analysis of elastic and viscoelastic structures.
Creator
Fang, Jianjie, Florida Atlantic University, Elishakoff, Isaac, College of Engineering and Computer Science, Department of Ocean and Mechanical Engineering
Abstract/Description
This dissertation deals with the identification of boundary conditions of elastic structures, and nonlinear random vibration analysis of elastic and viscoelastic structures through a new energy-based equivalent linearization technique. In the part of convex identification, convex models are utilized to represent the degree of uncertainty in the boundary condition modification. This means that the identification is actually the identification of the convex model to which the actual boundary...
Show moreThis dissertation deals with the identification of boundary conditions of elastic structures, and nonlinear random vibration analysis of elastic and viscoelastic structures through a new energy-based equivalent linearization technique. In the part of convex identification, convex models are utilized to represent the degree of uncertainty in the boundary condition modification. This means that the identification is actually the identification of the convex model to which the actual boundary stiffness profile belongs. Two examples are presented to illustrate the application of the method. For the beam example the finite element analysis is performed to evaluate the frequencies of a beam with any specific boundary conditions. For the plate example, the Bolotin's dynamic edge effect method, generalized by Elishakoff, is employed to determine the approximate natural frequencies and normal modes of elastically supported isotropic, uniform rectangular plates. In the part of nonlinear random analysis, first a systematic finite element analysis procedure, based on the element's energy formulation, through conventional stochastic linearization technique, is proposed. The procedure is applicable to a wide range of nonlinear random vibration problem as long as element's energy formulations are presented. Secondly, the new energy-based stochastic linearization method in finite element analysis setting is developed to improve the conventional stochastic linearization technique. The entire formulation is produced in detail for the first time. The theory is applied to beam problem subjected to space-wise and time-wise white noise excitations. Finally, the new energy-based stochastic linearization technique is applied to treat nonlinear vibration problems of viscoelastic beams.
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Date Issued
1996
PURL
http://purl.flvc.org/fcla/dt/12467
Subject Headings
Elasticity, Viscoelasticity, Structural dynamics--Mathematical models, Vibration--Mathematical models
Format
Document (PDF)
Dynamics of two-actor cooperation–competition conflict models
Title
Dynamics of two-actor cooperation–competition conflict models.
Creator
Liebovitch, Larry S., Naudot, Vincent, Vallacher, Robin R., Nowak, Andrzej, Bui-Wrzosinska, Lan, Coleman, Peter T.
Date Issued
2008-11-01
PURL
http://purl.flvc.org/fau/165475
Subject Headings
Nonlinear theories, Social systems--Mathematical models, Conflict management, Cooperativeness, Differential equations, Competition, Dynamics--Mathematical models
Format
Document (PDF)
Self-organizing dynamics of coupled map systems
Title
Self-organizing dynamics of coupled map systems.
Creator
Liebovitch, Larry S., Zochowski, Michal
Date Issued
1999-03
PURL
http://purl.flvc.org/fau/165481
Subject Headings
Dynamics--Mathematical models, Chaotic behavior in systems, Self-organizing maps, Self-organizing systems-Mathematical models
Format
Document (PDF)
Migration induced epidemics: dynamics of flux-based multipatch models
Title
Migration induced epidemics: dynamics of flux-based multipatch models.
Creator
Liebovitch, Larry S., Schwartz, Ira B.
Date Issued
2004
PURL
http://purl.flvc.org/FAU/165227
Subject Headings
Communicable diseases--Epidemiology--Mathematical models, Emerging infectious diseases, Epidemiologic Methods, Epidemiology, Biomathematics, Medicine-Mathematics, Dynamics-Mathematical models
Format
Document (PDF)
Wave Ship Interaction in Transforming Seas
Title
Wave Ship Interaction in Transforming Seas.
Creator
Gong, Fuxian, Dhanak, Manhar R., Florida Atlantic University, College of Engineering and Computer Science, Department of Ocean and Mechanical Engineering
Abstract/Description
In near-shore transforming seas, as waves approach the shoreline, wave shoaling and sometimes wave breaking take place due to the decreasing water depth. When a ship advances through the transforming seas, the ship body and waves interact with each other substantially and can lead to unknown motions of the ship hull. The physical process of how the wave transforms in the surf zone and how the vehicle actually behaves when it passes through the transforming seas is a complicated issue that...
