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 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 freeequilibrium 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.
Show less  Date Issued
 2020
 PURL
 http://purl.flvc.org/fau/fd/FA00013552
 Subject Headings
 Vector Borne Diseases, Mathematical models, Simulations, DynamicsMathematical models
 Format
 Document (PDF)
 Title
 Stability of an elliptical vortex in a timedependent 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 twodimensional elliptical vortices in a timedependent, 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 smallamplitude oscillations of the vortex core, so that the vortex is forced near its...
Show moreA theoretical study of the stability of twodimensional elliptical vortices in a timedependent, 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 smallamplitude 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.
Show less  Date Issued
 1992
 PURL
 http://purl.flvc.org/fcla/dt/14817
 Subject Headings
 VortexMotion, Fluid dynamicsMathematical models
 Format
 Document (PDF)
 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 energybased 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 energybased 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 energybased 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 spacewise and timewise white noise excitations. Finally, the new energybased stochastic linearization technique is applied to treat nonlinear vibration problems of viscoelastic beams.
Show less  Date Issued
 1996
 PURL
 http://purl.flvc.org/fcla/dt/12467
 Subject Headings
 Elasticity, Viscoelasticity, Structural dynamicsMathematical models, VibrationMathematical models
 Format
 Document (PDF)
 Title
 Dynamics of twoactor cooperation–competition conflict models.
 Creator
 Liebovitch, Larry S., Naudot, Vincent, Vallacher, Robin R., Nowak, Andrzej, BuiWrzosinska, Lan, Coleman, Peter T.
 Date Issued
 20081101
 PURL
 http://purl.flvc.org/fau/165475
 Subject Headings
 Nonlinear theories, Social systemsMathematical models, Conflict management, Cooperativeness, Differential equations, Competition, DynamicsMathematical models
 Format
 Document (PDF)
 Title
 Selforganizing dynamics of coupled map systems.
 Creator
 Liebovitch, Larry S., Zochowski, Michal
 Date Issued
 199903
 PURL
 http://purl.flvc.org/fau/165481
 Subject Headings
 DynamicsMathematical models, Chaotic behavior in systems, Selforganizing maps, Selforganizing systemsMathematical models
 Format
 Document (PDF)
 Title
 Migration induced epidemics: dynamics of fluxbased multipatch models.
 Creator
 Liebovitch, Larry S., Schwartz, Ira B.
 Date Issued
 2004
 PURL
 http://purl.flvc.org/FAU/165227
 Subject Headings
 Communicable diseasesEpidemiologyMathematical models, Emerging infectious diseases, Epidemiologic Methods, Epidemiology, Biomathematics, MedicineMathematics, DynamicsMathematical models
 Format
 Document (PDF)
 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 nearshore 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 nearshore 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 highspeed 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 degreeoffreedom (DoF) motion and the nearregion of the ship hull to deform as well as remesh. Nonconformal meshes with hybrid compositions of different cell types and various grid sizes are used in the simulations for different purposes. Five userdefined 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 nearshore 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 wavebreaking 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.
Show less  Date Issued
 2017
 PURL
 http://purl.flvc.org/fau/fd/FA00004916, http://purl.flvc.org/fau/fd/FA00004916
 Subject Headings
 HydrodynamicsMathematical models., Fluid dynamicsMathematical models., Ocean wavesMeasurement., Water wavesMeasurement., Coastal engineering.
 Format
 Document (PDF)
 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 pipesoil system response includes soil stresses around and above the buried pipes, vertical pipe crown diametral strain, and circumferential pipe wall strains. Modeling the pipesoil 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 pipesoil system response includes soil stresses around and above the buried pipes, vertical pipe crown diametral strain, and circumferential pipe wall strains. Modeling the pipesoil 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 twopoint, threepoint, and fourpoint loading configurations. The thin ring model predictions show good agreement with classical solutions specially valid for twopoint and threepoint loading configurations. Laboratory results were also in good agreement with the predictions. Laboratory results show that the maximum tensile strain for the fourpoint 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 pipesoil interface provides a reasonable prediction for soil pressures close to the buried pipes.
Show less  Date Issued
 2006
 PURL
 http://purl.flvc.org/fau/fd/FA00012573
 Subject Headings
 Structural analysis (Engineering), Pipe, PlasticDynamicsMathematical models, Underground pipelinesDesign and construction, Soilstructure interaction
 Format
 Document (PDF)
 Title
 Dynamical response of multipatch, fluxbased models to the input of infected people: epidemic response to initiated events.
 Creator
 Liebovitch, Larry S., Schwartz, Ira B., Rho, YoungAh
 Date Issued
 20080721
 PURL
 http://purl.flvc.org/FAU/165229
 Subject Headings
 Communicable diseasesEpidemiologyMathematical models, Epidemiologic Methods, Differential equations, DynamicsMathematical models, Spatial systemsMathematical models, Population dynamics, Emerging infectious diseases
 Format
 Document (PDF)