Show moreIn near-shore transforming seas, as waves approach the shoreline, wave shoaling and sometimes wave breaking take place due to the decreasing water depth. When a ship advances through the transforming seas, the ship body and waves interact with each other substantially and can lead to unknown motions of the ship hull. The physical process of how the wave transforms in the surf zone and how the vehicle actually behaves when it passes through the transforming seas is a complicated issue that triggers considerable research interest. The goal of my research is to characterize the dynamics of a high-speed surface ship model in transforming seas through a parametric numerical study of the shipwave interactions. In this study, the vehicle of interest is a surface effect ship (SES) and we aim to contribute to developing a methodology for simulating the transforming wave environment, including wave breaking, and its interactions with the SES. The thesis work uses a commercial software package ANSYS Fluent to generate numerical waves and model the interface between water and air using the volume of fluid (VoF) method. A ship motion solver and the dynamic mesh are used to enable the modeled ship to perform three degree-of-freedom (DoF) motion and the near-region of the ship hull to deform as well as re-mesh. Non-conformal meshes with hybrid compositions of different cell types and various grid sizes are used in the simulations for different purposes. Five user-defined functions (UDFs) are dynamically linked with the flow solver to incorporates ship/grid motions, wave damping and output of the numerical results. A series of steps were taken sequentially: 1) validation for ship motions including simulation of a static Wigley hull under steady flows to compare against previous experimental results by other researchers, and the comparison between the static SES model under steady flows and the moving SES model advancing in the calm water; 2) study of the ship with 3 DoF advancing in calm water of both constant depth and varying depth; 3) validation for numerical waves, including predictions of numerically progressive waves in both a regular tank and a tank with a sloped fringing reef to compare with theoretical and experimental results, respectively; 4) investigation of the transforming characteristics of the wave traveling over the sloped fringing reef, which mimics the near-shore wave environment and a study of the dynamics of the SES through transforming waves. We find that the flow solver used in this study reliably models the wave profiles along the ship hull. The comparison between a static SES in a current and a moving SES in calm water at the same Froude number shows that although the velocity fields around the vehicle are significantly different, the wave profiles inside and outside the rigid cushion of the vehicle are similar and the resistance force experienced by the vehicle in the two scenarios agree well over time. We conducted five numerical simulations of the vehicle traveling from shallow water to deep water across the transition zone for different Froude numbers. From the results, we find that as the Froude number increases, the wave resistance force on the vehicle becomes larger in both shallow water and deep water. In addition, the overall mean resistance force experienced by the vehicle over the whole trip increases with the Froude number. Statistical analysis of the wave motions suggests that the energy flux decreases dramatically in the onshore direction as the waves break. The more severe the wave-breaking process, the greater the decrease in energy flux. Both the increase of Froude number and the wave steepness apparently increase the resistance force on the vehicle in the shallow water. This thesis work captures the impact of the transforming characteristics of the waves and closely replicates the behavior of how waves interact with a ship in transforming seas through numerical modeling and simulation.
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Date Issued
2017
PURL
http://purl.flvc.org/fau/fd/FA00004916, http://purl.flvc.org/fau/fd/FA00004916
Subject Headings
Hydrodynamics--Mathematical models., Fluid dynamics--Mathematical models., Ocean waves--Measurement., Water waves--Measurement., Coastal engineering.
Format
Document (PDF)
Modeling of Flexible Pipe for Culvert Application under Shallow Burial Condition
Title
Modeling of Flexible Pipe for Culvert Application under Shallow Burial Condition.
Creator
Limpeteeprakarn, Terdkiat, Carlsson, Leif A., Florida Atlantic University, College of Engineering and Computer Science, Department of Civil, Environmental and Geomatics Engineering
Abstract/Description
Flexible thermoplastic p1pes under field and laboratory loading conditions have been examined in the present study. The flexible pipes were tested under truck loading application with shallow soil cover. The pipe-soil system response includes soil stresses around and above the buried pipes, vertical pipe crown diametral strain, and circumferential pipe wall strains. Modeling the pipe-soil system is made using plane strain and thin ring assumptions. A thin ring model using Castigliano's...
Show moreFlexible thermoplastic p1pes under field and laboratory loading conditions have been examined in the present study. The flexible pipes were tested under truck loading application with shallow soil cover. The pipe-soil system response includes soil stresses around and above the buried pipes, vertical pipe crown diametral strain, and circumferential pipe wall strains. Modeling the pipe-soil system is made using plane strain and thin ring assumptions. A thin ring model using Castigliano's theorem is developed to analyze the behavior and response of a flexible pipe under well defined loading conditions and simulate the behavior of the buried pipe under the live load application. Laboratory work was carried out to study the pipe behavior and response under two-point, three-point, and four-point loading configurations. The thin ring model predictions show good agreement with classical solutions specially valid for two-point and three-point loading configurations. Laboratory results were also in good agreement with the predictions. Laboratory results show that the maximum tensile strain for the four-point loading test occurs at inner pipe crown region. Comprehensive efforts were made to correlate the thin ring model predictions with the field test results; however, it appears that the thin ring model cannot be used to simulate the effect of the live load application. A major source of the differences between the predicted and measured values is attributed to the applied load magnitude. A further investigation was carried out to examine the applicability of the model to study the general pipe behavior. The predicted hoop pipe wall strain profile was found to be similar to that of the reported strain profile by Rogers under overall poor soil support condition. Comparison of soil stress distribution shows that the 2D prediction approach provides nonconservative results while the FE analysis agrees more favorably with the measured pressure data. Overall, FE analysis shows that a linearly elastic isotropic model for the surrounding soil and flexible pipes with a fully bonded pipe-soil interface provides a reasonable prediction for soil pressures close to the buried pipes.
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Date Issued
2006
PURL
http://purl.flvc.org/fau/fd/FA00012573
Subject Headings
Structural analysis (Engineering), Pipe, Plastic--Dynamics--Mathematical models, Underground pipelines--Design and construction, Soil-structure interaction
Format
Document (PDF)
Dynamical response of multi-patch, flux-based models to the input of infected people: epidemic response to initiated events
Title
Dynamical response of multi-patch, flux-based models to the input of infected people: epidemic response to initiated events.
Creator
Liebovitch, Larry S., Schwartz, Ira B., Rho, Young-Ah
Date Issued
2008-07-21
PURL
http://purl.flvc.org/FAU/165229
Subject Headings
Communicable diseases--Epidemiology--Mathematical models, Epidemiologic Methods, Differential equations, Dynamics--Mathematical models, Spatial systems--Mathematical models, Population dynamics, Emerging infectious diseases
Format
Document (PDF)